homog2d_test.cpp File Reference

A test file for homog2d, needs Catch2, v2 (single header file version), see https://github.com/catchorg/Catch2
Run with $ make test More...

#include "catch.hpp"
#include "../homog2d.hpp"
#include "figures_test/polyline_inside_a1.code"
#include "figures_test/polyline_inside_a2.code"
#include "figures_test/polyline_inside_a3.code"
#include "figures_test/polyline_inside_a4.code"
#include "figures_test/polyline_inside_b1.code"
#include "figures_test/polyline_inside_b2.code"
#include "figures_test/polyline_inside_b3.code"
#include "figures_test/frect_intersect_1.code"
#include "figures_test/frect_intersect_2.code"
#include "figures_test/frect_intersect_3.code"
#include "figures_test/frect_intersect_4.code"
#include "figures_test/frect_intersect_5.code"
#include "figures_test/frect_intersect_6.code"
#include "figures_test/frect_intersect_7.code"
#include "figures_test/frect_intersect_8.code"
#include "figures_test/frect_intersect_9.code"
#include "figures_test/frect_intersect_10.code"
#include "figures_test/frect_intersect_11.code"
#include "figures_test/frect_intersect_12.code"
#include "figures_test/frect_intersect_13.code"
#include "figures_test/polyline_min_1O.code"
#include "figures_test/polyline_min_1C.code"
#include "figures_test/polyline_min_2O.code"
#include "figures_test/polyline_min_2C.code"
#include "figures_test/polyline_min_3O.code"
#include "figures_test/polyline_min_3C.code"
#include "figures_test/polyline_comp_1a.code"
#include "figures_test/polyline_comp_1b.code"
#include "figures_test/polyline_chull_1.code"

Include dependency graph for homog2d_test.cpp:

Macros
#define	CATCH_CONFIG_RUNNER
#define	HOMOG2D_BIND_X   xxx
	see test [gen_bind] More...
#define	HOMOG2D_TEST_MODE
#define	LOCALLOG(a)
#define	NUMTYPE   double
	Numerical type for object storage for tests. This is usually defined by makefile. (The internal numerical type for the library is defined by HOMOG2D_INUMTYPE) More...
#define	STR(s)   #s
#define	XSTR(s)   STR(s)

Functions
	CHECK (s1.getPointAt(0)==Point2d_< NUMTYPE >(0, 0))
	CHECK (s1.getPointAt(5)==Point2d_< NUMTYPE >(5, 0))
	CHECK (s1.getPointAt(10)==Point2d_< NUMTYPE >(10, 0))
	CHECK (s1.getPointAt(20)==Point2d_< NUMTYPE >(20, 0))
	CHECK (pol.size()==5)
	CHECK (opol.size()==0)
	CHECK (cpol.size()==0)
	CHECK (cir.size()==1)
	CHECK (ell.size()==1)
	CHECK (rect.size()==4)
	CHECK (seg.size()==2)
	CHECK (li.size()==0)
	CHECK (pt.size()==1)
	CHECK (size(opol)==0)
	CHECK (size(cpol)==0)
	CHECK (size(cir)==1)
	CHECK (size(ell)==1)
	CHECK (size(rect)==4)
	CHECK (size(seg)==2)
	CHECK (size(li)==0)
	CHECK (size(pt)==1)
	CHECK_THROWS (CPolyline(-5, 5u))
	CHECK_THROWS (CPolyline(1, 2u))
	CHECK_THROWS (CPolyline(0, 5u))
	CHECK_THROWS (pol.set(1, 2u))
	CHECK_THROWS (pol.set(0, 5u))
	CHECK_THROWS (pol.set(-5, 5u))
	CHECK_THROWS (pol.set(5, 0u))
template<typename PT , typename CONT >
void	checkSizeNF (const PT &pt, const CONT &cont)
long double	computeDistTransformedLined (Homogr_< NUMTYPE > &H, Point2d_< NUMTYPE > pt1)
	Computation of the line passed through H^{-T} and computation of the distance between the resulting line and the transformed point. Should be 0, always. More...
std::string	FullPrecision (long double d)
template<typename I >
void	local_draw_test (img::Image< I > &im, std::string fn)
	Make sure all drawing functions and member functions are implemented. More...
	local_draw_test (im, "BUILD/dummy_draw.svg")
	local_draw_test (im, "BUILD/dummy_draw.png")
template<typename I , typename T >
void	local_draw_test2 (img::Image< I > &im, T &t)
	Helper function for local_draw_test() More...
int	main (int argc, char *argv[])
template<typename T , typename U >
void	polytest_1 (const base::PolylineBase< T, U > &pl1)
pol	set (8, 4u)
	TEST_CASE ("numerical types access", "[types-access]")
	TEST_CASE ("comparison testing", "[comparison-test]")
	TEST_CASE ("types testing 1", "[test-types-1]")
	TEST_CASE ("types testing 2", "[test-types-2]")
	TEST_CASE ("normalization", "[normaliz]")
	TEST_CASE ("homogeneous coordinates testing", "[homogeneous]")
	TEST_CASE ("infinity point", "[points-inf]")
	TEST_CASE ("types testing 3", "[test-types-3]")
	TEST_CASE ("stream operator << test", "[streamingop-test]")
	TEST_CASE ("line/point distance", "[lp-dist]")
	TEST_CASE ("side-pt-line", "[side-pt-line]")
	TEST_CASE ("test1", "[test1]")
	TEST_CASE ("build point line from container", "[build-cont]")
	TEST_CASE ("test throw", "[test_thr]")
	TEST_CASE ("test parallel", "[test_para]")
	TEST_CASE ("dist2points", "[t_d2p]")
	TEST_CASE ("Homogr constructors", "[testHC]")
	TEST_CASE ("test Homogr", "[testH]")
	TEST_CASE ("matrix inversion", "[testH3]")
	TEST_CASE ("line transformation", "[testH3]")
	TEST_CASE ("matrix chained operations", "[testH2]")
	TEST_CASE ("getPoints", "[test_points]")
	TEST_CASE ("getAngle", "[test_angle]")
	TEST_CASE ("getCorrectPoints", "[gcpts]")
	TEST_CASE ("IsInside - manual", "[IsInside_man]")
	TEST_CASE ("Polyline IsInside Polyline", "[tpolipol]")
	TEST_CASE ("Point2d IsInside Polyline", "[tptipol]")
	TEST_CASE ("Line2d IsInside something", "[tlir]")
	TEST_CASE ("Point2d IsInside Circle", "[tptic]")
	TEST_CASE ("Point2d IsInside FRect", "[tptir]")
	TEST_CASE ("Segment IsInside FRect", "[tsir]")
	TEST_CASE ("Circle IsInside FRect", "[tcir]")
	TEST_CASE ("Circle IsInside Circle", "[tcic]")
	TEST_CASE ("Intersection", "[int_all]")
	TEST_CASE ("Line/Line intersection", "[int_LL]")
	TEST_CASE ("Segment/Segment intersection", "[int_SS]")
	TEST_CASE ("Circle/Circle intersection", "[int_CC]")
	TEST_CASE ("FRect/FRect intersection", "[int_FF]")
	TEST_CASE ("IoU of 2 rectangles", "[IOU_RECT]")
	TEST_CASE ("Circle/Segment intersection", "[int_CS]")
	TEST_CASE ("Circle/FRect intersection", "[int_CF]")
	TEST_CASE ("Circle/Line intersection", "[int_CL]")
	TEST_CASE ("Line/Segment intersection", "[int_LS]")
	TEST_CASE ("Line/FRect intersection", "[int_LF]")
	TEST_CASE ("Colinearity", "[colinearity]")
	TEST_CASE ("Line2d", "[line1]")
	TEST_CASE ("Circle", "[cir1]")
	TEST_CASE ("Circle from points", "[cir2]")
	TEST_CASE ("Ellipse", "[ell1]")
	TEST_CASE ("OSegment point side", "[oseg-pt-side]")
	TEST_CASE ("Segment", "[seg1]")
	TEST_CASE ("Translate", "[trans]")
	TEST_CASE ("MoveTo", "[moveto]")
	TEST_CASE ("Segment-split-1", "[seg-split-1]")
	TEST_CASE ("Segment-split-2", "[seg-split-2]")
	TEST_CASE ("Segment 2", "[seg2]")
	TEST_CASE ("Segment extended", "[seg_extended]")
	TEST_CASE ("Segment orthogonal", "[seg_orthog]")
	TEST_CASE ("min/max of two objects", "[minmax]")
	TEST_CASE ("generalized bounding box of two objects", "[gen-BB]")
	TEST_CASE ("bounding box of container", "[BB-cont]")
	TEST_CASE ("common bounding box with points ", "[point2d-BB]")
	TEST_CASE ("FRect pair bounding box", "[frect-BB]")
	TEST_CASE ("bounding box of two objects", "[getBB-pair]")
	TEST_CASE ("FRect", "[frect]")
	TEST_CASE ("FRect extended", "[frect-ext]")
	TEST_CASE ("FRect diagonals", "[frect-diags]")
	TEST_CASE ("Polyline comparison 1", "[polyline-comparison-1]")
	TEST_CASE ("Polyline minimization", "[polyline-min]")
	TEST_CASE ("Polyline", "[polyline]")
	TEST_CASE ("Polyline setParallelogram", "[polyline-setParallelogram]")
	TEST_CASE ("Polyline get extreme point", "[polyline-getExtremePoint]")
	TEST_CASE ("Bounding Box of set of objects", "[BB-cont]")
	TEST_CASE ("getCenters() and getLines()", "[getCenters]")
	TEST_CASE ("Polygon convexity", "[polyline-convex]")
	TEST_CASE ("Polygon orientation", "[polyline-orient]")
	TEST_CASE ("Polyline basic", "[polyline-basic]")
	TEST_CASE ("Polyline fullstep rotation", "[polyline-rot]")
	TEST_CASE ("Polygon area", "[polyline-area]")
	TEST_CASE ("Polyline comparison 2", "[polyline-comp-2]")
	TEST_CASE ("convex hull", "[conv_hull]")
	TEST_CASE ("nearest/farthest points", "[nfp]")
	TEST_CASE ("pts_inside", "[ptsins]")
	TEST_CASE ("variant conversion tests", "[varconv]")
	TEST_CASE ("variant-based polymorphism", "[polymorph_1]")
	TEST_CASE ("SVG_Import_1", "[svg_import_1]")
	TEST_CASE ("SVG Import Ellipse", "[svg_import_ell]")
	TEST_CASE ("SVG Import path 1", "[svg_import_path_1]")
	TEST_CASE ("boost geometry point import", "[bg-pt-import]")
	TEST_CASE ("boost geometry point export", "[bg-pt-export]")
	TEST_CASE ("boost geometry vector point export", "[bg-vpt-export]")
	TEST_CASE ("Opencv build H", "[test_opencv2]")
	TEST_CASE ("Opencv binding", "[test_opencv]")

Variables
Circle	cir
CPolyline	cpol
Ellipse	ell
double	g_epsilon = std::numeric_limits<NUMTYPE>::epsilon()*10000.
Line2d	li
CPolyline	pol (5, 5u)
Point2d	pt
FRect	rect
Segment	seg

Detailed Description

A test file for homog2d, needs Catch2, v2 (single header file version), see https://github.com/catchorg/Catch2
Run with $ make test

This file holds mostly "general" tests.

It also holds some tests that are only related to the OpenCv binding Thus, they are run only if the symbol HOMOG2D_USE_OPENCV is defined.
This latter part starts around line 3350.
Run with $ make test USE_OPENCV=Y

It also holds some tests that are only related to the SVG import feature, that requires the tinyxml2 library, and that the symbol HOMOG2D_USE_SVG_IMPORT is defined.
Run with $ make test USE_TINYXML2=Y

Macro Definition Documentation

CATCH_CONFIG_RUNNER

#define CATCH_CONFIG_RUNNER

HOMOG2D_BIND_X

#define HOMOG2D_BIND_X   xxx

see test [gen_bind]

HOMOG2D_TEST_MODE

#define HOMOG2D_TEST_MODE

LOCALLOG

#define LOCALLOG

(

a

)

NUMTYPE

#define NUMTYPE   double

Numerical type for object storage for tests. This is usually defined by makefile. (The internal numerical type for the library is defined by HOMOG2D_INUMTYPE)

STR

#define STR

(

s

)

#s

XSTR

#define XSTR

(

s

)

STR(s)

Function Documentation

CHECK() [1/21]

CHECK

(

s1.

getPointAt0 = =Point2d_< NUMTYPE >(0, 0)

)

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CHECK() [2/21]

CHECK

(

s1.

getPointAt5 = =Point2d_< NUMTYPE >(5, 0)

)

CHECK() [3/21]

CHECK

(

s1.

getPointAt10 = =Point2d_< NUMTYPE >(10, 0)

)

CHECK() [4/21]

CHECK

(

s1.

getPointAt20 = =Point2d_< NUMTYPE >(20, 0)

)

CHECK() [5/21]

CHECK

(

pol.

size() = =5

)

CHECK() [6/21]

CHECK

(

opol.

size() = =0

)

CHECK() [7/21]

CHECK

(

cpol.

size() = =0

)

CHECK() [8/21]

CHECK

(

cir.

size() = =1

)

CHECK() [9/21]

CHECK

(

ell.

size() = =1

)

CHECK() [10/21]

CHECK

(

rect.

size() = =4

)

CHECK() [11/21]

CHECK

(

seg.

size() = =2

)

CHECK() [12/21]

CHECK

(

li.

size() = =0

)

CHECK() [13/21]

CHECK

(

pt.

size() = =1

)

CHECK() [14/21]

CHECK

(

size(opol)

= =0

)

CHECK() [15/21]

CHECK

(

size(cpol)

= =0

)

CHECK() [16/21]

CHECK

(

size(cir)

= =1

)

CHECK() [17/21]

CHECK

(

size(ell)

= =1

)

CHECK() [18/21]

CHECK

(

size(rect)

= =4

)

CHECK() [19/21]

CHECK

(

size(seg)

= =2

)

CHECK() [20/21]

CHECK

(

size(li)

= =0

)

CHECK() [21/21]

CHECK

(

size(pt)

= =1

)

CHECK_THROWS() [1/7]

CHECK_THROWS

(

CPolyline(-5, 5u)

)

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CHECK_THROWS() [2/7]

CHECK_THROWS

(

CPolyline(1, 2u)

)

CHECK_THROWS() [3/7]

CHECK_THROWS

(

CPolyline(0, 5u)

)

CHECK_THROWS() [4/7]

CHECK_THROWS

(

pol.

set1, 2u

)

CHECK_THROWS() [5/7]

CHECK_THROWS

(

pol.

set0, 5u

)

CHECK_THROWS() [6/7]

CHECK_THROWS

(

pol.

set-5, 5u

)

CHECK_THROWS() [7/7]

CHECK_THROWS

(

pol.

set5, 0u

)

checkSizeNF()

template<typename PT , typename CONT >

void checkSizeNF	(	const PT &	pt,
		const CONT &	cont
	)

{
    CHECK_THROWS( findFarthestPoint(        pt, cont ) );
    CHECK_THROWS( findNearestPoint(         pt, cont ) );
    CHECK_THROWS( findNearestFarthestPoint( pt, cont ) );
}

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computeDistTransformedLined()

long double computeDistTransformedLined	(	Homogr_< NUMTYPE > &	H,
		Point2d_< NUMTYPE >	pt1
	)

Computation of the line passed through H^{-T} and computation of the distance between the resulting line and the transformed point. Should be 0, always.

{
    Line2d_<NUMTYPE> line1( pt1 );       // line from (0,0) to pt1
    Point2d_<NUMTYPE> pt2 = H * pt1;     // move the point with H
//  H.inverse().transpose();             // not needed, done automatically since release 2.4 !
    Line2d_<NUMTYPE> line2 = H * line1;  // move the line with H^{-T}
    return line2.distTo( pt2 );          // should be 0 !
}

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FullPrecision()

std::string FullPrecision

(

long double

d

)

{
    auto s = std::ostringstream{};
    s << std::scientific << std::setprecision( std::numeric_limits<long double>::max_digits10 ) << d;
    return s.str();
}

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local_draw_test() [1/3]

template<typename I >

void local_draw_test	(	img::Image< I > &	im,
		std::string	fn
	)

Make sure all drawing functions and member functions are implemented.

No tests here, actually only checking that it builds fine

{
    FRect      r; local_draw_test2( im, r );
    Segment    s(50,50,100,100);
    local_draw_test2( im, s );
    Circle     c; local_draw_test2( im, c );
    Line2d    li; local_draw_test2( im, li );
    Point2d   pt; local_draw_test2( im, pt );
    Ellipse   el; local_draw_test2( im, el );
    CPolyline cp; local_draw_test2( im, cp );
    OPolyline op; local_draw_test2( im, op );

    im.write( fn );
}

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local_draw_test() [2/3]

local_draw_test	(	im	,
		"BUILD/dummy_draw.svg"
	)

local_draw_test() [3/3]

local_draw_test	(	im	,
		"BUILD/dummy_draw.png"
	)

local_draw_test2()

template<typename I , typename T >

void local_draw_test2	(	img::Image< I > &	im,
		T &	t
	)

Helper function for local_draw_test()

{
    t.draw( im );
    im.draw( t );
    draw( im, t );

    img::DrawParams dp;
    t.draw( im, dp );
    im.draw( t, dp );
    draw( im, t, dp );

    std::vector<T> v;
    t.translate( 50,20 );
    v.push_back(t);
    t.translate( 50,20 );
    v.push_back(t);
    draw( im, v );
    draw( im, v, dp );

    std::list<T> l;
    l.push_back(t);
    l.push_back(t);
    draw( im, l );
    draw( im, l, dp );

    std::array<T,2> a;
    a[0]=t;
    a[1]=t;
    draw( im, a );
    draw( im, a, dp );
}

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main()

int main	(	int	argc,
		char *	argv[]
	)

{
    std::cout << "START TESTS:"
        << "\n - homog2d version: " << HOMOG2D_VERSION
        << "\n - numerical type: " << XSTR(NUMTYPE)
        << "\n - internal numerical type=" << XSTR(HOMOG2D_INUMTYPE)
        << "\n - Catch lib version: " << CATCH_VERSION_MAJOR << '.' << CATCH_VERSION_MINOR << '.' << CATCH_VERSION_PATCH
        << "\n - build options:"

        << "\n  - HOMOG2D_OPTIMIZE_SPEED: "
#ifdef HOMOG2D_OPTIMIZE_SPEED
        << "YES"
#else
        << "NO"
#endif

        << "\n  - HOMOG2D_USE_OPENCV: "
#ifdef HOMOG2D_USE_OPENCV
        << "YES"
#else
        << "NO"
#endif

        << "\n  - HOMOG2D_USE_SVG_IMPORT: "
#ifdef HOMOG2D_USE_SVG_IMPORT
        << "YES"
#else
        << "NO"
#endif

        << "\n  - HOMOG2D_ENABLE_PRTP: "
#ifdef HOMOG2D_ENABLE_PRTP
        << "YES"
#else
        << "NO"
#endif

        << "\n  - HOMOG2D_ENABLE_VRTP: "
#ifdef HOMOG2D_ENABLE_VRTP
        << "YES"
#else
        << "NO"
#endif
        << '\n';

    Catch::StringMaker<float>::precision = 25;
    Catch::StringMaker<double>::precision = 25;

// removed until PR merged into next release, see https://github.com/catchorg/Catch2/pull/2245
//  Catch::StringMaker<long double>::precision = 25;

// we need to have a bigger threshold value for "float" type, as it has a lot less precision
    if( std::string( XSTR(NUMTYPE) ) == "float" )
        thr::nullDistance() = 1E-6;

    thr::printThresholds( std::cout );

    return Catch::Session().run( argc, argv );
}

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polytest_1()

template<typename T , typename U >

void polytest_1

(

const base::PolylineBase< T, U > &

pl1

)

{
    CHECK( pl1.isSimple() == false );
    CHECK( isSimple(pl1)  == false );

    CHECK( pl1.size() == 0 );
    CHECK( size(pl1)  == 0 );

    CHECK( pl1.nbSegs() == 0 );
    CHECK( nbSegs(pl1)  == 0 );

    CHECK( pl1.length() == 0 );
    CHECK( length(pl1)  == 0 );

    CHECK( pl1.area()   == 0 );
    CHECK( area(pl1)    == 0 );

    CHECK_THROWS( centroid(pl1) ); // unable
    CHECK_THROWS( pl1.centroid() ); // unable
}

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set()

pol set	(	8	,
		4u
	)

TEST_CASE() [1/93]

TEST_CASE	(	"numerical types access"	,
		""	[types-access]
	)

{
    Point2dF ptF;
    Point2dD ptD;
    Point2dL ptL;

    Line2dF liF;
    Line2dD liD;
    Line2dL liL;

    HomogrF HF;
    HomogrD HD;
    HomogrL HL;

    FRectF rF;
    FRectD rD;
    FRectL rL;

    SegmentF sF;
    SegmentD sD;
    SegmentL sL;

    CircleF cF;
    CircleD cD;
    CircleL cL;

    OPolylineF poF;
    OPolylineD poD;
    OPolylineL poL;

    CPolylineF pcF;
    CPolylineD pcD;
    CPolylineL pcL;

    EllipseF eF;
    EllipseD eD;
    EllipseL eL;

    CHECK( ptF.dtype() == dtype(ptF) );

    CHECK( ptF.dtype() == Dtype::Float );
    CHECK( liF.dtype() == Dtype::Float );
    CHECK( HF.dtype()  == Dtype::Float );
    CHECK( rF.dtype()  == Dtype::Float );
    CHECK( sF.dtype()  == Dtype::Float );
    CHECK( cF.dtype()  == Dtype::Float );
    CHECK( poF.dtype() == Dtype::Float );
    CHECK( pcF.dtype() == Dtype::Float );
    CHECK( eF.dtype()  == Dtype::Float );

    CHECK( ptD.dtype() == Dtype::Double );
    CHECK( liD.dtype() == Dtype::Double );
    CHECK( HD.dtype()  == Dtype::Double );
    CHECK( rD.dtype()  == Dtype::Double );
    CHECK( sD.dtype()  == Dtype::Double );
    CHECK( cD.dtype()  == Dtype::Double );
    CHECK( poD.dtype() == Dtype::Double );
    CHECK( pcD.dtype() == Dtype::Double );
    CHECK( eD.dtype()  == Dtype::Double );

    CHECK( dtype(ptD) == Dtype::Double );
    CHECK( dtype(liD) == Dtype::Double );
    CHECK( dtype(HF)  == Dtype::Float );
    CHECK( dtype(rF)  == Dtype::Float );

    CHECK( dsize(ptF).first  == ptF.dsize().first );
    CHECK( dsize(ptD).first  == ptD.dsize().first );
    CHECK( dsize(ptL).first  == ptL.dsize().first );

    CHECK( dsize(ptF).second  == ptF.dsize().second );
    CHECK( dsize(ptD).second  == ptD.dsize().second );
    CHECK( dsize(ptL).second  == ptL.dsize().second );

    CHECK( dsize(ptF).first  == 24 );
    CHECK( dsize(ptF).second == 7  );

    CHECK( dsize(ptD).first  == 53 );
    CHECK( dsize(ptD).second == 10 );

    CHECK( dsize(ptL).first  == 64 );
    CHECK( dsize(ptL).second == 63 );
}

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TEST_CASE() [2/93]

TEST_CASE	(	"comparison testing"	,
		""	[comparison-test]
	)

