Math Utilities class. More...

Static Public Member Functions
static float	GetHorizontalFieldOfViewRadians ()
	Get the horizontal FOV from the stereo camera More...

static bool	IsInFOV (Vector3 position)
	Returns if a point will be rendered on the screen in either eye More...

static Vector3	TransformPointFromTo (Transform from, Transform to, Vector3 ptInFrom)
	Takes a point in the coordinate space specified by the "from" transform and transforms it to be the correct point in the coordinate space specified by the "to" transform applies rotation, scale and translation More...

static Vector3	TransformDirectionFromTo (Transform from, Transform to, Vector3 dirInFrom)
	Takes a direction in the coordinate space specified by the "from" transform and transforms it to be the correct direction in the coordinate space specified by the "to" transform applies rotation only, no translation or scale More...

static Vector3	TransformVectorFromTo (Transform from, Transform to, Vector3 vecInFrom)
	Takes a vectpr in the coordinate space specified by the "from" transform and transforms it to be the correct direction in the coordinate space specified by the "to" transform applies rotation and scale, no translation More...

static Ray	TransformRayFromTo (Transform from, Transform to, Ray rayToConvert)
	Takes a ray in the coordinate space specified by the "from" transform and transforms it to be the correct ray in the coordinate space specified by the "to" transform More...

static Quaternion	QuaternionFromMatrix (Matrix4x4 m)
	Creates a quaternion containing the rotation from the input matrix. More...

static void	ToTranslationRotation (Matrix4x4 unityMtx, out Vector3 translation, out Quaternion rotation)
	Extract the translation and rotation components of a Unity matrix More...

static Vector3	XZProject (Vector3 v)
	Project vector onto XZ plane More...

static Vector3	YZProject (Vector3 v)
	Project vector onto YZ plane More...

static Vector3	XYProject (Vector3 v)
	Project vector onto XY plane More...

static float	DistanceOfPointToLine (Vector3 point, Vector3 linePointA, Vector3 linePointB)
	Returns the distance between a point and an infinite line defined by two points; linePointA and linePointB More...

static Vector3	ClosestPointOnLineToPoint (Vector3 point, Vector3 linePointA, Vector3 linePointB)

static float	DistanceOfPointToLineSegment (Vector3 point, Vector3 lineStart, Vector3 lineEnd)

static Vector3	ClosestPointOnLineSegmentToPoint (Vector3 point, Vector3 lineStart, Vector3 lineEnd)

static bool	TestPlanesAABB (Plane[] planes, int planeMask, Bounds bounds, out bool entirelyInside)

static bool	InRange (Vector2 vec, Vector2 lower, Vector2 upper)
	Tests component-wise if a Vector2 is in a given range More...

static bool	InRange (Vector3 vec, Vector3 lower, Vector3 upper)
	Tests component-wise if a Vector3 is in a given range More...

static Matrix4x4	Add (Matrix4x4 a, Matrix4x4 b)
	Element-wise addition of two Matrix4x4s - extension method More...

static Matrix4x4	Subtract (Matrix4x4 a, Matrix4x4 b)
	Element-wise subtraction of two Matrix4x4s - extension method More...

static float	DistanceOfPointToLine (Ray ray, Vector3 point)
	find unsigned distance of 3D point to an infinite line More...

static Vector3	NearestPointToLines (Ray p, Ray q)
	Find 3D point that minimizes distance to 2 lines, midpoint of the shortest perpendicular line segment between them More...

static Vector3	NearestPointToLinesRANSAC (List< Ray > rays, int ransac_iterations, float ransac_threshold, out int numActualInliers)
	Find 3D point that minimizes distance to a set of 2 or more lines, ignoring outliers More...

static Vector3	NearestPointToLinesLeastSquares (IEnumerable< Ray > rays)
	Find 3D point that minimizes distance to a set of 2 or more lines More...

Detailed Description

Math Utilities class.

Definition at line 13 of file MathUtils.cs.

Member Function Documentation

§ Add()

static Matrix4x4 HoloToolkit.Unity.MathUtils.Add	(	Matrix4x4	a,
		Matrix4x4	b
	)

static

Element-wise addition of two Matrix4x4s - extension method

Parameters

a	matrix
b	matrix

Returns: element-wise (a+b)

Definition at line 289 of file MathUtils.cs.

§ ClosestPointOnLineSegmentToPoint()

static Vector3 HoloToolkit.Unity.MathUtils.ClosestPointOnLineSegmentToPoint	(	Vector3	point,
		Vector3	lineStart,
		Vector3	lineEnd
	)

static

Definition at line 190 of file MathUtils.cs.