{
    {
        Segment_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
    {
        Circle_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
    {
        FRect_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
    {
        Line2d_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
    {
        Point2d_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
    {
        Ellipse_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
    {
        CPolyline_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
    {
        OPolyline_<NUMTYPE>
        a1, a2; CHECK( a1 == a2 );
    }
}

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TEST_CASE() [3/93]

TEST_CASE	(	"types testing 1"	,
		""	[test-types-1]
	)

{
    INFO( "type size" )
    {
        Point2dF ptF;
        Point2dD ptD;
        Point2dL ptL;

        Line2dF liF;
        Line2dD liD;
        Line2dL liL;

        HomogrF HF;
        HomogrD HD;
        HomogrL HL;

        Point2d pt(4.,5); // checking with 2 different types
        Point2d_<float> pt2F1;
        Point2d_<double> pt2F2;
        Point2d_<long double> pt2F3;
        pt2F1.set(4.,5); // checking with 2 different types

        CHECK( ptF.type() == Type::Point2d );
        CHECK( liF.type() == Type::Line2d );
    }

    Point2dD ptD0(1,1);
    Point2dF ptF0(2,2);
    Point2dL ptL0(3,3);

    Line2dD li_D0(1,1);
    Line2dF li_F0(2,2);
    Line2dL li_L0(3,3);
}

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TEST_CASE() [4/93]

TEST_CASE	(	"types testing 2"	,
		""	[test-types-2]
	)

{
    Point2dD ptD0(1,1);
    Point2dF ptF0(2,2);
    Point2dL ptL0(3,3);

    INFO( "numerical type conversions (assignment)" )
    {
        Point2dD ptD(4,4);
        Point2dF ptF(5,5);
        Point2dL ptL(6,6);

        ptL = ptD0;
        CHECK( ptL.getX() == 1. );
        ptL = ptF0;
        CHECK( ptL.getX() == 2. );

        ptF = ptD0;
        CHECK( ptF.getX() == 1. );
        ptF = ptL0;
        CHECK( ptF.getX() == 3. );

        ptD = ptF0;
        CHECK( ptD.getX() == 2. );
        ptD = ptL0;
        CHECK( ptD.getX() == 3. );

        CircleF cf;
        CircleD cd;
        CircleL cl;
        cl = cd;
        cf = cd;
        cd = cf;
        cl = cf;
        cf = cl;
        cd = cl;

        SegmentF sf;
        SegmentD sd;
        SegmentL sl;
        sl = sd;
        sf = sd;
        sd = sf;
        sl = sf;
        sf = sl;
        sd = sl;

        FRectF rf;
        FRectD rd;
        FRectL rl;
        rl = rd;
        rf = rd;
        rd = rf;
        rl = rf;
        rf = rl;
        rd = rl;

        OPolylineF pof;
        OPolylineD pod;
        OPolylineL pol;

        pol = pod;
        pof = pod;
        pod = pof;
        pol = pof;
        pof = pol;
        pod = pol;
    }
}

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TEST_CASE() [5/93]

TEST_CASE	(	"normalization"	,
		""	[normaliz]
	)

{
    Point2d_<NUMTYPE> pt1(1,2,3);
    CHECK( pt1.get() == std::array<NUMTYPE,3>{1,2,3} );
    Point2d_<NUMTYPE> pt2(-1,2,3);
    CHECK( pt2.get() == std::array<NUMTYPE,3>{1,-2,-3} );
}

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TEST_CASE() [6/93]

TEST_CASE	(	"homogeneous coordinates testing"	,
		""	[homogeneous]
	)

{
    {
        Point2d_<NUMTYPE> pt1(2,2,1);
        Point2d_<NUMTYPE> pt2(4,4,2);
        CHECK( pt1 == pt2 );
        pt2.set(8,8,4);
        CHECK( pt1 == pt2 );

        Line2d_<NUMTYPE> li1(0,1,0);
        Line2d_<NUMTYPE> li2(0,2,0);
        CHECK( li1 == li2 );
        li2.set(0,4,0);
        CHECK( li1 == li2 );

        Line2d_<NUMTYPE> li3(3,4,5);
        Line2d_<NUMTYPE> li4(6,8,10);
        CHECK( li3 == li4 );
    }
    {
        INFO( "constructors using a container of values as single argument" );

        std::array<float,3> arr{3,2,1};
        Point2d_<NUMTYPE> pt1(arr);
        CHECK( pt1 == Point2d_<NUMTYPE>(3,2,1) );

        std::vector<float> vec{3,2,1};
        Point2d_<NUMTYPE> pt2(vec);
        CHECK( pt2 == Point2d_<NUMTYPE>(3,2,1) );
    }
}

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TEST_CASE() [7/93]

TEST_CASE	(	"infinity point"	,
		""	[points-inf]
	)

{
    Line2d liH( LineDir::H, Point2d() ); // horizontal line at y=0
    CHECK_THROWS( Point2d(0,0,0) );
    CHECK_THROWS( Line2d(0,0,0) );

    Point2d pt1(1,0,0);
    Point2d pt2(-1,0,0);
    CHECK( pt1.isInf() );
    CHECK( pt2.isInf() );

    auto li1 = pt1 * Point2d();
    CHECK( li1 == liH );
    auto li2 = pt2 * Point2d();
    CHECK( li2 == liH );

    Point2d pt3(3,3,0);  // infinite points at an angle of 45°
    auto li3 = pt3 * Point2d();
    CHECK( std::abs(li3.getAngle( liH ) - M_PI/4.) < g_epsilon );

    Segment seg( Point2d(), pt1 );
    auto ppts = seg.getPts();

    auto line = seg.getLine();
    CHECK( line == liH );
}

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TEST_CASE() [8/93]

TEST_CASE	(	"types testing 3"	,
		""	[test-types-3]
	)

The goal of these is to make sure that the conversion (float to double, ...) does not trigger a build failure. The checking is only there to avoid a warning about "unused variable".

Todo:

Once we switch to C++17, we can remove the checking and use: https://en.cppreference.com/w/cpp/language/attributes/maybe_unused

{
    Point2dD ptD0(1,1); // double
    Point2dF ptF0(2,2); // float
    Point2dL ptL0(3,3); // long

    INFO( "numerical type conversions (copy-constructor)" )
    {
        Point2dL ptL1 = ptD0; // double to long
        Point2dL ptL2 = ptF0; // float to long
        CHECK( ptL1.getX() == 1. );
        CHECK( ptL2.getX() == 2. );

        Point2dF ptF1 = ptD0;
        Point2dF ptF2 = ptL0;
        CHECK( ptF1.getX() == 1. );
        CHECK( ptF2.getX() == 3. );

        Point2dD ptD1 = ptF0;
        Point2dD ptD2 = ptL0;
        CHECK( ptD1.getX() == 2. );
        CHECK( ptD2.getX() == 3. );

        CircleL cl;
        CircleF cf;
        CircleD cd;

        CircleL cl2 = cd;
        CircleF cf2 = cd;
        CircleD cd2 = cd;

        CircleL cl3 = cf;
        CircleF cf3 = cf;
        CircleD cd3 = cf;

        CircleL cl4 = cl;
        CircleF cf4 = cl;
        CircleD cd4 = cl;

        SegmentL sl;
        SegmentF sf;
        SegmentD sd;

        SegmentL sl2 = sd;
        SegmentF sf2 = sd;
        SegmentD sd2 = sd;

        SegmentL sl3 = sf;
        SegmentF sf3 = sf;
        SegmentD sd3 = sf;

        SegmentL sl4 = sl;
        SegmentF sf4 = sl;
        SegmentD sd4 = sl;

        FRectL rl;
        FRectF rf;
        FRectD rd;

        FRectL rl2 = rd;
        FRectF rf2 = rd;
        FRectD rd2 = rd;

        FRectL rl3 = rf;
        FRectF rf3 = rf;
        FRectD rd3 = rf;

        FRectL rl4 = rl;
        FRectF rf4 = rl;
        FRectD rd4 = rl;

        OPolylineL pol;
        OPolylineF pof;
        OPolylineD pod;

        OPolylineL pol2 = pod;
        OPolylineF pof2 = pod;
        OPolylineD pod2 = pod;

        OPolylineL pol3 = pof;
        OPolylineF pof3 = pof;
        OPolylineD pod3 = pof;

        OPolylineL pol4 = pol;
        OPolylineF pof4 = pol;
        OPolylineD pod4 = pol;

        CPolylineL pcl;
        CPolylineF pcf;
        CPolylineD pcd;

        CPolylineL pcl2 = pcd;
        CPolylineF pcf2 = pcd;
        CPolylineD pcd2 = pcd;

        CPolylineL pcl3 = pcf;
        CPolylineF pcf3 = pcf;
        CPolylineD pcd3 = pcf;

        CPolylineL pcl4 = pcl;
        CPolylineF pcf4 = pcl;
        CPolylineD pcd4 = pcl;

        EllipseL elll;
        EllipseF ellf;
        EllipseD elld;

        EllipseL elll2 = elld;
        EllipseF ellf2 = elld;
        EllipseD elld2 = elld;

        EllipseL elll3 = ellf;
        EllipseF ellf3 = ellf;
        EllipseD elld3 = ellf;

        EllipseL elll4 = elll;
        EllipseF ellf4 = elll;
        EllipseD elld4 = elll;

        Line2dD li_D0(1,1);
        Line2dF li_F0(2,2);
        Line2dL li_L0(3,3);

        Line2dD li_D1 = li_F0; CHECK( li_D1.get()[2] == 0. );
        Line2dD li_L1 = li_F0; CHECK( li_L1.get()[2] == 0. );

        Line2dD li_F2 = li_D0; CHECK( li_F2.get()[2] == 0. );
        Line2dD li_L2 = li_D0; CHECK( li_L2.get()[2] == 0. );

        Line2dD li_F3 = li_L0; CHECK( li_F3.get()[2] == 0. );
        Line2dD li_D3 = li_L0; CHECK( li_D3.get()[2] == 0. );
    }
}

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TEST_CASE() [9/93]

TEST_CASE	(	"stream operator << test"	,
		""	[streamingop-test]
	)

{
    Line2d li;
    Point2d pt;
    Segment seg;
    OSegment vec;
    Circle cir;
    Ellipse ell;
    CPolyline cpol;
    OPolyline opol;
// just to make sure that this builds !
    std::ostringstream oss;
    oss << li << pt << seg << vec << cir << cpol << opol << ell;
    std::ostringstream oss2;
    oss2 << cpol;
    CHECK( oss2.str() == "CPolyline: empty" );
}

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TEST_CASE() [10/93]

TEST_CASE	(	"line/point distance"	,
		""	[lp-dist]
	)

{
    size_t n = 1E6;  // nb of runs
    size_t c1{};
    size_t c2{};
    long double sum1{};
    long double sum2{};
    float k = 1;
    std::srand( time(0) );
    for( size_t i=0; i<n; i++ )
    {
        Point2d_<NUMTYPE> pt1(
            1.0*rand()/RAND_MAX * k,
            1.0*rand()/RAND_MAX * k
        );
        Point2d_<NUMTYPE> pt2(
            1.0*rand()/RAND_MAX * k,
            1.0*rand()/RAND_MAX * k
        );
        auto li = pt1 * pt2;
        auto d1 = li.distTo(pt1);
        auto d2 = li.distTo(pt2);
        if( d1 > thr::nullDistance() )
        {
//          std::cerr << ": distance check failure 1, value " << d1 << " > thres (" << thr::nullDistance()  << ")\n";
            sum1 += d1;
            c1++;
        }
        if( li.distTo(pt2) > thr::nullDistance() )
        {
//          std::cerr << "distance check failure 2, value " << d2 << " > thres (" << thr::nullDistance()  << ")\n";
            sum2 += d2;
            c2++;
        }
    }
    if( c1 != 0 || c2 != 0  )
    {
        std::cout << "line/point distance test failures with thres=" << thr::nullDistance()
            << "\n nb1=" << c1 << ", nb2=" << c2  << " failures over total nb of tests=" << n
            << "\n- mean distance: d1=" << sum1 / c1
            << "\n- mean distance: d2=" << sum2 / c2
            << '\n';
    }
    CHECK( c1 == 0 );
    CHECK( c2 == 0 );
}

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TEST_CASE() [11/93]

TEST_CASE	(	"side-pt-line"	,
		""	[side-pt-line]
	)

{
    Line2d_<NUMTYPE> li; // vertical line at x=0
    {
        Point2d_<NUMTYPE> pt;
        CHECK( side(pt,li) == 0 );
    }
    {
        Point2d_<NUMTYPE> pt(1,0);
        CHECK( side(pt,li) == 1 );
    }
    {
        Point2d_<NUMTYPE> pt(-1,0);
        CHECK( side(pt,li) == -1 );
    }
}

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TEST_CASE() [12/93]

TEST_CASE	(	"test1"	,
		""	[test1]
	)

{
    Point2d_<NUMTYPE> ptA1; // 0,0
    CHECK( ptA1 == Point2d_<NUMTYPE>(0,0) );

    Point2d_<NUMTYPE> ptA2(2,2);
    CHECK( ptA2.getX() == 2. );
    CHECK( ptA2.getY() == 2. );

    { // build line from one point, other one will be (0,0)
        Line2d_<NUMTYPE> lA1( ptA2 );
        CHECK( lA1.distTo( ptA1 ) == 0 );
        CHECK( lA1.distTo( ptA2 ) == 0 );

        CHECK( ptA1.distTo( lA1 ) == 0 );
        CHECK( ptA2.distTo( lA1 ) == 0 );
    }

    { // build line from two points
        Line2d_<NUMTYPE> lA1 = ptA1 * ptA2;
        Line2d_<NUMTYPE> lA2 = ptA2 * ptA1;

        CHECK( lA1 == lA2 );
        CHECK( lA1.getAngle(lA2) == 0. );
        CHECK( lA2.getAngle(lA1) == 0. );
        CHECK( getAngle(lA1,lA2) == 0. );

        Point2d_<NUMTYPE> ptB1(0,2);
        Point2d_<NUMTYPE> ptB2(2,0);
        Line2d_<NUMTYPE>  lB = ptB1 * ptB2;

        auto v1 = lB.getCoord( GivenCoord::X, 1 );
        CHECK( v1 == 1. );
        CHECK( lB.getPoint( GivenCoord::X, 1) == Point2d_<NUMTYPE>(1,1) );
    }
    {
// build point from two diagonal lines
        Line2d_<NUMTYPE> liA( Point2d(0,0), Point2d(2,2) );
        Line2d_<NUMTYPE> liB( Point2d(0,2), Point2d(2,0) );
        CHECK( Line2d_<NUMTYPE>() != liA );

        auto mA1 = liA * liB;
        auto mA2 = liB * liA;
        CHECK( mA1 == Point2d_<NUMTYPE>(1.,1.) );
        CHECK( mA2 == Point2d_<NUMTYPE>(1.,1.) );
        CHECK( mA1 != Point2d_<NUMTYPE>() );

// build point from two H/V lines
        Line2d_<NUMTYPE> lv0( 0, 1 );  // vertical, x=0
        Line2d_<NUMTYPE> lh0( 1, 0 );  // horizontal, x=0

        CHECK( lv0 * lh0 == Point2d_<NUMTYPE>(0.,0.) );
        CHECK( lh0 * lv0 == Point2d_<NUMTYPE>(0.,0.) );

        Line2d_<NUMTYPE> lv2( Point2d(2,0), Point2d(2,2) ); // vertical, x=2
        Line2d_<NUMTYPE> lh2( Point2d(0,2), Point2d(2,2) ); // horizontal, y=2

        CHECK( lv2*lh2 == Point2d_<NUMTYPE>(2.,2.) );

        CHECK( lv0*liA == Point2d_<NUMTYPE>() );
        CHECK( lh0*liA == Point2d_<NUMTYPE>() );

        CHECK( lv0*liB == Point2d_<NUMTYPE>(0,2) );
        CHECK( lh0*liB == Point2d_<NUMTYPE>(2,0) );

        CHECK( lv2*liA == Point2d_<NUMTYPE>(2.,2.) );
        CHECK( lh2*liA == Point2d_<NUMTYPE>(2.,2.) );

        CHECK( lv2*liB == Point2d_<NUMTYPE>(2.,0.) );
        CHECK( lh2*liB == Point2d_<NUMTYPE>(0.,2.) );
    }

    { // test of getOrthogonal()
        Line2d_<NUMTYPE> lV; // vertical line at x=0

// get orthogonal line at y=100
        Line2d_<NUMTYPE> li2 = lV.getOrthogLine( GivenCoord::Y, 100 );
        CHECK( li2.getAngle( lV ) == Approx(M_PI/2.) );
        CHECK( getAngle( li2,lV ) == Approx(M_PI/2.) );

        Line2d_<NUMTYPE> lH2(1,0);                // build horizontal line
        Line2d_<NUMTYPE> lH3 = lH2;
        CHECK( lH2.getAngle(lH3) == 0. );
    }
    {
        Line2d_<NUMTYPE> li(4,2);
        CHECK( li.getCoord( GivenCoord::X, 2 ) == 1 );
        CHECK( li.getCoord( GivenCoord::Y, 1 ) == 2 );
        CHECK( li.getPoint( GivenCoord::X, 2 ) == Point2d_<NUMTYPE>(2,1) );
        CHECK( li.getPoint( GivenCoord::Y, 1 ) == Point2d_<NUMTYPE>(2,1) );
    }
    {
        Line2d_<NUMTYPE> liv1( LineDir::V, 10. );
        Line2d_<NUMTYPE> liv2( Point2d(10,0), Point2d(10,20) );
        CHECK( liv1 == liv2 );
        Line2d_<NUMTYPE> lih1( LineDir::H, 10. );
        Line2d_<NUMTYPE> lih2( Point2d(0,10), Point2d(20,10) );
        CHECK( lih1 == lih2 );
    }
}

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TEST_CASE() [13/93]

TEST_CASE	(	"build point line from container"	,
		""	[build-cont]
	)

{
    std::array<double,3> arr{3,2,1};
    Point2d_<NUMTYPE> pt( arr );
    CHECK( pt == Point2d(3,2,1) );
}

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TEST_CASE() [14/93]

TEST_CASE	(	"test throw"	,
		""	[test_thr]
	)

{
    Line2d li;
    CHECK_THROWS( li.getCoord( GivenCoord::X, 0 ) );

    INFO("Lines and points");
    {
        Line2d_<NUMTYPE> v1,v2; // 2 identical vertical lines
        CHECK_THROWS( v1*v2 );

        Point2d_<NUMTYPE> p1,p2;
        CHECK_THROWS( p1*p2 ); // same points can't define a line
    }
    INFO("rectangle constructor")
    {
        Point2d_<NUMTYPE> p1, p2;
        CHECK_THROWS( FRect( p1,p2) );
        p2.set( 1, 1);
        CHECK_NOTHROW( FRect( p1,p2) );
        CHECK( FRect_<NUMTYPE>( p1,p2).getPts()==std::make_pair(Point2d_<NUMTYPE>(0,0),Point2d_<NUMTYPE>(1,1) ) );
        p1.set( 4, 4 );
        p2.set( 5, 5 );
        CHECK_NOTHROW( FRect( p1,p2) );
        p1.set( 4, 5 );
        p2.set( 5, 4 );
        CHECK_NOTHROW( FRect( p1,p2) );
        p1.set( 5, 4 );
        p2.set( 4, 5 );
        CHECK_NOTHROW( FRect( p1,p2) );

        p1.set( 4, 4 );
        p2.set( 5, 4 );
        CHECK_THROWS( FRect( p1,p2) );
        p2.set( 4, 5 );
        CHECK_THROWS( FRect( p1,p2) );
    }
    INFO("circle constructor")           // 0 not allowed as radius
    {
        Point2d_<NUMTYPE> pt;
        CHECK_THROWS(  Circle_<NUMTYPE> ( pt, 0 ) );
        CHECK_THROWS(  Circle_<NUMTYPE> ( pt, thr::nullDistance()/1.1 ) );
        CHECK_NOTHROW( Circle_<NUMTYPE> ( pt, thr::nullDistance()*1.1 ) );
    }
    INFO("segment constructor")           // can't have identical points
    {
        CHECK_THROWS( Segment_<NUMTYPE> ( Point2d(), Point2d() ) );
        CHECK_THROWS( Segment_<NUMTYPE> ( Point2d_<NUMTYPE>(1,5), Point2d_<NUMTYPE>(1,5) ) );
    }
}

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TEST_CASE() [15/93]

TEST_CASE	(	"test parallel"	,
		""	[test_para]
	)

{
    INFO( "Checking angle" )
    {
        Line2d_<NUMTYPE> l1;                                                   // vertical line
        Line2d_<NUMTYPE> l2a( Point2d_<NUMTYPE>(0,0),Point2d_<NUMTYPE>(1,1) ); // 45° line, starting at (0,0)
        CHECK( getAngle( l1, l2a ) == Approx( M_PI/4. ) );

        Line2d_<NUMTYPE> l2b( Point2d_<NUMTYPE>(3,0),Point2d_<NUMTYPE>(4,1) ); // 45° line, starting at (3,0)
        CHECK( getAngle( l1, l2b ) == Approx( M_PI/4. ) );

//      l2b.addOffset( LineOffset::horiz, 10. );
//      CHECK( getAngle( l1, l2b ) == Approx( M_PI/4. ) );
//      l2b.addOffset( LineOffset::vert, 10. );
//      CHECK( getAngle( l1, l2b ) == Approx( M_PI/4. ) );
    }

    INFO( "Checking parallel lines" )
    {
        Line2d_<NUMTYPE> l1, l1b; // vertical line
        CHECK( l1.isParallelTo(l1b) );
        {
            Line2d_<NUMTYPE> l2a(Point2d_<NUMTYPE>(1.,0.), Point2d_<NUMTYPE>(1.0005,1.) ); // almost vertical line
            CHECK( l1.isParallelTo(l2a) == true );

            Line2d_<NUMTYPE> l2b(Point2d_<NUMTYPE>(1.,0.), Point2d_<NUMTYPE>(1.002,1.) ); // almost vertical line
            CHECK( l1.isParallelTo(l2b) == false );
        }
        thr::nullAngleValue() = 0.01;
        {
            Line2d_<NUMTYPE> l2a(Point2d_<NUMTYPE>(1.,0.), Point2d_<NUMTYPE>(1.0005,1.) ); // almost vertical line
            INFO( "angle=" << getAngle( l1,l2a) );
            CHECK( l1.isParallelTo(l2a) == true );

            Line2d_<NUMTYPE> l2b(Point2d_<NUMTYPE>(1.,0.), Point2d_<NUMTYPE>(1.02,1.) ); // almost vertical line
            INFO( "angle=" << getAngle( l1,l2b) );
            CHECK( l1.isParallelTo(l2b) == false );
        }
        //l1.isParallelTo( Point2d() ); // NO BUILD
    }
    INFO( "Vertical line at x=0" )
    {
        Line2d_<NUMTYPE> l1; // vertical line

        Line2d_<NUMTYPE> l2 = l1.getParallelLine( Point2d_<NUMTYPE>(1,1) );
        CHECK_THROWS( l1 * l2 ); // two parallel lines never cross
        CHECK( l2.distTo( Point2d_<NUMTYPE>(0,0) ) == 1. );
        CHECK( l2.distTo( Point2d_<NUMTYPE>(0,2) ) == 1. );
        CHECK( getAngle(l2,l1) == 0. );

        Line2d_<NUMTYPE> l3 = l1.getParallelLine( Point2d_<NUMTYPE>(0,0) );
        CHECK( l3.distTo( Point2d_<NUMTYPE>(0,0) ) == 0. );
        CHECK( l3.distTo( Point2d_<NUMTYPE>(0,2) ) == 0. );
        CHECK( getAngle(l3,l1) == 0. );
    }
    INFO( "dist parallel lines" )
    {
        Line2d_<NUMTYPE> l1;                                // vertical line at x=0
        Line2d_<NUMTYPE> l2( Point2d(1,0), Point2d(1,10) ); // vertical line at x=1
        CHECK( getParallelDistance( l1, l2 ) == 1. );
        Line2d_<NUMTYPE> l3( Point2d(-3,0), Point2d(-3,-10) ); // vertical line at x=1
        CHECK( getParallelDistance( l1, l3 ) == 3. );
        CHECK( getParallelDistance( l2, l3 ) == 4. );

        Line2d_<NUMTYPE> l4( LineDir::H, 1 );    // horizontal line
        CHECK_THROWS( getParallelDistance( l1, l4 ) );
    }
}

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TEST_CASE() [16/93]

TEST_CASE	(	"dist2points"	,
		""	[t_d2p]
	)

{
    Line2d_<NUMTYPE> li(2,1);
    auto d = li.distTo( Point2d_<NUMTYPE>() );
    CHECK( d == 0. );

    auto d2 = li.distTo( Point2d_<NUMTYPE>(4,2) );
    CHECK( d2 == 0. );

    CHECK( li.getCoord( GivenCoord::X, 0. ) == 0. );
    CHECK( li.getCoord( GivenCoord::X, 2. ) == 1. );

    CHECK( li.getCoord( GivenCoord::Y, 0. ) == 0. );
    CHECK( li.getCoord( GivenCoord::Y, 1. ) == 2. );

    Point2d_<NUMTYPE> p1( 3,3);
    Point2d_<NUMTYPE> p2( 4,4);
    auto r = std::abs( p1.distTo( p2 ) - std::sqrt(2.) );
    CHECK( r < thr::nullDistance() );
}

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TEST_CASE() [17/93]

TEST_CASE	(	"Homogr constructors"	,
		""	[testHC]
	)

{
    {
        auto angle = 0.5;
        Homogr H0,H1( angle ); // set rotation with constructor
        H0.setRotation( angle );
        Line2d_<NUMTYPE> li1;
        Line2d_<NUMTYPE> li2 = H0 * li1;
        auto angle2 = getAngle( li1, li2 );
        CHECK( std::fabs(angle2 - angle) < thr::nullAngleValue() );
//      std::cout << std::setprecision( std::numeric_limits<double>::digits10 ) << std::scientific << "angle2=" << angle2 << " angle=" << angle << "\n";
    }
    {
        Homogr H0( 4. , 7. );
        CHECK( H0.value( 0, 2 ) == 4. );
        CHECK( H0.value( 1, 2 ) == 7. );
    }
}

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TEST_CASE() [18/93]

TEST_CASE	(	"test Homogr"	,
		""	[testH]
	)

{
    {
        Homogr H1,H2;
        auto H = H1*H2;
        CHECK( H == H1 );
    }
    {
        std::vector<std::vector<float>> m1a(3);
        for( auto& li: m1a)
            li.resize(3,1);
        Homogr_<NUMTYPE> H1a(m1a);

        std::vector<std::vector<double>> m1b(3);
        for( auto& li: m1b)
            li.resize(3,1);
        Homogr_<NUMTYPE> H1b(m1b);

        std::vector<std::vector<int>> m1c(3);
        for( auto& li: m1c)
            li.resize(3,1);
        Homogr_<NUMTYPE> H1c(m1c);

        std::array<std::array<float,3>,3> m2a;
        m2a[2][2] = 1.;
        Homogr_<NUMTYPE> H2a(m2a);

        std::array<std::array<double,3>,3> m2b;
        m2b[2][2] = 1.;
        Homogr_<NUMTYPE> H2b(m2b);

        std::array<std::array<int,3>,3> m2c;
        m2c[2][2] = 1.;
        Homogr_<NUMTYPE> H2c(m2c);
    }
    { // test of operator * for points
        Homogr_<NUMTYPE> H;
        Point2d_<NUMTYPE> pt1(1,1);
        H.setTranslation( 3., 2. );

        auto pt2 = H * pt1;

        CHECK( pt2.getX() == 4. );
        CHECK( pt2.getY() == 3. );

        H.setRotation( M_PI/2. );
        auto pt3 = H * pt1;

        CHECK( pt3.getX() == Approx( -1. ) );
        CHECK( pt3.getY() == Approx(  1. ) );
    }
    { // test of operator * for container holding points, using applyTo()
        Homogr_<NUMTYPE> H;
        H.setTranslation(5,6);

        std::vector<Point2d> v_pt(3);  // 3 points at (0,0)
        H.applyTo( v_pt );             // translate them all to (+5,+6)
        CHECK( v_pt[2].getX() == 5 );
        CHECK( v_pt[2].getY() == 6 );
        CHECK( v_pt[0].getX() == 5 );
        CHECK( v_pt[0].getY() == 6 );
        auto v_pt2 = H * v_pt;
        CHECK( v_pt2.size() == 3 );
        CHECK( v_pt2[2].getX() == 10 );
        CHECK( v_pt2[2].getY() == 12 );
        CHECK( v_pt2[0].getX() == 10 );
        CHECK( v_pt2[0].getY() == 12 );

        std::array<Point2d,3> a_pt;
        H.applyTo( a_pt );
        CHECK( a_pt[2].getX() == 5 );

        std::list<Point2d> l_pt(3);
        H.applyTo( l_pt );
        CHECK( std::begin(l_pt)->getX() == 5 );
    }
    { // test of operator * for container holding points
        Homogr_<NUMTYPE> H;
        H.setTranslation(5,6);

        std::vector<Point2d> v_pt(3);
        auto vpt2 = H * v_pt;
        CHECK( vpt2.size() == 3 );

        std::array<Point2d,3> a_pt;
        auto vpt3 = H * a_pt;
        CHECK( vpt3.size() == 3 );

        std::list<Point2d> l_pt(3);
        auto vpt4 = H * l_pt;
        CHECK( vpt4.size() == 3 );
    }
}

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TEST_CASE() [19/93]

TEST_CASE	(	"matrix inversion"	,
		""	[testH3]
	)

{
    Homogr_<NUMTYPE> H;
    {
        Homogr_<NUMTYPE> HR=H;
        HR.inverse();
        CHECK( HR == H );
        HR.transpose();
        CHECK( HR == H );
    }

    { // sample inversion
// checked with https://ncalculators.com/matrix/inverse-matrix.htm
        H = std::vector<std::vector<double>>{
            { 1, -1,  2 },
            { 4,  0,  6 },
            { 5,  1, -1 }
        };

        Homogr_<NUMTYPE> H2;

        H2 = H;        // transposing twice = original matrix
        H2.transpose();
        H2.transpose();
        CHECK( H == H2 );

        H2 = H;        // transposing twice = original matrix
        H2.transpose().transpose();
        CHECK( H == H2 );

        H2 = H;        // inverting twice = original matrix
        H2.inverse();
        Homogr_<NUMTYPE> HI = std::vector<std::vector<NUMTYPE>>{
                { -3./2,   1./4,  -3./2 },
                { 17./2, -11./4,   1./2 },
                {  1.  ,  -3./2,   1.   }
            };
        CHECK( H2 == HI );
        H2.inverse();
        CHECK( H == H2 );

        H2 = H;        // inverting twice = original matrix
        H2.inverse().inverse();
        CHECK( H == H2 );

        H2 = H;
        H.inverse();
        Homogr_<NUMTYPE> HR = std::vector<std::vector<double>>{
            {   6, - 1,  6 },
            { -34,  11, -2 },
            { - 4,   6, -4 }
        };
        CHECK( HR == H );

        H.transpose();
        H2.inverse().transpose();
        CHECK( H == H2 );
    }
}

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TEST_CASE() [20/93]

TEST_CASE	(	"line transformation"	,
		""	[testH3]
	)

{
    {
        Line2d_<NUMTYPE> d1( 5, 6 ); // line from (0,0) to (5,6)
        Point2d_<NUMTYPE> pt1( 5, 6);  // point is on line
        CHECK( d1.distTo( pt1 ) < g_epsilon );
    }
    Point2d_<NUMTYPE> pt( 5, 6);
    Homogr_<NUMTYPE> H;
    {
        H.setTranslation(4,5);
        auto d = computeDistTransformedLined( H , pt );
        LOCALLOG( "T(4,5): d=" << FullPrecision(d) );
        CHECK( d < g_epsilon );
        H.setTranslation(4000,5);
        auto d2 = computeDistTransformedLined( H , pt );
        LOCALLOG( "T(4000,5): d=" << FullPrecision(d2) );
        CHECK( d2 < g_epsilon );
        H.setTranslation(4,5000);
        auto d3 = computeDistTransformedLined( H , pt );
        LOCALLOG( "T(4,5000): d=" << FullPrecision(d3) );
        CHECK( d3 < g_epsilon );
    }
    {
        H.setRotation( 22.*M_PI/180. );
        auto d = computeDistTransformedLined( H , pt );
        LOCALLOG( "rotation: d=" << FullPrecision(d) );
        CHECK( d < g_epsilon );
    }
    {
        H.setScale(0.4, 4.2);
        auto d = computeDistTransformedLined( H , pt );
        LOCALLOG( "scale: d=" << FullPrecision(d) );
        CHECK( d < g_epsilon );
    }
    {
        H.setRotation( 1.456 ).addTranslation(4,5).addScale( 0.4, 1.2 ); // some random transformation
        auto d = computeDistTransformedLined( H , pt );
        LOCALLOG( "complex transformation: d=" << FullPrecision(d) );
        CHECK( d < g_epsilon );
    }
}

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TEST_CASE() [21/93]

TEST_CASE	(	"matrix chained operations"	,
		""	[testH2]
	)

{
    Homogr H1,H2;
    CHECK( H1 == H2 );
    H1.addTranslation(4,5).addRotation( 1 ).addScale( 5,6);
    H2.addRotation( 1 ).addTranslation(4,5).addScale( 5,6);
    CHECK( H1 != H2 );
}

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TEST_CASE() [22/93]

TEST_CASE	(	"getPoints"	,
		""	[test_points]
	)

{
    Line2d_<NUMTYPE> liV; // vertical line
    auto pp = liV.getPoints( GivenCoord::Y, 0.0, 2.0 ); // get points at a distance 2 from (0,0)
    CHECK( pp.first  == Point2d_<NUMTYPE>(0,-2) );
    CHECK( pp.second == Point2d_<NUMTYPE>(0,+2) );

    pp = liV.getPoints( GivenCoord::Y, 3.0, 2.0 ); // get points at a distance 2 from (0,3)
    CHECK( pp.first  == Point2d_<NUMTYPE>(0,+1) );
    CHECK( pp.second == Point2d_<NUMTYPE>(0,+5) );

    Line2d_<NUMTYPE> liH(1,0); // horizontal line
    pp = liH.getPoints( GivenCoord::X, 0.0, 2.0 ); // get points at a distance 2 from (0,0)
    CHECK( pp.first  == Point2d_<NUMTYPE>(-2,0) );
    CHECK( pp.second == Point2d_<NUMTYPE>(+2,0) );

    pp = liH.getPoints( GivenCoord::X, 3.0, 2.0 ); // get points at a distance 2 from (3,0)
    CHECK( pp.first  == Point2d_<NUMTYPE>(+1,0) );
    CHECK( pp.second == Point2d_<NUMTYPE>(+5,0) );

    Line2d_<NUMTYPE> li( 1, 1 );                   // line with slope [1,1] starting from (0,0)
    auto k = 1.0 / std::sqrt(2.);
    pp = li.getPoints( GivenCoord::X, 5.0, 1.0 ); // get points at a distance 1 from (5,0)
    CHECK( pp.first  == Point2d_<NUMTYPE>( 5-k, 5-k ) );
    CHECK( pp.second == Point2d_<NUMTYPE>( 5+k, 5+k ) );

    li = Point2d_<NUMTYPE>(3,1) * Point2d_<NUMTYPE>(4,2); // line with slope [1,1] starting from (3,1)

    pp = li.getPoints( GivenCoord::X, 5.0, 1.0 ); // get points at a distance 2 from (3,0)
    CHECK( pp.first  == Point2d_<NUMTYPE>( 5-k, 3-k ) );
    CHECK( pp.second == Point2d_<NUMTYPE>( 5+k, 3+k ) );
}

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TEST_CASE() [23/93]

TEST_CASE	(	"getAngle"	,
		""	[test_angle]
	)

{
    Line2d_<NUMTYPE> lid(1,1); // diagonal line going through (0,0)
    Line2d_<NUMTYPE> lih(1,0); // horizontal line
    Line2d_<NUMTYPE> liv;     // vertical line
    CHECK( lih.getAngle(lid) == Approx(M_PI/4.) );
    CHECK( liv.getAngle(lid) == Approx(M_PI/4.) );
    CHECK( liv.getAngle(lih) == Approx(M_PI/2.) );

    CHECK( getAngle(lih,lid) == Approx(M_PI/4.) );
    CHECK( getAngle(liv,lid) == Approx(M_PI/4.) );
    CHECK( getAngle(lih,liv) == Approx(M_PI/2.) );
//  liv.getAngle( Point2d() );          // NO BUILD
//  getAngle( liv, Point2d() );         // NO BUILD
}

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TEST_CASE() [24/93]

TEST_CASE	(	"getCorrectPoints"	,
		""	[gcpts]
	)

{
    {
        auto p1 = detail::getCorrectPoints( Point2d(0,0), Point2d(5,5) );
        CHECK( p1.first  == Point2d(0,0) );
        CHECK( p1.second == Point2d(5,5) );
    }
    {
        auto p1 = detail::getCorrectPoints( Point2d(0,5), Point2d(5,0) );
        CHECK( p1.first  == Point2d(0,0) );
        CHECK( p1.second == Point2d(5,5) );
    }
    {
        auto p1 = detail::getCorrectPoints( Point2d(5,0), Point2d(0,5) );
        CHECK( p1.first  == Point2d(0,0) );
        CHECK( p1.second == Point2d(5,5) );
    }
    {
        auto p1 = detail::getCorrectPoints( Point2d(5,5), Point2d(0,0) );
        CHECK( p1.first  == Point2d(0,0) );
        CHECK( p1.second == Point2d(5,5) );
    }
}

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TEST_CASE() [25/93]

TEST_CASE	(	"IsInside - manual"	,
		""	[IsInside_man]
	)

{
    Point2d pt1(10,10),pt2(10,10);
    Line2d li1, li2;
    FRect rect1, rect2;
    Circle cir1, cir2;
    Segment seg1, seg2;
    Ellipse ell1(5.,5.), ell2(3,4);
    CPolyline cpol1,cpol2;
    OPolyline opol1,opol2;

    CHECK( !pt2.isInside( pt1 ) );
    CHECK( !pt2.isInside( li1 ) );
    CHECK( !pt2.isInside( rect1 ) );
    CHECK( !pt2.isInside( cir1 ) );
    CHECK( !pt2.isInside( ell1  ) );
    CHECK( !pt2.isInside( cpol1 ) );
    CHECK( !pt2.isInside( opol1 ) );

    CHECK( !li2.isInside( pt1 ) );
    CHECK( !li2.isInside( li1 ) );
    CHECK( !li2.isInside( rect1 ) );
    CHECK( !li2.isInside( cir1 ) );
    CHECK( !li2.isInside( ell1  ) );
    CHECK( !li2.isInside( cpol1 ) );
    CHECK( !li2.isInside( opol1 ) );

    CHECK( !rect2.isInside( pt1 ) );
    CHECK( !rect2.isInside( li1 ) );
    CHECK( !rect2.isInside( rect1 ) );
    CHECK( !rect2.isInside( cir1 ) );
    CHECK( !rect2.isInside( ell1  ) );
    CHECK( !rect2.isInside( cpol1 ) );
    CHECK( !rect2.isInside( opol1 ) );

    CHECK( !cir2.isInside( pt1 ) );
    CHECK( !cir2.isInside( li1 ) );
    CHECK( !cir2.isInside( rect1 ) );
    CHECK( !cir2.isInside( cir1 ) );
    CHECK( !cir2.isInside( ell1  ) );
    CHECK( !cir2.isInside( cpol1 ) );
    CHECK( !cir2.isInside( opol1 ) );

    CHECK( !seg2.isInside( pt1 ) );
    CHECK( !seg2.isInside( li1 ) );
    CHECK( !seg2.isInside( rect1 ) );
    CHECK( !seg2.isInside( cir1 ) );
    CHECK( !seg2.isInside( ell1  ) );
    CHECK( !seg2.isInside( cpol1 ) );
    CHECK( !seg2.isInside( opol1 ) );

    CHECK( !ell2.isInside( pt1 ) );
    CHECK( !ell2.isInside( li1 ) );
    CHECK( !ell2.isInside( rect1 ) );
    CHECK( !ell2.isInside( cir1 ) );
    CHECK( !ell2.isInside( ell1  ) );
    CHECK( !ell2.isInside( cpol1 ) );
    CHECK( !ell2.isInside( opol1 ) );

    CHECK( !cpol2.isInside( pt1 ) );
    CHECK( !cpol2.isInside( li1 ) );
    CHECK( !cpol2.isInside( rect1 ) );
    CHECK( !cpol2.isInside( cir1 ) );
    CHECK( !cpol2.isInside( ell1  ) );
    CHECK( !cpol2.isInside( cpol1 ) );
    CHECK( !cpol2.isInside( opol1 ) );

    CHECK( !opol2.isInside( pt1 ) );
    CHECK( !opol2.isInside( li1 ) );
    CHECK( !opol2.isInside( rect1 ) );
    CHECK( !opol2.isInside( cir1 ) );
    CHECK( !opol2.isInside( ell1  ) );
    CHECK( !opol2.isInside( cpol1 ) );
    CHECK( !opol2.isInside( opol1 ) );
}

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TEST_CASE() [26/93]

TEST_CASE	(	"Polyline IsInside Polyline"	,
		""	[tpolipol]
	)

{
    { // checking https://github.com/skramm/homog2d/issues/10
        CPolyline_<HOMOG2D_INUMTYPE> p1(std::vector<Point2d>{
            Point2d(-2, 2),
            Point2d(-2,-2),
            Point2d( 2,-2),
            Point2d( 2, 2),
        });
        CPolyline_<HOMOG2D_INUMTYPE> p2(std::vector<Point2d>{
            Point2d(-5, 5),
            Point2d(-5,-5),
            Point2d( 5,-5),
            Point2d( 5, 5)
        });
        CHECK( p2.isInside( p1 ) == false );
        CHECK( p1.isInside( p2 ) == true );
    }
    { // one inside the other
        #include "figures_test/polyline_inside_a1.code"
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == true );
    }
    { // simple intersection, one point outside
        #include "figures_test/polyline_inside_a2.code"
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == false );
    }
    { // nothing common
        #include "figures_test/polyline_inside_a3.code"
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == false );
    }
    { // all points inside, but some intersections
        #include "figures_test/polyline_inside_a4.code"
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == false );
    }

    { // Open polyline inside a closed polyline
        #include "figures_test/polyline_inside_b1.code"
        CHECK( pl2.isInside( pl ) == true );
        CHECK( pl.isInside( pl2 ) == false );
    }
    { // Open polyline inside a closed polyline, but one point outside
        #include "figures_test/polyline_inside_b2.code"
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == false );
    }
    { // Open polyline with no common with closed polyline
        #include "figures_test/polyline_inside_b3.code"
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == false );
    }

    { // two Open polylines
        OPolyline_<HOMOG2D_INUMTYPE> pl(std::vector<Point2d_<HOMOG2D_INUMTYPE>>{
            {1,2},{1,1},{2,2}
        });
        OPolyline_<HOMOG2D_INUMTYPE> pl2(std::vector<Point2d_<HOMOG2D_INUMTYPE>>{
            {3,3},{3,2},{4,2}
        });
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == false );
    }
    { // two Open polylines
        OPolyline_<HOMOG2D_INUMTYPE> pl(std::vector<Point2d_<HOMOG2D_INUMTYPE>>{
            {1,1},{5,1},{5,5},{1,5}
        });
        OPolyline_<HOMOG2D_INUMTYPE> pl2(std::vector<Point2d_<HOMOG2D_INUMTYPE>>{
            {3,3},{3,2},{4,2}
        });
        CHECK( pl2.isInside( pl ) == false );
        CHECK( pl.isInside( pl2 ) == false );
    }
}

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TEST_CASE() [27/93]

TEST_CASE	(	"Point2d IsInside Polyline"	,
		""	[tptipol]
	)

{
    Point2d_<HOMOG2D_INUMTYPE> pt;

    OPolyline_<HOMOG2D_INUMTYPE> opol{ std::vector<Point2d>{ {0,0}, {3,4}, {1,8} } };
    CHECK( !pt.isInside( opol ) );

    {
        CPolyline_<HOMOG2D_INUMTYPE> cpol{ FRect_<HOMOG2D_INUMTYPE>() };  // polygon (0,0)-(1,0)-(1,1)-(0,1)

        pt.set( 0, 0 );
        CHECK( !pt.isInside( cpol ) );  // equal to one of the points
        pt.set( .2, .3 );
        CHECK( pt.isInside( cpol ) );
        pt.set( 1,0 );
        CHECK( !pt.isInside( cpol ) );
        pt.set( .5, 0. );
        CHECK( !pt.isInside( cpol ) );
    }
    {
//      CPolyline_<HOMOG2D_INUMTYPE> cpol{ {1,0},{2,1},{1,2},{0,1} };
        CPolyline_<HOMOG2D_INUMTYPE> cpol{ std::vector<Point2d>{ {1,0},{2,1},{1,2},{0,1} } };

        pt.set( 1,1 );
        CHECK( pt.isInside( cpol ) );
    }
}

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TEST_CASE() [28/93]

TEST_CASE	(	"Line2d IsInside something"	,
		""	[tlir]
	)

{
    Point2d_<NUMTYPE> pt1(2,10);
    Point2d_<NUMTYPE> pt2(10,2);
    auto li = pt1*pt2;
    CHECK( li.isInside( pt1, pt2 ) == false );

    Circle_<NUMTYPE> c( 4, 5, 2 );
    CHECK( li.isInside( c ) == false );

    Ellipse_<NUMTYPE> ell(pt1);
    CHECK( li.isInside( ell ) == false );
}

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TEST_CASE() [29/93]

TEST_CASE	(	"Point2d IsInside Circle"	,
		""	[tptic]
	)

{
    Circle_<NUMTYPE> c1(10.);
    Circle_<NUMTYPE> c2(2.);
    {
        Point2d p1( 3,3 );          // point inside circle
        CHECK( p1.isInside(c1) );
        CHECK( !p1.isInside(c2) );
        CHECK( p1.isInside(  Point2d(0,0), 8 ) );
        CHECK( !p1.isInside( Point2d(0,0), 2 ) );
    }
    {
        Point2d p1( 10, 0 );          // point on the edge of circle
        CHECK( !p1.isInside(c1) );
        Point2d p2( 0, 10 );          // point on the edge of circle
        CHECK( !p2.isInside(c1) );
    }
}

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TEST_CASE() [30/93]

TEST_CASE	(	"Point2d IsInside FRect"	,
		""	[tptir]
	)

{
    Point2d_<NUMTYPE> pt1(2,10);
    Point2d_<NUMTYPE> pt2(10,2);

//  Line2d_<NUMTYPE> li;                              // THIS DOES NOT BUILD (on purpose)
//  li.isInside( pt1, pt2 );       // (but we can't test this...)

    Point2d_<NUMTYPE> pt; // (0,0)
    CHECK( pt.isInside( pt1, pt2 ) == false );
    pt.set(5,5);
    CHECK( pt.isInside( pt1, pt2 ) == true );

    pt.set(10,5);                                         // on the edge
    CHECK( pt.isInside( pt1, pt2 ) == false );
    pt.set(5,10);
    CHECK( pt.isInside( pt1, pt2 ) == false );

    pt.set(4.999,9.99);
    CHECK( pt.isInside( pt1, pt2 ) == true );

    CHECK( Point2d_<NUMTYPE>( 2, 2).isInside( pt1, pt2 ) == false );
    CHECK( Point2d_<NUMTYPE>( 2,10).isInside( pt1, pt2 ) == false );
    CHECK( Point2d_<NUMTYPE>(10, 2).isInside( pt1, pt2 ) == false );
    CHECK( Point2d_<NUMTYPE>(10,10).isInside( pt1, pt2 ) == false );
}

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TEST_CASE() [31/93]

TEST_CASE	(	"Segment IsInside FRect"	,
		""	[tsir]
	)

{
    FRect_<NUMTYPE> r(2,3, 10,10);
    CHECK( r.length() == 30 );
    CHECK( r.area()   == 56 );
    CHECK( r.width()  == 8 );
    CHECK( r.height() == 7 );

    CHECK( Segment_<NUMTYPE>( 0,0, 5,0 ).isInside( r )           == false ); // outside
    CHECK( Segment_<NUMTYPE>( 2,5, 4,5 ).isInside( r )           == false ); // on the contour
    CHECK( Segment_<NUMTYPE>( 2.00001, 5., 4.,5. ).isInside( r ) == true );
    CHECK( Segment_<NUMTYPE>( 3,5, 4,5 ).isInside( r )           == true );
}

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TEST_CASE() [32/93]

TEST_CASE	(	"Circle IsInside FRect"	,
		""	[tcir]
	)

{
    FRect_<NUMTYPE> r(2,3, 10,10);
    CHECK( Circle_<NUMTYPE>( 5,5, 2 ).isInside( r ) == false );   // touches rectangle at (5,3)
    CHECK( Circle_<NUMTYPE>( 5,5, 1 ).isInside( r ) == true );
    CHECK( Circle_<NUMTYPE>( 6,6, 2 ).isInside( r ) == true );
    CHECK( Circle_<NUMTYPE>().isInside( r )         == false );

    CHECK( Circle( 6,6, 22 ).isInside( r ) == false);
    CHECK( r.isInside( Circle( 6,6, 22 ) ) == true );

    std::vector<Point2d> vecpt{ {3,3},{4,4} };
    CPolyline pl(vecpt);
    CHECK( pl.isInside( r ) == false );  // on contour
}

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TEST_CASE() [33/93]

TEST_CASE	(	"Circle IsInside Circle"	,
		""	[tcic]
	)

{
    Circle_<NUMTYPE> c1(10.);
    Circle_<NUMTYPE> c2(2.);
    {
        CHECK( c2.isInside(c1) );  // circle inside circle
        CHECK( !c1.isInside(c2) );
        CHECK( !c1.isInside(c1) );
        CHECK( c1 != c2 );
        CHECK( c1 == c1 );
    }
    {
        Circle_<NUMTYPE> cA( Point2d(),   10.);
        CHECK( cA.radius() == 10. );
        cA.radius() = 12;
        CHECK( cA.radius() == 12. );
        CHECK( cA.center() == Point2d(0,0) );

        Circle_<NUMTYPE> cB( Point2d(5,0), 2.);
        auto seg = getSegment( cA, cB );
        CHECK( seg.getPts().first  == Point2d(0,0) );
        CHECK( seg.getPts().second == Point2d(5,0) );
        CHECK( seg.length() == 5 );
    }
}

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TEST_CASE() [34/93]

TEST_CASE	(	"Intersection"	,
		""	[int_all]
	)

{
    FRect    r1,r2;
    Circle   c1,c2;
    Segment  s1,s2;
    Line2d   l1,l2;
    OPolyline po1,po2;
    CPolyline pc1,pc2;

    CHECK( !r1.intersects( r2 )() ); // intersection with object of same type
    CHECK( !c1.intersects( c2 )() );
    CHECK( !s1.intersects( s2 )() );
    CHECK( !l1.intersects( l2 )() );
    CHECK( !po1.intersects( po2 )() );
    CHECK( !pc1.intersects( pc2 )() );

    CHECK( r1.intersects( c2 )() );
    CHECK( r1.intersects( s2 )() );
    CHECK( r1.intersects( l2 )() );
    CHECK( !r1.intersects( po2 )() );  // polyline is empty, so no intersection
    CHECK( !r1.intersects( pc2 )() );  // polyline is empty, so no intersection

    CHECK( c1.intersects( r2 )() );
    CHECK( c1.intersects( s2 )() );
    CHECK( c1.intersects( l2 )() );
    CHECK( !c1.intersects( po2 )() );  // polyline is empty, so no intersection
    CHECK( !c1.intersects( pc2 )() );  // polyline is empty, so no intersection

    CHECK( s1.intersects( r2 )() );
    CHECK( s1.intersects( c2 )() );
    CHECK( s1.intersects( l2 )() );
    CHECK( !s1.intersects( po2 )() );  // polyline is empty, so no intersection
    CHECK( !s1.intersects( pc2 )() );  // polyline is empty, so no intersection

    CHECK( l1.intersects( r2 )() );
    CHECK( l1.intersects( c2 )() );
    CHECK( l1.intersects( s2 )() );
    CHECK( !l1.intersects( po2 )() );  // polyline is empty, so no intersection
    CHECK( !l1.intersects( pc2 )() );  // polyline is empty, so no intersection

    CHECK( !po1.intersects( r2 )() );
    CHECK( !po1.intersects( c2 )() );
    CHECK( !po1.intersects( s2 )() );
    CHECK( !po1.intersects( l2 )() );
    CHECK( !po1.intersects( pc2 )() );

    CHECK( !pc1.intersects( r2 )() );
    CHECK( !pc1.intersects( c2 )() );
    CHECK( !pc1.intersects( s2 )() );
    CHECK( !pc1.intersects( l2 )() );
    CHECK( !pc1.intersects( po2 )() );
}

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TEST_CASE() [35/93]

TEST_CASE	(	"Line/Line intersection"	,
		""	[int_LL]
	)

{
    Line2d_<NUMTYPE> liv1,liv3;
    Line2d_<NUMTYPE> liv2( Point2d(5,0), Point2d(5,10) );
    Line2d_<NUMTYPE> lih( Point2d(0,0), Point2d(1,0) );
    CHECK(  liv1.intersects( lih  )() );
    CHECK( !liv1.intersects( liv2 )() );
    CHECK(  lih.intersects(  liv2 )() );
    CHECK( !liv1.intersects( liv3 )() );

    auto i1 = liv1.intersects( lih  );
    auto i2 = liv1.intersects( liv2 );
    auto i3 = lih.intersects(  liv2 );

    CHECK(  i1() );
    CHECK( !i2() );
    CHECK(  i3() );

    CHECK( i1.size()==1 );
    CHECK( i2.size()==0 );
    CHECK( i3.size()==1 );
}

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TEST_CASE() [36/93]

TEST_CASE	(	"Segment/Segment intersection"	,
		""	[int_SS]
	)

{
    Segment_<NUMTYPE> s1,s2;
    {
        CHECK( s1 == s2 );
        auto si = s1.intersects(s2);
        CHECK( si() == false );
        CHECK( si.size() == 0 );
    }
    {
        s1.set( Point2d(0,0), Point2d(4,4) ); // diagonal
        s2.set( Point2d(0,4), Point2d(4,0) );
        auto si = s1.intersects(s2);
        CHECK( si() == true );
        CHECK( si.size() == 1 );
        CHECK( si.get() == Point2d(2,2) );
    }
    {
        s1.set( Point2d(0,0), Point2d(10,0) ); // overlapping (complete
        s2.set( Point2d(5,0), Point2d(15,0) );
        auto si = s1.intersects(s2);
        CHECK( si() == false );
        CHECK( si.size() == 0 );
    }
    {
        s1.set( Point2d(0,0), Point2d(0,1) );  // vertical
        s2.set( Point2d(1,1), Point2d(0,1) );  // horizontal
        auto si = s1.intersects(s2);
        CHECK( si() );
        CHECK( si.size() == 1 );
        CHECK( si.get() == Point2d(0,1) );
    }
    {
        s1.set( Point2d(0,0), Point2d(0,2) );  // vertical

        s2.set( Point2d(1,1), Point2d(0,1) );  // horizontal, touches the other one in the middle
        {
            auto si = s1.intersects(s2);
            CHECK( si() );
            CHECK( si.size() == 1 );
            CHECK( si.get() == Point2d(0,1) );
        }
        s2.set( Point2d(0,0), Point2d(1,0) );  // horizontal, touches the edge of other one
        {
            auto si = s1.intersects(s2);
            CHECK( si() );
            CHECK( si.size() == 1 );
            CHECK( si.get() == Point2d(0,0) );
        }
        s2.set( Point2d(1,1), Point2d(0,1) );  // horizontal, touches the edge of other one
        {
            auto si = s1.intersects(s2);
            CHECK( si() );
            CHECK( si.size() == 1 );
            CHECK( si.get() == Point2d(0,1) );
        }
        s2.set( Point2d(-1,1), Point2d(0,1) );  // horizontal, touches the edge of other one
        {
            auto si = s1.intersects(s2);
            CHECK( si() );
            CHECK( si.size() == 1 );
            CHECK( si.get() == Point2d(0,1) );
        }
    }
    {
        s1.set( 0., 0., 1., 0. );
        s2.set( 1., 1., 1., -1E-05 );
        {
            auto si = s1.intersects(s2);
            CHECK( si() );
            CHECK( si.size() == 1 );
            CHECK( si.get() == Point2d(1,0) );
        }
        s2.set( 1., 1., 1., +1E-05 );
        {
            CHECK( !s1.intersects(s2)() );
        }
    }
}

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TEST_CASE() [37/93]

TEST_CASE	(	"Circle/Circle intersection"	,
		""	[int_CC]
	)

{
    {
        Circle_<NUMTYPE> cA, cB;
        CHECK( cA == cB );                 // identical circles do
        CHECK( !cA.intersects(cB)() );     // not intersect
    }
    {
        Circle_<NUMTYPE> cA;
        Circle_<NUMTYPE> cB( Point2d(5,5), 2 );
        CHECK( cA != cB );
        CHECK( !cA.intersects(cB)() );
    }
    {
        Circle_<NUMTYPE> cA( Point2d(0,0), 2 );
        Circle_<NUMTYPE> cB( Point2d(3,0), 2 );
        CHECK( cA != cB );
        CHECK( cA.intersects(cB)() );
        CHECK( cA.intersects(cB).size() == 2 );
    }
    {
        Circle_<NUMTYPE> cA( Point2d(0,0), 1 );
        Circle_<NUMTYPE> cB( Point2d(2,0), 1 );
        CHECK( cA != cB );
        CHECK( cA.intersects(cB)() );
        auto inter = cA.intersects(cB);
        CHECK( inter() == true );
        CHECK( inter.size() == 1 );
//      CHECK( inter.get().first  == Point2d(1,0) );
//      CHECK( inter.get().second == Point2d(1,0) );
        CHECK( inter.get()[0] == Point2d(1,0) );
    }
}

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TEST_CASE() [38/93]

TEST_CASE	(	"FRect/FRect intersection"	,
		""	[int_FF]
	)

{
    {                                   // identical rectangles
        FRect_<NUMTYPE> r1, r2;
        CHECK( r1 == r2 );
        CHECK( !r1.intersects(r2)() ); // no intersection !
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 0 );

        auto i1 = intersectArea(r1,r2);
        CHECK( i1() == true );
        CHECK( i1.get() == r1 );

        auto u1 = unionArea(r1,r2);
        CHECK( u1.size() == 4 );      // 4 points
        CHECK( u1 == CPolyline(r1) );  // same
    }
    {
#include "figures_test/frect_intersect_1.code"
        CHECK( r1 != r2 );
        CHECK( r1.height() == r2.height() );
        CHECK( !r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 0 );

        auto a = r1.intersectArea(r2);
        CHECK( a() == false );       // no intersection !
        auto b = r1&r2;
        CHECK( b() == false );       // no intersection !

        auto u1 = unionArea(r1,r2);
        CHECK( u1.size() == 0 );     // empty
    }
    {
#include "figures_test/frect_intersect_2.code"
        CHECK( r1 != r2 );
        CHECK( r1.width()  == r2.width() );
        CHECK( r1.height() == r2.height() );
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 2 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d(2,2) );
        CHECK( vpts[1] == Point2d(3,1) );

        auto rect_inter = r1.intersectArea(r2);
        CHECK( rect_inter() == true );
        CHECK( rect_inter.get() == FRect(2,1, 3,2) );
        auto rect_inter2 = r1&r2;
        CHECK( rect_inter2() == true );
        CHECK( rect_inter2.get() == FRect(2,1, 3,2) );

        auto u1 = unionArea(r1,r2);
//      Polyline p{ [0,0],[1,1] };
        CHECK( u1.size() == 8 );
    }

    {      // 4 intersection points
#include "figures_test/frect_intersect_3.code"
        CHECK( r1 != r2 );
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 4 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d(2,2) );
        CHECK( vpts[1] == Point2d(2,4) );
        CHECK( vpts[2] == Point2d(4,2) );
        CHECK( vpts[3] == Point2d(4,4) );

        auto rect_inter = r1.intersectArea(r2);
        CHECK( rect_inter() == true );
        CHECK( rect_inter.get() == FRect(2,2, 4,4) );

        auto u1 = unionArea(r1,r2);
//      Polyline p{ [0,0],[1,1] };
        CHECK( u1.size() == 12 );
    }

    {     // horizontal segment overlap
#include "figures_test/frect_intersect_4.code"
        CHECK( r1 != r2 );
        CHECK( r1.width()  == r2.width() );
        CHECK( r1.height() == r2.height() );
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 4 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d(3,1) );
        CHECK( vpts[1] == Point2d(3,3) );
        CHECK( vpts[2] == Point2d(4,1) );
        CHECK( vpts[3] == Point2d(4,3) );

        auto rect_inter = r1.intersectArea(r2);
        CHECK( rect_inter() == true );
        CHECK( rect_inter.get() == FRect(3,1, 4,3) );

        auto u1 = unionArea(r1,r2);
//      Polyline p{ [0,0],[1,1] };
        CHECK( u1.size() == 4 );
    }
    {     // common vertical segment
#include "figures_test/frect_intersect_5.code"
        CHECK( r1 != r2 );
        CHECK( r1.width()  != r2.width() );
        CHECK( r1.height() == r2.height() );
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters() == true );
        CHECK( inters.size() == 2 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 3,0 ) );
        CHECK( vpts[1] == Point2d( 3,2 ) );
        CHECK( r1.intersectArea(r2)() == false ); // no area intersection

        r2.translate( 0.000001, 0 );         // move it a bit left
        inters = r1.intersects(r2);          // => no more intersection
        CHECK( inters() == false );
        CHECK( inters.size() == 0 );
        CHECK( r1.intersectArea(r2)() == false ); // still no intersection

        auto u1 = unionArea(r1,r2);
        CHECK( u1.size() == 0 );
    }
    {     // two rectangles joined by corner at 3,2
#include "figures_test/frect_intersect_6.code"
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 1 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 3,2 ) );
        CHECK( r1.intersectArea(r2)() == false ); // only one point !

        auto u1 = unionArea(r1,r2);
        CHECK( u1.size() == 8 );
    }
    {     // two rectangles
#include "figures_test/frect_intersect_7.code"
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 2 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 2,2 ) );
        CHECK( vpts[1] == Point2d( 4,2 ) );

        auto rect_inter = r1.intersectArea(r2);
        CHECK( rect_inter() == true );
        CHECK( rect_inter.get() == FRect(2,2, 4,3) );
    }
    {     // two rectangles with a single common segment
#include "figures_test/frect_intersect_8.code"
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 3 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 3,3 ) );
        CHECK( vpts[1] == Point2d( 4,2 ) );
        CHECK( vpts[2] == Point2d( 4,3 ) );
//      auto rect_inter = r1.intersectArea(r2);
//      CHECK( rect_inter == FRect(3,2, 4,3) );
    }
    {     // two rectangles with a single common segment
#include "figures_test/frect_intersect_9.code"
        CHECK( r1.intersects(r2)() );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 3 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 3,3 ) );
        CHECK( vpts[1] == Point2d( 4,2 ) );
        CHECK( vpts[2] == Point2d( 4,3 ) );
//      auto rect_inter = r1.intersectArea(r2);
//      CHECK( rect_inter == FRect(3,2, 4,3) );
    }

    { // one rectangle inside the other
#include "figures_test/frect_intersect_10.code"
        CHECK( r1.intersects(r2)() == false );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 0 );
        auto inters2 = r1.intersectArea(r2);
        CHECK( inters2() == true );
        CHECK( inters2.get() == r2 );
    }
    { // one rectangle inside the other, with a common segment
#include "figures_test/frect_intersect_11.code"
        CHECK( r1.intersects(r2)() == true );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 2 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 2,3 ) );
        CHECK( vpts[1] == Point2d( 3,3 ) );
        CHECK( r1.intersectArea(r2)() == true );
        auto inter=r1.intersectArea(r2);
        CHECK( inter.get() == r2 );
    }

// this below needs to be expanded
    {
#include "figures_test/frect_intersect_12.code"
        CHECK( r1.intersects(r2)() == true );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 3 );
        auto vpts = inters.get();
//      priv::printVector( vpts, "intersection points demo12" );
        CHECK( vpts[0] == Point2d( 2,0 ) );
        CHECK( vpts[1] == Point2d( 2,2 ) );
        CHECK( vpts[2] == Point2d( 3,0 ) );
        CHECK( r1.intersectArea(r2)() == true );
//      auto inter=r1.intersectArea(r2);
//      CHECK( inter.get() == r2 );
    }

// this below needs to be expanded
    {
#include "figures_test/frect_intersect_13.code"
        CHECK( r1.intersects(r2)() == true );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 2 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 3,0 ) );
        CHECK( vpts[1] == Point2d( 3,2 ) );
        CHECK( r1.intersectArea(r2)() == false );
//      auto inter=r1.intersectArea(r2);
//      CHECK( inter.get() == r2 );
    }
}

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TEST_CASE() [39/93]

TEST_CASE	(	"IoU of 2 rectangles"	,
		""	[IOU_RECT]
	)

{
    FRect_<NUMTYPE> r1( 0,0,1,1 );
    FRect_<NUMTYPE> r2( 2,2,3,3 );
    CHECK( IoU(r1,r2) == 0. );
    r1.set(0,0,2,2);
    CHECK( IoU(r1,r2) == 0. );

    r2.set(1,0,3,2);
    CHECK( IoU(r1,r2) == Approx(1./3.) );
}

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TEST_CASE() [40/93]

TEST_CASE	(	"Circle/Segment intersection"	,
		""	[int_CS]
	)

{
    Circle_<NUMTYPE> c1( Point2d(1,1), 1 ); // circle centered on 1,1, going horizontally from 0 to 2 at y=0
    {
        Segment_<NUMTYPE> s1( Point2d(0,20),Point2d(2,20) ); // horizontal segment at y=20

        CHECK( !c1.intersects( s1 )() );
        CHECK( !s1.intersects( c1 )() );
        auto int_a = c1.intersects( s1 );
        auto int_b = s1.intersects( c1 );
        CHECK( !int_a() );
        CHECK( !int_b() );
        CHECK( int_a.size() == 0 );
        CHECK( int_b.size() == 0 );

        Segment_<NUMTYPE> s2( Point2d(10,0),Point2d(10,20) ); // vertical segment at x=10
        CHECK( !c1.intersects( s2 )() );
        CHECK( !s2.intersects( c1 )() );
        auto int_a2 = c1.intersects( s2 );
        auto int_b2 = s2.intersects( c1 );
        CHECK( int_a2.size() == 0 );
        CHECK( int_b2.size() == 0 );
        CHECK( !int_a2() );
        CHECK( !int_b2() );
    }
    {
        Segment_<NUMTYPE> s2( Point2d(-5,1),Point2d(+5,1) ); // horizontal segment at y=1

        CHECK( c1.intersects( s2 )() );
        CHECK( s2.intersects( c1 )() );

        auto int_a = c1.intersects( s2 );
        auto int_b = s2.intersects( c1 );
        CHECK( int_a() );
        CHECK( int_b() );
        CHECK( int_a.size() == 2 );
        CHECK( int_b.size() == 2 );
        CHECK( int_a.get()[0] == Point2d_<NUMTYPE>(0,1) );
        CHECK( int_b.get()[1] == Point2d_<NUMTYPE>(2,1) );
    }
    {
        Segment_<NUMTYPE> s2( Point2d(-5,1),Point2d(1,1) ); // horizontal segment at y=1

        CHECK( c1.intersects( s2 )() );
        CHECK( s2.intersects( c1 )() );

        auto int_a = c1.intersects( s2 );
        auto int_b = s2.intersects( c1 );
        CHECK( int_a() );
        CHECK( int_b() );
        CHECK( int_a.size() == 1 );
        CHECK( int_b.size() == 1 );
        CHECK( int_a.get()[0] == Point2d_<NUMTYPE>(0,1) );
    }
    {
        Segment_<NUMTYPE> s2( Point2d(2,0),Point2d(4,0) ); // horizontal segment at y=0, outside circle

        CHECK( !c1.intersects( s2 )() );
        CHECK( !s2.intersects( c1 )() );

        auto int_a = c1.intersects( s2 );
        auto int_b = s2.intersects( c1 );
        CHECK( int_a() == false );
        CHECK( int_b() == false );
        CHECK( int_a.size() == 0 );
        CHECK( int_b.size() == 0 );
    }
    {
        Segment_<NUMTYPE> s2( Point2d(2,1),Point2d(4,1) ); // horizontal segment at y=0, touching edge of circle at (1,1)

        CHECK( c1.intersects( s2 )() );
        CHECK( s2.intersects( c1 )() );

        auto int_a = c1.intersects( s2 );
        auto int_b = s2.intersects( c1 );
        CHECK( int_a() );
        CHECK( int_b() );
        CHECK( int_a.size() == 1 );
        CHECK( int_b.size() == 1 );
        CHECK( int_a.get()[0] == Point2d_<NUMTYPE>(2,1) );
    }
}

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TEST_CASE() [41/93]

TEST_CASE	(	"Circle/FRect intersection"	,
		""	[int_CF]
	)

{
    {
//#include "figures_test/circle_intersect_1.code"
        Circle_<NUMTYPE> r1( Point2d(1,1), 1 );
        FRect_<NUMTYPE> r2( Point2d(3,2), Point2d(4,3) );
        CHECK( r1.intersects(r2)() == false );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 0 );
    }
    {
//#include "figures_test/circle_intersect_2.code"
        Circle_<NUMTYPE> r1( Point2d(3,3), 2 );
        FRect_<NUMTYPE> r2( Point2d(3,2), Point2d(4,3) );
        CHECK( r1.intersects(r2)() == false );
    }
    {
        Circle_<NUMTYPE> r1;
        FRect_<NUMTYPE> r2( 0,0, 3,3 );
        CHECK( r1.intersects(r2)() == true );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 2 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 0,1 ) );
        CHECK( vpts[1] == Point2d( 1,0 ) );
    }
    {
        Circle_<NUMTYPE> r1; // (0,0) with radius=1
        FRect_<NUMTYPE> r2( 1,0, 3,3 );
        CHECK( r1.intersects(r2)() == true );
        auto inters = r1.intersects(r2);
        CHECK( inters.size() == 1 );
        auto vpts = inters.get();
        CHECK( vpts[0] == Point2d( 1,0 ) );
    }
}

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TEST_CASE() [42/93]

TEST_CASE	(	"Circle/Line intersection"	,
		""	[int_CL]
	)

{
    Line2d_<NUMTYPE> lid(1,1); // diagonal line going through (0,0)
    Line2d_<NUMTYPE> liv; // vertical line at x=0
    Line2d_<NUMTYPE> lih( Point2d(-1,0), Point2d(1,0) ); // horizontal line at y=0
    Point2d_<NUMTYPE> pt;
    {
        CHECK( lid.intersects( Point2d_<NUMTYPE>(), 0.5 )() );
        auto ri = lid.intersects( Point2d_<NUMTYPE>(), 0.5 );
        CHECK( ri() == true );
        auto ri2 = lid.intersects( Point2d_<NUMTYPE>(10,5), 1. );
        CHECK( ri2() == false );
        auto ri3 = lid.intersects( Circle_<NUMTYPE>(Point2d_<NUMTYPE>(), 0.5 ) );
        CHECK( ri3() == true );
        auto ri4 = lid.intersects( Circle_<NUMTYPE>(Point2d_<NUMTYPE>(10,5), 1. ) );
        CHECK( ri4() == false );
    }
    {
        auto rih = lih.intersects( pt, 1.0 );
        CHECK( rih() == true );
        CHECK( rih.get().first  == Point2d(-1,0) );
        CHECK( rih.get().second == Point2d(+1,0) );
    }
    {
        auto riv = liv.intersects( pt, 1.0 );
        CHECK( riv() == true );
        CHECK( riv.get().first  == Point2d(0,-1) );
        CHECK( riv.get().second == Point2d(0,+1) );
    }

    Circle_<NUMTYPE> cir2(45);
    CHECK( cir2.radius() == 45. );
    Circle_<NUMTYPE> cir3( Point2d(4,6),7);
    CHECK( cir3.radius() == 7. );
    {
        auto cl1 = cir2.intersects( liv );
        CHECK( cl1() == true );
        CHECK( cl1.get().first  == Point2d(0,-45) );
        CHECK( cl1.get().second == Point2d(0,+45) );
    }
    {
        Circle_<NUMTYPE> c4( Point2d(1,1),1);
        Line2d_<NUMTYPE> l4( Point2d(-5,1), Point2d(5,1));
        auto res1 = c4.intersects( l4 );
        CHECK( res1() == true );
        CHECK( res1.size() == 2 );
        CHECK( res1.get().first  == Point2d(0,1) );
        CHECK( res1.get().second == Point2d(2,1) );

        auto res2 = l4.intersects( c4 );
        CHECK( res2() == true );
        CHECK( res2.size() == 2 );
        CHECK( res2.get().first  == Point2d(0,1) );
        CHECK( res2.get().second == Point2d(2,1) );
    }
}

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TEST_CASE() [43/93]

TEST_CASE	(	"Line/Segment intersection"	,
		""	[int_LS]
	)

{
    Line2d_<NUMTYPE> li;             // vertical line x=0
    {
        Segment_<NUMTYPE> seg;           // (0,0 -- (1,1)
        CHECK( li.intersects( seg )() );
        CHECK( seg.intersects( li )() );
        auto ri1 = li.intersects( seg );
        auto ri2 = seg.intersects( li );
        CHECK( ri1.size() == 1 );
        CHECK( ri2.size() == 1 );

        CHECK( ri1.get() == Point2d(0,0) );
        CHECK( ri2.get() == Point2d(0,0) );
    }
    {
        Segment_<NUMTYPE> seg( 0,0, 0,2 );  // vertical x=0
        CHECK( !li.intersects( seg )() );
        CHECK( !seg.intersects( li )() );
    }
    {
        Segment_<NUMTYPE> seg( 1,0, 1,2 );
        CHECK( !li.intersects( seg )() );
        CHECK( !seg.intersects( li )() );
    }
}

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TEST_CASE() [44/93]

TEST_CASE	(	"Line/FRect intersection"	,
		""	[int_LF]
	)

{
    INFO( "with diagonal line" )
    {
        Line2d_<NUMTYPE> li(1,1); // diagonal line going through (0,0)
        Point2d_<NUMTYPE> pt1, pt2; // 0,0

        pt2.set(1,1);
        auto ri = li.intersects( FRect(pt1, pt2) );
        CHECK( ri() == true );
        CHECK( ri.size() == 2 );
        auto pts = ri.get();
        CHECK( pts[0] == pt1 );
        CHECK( pts[1] == pt2 );

        pt1.set( 5,0 );
        pt2.set( 6,1 );
        ri = li.intersects( FRect(pt1, pt2) );
        CHECK( ri() == false );
    }
    INFO( "with H/V line" )
    {
        Point2d_<NUMTYPE> pt1, pt2(1,1);                //  rectangle (0,0) - (1,1)
        FRect_<NUMTYPE> r1(pt1, pt2);
        Line2d_<NUMTYPE> li = Point2d_<NUMTYPE>() * Point2d_<NUMTYPE>(0,1); // vertical line at y=x
        auto ri1 = li.intersects( r1 );
        auto ri2 = r1.intersects( li );
        CHECK( ri1() == true );
        CHECK( ri2() == true );

        CHECK( ri1.size() == 2 );
        CHECK( ri2.size() == 2 );
        auto pts1 = ri1.get();
        auto pts2 = ri2.get();
        CHECK( pts1[0] == pt1 );
        CHECK( pts1[1] == Point2d(0,1) );

        CHECK( pts2[0] == pt1 );
        CHECK( pts2[1] == Point2d(0,1) );

        li = Point2d_<NUMTYPE>(1,0) * Point2d_<NUMTYPE>(1,1);     // vertical line at x=1
        ri1 = li.intersects( r1 );
        ri2 = r1.intersects( li );
        CHECK( ri1() == true );
        CHECK( ri2() == true );
        CHECK( ri1.size() == 2 );
        CHECK( ri2.size() == 2 );

        pts1 = ri1.get();
        CHECK( pts1[0] == Point2d(1,0) );
        CHECK( pts1[1] == Point2d(1,1) );

        li = Point2d_<NUMTYPE>() * Point2d_<NUMTYPE>(1,0);        // horizontal line at y=0
        ri1 = li.intersects( r1 );
        ri2 = r1.intersects( li );
        CHECK( ri1() == true );
        CHECK( ri2() == true );
        CHECK( ri1.size() == 2 );
        CHECK( ri2.size() == 2 );

        pts1 = ri1.get();
        CHECK( pts1[0] == pt1 );
        CHECK( pts1[1] == Point2d(1,0) );

        li = Point2d_<NUMTYPE>(-1,1) * Point2d_<NUMTYPE>(1,1);     // horizontal line at y=1
        ri1 = li.intersects( r1 );
        ri2 = r1.intersects( li );
        CHECK( ri1() == true );
        CHECK( ri2() == true );
        CHECK( ri1.size() == 2 );
        CHECK( ri2.size() == 2 );

        pts1 = ri1.get();
        CHECK( pts1[0] == Point2d(0,1) );
        CHECK( pts1[1] == Point2d(1,1) );

        li = Point2d_<NUMTYPE>(-1.,.5) * Point2d_<NUMTYPE>(2.,.5);     // horizontal line at y=0.5
        ri1 = li.intersects( r1 );
        ri2 = r1.intersects( li );
        CHECK( ri1() == true );
        CHECK( ri2() == true );
        CHECK( ri1.size() == 2 );
        CHECK( ri2.size() == 2 );

        pts1 = ri1.get();
        CHECK( pts1[0] == Point2d(0.,.5) );
        CHECK( pts1[1] == Point2d(1.,.5) );
    }
    INFO( "single point intersection" )
    {
        FRect_<NUMTYPE> r1( 0,0,1,1 );
        Line2d_<NUMTYPE> li( -1,+1, +1,-1 );
        auto inter = r1.intersects( li );
        CHECK( inter.size() == 1 );
        auto pts = inter.get();
        CHECK( pts[0] == Point2d(0,0) );
    }
}

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TEST_CASE() [45/93]

TEST_CASE	(	"Colinearity"	,
		""	[colinearity]
	)

{
    Point2d p00(0,0), p01(0,1), p30(3,0);
    Point2d pt1, pt2, pt3;

    {
        pt1 = p01; pt2 = p00; pt3 = p30;   // case A
        auto arr = priv::getLargestDistancePoints( pt1, pt2, pt3 );
        CHECK( arr[0]==pt3 );
        CHECK( arr[1]==pt1 );
        CHECK( arr[2]==pt2 );
    }
    {
        pt1 = p01; pt2 = p30; pt3 = p00;   // case B
        auto arr = priv::getLargestDistancePoints( pt1, pt2, pt3 );
        CHECK( arr[0]==pt2 );
        CHECK( arr[1]==pt1 );
        CHECK( arr[2]==pt3 );
    }
    {
        pt1 = p00; pt2 = p01; pt3 = p30;   // case C
        auto arr = priv::getLargestDistancePoints( pt1, pt2, pt3 );
        CHECK( arr[0]==pt3 );
        CHECK( arr[1]==pt2 );
        CHECK( arr[2]==pt1 );
    }
    {
        pt1 = p30; pt2 = p01; pt3 = p00;   // case D
        auto arr = priv::getLargestDistancePoints( pt1, pt2, pt3 );
        CHECK( arr[0]==pt1 );
        CHECK( arr[1]==pt2 );
        CHECK( arr[2]==pt3 );
    }
    {
        pt1 = p00; pt2 = p30; pt3 = p01;   // case E
        auto arr = priv::getLargestDistancePoints( pt1, pt2, pt3 );
        CHECK( arr[0]==pt2 );
        CHECK( arr[1]==pt3 );
        CHECK( arr[2]==pt1 );
    }
    {
        pt1 = p30; pt2 = p00; pt3 = p01;   // case F
        auto arr = priv::getLargestDistancePoints( pt1, pt2, pt3 );
        CHECK( arr[0]==pt1 );
        CHECK( arr[1]==pt3 );
        CHECK( arr[2]==pt2 );
    }
    {
        Point2d p1(0,0), p2(1,0), p3(4,0);
        CHECK( areCollinear( p1, p2, p3 ) );
    }
    {
        Point2d p1(1,0), p2(0,0), p3(4,0);
        CHECK( areCollinear( p1, p2, p3 ) );
    }
    {
        Point2d p1(1,0), p2(0,0), p3(4,1E-3);
        CHECK( !areCollinear( p1, p2, p3 ) );
    }
}

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TEST_CASE() [46/93]

TEST_CASE	(	"Line2d"	,
		""	[line1]
	)

{
    Line2d_<NUMTYPE> li;
    CHECK( li.area() == 0. );
    CHECK_THROWS( li.length() );
}

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TEST_CASE() [47/93]

TEST_CASE	(	"Circle"	,
		""	[cir1]
	)

?

{
    {
        Circle_<NUMTYPE> c1;       // Default constructor
        CHECK( c1.center() == Point2d(0,0) );
        CHECK( center(c1)  == Point2d(0,0) );
        CHECK( c1.radius() == 1. );
        CHECK( radius(c1)  == 1. );
        CHECK( c1.getBB() == FRect(-1,-1,1,1 ) );
        CHECK( getBB(c1)  == FRect(-1,-1,1,1 ) );

        CHECK( c1.area()   == area(c1) );
        CHECK( c1.length() == length(c1) );
    }
    {
        int i = 44;
        Circle_<NUMTYPE> c1(i);  // 1-arg Constructor - radius
        CHECK( c1.center() == Point2d(0,0) );
        CHECK( c1.radius() == i );
        CHECK( c1.getBB() == FRect(-i,-i,i,i) );
        CHECK( getBB(c1)  == FRect(-i,-i,i,i) );
        c1.set( 454 );
        CHECK( c1.center() == Point2d(0,0) );
        CHECK( c1.radius() == 454 );
    }
    {
        Point2d_<NUMTYPE> pt( 4,5);
        Circle_<NUMTYPE> c2(pt);  // 1-arg Constructor - center
        CHECK( c2.center() == Point2d(4,5) );
        CHECK( c2.radius() == 1 );

        CHECK( center(c2) == Point2d(4,5) );  // free functions call
        CHECK( radius(c2) == 1 );

        c2.set( Point2d_<NUMTYPE>(18,22) );
        CHECK( c2.center() == Point2d(18,22) );
        CHECK( c2.radius() == 1 );
    }
    {
        Point2d_<NUMTYPE> pt1(0,0), pt2(4,0);
        Circle_<NUMTYPE> c1(pt1,pt2);  // 2-args constructor: 2 points
        CHECK( c1.center() == Point2d(2,0) );
        CHECK( c1.radius() == 2. );
        c1.set( Point2d(1,1), Point2d(1,5) );
        CHECK( c1.center() == Point2d(1,3) );
        CHECK( c1.radius() == 2. );
    }
    {
        Point2d_<NUMTYPE> pt1(4,5);
        Circle_<NUMTYPE> c2(pt1,3);  // 2-args constructor - center and radius
        CHECK( c2.center() == pt1 );
        CHECK( c2.radius() == 3 );

        c2.set( Point2d_<NUMTYPE>(42,24), 18 );
        CHECK( c2.center() == Point2d_<NUMTYPE>(42,24) );
        CHECK( c2.radius() == 18 );
    }
    {
        Circle_<NUMTYPE> c1(1,2,3);  // 3-args constructor: x0, y0, radius
        CHECK( c1.center() == Point2d(1,2) );
        CHECK( c1.radius() == 3 );

        c1.set( 11, 22, 33 );
        CHECK( c1.center() == Point2d(11,22) );
        CHECK( c1.radius() == 33 );
    }
    {
        CHECK_THROWS( Circle_<NUMTYPE>(1,2,0.) ); 
        CHECK_THROWS( Circle_<NUMTYPE>(1,2,-1.) );
    }
    {
        Point2d_<NUMTYPE> pt1(4,5), pt2(6,7), pt3; // 3-args constructor: 3 points
        Circle_<NUMTYPE> c1(pt1,pt2,pt3);  // 2-args constructor: 2 points

        c1.set( Point2d(4,5), Point2d(6,7), Point2d(2,2) );

        CHECK_THROWS( c1.set( Point2d(4,5), Point2d(4,5) ) );               // points must be different !
        CHECK_THROWS( c1.set( Point2d(4,5), Point2d(4,5), Point2d(2,2) ) );
        CHECK_THROWS( Circle( Point2d(4,5), Point2d(4,5), Point2d(2,2) ) );
        CHECK_THROWS( Circle( Point2d(4,5), Point2d(4,5) ) );
    }
    {
        Circle_<NUMTYPE> c1;

        CHECK( c1.radius() == 1 );
        c1.radius() = 2;                // member function call
        CHECK( c1.radius() == 2 );
        radius(c1) = 3;                 // free function call
        CHECK( radius(c1) == 3 );

        CHECK( center(c1) == Point2d() );
        c1.center() = Point2d(3,4);            // member function call
        CHECK( center(c1) == Point2d(3,4) );
        center(c1) = Point2d(5,6);             // free function call
        CHECK( center(c1) == Point2d(5,6) );
    }
}

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TEST_CASE() [48/93]

TEST_CASE	(	"Circle from points"	,
		""	[cir2]
	)

{
    {
        INFO( "circle from 2 pts");
        std::vector<Point2d_<NUMTYPE>> pts1{ {0,0}, {2,0} };
        std::vector<Point2d_<NUMTYPE>> pts2{ {0,3}, {4,3} };
// check using constructor
        Circle_<NUMTYPE> c1(pts1);
        CHECK( c1.center() == Point2d(1,0) );
        CHECK( c1.radius() == 1. );
        Circle_<NUMTYPE> c2(pts2);
        CHECK( c2.center() == Point2d(2,3) );
        CHECK( c2.radius() == 2. );
// check using "set" function
        c1.set(pts2);
        CHECK( c1.center() == Point2d(2,3) );
        CHECK( c1.radius() == 2. );
        c2.set(pts1);
        CHECK( c2.center() == Point2d(1,0) );
        CHECK( c2.radius() == 1. );
    }
    {
        INFO( "circle from 4 pts");
        std::vector<Point2d_<NUMTYPE>> pts1{ {0,4}, {4,0}, {0,-4}, {0,0} };
        Circle_<NUMTYPE> c1(pts1);
        CHECK( c1.center() == Point2d(0,0) );
        CHECK( c1.radius() == 4. );
        c1.set(pts1);
        CHECK( c1.center() == Point2d(0,0) );
        CHECK( c1.radius() == 4. );

        std::vector<Point2d_<NUMTYPE>> pts2{ {0,4} };
        CHECK_THROWS( Circle_<NUMTYPE>(pts2) ); // 1 point not allowed
        std::vector<Point2d_<NUMTYPE>> pts3;
        CHECK_THROWS( Circle_<NUMTYPE>(pts3) ); // 0 points not allowed
    }
}

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TEST_CASE() [49/93]

TEST_CASE	(	"Ellipse"	,
		""	[ell1]
	)

{
    {
        Ellipse_<NUMTYPE> el;
        CHECK( el.getCenter() == Point2d(0,0) );
        CHECK( getCenter(el)  == Point2d(0,0) );
        CHECK( el.getMajMin().first == 2.0 );
        CHECK( el.getMajMin().second == 1.0 );
        CHECK( el.angle() == 0.0 );
        CHECK( angle(el)  == 0.0 );
        CHECK( el.isCircle() == false );
        CHECK( isCircle(el) == false );
    //  CHECK( el.getBB() == Point2d(0,0) );
    }
    {
        Circle c(1,2,3);
        Ellipse_<NUMTYPE> el(c);
        CHECK( el.getCenter() == Point2d(1,2) );
        CHECK( getCenter(el)  == Point2d(1,2) );
        CHECK( el.getMajMin().first == 3.0 );
        CHECK( el.getMajMin().second == 3.0 );
        CHECK( el.angle() == 0.0 );
        CHECK( angle(el)  == 0.0 );
        CHECK( el.isCircle() == true );
        CHECK( isCircle(el) == true );
    }

    {
        Ellipse_<NUMTYPE> el(1,2,3.0,3.00001);
        CHECK( el.getCenter() == Point2d(1,2) );
        CHECK( el.isCircle() == false );       // using default threshold
        CHECK( isCircle(el) == false );

        CHECK( el.isCircle(1E-3) == true );    // using arbitrary threshold
        CHECK( isCircle(el,1E-3) == true );
    }

    {
        Ellipse_<NUMTYPE> el(4,5,6,7);
        CHECK( el.getCenter() == Point2d(4,5) );
        CHECK( el.getMajMin().first  == Approx(7.0) );
        CHECK( el.getMajMin().second == Approx(6.0) );
        CHECK( el.angle() == 0.0 );
        CHECK( el.isCircle() == false );
    }
    {
        Ellipse_<NUMTYPE> el(4,5, 6, 7, 1 /*rad.*/ );
        CHECK( el.getCenter() == Point2d(4,5) );
        CHECK( el.getMajMin().first  == Approx(7.0) );
        CHECK( el.getMajMin().second == Approx(6.0) );
        CHECK( el.angle() == Approx(1.0) );
        CHECK( el.isCircle() == false );
    }
}

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TEST_CASE() [50/93]

TEST_CASE	(	"OSegment point side"	,
		""	[oseg-pt-side]
	)

{
    OSegment_<NUMTYPE> s1( 0,0,10,0);
    Point2d_<NUMTYPE> pt;
    CHECK( s1.getPointSide(pt) == PointSide::Neither );
    pt.translate(1,1);
    CHECK( s1.getPointSide(pt) == PointSide::Left );
    pt.translate(0,-5);
    CHECK( s1.getPointSide(pt) == PointSide::Right );

    pt.set(0,0);
    s1.set( 1,0, 1,10 );
    CHECK( s1.getPointSide(pt) == PointSide::Left );
}

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TEST_CASE() [51/93]

TEST_CASE	(	"Segment"	,
		""	[seg1]
	)

{
    {                              // test order of points
        Point2d p1(43,8);
        Point2d p2(43,18);
        Point2d p3(5,55);
        {
            Segment_<NUMTYPE> s( p1, p2 );   // same x value
            CHECK( s.getPts().first == p1 );
            CHECK( s.getPts().second == p2 );

            s.translate( 2, 3 );
            CHECK( s.getPts().first == Point2d(45,11) );
            CHECK( s.getPts().second == Point2d(45,21) );

            translate( s, -2, -3 );
            CHECK( s.getPts().first == Point2d(43,8) );
            CHECK( s.getPts().second == Point2d(43,18) );
        }
        {
            Segment_<NUMTYPE> s( p2, p1 );   // same x value
            CHECK( s.getPts().first == p1 );
            CHECK( s.getPts().second == p2 );
        }
        {
            Segment_<NUMTYPE> s( p1, p3 );
            CHECK( s.getPts().first == p3 );
            CHECK( s.getPts().second == p1 );
        }
        {
            Segment_<NUMTYPE> s( p3, p1 );
            CHECK( s.getPts().first == p3 );
            CHECK( s.getPts().second == p1 );
        }
    }
    {
        Point2d_<NUMTYPE> p1( 4,5 );
        Point2d_<NUMTYPE> p2( 1,2 );
        auto ppts = std::make_pair( p1, p2 );
        Segment_<NUMTYPE> s( ppts );
        CHECK( s.getPts().first  == p2 );
        CHECK( s.getPts().second == p1 );
        s.set( ppts );
    }
    {
        Line2d_<NUMTYPE> li( Point2d(0,0), Point2d(2,2) );
        Segment_<NUMTYPE> s1( Point2d(0,0), Point2d(2,2) );
        Segment_<NUMTYPE> s2( Point2d(2,2), Point2d(0,0) );
        CHECK( s1 == s2 );
        CHECK( s1.isParallelTo(s2) );
        Line2d_<NUMTYPE> l1( Point2d(10,0), Point2d(12,2) );
        CHECK( s1.isParallelTo(l1) );
        CHECK( l1.isParallelTo(s1) );
        CHECK( l1.getAngle( s1 ) == Approx(0) );
        CHECK( s1.getAngle( l1 ) == Approx(0) );
        CHECK( s1.getAngle( s2 ) == Approx(0) );
        CHECK( getAngle( s1, s2 ) == Approx(0) );
        CHECK( getAngle( li, s2 ) == Approx(0) );
        CHECK( getAngle( s2, li ) == Approx(0) );
    }
    {
        Segment_<NUMTYPE> s1( Point2d(0,0), Point2d(3,4) );
        CHECK( s1.length() == 5 );
        CHECK( s1.area() == 0 );

        Segment_<NUMTYPE> s2( Point2d(9,9), Point2d(8,8) );
        auto pts = s2.getPts();
        CHECK( pts.first  == Point2d_<NUMTYPE>(8,8) );
        CHECK( pts.second == Point2d_<NUMTYPE>(9,9) );
    }
    {
        Segment_<NUMTYPE> s1( Point2d(0,0), Point2d(2,2) );
        Segment_<NUMTYPE> s2( Point2d(2,0), Point2d(0,2) );
        auto si = s1.intersects(s2);
        CHECK( si() == true );
        CHECK( si.get() == Point2d_<NUMTYPE>(1,1) );

        auto pt = s1.getCenter();
        CHECK( pt == Point2d_<NUMTYPE>(1,1) );
    }
    {
        Segment_<NUMTYPE> s1( Point2d(0,0), Point2d(2,2) );
        Segment_<NUMTYPE> s2( Point2d(2,0), Point2d(0,2) );
        auto bis = s1.getBisector();
        CHECK( bis == s2.getLine() );
    }
    {  // test that points on a line at equal distance from a point, when
        // transformed in a segment, we get back as middle point the same one.
        Line2d li(9,9);   // diagonal line (0,0) - (9,9)
        auto ppts = li.getPoints( GivenCoord::X, 5, 1 );
        Segment_<NUMTYPE> s1( ppts.first, ppts.second );
        CHECK( s1.getCenter() == Point2d_<NUMTYPE>(5,5) );
    }
}

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TEST_CASE() [52/93]

TEST_CASE	(	"Translate"	,
		""	[trans]
	)

{
    INFO( "Translate Circle" );
    Circle_<NUMTYPE> c(5,5,10);
    c.translate(-1,+1);
    CHECK( c.center() == Point2d(4,6) );
    translate( c, +1, -1 );
    CHECK( c.center() == Point2d(5,5) );

    translate( c, std::make_pair(2,3) );
    CHECK( c.center() == Point2d(7,8) );
    c.translate( std::make_pair(-2,-3) );
    CHECK( c.center() == Point2d(5,5) );

    INFO( "Translate Point" );
    Point2d_<NUMTYPE> pt(4,5);
    pt.translate(-1,+1);
    CHECK( pt == Point2d(3,6) );
    translate(pt,+1,-1);
    CHECK( pt == Point2d(4,5) );

    translate( pt, std::make_pair(2,3) );
    CHECK( pt == Point2d(6,8) );
    pt.translate( std::make_pair(-2,-3) );
    CHECK( pt == Point2d(4,5) );
}

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TEST_CASE() [53/93]

TEST_CASE	(	"MoveTo"	,
		""	[moveto]
	)

{
    INFO( "MoveTo Circle" );
    Circle_<NUMTYPE> c(5,5,10);
    c.moveTo( 9,8 );
    CHECK( c.center() == Point2d(9,8) );
    moveTo(c,8,9);
    CHECK( c.center() == Point2d(8,9) );

    Point2d_<NUMTYPE> pt1(1,1);
    moveTo(c,pt1);
    CHECK( c.center() == pt1 );
    Point2d_<NUMTYPE> pt2(3,3);
    c.moveTo(pt2);
    CHECK( c.center() == pt2 );

//  INFO( "MoveTo Segment" );


}

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TEST_CASE() [54/93]

TEST_CASE	(	"Segment-split-1"	,
		""	[seg-split-1]
	)

{
    Segment_<NUMTYPE>  s1( Point2d(0,0), Point2d(20,0) );
    OSegment_<NUMTYPE> s2( Point2d(0,0), Point2d(20,0) );
    {
        auto psegs1 = s1.split();
        auto psegs2 = split(s1);
        CHECK( psegs1 == psegs2 );
        CHECK( psegs1.first  == Segment_<NUMTYPE>( Point2d(0,0), Point2d(10,0) ) );
        CHECK( psegs1.second == Segment_<NUMTYPE>( Point2d(10,0), Point2d(20,0) ) );
    }
    {
        auto psegs1 = s2.split();
        auto psegs2 = split(s2);
        CHECK( psegs1 == psegs2 );
        CHECK( psegs1.first  == OSegment_<NUMTYPE>( Point2d(0,0), Point2d(10,0) ) );
        CHECK( psegs1.second == OSegment_<NUMTYPE>( Point2d(10,0), Point2d(20,0) ) );
    }
}

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TEST_CASE() [55/93]

TEST_CASE	(	"Segment-split-2"	,
		""	[seg-split-2]
	)

{
    OSegment_<NUMTYPE> s1( Point2d(0,0), Point2d(20,0) );

    CHECK_THROWS( s1.split(-4) );
    CHECK_THROWS( s1.split(0) );
    CHECK_THROWS( s1.split(20) );

    CHECK_THROWS( split(s1,-4) );
    CHECK_THROWS( split(s1,0) );
    CHECK_THROWS( split(s1,20) );

    auto psegs1 = s1.split(4);
    auto psegs2 = split(s1,4);
    CHECK( psegs1 == psegs2 );
    CHECK( psegs1.first  == OSegment_<NUMTYPE>( Point2d(0,0), Point2d(4,0) ) );
    CHECK( psegs1.second == OSegment_<NUMTYPE>( Point2d(4,0), Point2d(20,0) ) );
}

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TEST_CASE() [56/93]

TEST_CASE	(	"Segment 2"	,
		""	[seg2]
	)

{
    {
        Segment_<HOMOG2D_INUMTYPE> seg (0,0,1,0); // horizontal segment
        auto psegs  = seg.getParallelSegs(1.);
        auto psegs2 = seg.getParallelSegs(1.);
        CHECK( psegs == psegs2 );
        CHECK( psegs.first  == Segment(0,-1,1,-1) );
        CHECK( psegs.second == Segment(0,+1,1,+1) );
    }
    {
        Segment_<HOMOG2D_INUMTYPE> seg (0,0,0,1); // vertical segment
        auto psegs = seg.getParallelSegs(1.);
        CHECK( psegs.first  == Segment(-1,0,-1,+1) );
        CHECK( psegs.second == Segment(+1,0,+1,+1) );
    }
}

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TEST_CASE() [57/93]

TEST_CASE	(	"Segment extended"	,
		""	[seg_extended]
	)

{
    Segment_<HOMOG2D_INUMTYPE> seg(0,0,1,0);
    auto s2 = seg.getExtended();
    CHECK( s2.length() == 3. );
    CHECK( s2.getPts().first == Point2d(-1,0) );
    CHECK( s2.getPts().second == Point2d(2,0) );

    auto s3 = getExtended(seg);
    CHECK( s3.length() == 3. );
    CHECK( s3.getPts().first == Point2d(-1,0) );
    CHECK( s3.getPts().second == Point2d(2,0) );
}

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TEST_CASE() [58/93]

TEST_CASE	(	"Segment orthogonal"	,
		""	[seg_orthog]
	)

{
    Segment_<HOMOG2D_INUMTYPE> seg(0,0,1,0);
    auto pts  = seg.getOrthogPts();
    auto pts2 = getOrthogPts(seg);
    CHECK( pts2 == pts );
    auto pol = CPolyline(pts);
    CHECK( pol == CPolyline( std::vector<Point2d>{ {0,-1},{1,-1},{1,1},{0,1} } ) );

    auto osegs  = seg.getOrthogSegs();
    auto osegs2 = getOrthogSegs(seg);
    CHECK( osegs2 == osegs );
    std::array<Segment_<HOMOG2D_INUMTYPE>,4> gt;
    gt[0] = Segment( 0,0,0,+1 );
    gt[1] = Segment( 0,0,0,-1 );
    gt[2] = Segment( 1,0,1,+1 );
    gt[3] = Segment( 1,0,1,-1 );
    std::sort( gt.begin(), gt.end() );
    std::sort( osegs.begin(), osegs.end() );
    CHECK( gt == osegs );
}

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TEST_CASE() [59/93]

TEST_CASE	(	"min/max of two objects"	,
		""	[minmax]
	)

{
    Point2d_<NUMTYPE> pt0(0,0), pt1(1,1), pt2(2,2), pt3(3,3);
    auto pp1 = std::make_pair( pt0,pt1 );
    auto pp2 = std::make_pair( pt2,pt3 );
    auto ppts = getMinMax( pp1, pp2 );
    CHECK( ppts.first  == Point2d_<NUMTYPE>(0,0) );
    CHECK( ppts.second == Point2d_<NUMTYPE>(3,3) );
// TODO: EXTEND
}

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TEST_CASE() [60/93]

TEST_CASE	(	"generalized bounding box of two objects"	,
		""	[gen-BB]
	)

{
    Point2d_<NUMTYPE> pt,pt2(1,1);
    FRect_<NUMTYPE> re,re2;
    Segment_<NUMTYPE> se,se2(1,0,0,1);
    CPolyline_<NUMTYPE> pc,pc2;
    OPolyline_<NUMTYPE> po,po2;
    Ellipse_<NUMTYPE> el,el2;

    CHECK( getBB(pt,pt2) == FRect_<NUMTYPE>() ); // (0,0) - (1,1)
    CHECK( getBB(se,se2) == FRect_<NUMTYPE>() ); // [(0,0) - (1,1)] - [(1,0) - (0,1)]
    CHECK( getBB(se,se)  == FRect_<NUMTYPE>() ); // identical segments, but they cover some area
    CHECK( getBB(re,re2) == FRect_<NUMTYPE>() );
    CHECK( getBB(se,se2) == FRect_<NUMTYPE>() );
    CHECK( getBB(el,el2) == getBB(el) ); // identical

    CHECK_THROWS( getBB(pc,pc2) ); // empty
    CHECK_THROWS( getBB(pt,pt) ); // identical points   => no BB

    pt2.set(0,1);
    CHECK_THROWS( getBB(pt,pt2) ); // one of the coordinates is identical

    se.set( 0,0,1,0 );
    se2.set( 10,0,11,0 );
    CHECK_THROWS( getBB(se,se)  ); // segments are colinear
    CHECK_THROWS( getBB(se,se2) ); // segments are colinear

    pt2.set(0,0);
    CHECK_THROWS( getBB(se,pt2) ); // no area

    pc.set(  std::vector<Point2d_<NUMTYPE>>{ {0,0},{1,0} } );
    CHECK_THROWS( getBB(pc) );         // no area
    CHECK_THROWS( getBB(pc, pc2) );    // no area, and second is empty

    pc2.set( std::vector<Point2d_<NUMTYPE>>{ {5,0},{6,0} } );
    CHECK_THROWS( getBB(pc,pc2) ); // colinear

    pc2.set( std::vector<Point2d_<NUMTYPE>>{ {5,1},{6,1} } );
    CHECK( getBB(pc,pc2) == FRect_<NUMTYPE>(0,0,6,1) );
}

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TEST_CASE() [61/93]

TEST_CASE	(	"bounding box of container"	,
		""	[BB-cont]
	)

{
    {
        std::vector<Point2d_<NUMTYPE>> vec(3);
        vec[0] = Point2d_<NUMTYPE>(1,1);
        vec[1] = Point2d_<NUMTYPE>(5,6);
        vec[2] = Point2d_<NUMTYPE>(3,2);
        CHECK( getBB(vec) == FRect_<NUMTYPE>(1,1,5,6) );
    }
    {
        std::array<Point2d_<NUMTYPE>,3> vec;
        vec[0] = Point2d_<NUMTYPE>(1,1);
        vec[1] = Point2d_<NUMTYPE>(5,6);
        vec[2] = Point2d_<NUMTYPE>(3,2);
        CHECK( getBB(vec) == FRect_<NUMTYPE>(1,1,5,6) );
    }
    {
        std::list<Point2d_<NUMTYPE>> vec;
        vec.emplace_back( Point2d_<NUMTYPE>(1,1) );
        vec.emplace_back( Point2d_<NUMTYPE>(5,6) );
        vec.emplace_back( Point2d_<NUMTYPE>(3,2) );
        CHECK( getBB(vec) == FRect_<NUMTYPE>(1,1,5,6) );
    }
    {
        std::vector<Line2d_<NUMTYPE>> vec(3);  // cannot get BB of a set of lines
        CHECK_THROWS( getBB(vec) );
    }
    {
        std::vector<FRect_<NUMTYPE>> vec(3);
        vec[0] = FRect_<NUMTYPE>(1,1,2,2);
        vec[1] = FRect_<NUMTYPE>(5,6,10,11);
        vec[2] = FRect_<NUMTYPE>(3,2,4,5);
        CHECK( getBB(vec) == FRect_<NUMTYPE>(1,1,10,11) );
    }
    {
        std::vector<Segment_<NUMTYPE>> vec(3);
        vec[0] = Segment_<NUMTYPE>(1,1,2,2);
        vec[1] = Segment_<NUMTYPE>(5,6,10,11);
        vec[2] = Segment_<NUMTYPE>(3,2,4,5);
        CHECK( getBB(vec) == FRect_<NUMTYPE>(1,1,10,11) );
    }
    {
        std::vector<Circle_<NUMTYPE>> vec(3);
        vec[0] = Circle_<NUMTYPE>(1,1,1);
        vec[1] = Circle_<NUMTYPE>(5,3,2);
        vec[2] = Circle_<NUMTYPE>(10,11,2);
        CHECK( getBB(vec) == FRect_<NUMTYPE>(0,0,12,13) );
    }
#ifdef HOMOG2D_ENABLE_VRTP
    {
        std::vector<CommonType_<NUMTYPE>> vec(4);
        vec[0] = Circle_<NUMTYPE>(3,4,1);
        vec[1] = Segment_<NUMTYPE>(5,3,2,8);
        vec[2] = FRect_<NUMTYPE>(10,11,2,2);
        vec[3] = Line2d_<NUMTYPE>();
        CHECK( getBB(vec) == FRect_<NUMTYPE>(10,11,2,2) );
    }
#endif
}

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TEST_CASE() [62/93]

TEST_CASE	(	"common bounding box with points "	,
		""	[point2d-BB]
	)

{
    Point2d_<NUMTYPE> pt;
    FRect_<NUMTYPE> r1;
    CHECK( getBB( pt, r1 ) == r1 );
    CHECK( getBB( r1, pt ) == r1 );
    Segment_<NUMTYPE> seg( 0,0,1,1);
    CHECK( getBB( seg, pt ) == r1 );
    CHECK( getBB( pt, seg ) == r1 );

    Circle_<NUMTYPE> cir;
    pt.set( 10,0);
    CHECK( getBB( pt, cir ) == FRect_<NUMTYPE>(-1.,-1.,+10.,+1. ) );
}

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TEST_CASE() [63/93]

TEST_CASE	(	"FRect pair bounding box"	,
		""	[frect-BB]
	)

{
    {                              // two identical rectangles
        FRect_<NUMTYPE> r1, r2;
        CHECK( getBB(r1,r2) == r1 );
    }
    {                                  // one bottom left, the other top right
        FRect_<NUMTYPE> r1(0,0, 1,1);
        FRect_<NUMTYPE> r2(2,2, 4,4);
        CHECK( getBB(r1,r2) == FRect_<NUMTYPE>(0,0,4,4) );
    }
    {                                 // one top left, the other bottom right
        FRect_<NUMTYPE> r1(0,2, 1,3);
        FRect_<NUMTYPE> r2(2,0, 4,1);
        CHECK( getBB(r1,r2) == FRect_<NUMTYPE>(0,0,4,3) );
    }
    {                                 // one inside the other
        FRect_<NUMTYPE> r1(0,0, 5,5);
        FRect_<NUMTYPE> r2(1,1, 3,3);
        CHECK( getBB(r1,r2) == FRect_<NUMTYPE>(0,0,5,5) );
    }
    {                                 // one inside the other, with a common edge
        FRect_<NUMTYPE> r1(0,0, 5,5);
        FRect_<NUMTYPE> r2(1,0, 3,3);
        CHECK( getBB(r1,r2) == FRect_<NUMTYPE>(0,0,5,5) );
    }

// test for rectangle of different types
    {                                 // one inside the other, with a common edge
        FRect_<float> r1(0,0, 5,5);
        FRect_<double> r2(1,0, 3,3);
        auto bb = getBB(r1,r2);
        CHECK( bb == FRect_<long double>(0,0,5,5) );
        CHECK( bb.dtype() == Dtype::Float );
    }
}

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TEST_CASE() [64/93]

TEST_CASE	(	"bounding box of two objects"	,
		""	[getBB-pair]
	)

{
    FRect_<NUMTYPE> r1(0,3, 2,0);
    FRect_<NUMTYPE> r2(4,5, 6,8);
    FRect_<NUMTYPE> bbr(0,0, 6,8);
    CHECK( bbr == getBB( r1,r2 ) );
    {                                    // distant segments
        Segment_<NUMTYPE> s1(0,3, 2,0);
        Segment_<NUMTYPE> s2(4,5, 6,8);
        FRect_<NUMTYPE> bbs(0,0, 6,8);
        CHECK( bbs == getBB( s1,s2 ) );
    }
    {                                    // crossing segments
        Segment_<NUMTYPE> s1(0,0, 5,5);
        Segment_<NUMTYPE> s2(0,6, 4,0);
        FRect_<NUMTYPE> bbs(0,0, 5,6);
        CHECK( bbs == getBB( s1,s2 ) );
    }

    {                                  // one circle inside the other
        Circle_<NUMTYPE> c1(0,0, 2);
        Circle_<NUMTYPE> c2(0,1, 4);
        FRect_<NUMTYPE> bbc(-4,-3, +4,5);
        CHECK( bbc == getBB( c1,c2 ) );
    }
    {                                  // two distant circles
        Circle_<NUMTYPE> c1(5,5, 2);
        Circle_<NUMTYPE> c2(0,0, 1);
        FRect_<NUMTYPE> bbc(-1,-1, 7,7);
        CHECK( bbc == getBB( c1,c2 ) );
    }
    {  // CPolyline / Frect
        CPolyline_<NUMTYPE> po( std::vector<Point2d>{ {0,0}, {1,1}, {3,2} } );
        FRect_<NUMTYPE> rect;
        CHECK( getBB(po,rect) == FRect_<NUMTYPE>(0,0,3,2) );
    }
    {  // OPolyline / Frect
        OPolyline_<NUMTYPE> po( std::vector<Point2d>{ {0,0}, {1,1}, {3,2} } );
        FRect_<NUMTYPE> rect;
        CHECK( getBB(po,rect) == FRect_<NUMTYPE>(0,0,3,2) );
    }
    {  // OPolyline / Segment
        OPolyline_<NUMTYPE> po( std::vector<Point2d>{ {0,0}, {1,1}, {3,2} } );
        Segment_<NUMTYPE> seg; // [0,0]-[1,1]
        CHECK( getBB(seg,po) == FRect_<NUMTYPE>(0,0,3,2) );
    }
    {  // 2 CPolyline, one is empty
        CPolyline_<NUMTYPE> po1( std::vector<Point2d>{ {0,0}, {1,1}, {3,2} } );
        CPolyline_<NUMTYPE> po2;
        CHECK( getBB(po1,po2) == getBB(po1) );
    }
    {  // Circle / Frect
        Circle_<NUMTYPE> cir( 5,5,3 ); // center at 5,5, radius=3
        FRect_<NUMTYPE> rect; // (0,0)--(1,1)
        CHECK( getBB(cir,rect) == FRect_<NUMTYPE>(0,0,8,8) );
    }
    {  // Circle / Segment
        Circle_<NUMTYPE> cir( 5,5,3 ); // center at 5,5, radius=3
        Segment_<NUMTYPE> seg(10,20,30,40);
        CHECK( getBB(cir,seg) == FRect_<NUMTYPE>(2,2,30,40) );
    }
    {  // Circle / Circle (one inside the other)
        Circle_<NUMTYPE> cir1( 5,5,3 ); // center at 5,5, radius=3
        Circle_<NUMTYPE> cir2( 5,5,1 ); // center at 5,5, radius=1
        CHECK( getBB(cir1,cir2) == FRect_<NUMTYPE>(2,2,8,8) );
    }
    {  // two identical Circles
        Circle_<NUMTYPE> cir1,cir2;
        CHECK( getBB(cir1,cir2) == FRect_<NUMTYPE>(-1,-1,1,1) );
    }
    {  // two identical Ellipses
        Ellipse_<NUMTYPE> e1,e2;
        CHECK( getBB(e1,e2) == FRect_<NUMTYPE>(-2,-1,2,1) );
    }
}

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TEST_CASE() [65/93]

TEST_CASE	(	"FRect"	,
		""	[frect]
	)

{
    {
        FRect_<NUMTYPE> r1;
        CHECK( r1.width()  == 1. );
        CHECK( r1.height() == 1. );
        CHECK( r1.length() == 4 );
        CHECK( r1.area()   == 1 );
        CHECK( r1.getCenter() == Point2d(0.5,0.5) );

// free functions
        CHECK( width(r1)  == 1. );
        CHECK( height(r1) == 1. );
        CHECK( length(r1) == 4 );
        CHECK( area(r1)   == 1 );
        CHECK( getCenter(r1) == Point2d(0.5,0.5) );

        auto p_pts = r1.getPts();
        CHECK( p_pts.first  == Point2d() );
        CHECK( p_pts.second == Point2d(1.,1.) );

        auto pts = r1.get4Pts();
        CHECK( pts[0] == Point2d(0,0) );
        CHECK( pts[1] == Point2d(0,1) );
        CHECK( pts[2] == Point2d(1,1) );
        CHECK( pts[3] == Point2d(1,0) );
    }
    CHECK_THROWS( FRect_<NUMTYPE>( Point2d(4,5), Point2d(4,2) ) );
    {
        FRect_<NUMTYPE> r2a( Point2d(6,5), Point2d(1,2) );
        FRect_<NUMTYPE> r2b( Point2d(6,2), Point2d(1,5) );
        CHECK( r2a == r2b );

        CHECK( r2a.width() == 5. );
        CHECK( r2a.height() == 3. );
        auto p_pts = r2b.getPts();
        CHECK( p_pts.first  == Point2d(1,2) );
        CHECK( p_pts.second == Point2d(6,5) );

        auto pts = r2b.get4Pts();
        CHECK( pts[0] == Point2d(1,2) );
        CHECK( pts[1] == Point2d(1,5) );
        CHECK( pts[2] == Point2d(6,5) );
        CHECK( pts[3] == Point2d(6,2) );
    }
    {
        FRect_<NUMTYPE> r;
        auto s = r.getSegs();
        auto s2 = getSegs( r );
        CHECK( s == s2 );
        CHECK( s[0] == Segment(0,0, 0,1) );
        CHECK( s[1] == Segment(0,1, 1,1) );
        CHECK( s[2] == Segment(1,1, 1,0) );
        CHECK( s[3] == Segment(1,0, 0,0) );
    }
    {
        FRect_<NUMTYPE> r( Point2d(0,0), 100, 50 );
        CHECK( r.width()  == 100 );
        CHECK( r.height() == 50 );
        CHECK( r.length() == 300 );
        CHECK( r.area() == 5000 );
        CHECK( r.getCenter() == Point2d(0,0) );
    }
    {
        FRect_<NUMTYPE> r1( 0,0, 5, 3 );
        FRect_<NUMTYPE> r2( 2,3, 7, 6 );
        CHECK( r1.size() == r2.size() );
        CHECK( size(r1) == size(r2) );
    }
}

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TEST_CASE() [66/93]

TEST_CASE	(	"FRect extended"	,
		""	[frect-ext]
	)

{
    FRect_<NUMTYPE> rect;
    auto r1a = rect.getExtended();
    auto r1b = getExtended(rect);
    CHECK( r1a == r1b );
    CHECK( r1a == FRect(-1,-1,2,2 ) );
    CHECK( r1a.area() == 9 * rect.area() );

    FRect_<NUMTYPE> rect2(4,5,6,6);
    CHECK( rect2.getExtended() == FRect(2,4,8,7) );
}

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TEST_CASE() [67/93]

TEST_CASE	(	"FRect diagonals"	,
		""	[frect-diags]
	)

{
    FRect_<NUMTYPE> r1;
    auto psegs1 = r1.getDiagonals();
    auto psegs2 = getDiagonals(r1);
    CHECK( psegs1 == psegs2 );

    CHECK( psegs1.first  == Segment(0,0,1,1) );
    CHECK( psegs1.second == Segment(0,1,1,0) );
}

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TEST_CASE() [68/93]

TEST_CASE	(	"Polyline comparison 1"	,
		""	[polyline-comparison-1]
	)

{
    std::vector<Point2d_<NUMTYPE>> vpt1{ {0,0}, {1,0}, {1,1}        };
    std::vector<Point2d_<NUMTYPE>> vpt2{        {1,0}, {1,1}, {0,0} };
    {
        OPolyline opl1, opl2;
        opl1.set( vpt1 );
        opl2.set( vpt2 );
        CHECK( opl1 != opl2 );

        CPolyline cpl1, cpl2;
        cpl1.set( vpt1 );
        cpl2.set( vpt2 );
        CHECK( cpl1 == cpl2 );

        CHECK( opl1 != cpl1 ); // comparing polygons of different types is allowed
        CHECK( opl2 != cpl1 ); // (but will always return false)
    }
}

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TEST_CASE() [69/93]

TEST_CASE	(	"Polyline minimization"	,
		""	[polyline-min]
	)

{
    INFO( "Polyline pl2( IsClosed::No" );
    {
#include "figures_test/polyline_min_1O.code" // open

        CHECK( pl.size() == 3 );
        CHECK( pl.nbSegs() == 2 );
        pl.minimize();
        CHECK( pl.size() == 2 );
        CHECK( pl.nbSegs() == 1 );
    }
    {
#include "figures_test/polyline_min_1C.code"  // closed
        CHECK( pl.size()   == 3 );
        CHECK( pl.nbSegs() == 3 );
        pl.minimize();
        CHECK( pl.size()   == 2 );
        CHECK( pl.nbSegs() == 2 );
    }
    {
#include "figures_test/polyline_min_2O.code"// open
        CHECK( pl.size()   == 3 );
        CHECK( pl.nbSegs() == 2 );
        pl.minimize();
//      std::cout << "pl:" << pl << '\n';
        CHECK( pl.size()   == 3 ); // no change
        CHECK( pl.nbSegs() == 2 );
    }
    {
#include "figures_test/polyline_min_2C.code" // closed
        CHECK( pl.size()   == 3 );
        CHECK( pl.nbSegs() == 3 );
        pl.minimize();
        CHECK( pl.size()   == 3 );   // no change !
        CHECK( pl.nbSegs() == 3 );
    }
    {
#include "figures_test/polyline_min_3O.code" // open
        CHECK( pl.size()   == 4 );
        CHECK( pl.nbSegs() == 3 );
        pl.minimize();
//      std::cout << "pl:" << pl << '\n';
        CHECK( pl.size()   == 4 );     // no change
        CHECK( pl.nbSegs() == 3 );
    }
    {
#include "figures_test/polyline_min_3C.code" // closed
        CHECK( pl.size()   == 4 );
        CHECK( pl.nbSegs() == 4 );
        pl.minimize();
//      std::cout << "pl:" << pl << '\n';
        CHECK( pl.size()   == 3 );     // no change
        CHECK( pl.nbSegs() == 3 );
    }
}

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TEST_CASE() [70/93]

TEST_CASE	(	"Polyline"	,
		""	[polyline]
	)

{
    {                                 // default constructor
        OPolyline_<NUMTYPE> pl1;
        polytest_1( pl1 );
        CPolyline_<NUMTYPE> pl2;
        polytest_1( pl2 );
    }
    {
        CPolyline_<NUMTYPE> pc1;
        OPolyline_<NUMTYPE> po1;
        std::vector<Point2d> vpt{ {0,0} };
        CHECK_THROWS( pc1.set( vpt ) );  // can't hold only 1 point
        CHECK_THROWS( po1.set( vpt ) );
    }
    {
        std::vector<Point2d> vpt{ {0,0} };
        CHECK_THROWS( CPolyline_<NUMTYPE>( vpt ) ); // can(t build a polyline with a vector of size=1
        CHECK_THROWS( OPolyline_<NUMTYPE>( vpt ) );
    }
    {                           // build from Rectangle
        FRect r( 5,6, 7,8 );
        CPolyline_<NUMTYPE> pl1( r );

        CHECK( pl1.isSimple() == true );
        CHECK( isSimple(pl1)  == true );
        CHECK( pl1.size()   == 4 );
        CHECK( size(pl1)   == 4 );
        CHECK( pl1.nbSegs() == 4 );
        CHECK( nbSegs(pl1)  == 4 );
        CHECK( pl1.length() == 8 );
        CHECK( length(pl1)  == 8 );
        CHECK( pl1.area()   == 4 );
        CHECK( area(pl1)    == 4 );
        CHECK( pl1.centroid() == Point2d(6,7) );
        CHECK( centroid(pl1)  == Point2d(6,7) );

        auto vpts = pl1.getPts();
        CHECK( vpts.size() == 4 );
        CHECK( vpts[0] == Point2d(5,6) );

        pl1.translate(1,2);
        CHECK( pl1 == CPolyline_<NUMTYPE>( FRect( 6,8, 8,10 ) ) );
    }
    {                           // set from Rectangle
        FRect r( 5,6, 7,8 );
        CPolyline_<NUMTYPE> pl1;
        pl1.set(r);

        CHECK( pl1.isSimple() == true );
        CHECK( pl1.size() == 4 );
        CHECK( pl1.getPoint(0)  == Point2d(5,6) );
    }
    {
        OPolyline_<NUMTYPE> po1;
        CPolyline_<NUMTYPE> pc1;
        std::vector<Point2d> vpt{ {0,0},{2,2}, {2,2}, {4,3} };

        CHECK_THROWS( po1.set( vpt ) ); // cant have two contiguous identical points
        CHECK_THROWS( pc1.set( vpt ) ); // cant have two contiguous identical points
    }
    {
        std::vector<Point2d> vpt{ {0,0}, {1,1.5}, {3,5}, {1,4} };

        OPolyline_<NUMTYPE> po1(vpt);
        CPolyline_<NUMTYPE> pc1(vpt);

        CHECK( po1.isClosed() == false );
        CHECK( pc1.isClosed() == true );

        CHECK( po1.size() == 4 );
        CHECK( pc1.size() == 4 );

        CHECK( po1.nbSegs() == 3 );
        CHECK( pc1.nbSegs() == 4 );

        CHECK( po1.isSimple() == false );
        CHECK( pc1.isSimple() == true );

        CPolyline_<NUMTYPE> pc2(po1);
        CHECK( pc2.nbSegs()    == 4 );
        CHECK( pc2.isSimple() == true );

        FRect bb1( 0,0, 3,5);
        CHECK( getBB(po1) == bb1 );
        CHECK( getBB(pc1) == bb1 );
        CHECK( po1.getBB() == bb1 );
        CHECK( pc1.getBB() == bb1 );
    }
    {
        std::vector<Point2d> vpt{ {0,0}, {1,1}, {0,1}, {1,0} };
        CPolyline_<NUMTYPE> pc1(vpt);
        CHECK( pc1.isClosed() == true );
        CHECK( pc1.size() == 4 );
        CHECK( pc1.nbSegs() == 4 );
        CHECK( pc1.isSimple() == false ); // crossing segments

        pc1.translate(2,1.);
        CHECK( pc1.getPoint(0) == Point2d(2,1.) ); // (0,0) translated to (2,1)
    }
    {                                        // build from std::array
        std::array<Point2d,3> pts{{ {0,0}, {1,1}, {0,1} }};
        CPolyline_<NUMTYPE> pc(pts);
        OPolyline_<NUMTYPE> po(pts);
        CHECK( pc.isClosed() == true );
        CHECK( po.isClosed() == false );
        CHECK( pc.size() == 3 );
        CHECK( po.size() == 3 );
        CHECK( pc.nbSegs() == 3 );
        CHECK( po.nbSegs() == 2 );
    }
    {                                          // build from std::list
        std::list<Point2d> pts{ {0,0}, {1,1}, {0,1} };
        CPolyline_<NUMTYPE> pc(pts);
        OPolyline_<NUMTYPE> po(pts);
        CHECK( pc.isClosed() == true );
        CHECK( po.isClosed() == false );
        CHECK( pc.size() == 3 );
        CHECK( po.size() == 3 );
        CHECK( pc.nbSegs() == 3 );
        CHECK( po.nbSegs() == 2 );
    }
    {                   // build from segment
        Segment_<NUMTYPE> seg;
        CPolyline_<NUMTYPE> pc( seg );
        OPolyline_<NUMTYPE> po( seg );
        CHECK( pc.size() == 2 );
        CHECK( po.size() == 2 );
        CHECK( pc.getPoint(0) == Point2d(0,0) );
        CHECK( po.getPoint(0) == Point2d(0,0) );
        CHECK( pc.nbSegs() == 2 );
        CHECK( po.nbSegs() == 1 );
    }
    {                   // build from segment - 2
        Segment_<NUMTYPE> seg; // (0,0) - (1,1)
        CPolyline_<NUMTYPE> pc1( seg );
        OPolyline_<NUMTYPE> po1( seg );
        std::list<Point2d> pts{ {1,1},{0,0} };
        CPolyline_<NUMTYPE> pc2(pts);
        OPolyline_<NUMTYPE> po2(pts);
        CHECK( pc1 == pc2 );
        CHECK( po1 == po2 );
    }
}

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TEST_CASE() [71/93]

TEST_CASE	(	"Polyline setParallelogram"	,
		""	[polyline-setParallelogram]
	)

{
    {
        Point2d_<NUMTYPE> pt1(0,0);
        Point2d_<NUMTYPE> pt2(0,2);
        Point2d_<NUMTYPE> pt3(4,5);
        CPolyline_<NUMTYPE> pol;
        pol.setParallelogram( pt1, pt2, pt3 );

        std::vector<Point2d_<NUMTYPE>> vpts{ {0,0}, {0,2}, {4,5}, {4,3} };
        CPolyline_<NUMTYPE> pol2(vpts);
        CHECK( pol == pol2 );
    }
}

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TEST_CASE() [72/93]

TEST_CASE	(	"Polyline get extreme point"	,
		""	[polyline-getExtremePoint]
	)

{
    {
        CPolyline cp_empty;
        CHECK_THROWS( cp_empty.getLmPoint() );
    }
    {
        Point2d_<NUMTYPE> pt( 3, 4 );
        std::vector<Point2d_<NUMTYPE>> vpt{ pt };

        CHECK( getLmPoint(vpt).first == pt );
        CHECK( getRmPoint(vpt).first == pt );
        CHECK( getTmPoint(vpt).first == pt );
        CHECK( getBmPoint(vpt).first == pt );
        CHECK( getExtremePoint(CardDir::Left,vpt).first == pt );
    }
    {
        std::vector<Point2d_<NUMTYPE>> vpt{ {1,0}, {0,1}, {-1,0}, {0,-1} };
        CPolyline cp( vpt );
        CHECK( cp.size() == 4 );
        CHECK( cp.getLmPoint() == Point2d_<NUMTYPE>(-1,0) );
        CHECK( cp.getRmPoint() == Point2d_<NUMTYPE>(1,0) );
        CHECK( cp.getTmPoint() == Point2d_<NUMTYPE>(0,1) );
        CHECK( cp.getBmPoint() == Point2d_<NUMTYPE>(0,-1) );

        CHECK( getLmPoint(vpt).first == Point2d_<NUMTYPE>(-1,0) );
        CHECK( getRmPoint(vpt).first == Point2d_<NUMTYPE>(1,0) );
        CHECK( getTmPoint(vpt).first == Point2d_<NUMTYPE>(0,1) );
        CHECK( getBmPoint(vpt).first == Point2d_<NUMTYPE>(0,-1) );
    }
    {
        std::vector<Point2d_<NUMTYPE>> vpt{ {0,0}, {1,0}, {2,0}, {2,1}, {2,2}, {1,2}, {0,2}, {0,1} };
        CPolyline cp( vpt );
        CHECK( cp.size() == 8 );
        CHECK( cp.getLmPoint() == Point2d_<NUMTYPE>(0,0) );
        CHECK( cp.getRmPoint() == Point2d_<NUMTYPE>(2,0) );
        CHECK( cp.getTmPoint() == Point2d_<NUMTYPE>(0,2) );
        CHECK( cp.getBmPoint() == Point2d_<NUMTYPE>(0,0) );

        CHECK( getLmPoint(vpt).first == Point2d_<NUMTYPE>(0,0) );
        CHECK( getRmPoint(vpt).first == Point2d_<NUMTYPE>(2,0) );
        CHECK( getTmPoint(vpt).first == Point2d_<NUMTYPE>(0,2) );
        CHECK( getBmPoint(vpt).first == Point2d_<NUMTYPE>(0,0) );
    }
}

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TEST_CASE() [73/93]

TEST_CASE	(	"Bounding Box of set of objects"	,
		""	[BB-cont]
	)

{
    std::vector<Point2d> vpts1{ {0,0}, {1,1.5}, {3,5}, {1,4} };
    FRect bb1( 0,0, 3,5 );
    {
        CHECK( getBB(vpts1) == bb1 );

        CPolyline cpol( vpts1 );
        OPolyline opol( vpts1 );
        std::vector<CPolyline> vec_c{ cpol };
        std::vector<OPolyline> vec_o{ opol };
        CHECK( getBB(vec_c) == bb1 );
        CHECK( getBB(vec_o) == bb1 );
    }
    {
        std::vector<Segment> vseg;
        CHECK_THROWS( getBB(vseg) );
        vseg.emplace_back( Segment(0,0,0,1) );
        CHECK_THROWS( getBB(vseg) );     // no area !

        vseg.emplace_back( Segment(4,5,6,7) );
        FRect bb2( 0,0, 6,7 );
        CHECK( getBB(vseg) == bb2 );
    }
    {
        std::list<Circle> vcir;
        CHECK_THROWS( getBB(vcir) );     // empty !
        vcir.emplace_back( Circle(1,1,1) );
        FRect bb3( 0,0, 2,2 );
        CHECK( getBB(vcir) == bb3 );
    }
    {
        std::vector<Point2d> vpt{ {0,11} };
        CHECK_THROWS( getBB(vpt) );         // need at least 2 points !

        std::list<Point2d> lpt{ {2,11} };
        CHECK_THROWS( getBB(lpt) );         // need at least 2 points !

        std::array<Point2d,1> apt;
        apt[0] = Point2d{2,11};
        CHECK_THROWS( getBB(apt) );         // need at least 2 points !
    }
}

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TEST_CASE() [74/93]

TEST_CASE	(	"getCenters() and getLines()"	,
		""	[getCenters]
	)

{
    {
        std::vector<Segment> vec;
        auto out1 = getCenters( vec );
        CHECK( out1.empty() );

        vec.emplace_back( Segment( 0,0,2,0) );
        vec.emplace_back( Segment( 0,1,2,1) );
        auto out2 = getCenters( vec );
        CHECK( out2.size() == 2 );
        CHECK( out2[0] == Point2d(1,0) );
        CHECK( out2[1] == Point2d(1,1) );

        auto out3 = getLines( vec );
        CHECK( out3.size() == 2 );
        CHECK( out3[0] == Line2d( Point2d(0,0), Point2d(5,0) ) );
        CHECK( out3[1] == Line2d( Point2d(0,1), Point2d(5,1) ) );
    }
    {
        std::list<Circle> vec;
        auto out1 = getCenters( vec );
        CHECK( out1.empty() );

        vec.emplace_back( Circle( 0,0, 2) );
        vec.emplace_back( Circle( 1,1, 3) );
        auto out2 = getCenters( vec );
        CHECK( out2.size() == 2 );
        CHECK( out2[0] == Point2d(0,0) );
        CHECK( out2[1] == Point2d(1,1) );
    }
    {
        std::array<Ellipse,2> vec;
        auto out1 = getCenters( vec );
        CHECK( out1.size() == 2 );    // because input array has size=2

        vec[0] = Ellipse( 0,0, 2, 3 );
        vec[1] = Ellipse( 1,1, 3, 8 );
        auto out2 = getCenters( vec );
        CHECK( out2.size() == 2 );
        CHECK( out2[0] == Point2d(0,0) );
        CHECK( out2[1] == Point2d(1,1) );
    }
}

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TEST_CASE() [75/93]

TEST_CASE	(	"Polygon convexity"	,
		""	[polyline-convex]
	)

{
    OPolyline_<NUMTYPE> plo;
    CPolyline_<NUMTYPE> plc;
    CHECK( !plo.isConvex() );  // empty !!
    CHECK( !plc.isConvex() );

    CHECK( !isConvex(plc) ); // free function call
    CHECK( !isConvex(plo) );

    plo.set( std::vector<Point2d>{ {0,0}, {2,0} } );
    plc.set( std::vector<Point2d>{ {0,0}, {2,0} } );
    CHECK( !plo.isConvex() );  // 2 pts are fine, but not convex
    CHECK( !plc.isConvex() );

    plo.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,1} } );
    plc.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,1} } );
    CHECK( !plo.isConvex() );  // 3 pts ok, but open Polyline never convex
    CHECK( plc.isConvex() );

    plc.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,2}, {0,2} } );
    CHECK( plc.isConvex() );
    plc.set( std::vector<Point2d>{ {0,0}, {2,0}, {1,1}, {2,2}, {0,2} } );
    CHECK( !plc.isConvex() );

    plc.set( std::vector<Point2d>{ {2,2}, {2,-2}, {-2,-2}, {-2,2} } );
    CHECK( plc.isConvex() );
    plc.set( std::vector<Point2d>{ {2,2}, {2,-2}, {1,1}, {-2,2} } );
    CHECK( !plc.isConvex() );
}

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TEST_CASE() [76/93]

TEST_CASE	(	"Polygon orientation"	,
		""	[polyline-orient]
	)

{
    {
        CPolyline_<NUMTYPE> pl1;
        CPolyline_<NUMTYPE> pl2;                                             //  +-----+
        pl1.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,1}, {0,1} } );       //  |     |
        pl2.set( std::vector<Point2d>{ {0,0}, {0,1}, {2,1}, {2,0} } );       //  +-----+
        CHECK( pl1 == pl2 );   // is closed, so the points describe the same thing
    }
    {
        OPolyline_<NUMTYPE> pl1;
        OPolyline_<NUMTYPE> pl2;                                          //  +-----+     +-----+
        pl1.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,1}, {0,1} } );    //        | and |     |
        pl2.set( std::vector<Point2d>{ {0,0}, {0,1}, {2,1}, {2,0} } );    //  +-----+     +     +
        CHECK( pl1 != pl2 ); // is open, so they are different

        CPolyline_<NUMTYPE> plc1(pl1);
        CPolyline_<NUMTYPE> plc2(pl2);
        CHECK( plc1 == plc2 );
    }
    {
        std::vector<Point2d> v1{ {0,0}, {1,0}, {1,1} };
        std::vector<Point2d> v2{ {1,1}, {1,0}, {0,0} };

        CPolyline_<NUMTYPE> pl1(v1);
        CPolyline_<NUMTYPE> pl2(v2);
        CHECK( pl1 == pl2 );
        OPolyline_<NUMTYPE> po1(v1);
        OPolyline_<NUMTYPE> po2(v2);
        CHECK( po1 == po2 );
    }
}

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TEST_CASE() [77/93]

TEST_CASE	(	"Polyline basic"	,
		""	[polyline-basic]
	)

{
    std::vector<Point2d_<NUMTYPE>> vpts{ {0,0}, {1,0}, {1,1} };

    std::vector<Segment_<NUMTYPE>> vseg_o;
    std::vector<Segment_<NUMTYPE>> vseg_c;
    vseg_o.emplace_back( Segment_<NUMTYPE>( 0,0, 1,0 ) );
    vseg_o.emplace_back( Segment_<NUMTYPE>( 1,0, 1,1 ) );
    vseg_c = vseg_o;
    vseg_c.emplace_back( Segment_<NUMTYPE>( 1,1, 0,0 ) );

    CPolyline_<NUMTYPE> cpol(vpts);
    OPolyline_<NUMTYPE> opol(vpts);
    CHECK( cpol.isClosed() );
    CHECK( !opol.isClosed() );

    CHECK( cpol.size() == 3 );
    CHECK( opol.size() == 3 );

    CHECK( cpol.getPts() == vpts );
    CHECK( opol.getPts() == vpts );

    CHECK( cpol.getSegs() == vseg_c );
    CHECK( opol.getSegs() == vseg_o );

    std::vector<OSegment_<NUMTYPE>> voseg_o;                   // oriented segments
    std::vector<OSegment_<NUMTYPE>> voseg_c;

    auto os0 = OSegment_<NUMTYPE>( 0,0, 1,0 );
    auto os1 = OSegment_<NUMTYPE>( 1,0, 1,1 );
    auto os2 = OSegment_<NUMTYPE>( 1,1, 0,0 );
    voseg_o.emplace_back( os0 );
    voseg_o.emplace_back( os1 );
    voseg_c = voseg_o;
    voseg_c.emplace_back( os2 );

    CHECK( cpol.getOSegs() == voseg_c );
    CHECK( opol.getOSegs() == voseg_o );

    CHECK( cpol.getOSegment(0) == os0 );
    CHECK( opol.getOSegment(0) == os0 );

    CHECK( cpol.getOSegment(1) == os1 );
    CHECK( opol.getOSegment(1) == os1 );

    CHECK( cpol.getOSegment(2) == os2 );
    CHECK_THROWS( opol.getOSegment(2) );
    CHECK_THROWS( cpol.getOSegment(3) );
}

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TEST_CASE() [78/93]

TEST_CASE	(	"Polyline fullstep rotation"	,
		""	[polyline-rot]
	)

{
    OPolyline_<NUMTYPE> plo;
    CPolyline_<NUMTYPE> plc;
    OPolyline_<NUMTYPE> plo_ff;
    CPolyline_<NUMTYPE> plc_ff;
    std::vector<Point2d>  vpts{ {0,0}, {2,0}, {1,1} };
    {
        plo.set( vpts );
        plc.set( vpts );
        plo.rotate( Rotate::CCW );
        plc.rotate( Rotate::CCW );
        std::vector<Point2d> vpts2{ {0,0},{0,2},{-1,1} };
        OPolyline_<NUMTYPE> plo2( vpts2 );
        CPolyline_<NUMTYPE> plc2( vpts2 );
        CHECK( plo == plo2 );
        CHECK( plc == plc2 );

        plo_ff.set( vpts );
        plc_ff.set( vpts );
        rotate( plo_ff, Rotate::CCW );
        rotate( plc_ff, Rotate::CCW );
        CHECK( plo == plo_ff );
        CHECK( plc == plc_ff );
    }
    {
        plo.set( vpts );
        plc.set( vpts );
        plo.rotate( Rotate::VMirror );
        plc.rotate( Rotate::VMirror );
        std::vector<Point2d> vpts2{ {0,0},{-2,0},{-1,1} };
        OPolyline_<NUMTYPE> plo2( vpts2 );
        CPolyline_<NUMTYPE> plc2( vpts2 );
        CHECK( plo == plo2 );
        CHECK( plc == plc2 );
    }
    {
        plo.set( vpts );
        plc.set( vpts );
        plo.rotate( Rotate::HMirror );
        plc.rotate( Rotate::HMirror );
        std::vector<Point2d> vpts2{ {0,0},{2,0},{1,-1} };
        OPolyline_<NUMTYPE> plo2( vpts2 );
        CPolyline_<NUMTYPE> plc2( vpts2 );
        CHECK( plo == plo2 );
        CHECK( plc == plc2 );
    }
}

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TEST_CASE() [79/93]

TEST_CASE	(	"Polygon area"	,
		""	[polyline-area]
	)

{
    CPolyline_<NUMTYPE> pl1;
    {
        pl1.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,1}, {0,1} } );
        CHECK( pl1.size()   == 4 );
        CHECK( pl1.nbSegs() == 4 );
        CHECK( pl1.isSimple() == true );
        CHECK( pl1.area() == 2. );
    }
    {
        pl1.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,2}, {1,2}, {1,1}, {0,1} } );
        CHECK( pl1.size()   == 6 );
        CHECK( pl1.nbSegs() == 6 );
        CHECK( pl1.isSimple() == true );
        CHECK( pl1.area() == 3. );
    }
    OPolyline_<NUMTYPE> plo;
    plo.set( std::vector<Point2d>{ {0,0}, {2,0}, {2,1}, {0,1} } );
    CHECK( plo.isSimple() == false );
    CHECK( plo.area() == 0. );
}

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TEST_CASE() [80/93]

TEST_CASE	(	"Polyline comparison 2"	,
		""	[polyline-comp-2]
	)

{
    {
        OPolyline_<NUMTYPE> pa,pb;
        CHECK( pa == pb );
    }
    {
        CPolyline_<NUMTYPE> pa,pb;
        CHECK( pa == pb );
    }

    OPolyline_<NUMTYPE> pl2( std::vector<Point2d>{ {7,8},{3,4},{5,6}       } );
    OPolyline_<NUMTYPE> pl1( std::vector<Point2d>{       {3,4},{5,6},{7,8} } );

    {
        OPolyline_<NUMTYPE> p1 = pl1;
        OPolyline_<NUMTYPE> p2 = pl2;

        CHECK( p1.isClosed()     == false );
        CHECK( p1.isNormalized() == false );
        CHECK( p2.isNormalized() == false );
        CHECK( p1!=p2 );
    }
    {
        CPolyline_<NUMTYPE> p1 = pl1; // build a closed one from an open one
        CPolyline_<NUMTYPE> p2 = pl2;

        CHECK( p1.isClosed()     == true );
        CHECK( p1.isNormalized() == false );
        CHECK( p2.isNormalized() == false );
        CHECK( (p1==p2) == true );
        CHECK( p1.isNormalized() == true );
        CHECK( p2.isNormalized() == true );
    }
    {
        CPolyline_<NUMTYPE> p2( std::vector<Point2d>{ {1,2},{1,1},{2,1}       } );
        CPolyline_<NUMTYPE> p1( std::vector<Point2d>{       {1,1},{2,1},{1,2} } );

        CHECK( p1.getPoint(0) == Point2d_<NUMTYPE>(1,1) );
        CHECK( p2.getPoint(0) == Point2d_<NUMTYPE>(1,2) );
        CHECK( p1 == p2 ); // normalizing
        CHECK( p1.getPoint(0) == Point2d_<NUMTYPE>(1,1) );
        CHECK( p2.getPoint(0) == Point2d_<NUMTYPE>(1,1) );
    }
    {
        CPolyline pa, pb;
        {
#include "figures_test/polyline_comp_1a.code"
            pa = pl;
        }
        {
#include "figures_test/polyline_comp_1b.code"
            pb = pl;
        }
        CHECK( pa.size() == pb.size() );
        CHECK( pa != pb );
    }
}

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TEST_CASE() [81/93]

TEST_CASE	(	"convex hull"	,
		""	[conv_hull]
	)

{
    {
        CPolyline_<NUMTYPE> pl;

        pl.set( FRect_<NUMTYPE>(1,1,3,3) );
        CHECK( priv::chull::getPivotPoint(pl.getPts() ) == 0 );

        std::vector<Point2d> v1{ {0,0}, {2,0}, {2,2}, {1,2}, {1,1}, {0,1} };
        pl.set( v1 );
        CHECK( priv::chull::getPivotPoint(pl.getPts() ) == 0 );

        std::rotate( v1.begin(), v1.begin()+1, v1.end() );
        pl.set( v1 );
        CHECK( priv::chull::getPivotPoint(pl.getPts() ) == 5 );

        std::rotate( v1.begin(), v1.begin()+1, v1.end() );
        pl.set( v1 );
        CHECK( priv::chull::getPivotPoint(pl.getPts() ) == 4 );
    }
    {
#include "figures_test/polyline_chull_1.code"
        auto vp = pl.getPts();
        CHECK( priv::chull::getPivotPoint(pl.getPts() ) == 0 );
        auto vout = priv::chull::sortPoints( vp, 0 );
        CHECK( vout == std::vector<size_t>{ 0,1,2,3 } );
        auto ch = convexHull( pl );
        CHECK( ch == CPolyline(
                std::vector<Point2d>{
                    {0,0},{3,0},{0,3}
                }
            )
        );
    }
    {
        CPolyline pl1;
        auto ch1 = convexHull( pl1 );
        CHECK( ch1.size() == 0 );
        auto ch2 = pl1.convexHull();
        CHECK( ch2.size() == 0 );
    }
    {
        CPolyline pl1( std::vector<Point2d>{ {1,1}, {2,2} });
        auto ch1 = convexHull( pl1 );
        CHECK( ch1.size() == 2 );
        auto ch2 = pl1.convexHull();
        CHECK( ch2.size() == 2 );
    }
}

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TEST_CASE() [82/93]

TEST_CASE	(	"nearest/farthest points"	,
		""	[nfp]
	)

{
// 1 - make sure calling with empty container throws
    std::vector<Point2d_<NUMTYPE>> vec;
    std::vector<Point2d_<NUMTYPE>> lst;
    std::array<Point2d_<NUMTYPE>,0> arr0; // very unlikely, but... who knows?
    checkSizeNF( Point2d_<NUMTYPE>(), vec );
    checkSizeNF( Point2d_<NUMTYPE>(), lst );
    checkSizeNF( Point2d_<NUMTYPE>(), arr0 );

// 2 - make sure calling with container holding only 1 point also throws
    vec.emplace_back( Point2d_<NUMTYPE>() ); // add point (0,0)
    lst.emplace_back( Point2d_<NUMTYPE>() );
    std::array<Point2d_<NUMTYPE>,1> arr;

    checkSizeNF( Point2d_<NUMTYPE>(), vec );
    checkSizeNF( Point2d_<NUMTYPE>(), lst );
    checkSizeNF( Point2d_<NUMTYPE>(), arr );

// 3 - check behavior if query point is in the container (only for vector)
    {
        Point2d_<NUMTYPE> pt1(1,1);
        Point2d_<NUMTYPE> pt0;
        vec.emplace_back( pt1 );
        auto resN = findNearestPoint(  pt0, vec ); // check for (0,0)
        auto resF = findFarthestPoint( pt0, vec );
        CHECK( resN == 1 );                        // both will return
        CHECK( resF == 1 );                        // second point

        resN = findNearestPoint(  pt1, vec );  // check for (1,1)
        resF = findFarthestPoint( pt1, vec );
        CHECK( resN == 0 );                    // both will return
        CHECK( resF == 0 );                    // first point

        auto pres = findNearestFarthestPoint( pt0, vec );
        CHECK( pres.first  == 1 );
        CHECK( pres.second == 1 );
        auto pres2 = findNearestFarthestPoint( pt1, vec );
        CHECK( pres2.first  == 0 );
        CHECK( pres2.second == 0 );
    }

// 4 - check general behavior
    { //                                      0      1      2      3      4
        std::vector<Point2d_<NUMTYPE>> vec2{ {0,0}, {3,0}, {4,0}, {5,6}, {7,8} };
        Point2d_<NUMTYPE> qpt(4,5);
        auto pres = findNearestFarthestPoint( qpt, vec2 );
        auto resN = findNearestPoint(  qpt, vec2 );
        auto resF = findFarthestPoint( qpt, vec2 );
        CHECK( pres.first  == resN );
        CHECK( pres.second == resF );
        CHECK( 3 == resN );
        CHECK( 0 == resF );
    }
}

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TEST_CASE() [83/93]

TEST_CASE	(	"pts_inside"	,
		""	[ptsins]
	)

Todo:

20250201: add tests cases

{
    OPolyline opol;

}

TEST_CASE() [84/93]

TEST_CASE	(	"variant conversion tests"	,
		""	[varconv]
	)

{
    CommonType_<NUMTYPE> var;
    var = Circle_<NUMTYPE>{};
    Circle_<NUMTYPE> c = fct::VariantUnwrapper{var};
    // TODO
}

TEST_CASE() [85/93]

TEST_CASE	(	"variant-based polymorphism"	,
		""	[polymorph_1]
	)

{
    std::vector<CommonType_<NUMTYPE>> vvar;
    vvar.push_back( Circle_<NUMTYPE>{} );
    vvar.push_back( Segment_<NUMTYPE>{} );
    vvar.push_back( Line2d_<NUMTYPE>{} );

    {
        auto var0 = vvar[0];
        Circle_<NUMTYPE> c = fct::VariantUnwrapper{var0};
        CHECK( std::visit( fct::TypeFunct{}, var0 ) == Type::Circle );
        CHECK( c == Circle() );

        auto var1 = vvar[1];
        Segment_<NUMTYPE> s = fct::VariantUnwrapper{var1};
        CHECK( type( var1 ) == Type::Segment );
        CHECK( s == Segment() );

        auto var2 = vvar[2];
        Line2d_<NUMTYPE> l = fct::VariantUnwrapper{var2};
        CHECK( type( var2 ) == Type::Line2d );
    }
}

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TEST_CASE() [86/93]

TEST_CASE	(	"SVG_Import_1"	,
		""	[svg_import_1]
	)

Note

Here, we use only the "double" type, because that is the one used on import

{
    {
        Circle c( 50,50,20);
        img::Image<img::SvgImage> im(200,200);
        c.draw( im );
        im.write( "BUILD/test_svg_11.svg" );

        tinyxml2::XMLDocument doc;                // load the file that we just created
        doc.LoadFile( "BUILD/test_svg_11.svg" );

        h2d::svg::Visitor visitor;
        doc.Accept( &visitor );
        const auto& data = visitor.get();
        CHECK( data.size() == 1 );
        auto elem = data.at(0);
        CHECK( type( elem ) == Type::Circle );
        CircleD cir = fct::VariantUnwrapper{elem};
        CHECK( cir.radius() == 20 );
    }
    {                               // this test makes sure the <g> element is ignored
        tinyxml2::XMLDocument doc;
        doc.LoadFile( "misc/other/test_svg_import_1.svg" );
        h2d::svg::Visitor visitor;
        doc.Accept( &visitor );
        const auto& data = visitor.get();
        CHECK( data.size() == 3 );
        for( const auto& elem: data )
            CHECK( type( elem ) == Type::Circle );
    }
    {                            // read a file with 3 circles, one rect, one segment and a polygon
        tinyxml2::XMLDocument doc;
        doc.LoadFile( "misc/other/test_svg_import_2.svg" );
        h2d::svg::Visitor visitor;
        doc.Accept( &visitor );
        const auto& data = visitor.get();
        CHECK( data.size() == 6 );

        CHECK( type( data.at(3) ) == Type::Segment );
        CHECK( type( data.at(4) ) == Type::FRect );
        CHECK( type( data.at(5) ) == Type::CPolyline );
    }
}

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TEST_CASE() [87/93]

TEST_CASE	(	"SVG Import Ellipse"	,
		""	[svg_import_ell]
	)

{
    tinyxml2::XMLDocument doc;
    doc.LoadFile( "misc/other/test_svg_import_3.svg" );
    h2d::svg::Visitor visitor;
    doc.Accept( &visitor );
    const auto& data = visitor.get();
    CHECK( data.size() == 3 );
    for( const auto& p: data )
    {
        if( type( p ) == Type::Ellipse )
        {
            Ellipse ell( 150, 100, 60, 15, 20*M_PI/180. );
            const EllipseD ell2 = fct::VariantUnwrapper{ p };
            CHECK( ell == ell2 );
        }
    }
}

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TEST_CASE() [88/93]

TEST_CASE	(	"SVG Import path 1"	,
		""	[svg_import_path_1]
	)

{
    {                        // empty string
        const char* s1 = "";
        CHECK_THROWS( svg::svgp::parsePath( s1 ) );
    }
    {
        const char* s1 ="10 20 30 40";
        const auto& res = svg::svgp::parsePath( s1 );
        CHECK( res.first.size() == 1 ); // one vector
        CHECK( res.first[0].size() == 2 );  // holding two points
        CHECK( res.first[0][0] == Point2d(10,20) );
        CHECK( res.first[0][1] == Point2d(30,40) );
        CHECK( res.second == false );
    }

    {
        const char* s1 ="10 20 30 40z";
        auto res = svg::svgp::parsePath( s1 );
        CHECK( res.first.size() == 1 );
        CHECK( res.first[0].size() == 2 );
        CHECK( res.second == true );
    }
    {
        const char* s1 ="10 20 m 1 2 3 4z";  //relative and "Move To" (=>so two vectors in output)
        auto res = svg::svgp::parsePath( s1 );
        CHECK( res.first.size() == 2 );
        CHECK( res.first[0].size() == 1 );
        CHECK( res.first[1].size() == 2 );
        CHECK( res.first[0][0] == Point2d(10,20) );
        CHECK( res.first[1][0] == Point2d(11,22) );
        CHECK( res.first[1][1] == Point2d(14,26) );
        CHECK( res.second == true );
    }
    {
        const char* s1 ="10 20 H 30 40";  //horizontal line
        auto res = svg::svgp::parsePath( s1 );
        CHECK( res.first.size() == 1 );
        CHECK( res.first[0].size() == 3 );
        CHECK( res.first[0][0] == Point2d(10,20) );
        CHECK( res.first[0][1] == Point2d(30,20) );
        CHECK( res.first[0][2] == Point2d(40,20) );
        CHECK( res.second == false);
    }
    {
        const char* s1 ="10"; // missing second value
        CHECK_THROWS( svg::svgp::parsePath( s1 ) );
    }
    {
        const char* s1 ="10 20 30"; // missing second value
        CHECK_THROWS( svg::svgp::parsePath( s1 ) );
    }
    {
        const char* s1 ="M10 20 C 30"; // C command not handled
        CHECK_THROWS( svg::svgp::parsePath( s1 ) );
    }
}

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TEST_CASE() [89/93]

TEST_CASE	(	"boost geometry point import"	,
		""	[bg-pt-import]
	)

{
    namespace bg = boost::geometry;
    bg::model::point<double, 2, boost::geometry::cs::cartesian> ptb1(3,4);
    bg::model::d2::point_xy<double> ptb2(5,6);
    Point2d_<NUMTYPE> pt1(ptb1);
    Point2d_<NUMTYPE> pt2(ptb2);
    CHECK( pt1 == Point2d_<NUMTYPE>(3,4) );
    CHECK( pt2 == Point2d_<NUMTYPE>(5,6) );

    pt1 = ptb1;         // using assignment operator
    pt2 = ptb2;
    CHECK( pt1 == Point2d_<NUMTYPE>(3,4) );
    CHECK( pt2 == Point2d_<NUMTYPE>(5,6) );
}

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TEST_CASE() [90/93]

TEST_CASE	(	"boost geometry point export"	,
		""	[bg-pt-export]
	)

{
    Point2d_<NUMTYPE> ref1(3,4);
    Point2d_<NUMTYPE> ref2(5,6);
    namespace bg = boost::geometry;
    using point_t1 = bg::model::point<double, 2, bg::cs::cartesian>;
    using point_t2 = bg::model::d2::point_xy<double>;

    auto pt1 = getPt<point_t1>( ref1 );
    auto pt2 = getPt<point_t2>( ref2 );
    CHECK( bg::get<0>(pt1) == ref1.getX() );
    CHECK( bg::get<0>(pt2) == ref2.getX() );
}

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TEST_CASE() [91/93]

TEST_CASE	(	"boost geometry vector point export"	,
		""	[bg-vpt-export]
	)

{
    namespace bg = boost::geometry;
    std::vector<Point2d> vin;
    vin.push_back( Point2d(0.0, 0.0) );
    vin.push_back( Point2d(0.0, 5.0));
    vin.push_back( Point2d(5.0, 5.0));
    auto vout = getPts<bg::model::d2::point_xy<float>>(vin); // convert to a vector of boost geometry points
    CHECK( vout.size() == 3 );
}

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TEST_CASE() [92/93]

TEST_CASE	(	"Opencv build H"	,
		""	[test_opencv2]
	)

{
    std::vector<Point2d_<NUMTYPE>> v1(4);
    std::vector<Point2d_<NUMTYPE>> v2(4);
    Homogr_<NUMTYPE> H;
    H.buildFrom4Points( v1, v2 );
    buildFrom4Points( v1, v2 );
}

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TEST_CASE() [93/93]

TEST_CASE	(	"Opencv binding"	,
		""	[test_opencv]
	)

{
    cv::Mat mat_64 = cv::Mat::eye(3, 3, CV_64F);
    cv::Mat mat_32 = cv::Mat::eye(3, 3, CV_32F);
    INFO( "assignment operator()" )
    {
        cv::Mat cvmat = cv::Mat::ones(3,3, CV_32F );
        Homogr H;
        H = cvmat;
        CHECK( H.value(0,0) == 1.);
        CHECK( H.value(1,1) == 1.);
        CHECK( H.value(1,0) == 1.);
        CHECK( H.value(0,1) == 1.);

        cv::Mat cvmat2 = cv::Mat::ones(3,3, CV_32F );
        Homogr H2 = cvmat;
        CHECK( H2.value(0,0) == 1.);
        CHECK( H2.value(1,1) == 1.);
        CHECK( H2.value(1,0) == 1.);
        CHECK( H2.value(0,1) == 1.);

        H = mat_64;
        CHECK( H.value(0,0) == 1.);
        CHECK( H.value(1,1) == 1.);
        CHECK( H.value(1,0) == 0.);
        CHECK( H.value(0,1) == 0.);

        H = mat_32;
        CHECK( H.value(0,0) == 1.);
        CHECK( H.value(1,1) == 1.);
        CHECK( H.value(1,0) == 0.);
        CHECK( H.value(0,1) == 0.);
    }
    INFO( "default copyTo()" )
    {
        Homogr H;
        cv::Mat mat;
        CHECK_THROWS( H.copyTo( mat, 111 ) );
        CHECK_NOTHROW( H.copyTo( mat ) );
        CHECK( (
            (mat.at<double>(0,0) == 1.0)
            && (mat.at<double>(0,1) == 0.0)
            && (mat.at<double>(0,2) == 0.0)
        ) );
        CHECK( mat.channels() == 1 );
        CHECK( mat.type() == CV_64F );
    }
    INFO( "copyTo() with CV_64F" )
    {
        Homogr H;
        cv::Mat mat;
        H.copyTo( mat, CV_64F );
        CHECK( (
            (mat.at<double>(0,0) == 1.0)
            && (mat.at<double>(0,1) == 0.0)
            && (mat.at<double>(0,2) == 0.0)
        ) );
        CHECK( mat.channels() == 1 );
        CHECK( mat.type() == CV_64F );
    }
    INFO( "copyTo() with CV_32F" )
    {
        Homogr H;
        cv::Mat mat;
        H.copyTo( mat, CV_32F );
        CHECK( (
            (mat.at<float>(0,0) == 1.0)
            && (mat.at<float>(0,1) == 0.0)
            && (mat.at<float>(0,2) == 0.0)
        ) );
        CHECK( mat.channels() == 1 );
        CHECK( mat.type() == CV_32F );
    }
    INFO( "Copy to OpenCv points" )
    {
        Point2d_<NUMTYPE> pt(1.,2.);
        {                              // free function
            cv::Point2d cvpt1 = getCvPtd( pt );           // double
            CHECK( (cvpt1.x == 1. && cvpt1.y == 2.) );
            cv::Point2f cvpt2 = getCvPtf( pt );           // float
            CHECK( (cvpt2.x == 1. && cvpt2.y == 2.) );
            cv::Point2i cvpt3 = getCvPti( pt );           // integer point
            CHECK( (cvpt3.x == 1 && cvpt3.y == 2) );

            auto cvpt_1 = getPt<cv::Point2d>( pt );
            auto cvpt_2 = getPt<cv::Point2f>( pt );
            auto cvpt_3 = getPt<cv::Point2i>( pt );
        }
        {
            cv::Point2d cvpt1 = pt.getCvPtd() ;
            CHECK( (cvpt1.x == 1. && cvpt1.y == 2.) );
            cv::Point2f cvpt2 = pt.getCvPtf() ;
            CHECK( (cvpt2.x == 1. && cvpt2.y == 2.) );
            cv::Point2i cvpt3 = pt.getCvPti() ;          // integer point
            CHECK( (cvpt3.x == 1  && cvpt3.y == 2 ) );

            auto cvpt_1 = pt.getPt<cv::Point2d>();
            auto cvpt_2 = pt.getPt<cv::Point2f>();
            auto cvpt_3 = pt.getPt<cv::Point2i>();
        }
        { // input: vector of "double" points
          // converted into "float" Opencv points
            std::vector<Point2d> v{ Point2d(1,2), Point2d(5,6), Point2d(3,4) };
            auto vcv1 = getPts<cv::Point2d>( v );
            CHECK( vcv1.size() == 3 );
            auto vcv2 = getPts<cv::Point2f>( v );
            CHECK( vcv2.size() == 3 );
            auto vcv3 = getPts<cv::Point2i>( v );
            CHECK( vcv3.size() == 3 );
        }
    }
    INFO( "Fetch from OpenCv points" )
    {
        cv::Point2d ptd(1,2);
        cv::Point2f ptf(1,2);
        cv::Point2f pti(1,2);
        {                            // test of constructor
            Point2d p1(ptd);
            CHECK(( p1.getX() == 1. && p1.getY() == 2. ));
            Point2d_<NUMTYPE> p2(ptf);
            CHECK(( p2.getX() == 1. && p2.getY() == 2. ));
            Point2d_<NUMTYPE> p3(pti);
            CHECK(( p3.getX() == 1. && p3.getY() == 2. ));
        }
        {                            // test of assignment operator
            Point2d p1 = ptd;
            CHECK(( p1.getX() == 1 && p1.getY() == 2. ));
            Point2d_<NUMTYPE> p2 = ptf;
            CHECK(( p2.getX() == 1 && p2.getY() == 2. ));
            Point2d_<NUMTYPE> p3 = pti;
            CHECK(( p3.getX() == 1 && p3.getY() == 2. ));
        }
    }
    INFO( "Build line using OpenCv points" )
    {
        Line2d_<NUMTYPE> lia( cv::Point2d(100,200) );
//      Line2d_<NUMTYPE> lib( Point2d(100,200) );
//      CHECK( lia == lib );
    }
}

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Variable Documentation

cir

Circle cir

cpol

CPolyline cpol

Initial value:

{
    OPolyline opol

ell

Ellipse ell

g_epsilon

double g_epsilon = std::numeric_limits<NUMTYPE>::epsilon()*10000.

li

Line2d li

pol

CPolyline pol(5, 5u)

pt

Point2d pt

rect

FRect rect

seg

Segment seg