§ ClosestPointOnLineToPoint()

static Vector3 HoloToolkit.Unity.MathUtils.ClosestPointOnLineToPoint	(	Vector3	point,
		Vector3	linePointA,
		Vector3	linePointB
	)

static

Definition at line 170 of file MathUtils.cs.

§ DistanceOfPointToLine() [1/2]

static float HoloToolkit.Unity.MathUtils.DistanceOfPointToLine	(	Vector3	point,
		Vector3	linePointA,
		Vector3	linePointB
	)

static

Returns the distance between a point and an infinite line defined by two points; linePointA and linePointB

Parameters

point
linePointA
linePointB

Returns

Definition at line 164 of file MathUtils.cs.

§ DistanceOfPointToLine() [2/2]

static float HoloToolkit.Unity.MathUtils.DistanceOfPointToLine	(	Ray	ray,
		Vector3	point
	)

static

find unsigned distance of 3D point to an infinite line

Parameters

ray	ray that specifies an infinite line
point	3D point

Returns: unsigned perpendicular distance from point to line

Definition at line 321 of file MathUtils.cs.

§ DistanceOfPointToLineSegment()

static float HoloToolkit.Unity.MathUtils.DistanceOfPointToLineSegment	(	Vector3	point,
		Vector3	lineStart,
		Vector3	lineEnd
	)

static

Definition at line 184 of file MathUtils.cs.

§ GetHorizontalFieldOfViewRadians()

static float HoloToolkit.Unity.MathUtils.GetHorizontalFieldOfViewRadians ( )

static

Get the horizontal FOV from the stereo camera

Returns

Definition at line 20 of file MathUtils.cs.

§ InRange() [1/2]

static bool HoloToolkit.Unity.MathUtils.InRange	(	Vector2	vec,
		Vector2	lower,
		Vector2	upper
	)

static

Tests component-wise if a Vector2 is in a given range

Parameters

vec	The vector to test
lower	The lower bounds
upper	The upper bounds

Returns: true if in range, otherwise false

Definition at line 266 of file MathUtils.cs.

§ InRange() [2/2]

static bool HoloToolkit.Unity.MathUtils.InRange	(	Vector3	vec,
		Vector3	lower,
		Vector3	upper
	)

static

Tests component-wise if a Vector3 is in a given range

Parameters

vec	The vector to test
lower	The lower bounds
upper	The upper bounds

Returns: true if in range, otherwise false

Definition at line 278 of file MathUtils.cs.

§ IsInFOV()

static bool HoloToolkit.Unity.MathUtils.IsInFOV ( Vector3 position )

static

Returns if a point will be rendered on the screen in either eye

Parameters

position

Returns

Definition at line 31 of file MathUtils.cs.

§ NearestPointToLines()

static Vector3 HoloToolkit.Unity.MathUtils.NearestPointToLines	(	Ray	p,
		Ray	q
	)

static

Find 3D point that minimizes distance to 2 lines, midpoint of the shortest perpendicular line segment between them

Parameters

p	ray that specifies a line
q	ray that specifies a line

Returns: point nearest to the lines

Definition at line 332 of file MathUtils.cs.

§ NearestPointToLinesLeastSquares()

static Vector3 HoloToolkit.Unity.MathUtils.NearestPointToLinesLeastSquares ( IEnumerable< Ray > rays )

static

Find 3D point that minimizes distance to a set of 2 or more lines

Parameters

rays	each ray specifies an infinite line

Returns: point nearest to the set of lines

Definition at line 408 of file MathUtils.cs.

§ NearestPointToLinesRANSAC()

static Vector3 HoloToolkit.Unity.MathUtils.NearestPointToLinesRANSAC	(	List< Ray >	rays,
		int	ransac_iterations,
		float	ransac_threshold,
		out int	numActualInliers
	)

static

Find 3D point that minimizes distance to a set of 2 or more lines, ignoring outliers

Parameters

rays	list of rays, each specifying a line, must have at least 1
ransac_iterations	number of iterations: log(1-p)/log(1-(1-E)^s) where p is probability of at least one sample containing s points is all inliers E is proportion of outliers (1-ransac_ratio) e.g. p=0.999, ransac_ratio=0.54, s=2 ==> log(0.001)/(log(1-0.54^2) = 20
ransac_threshold	minimum distance from point to line for a line to be considered an inlier
numActualInliers	return number of inliers: lines that are within ransac_threshold of nearest point

Returns: point nearest to the set of lines, ignoring outliers

Definition at line 365 of file MathUtils.cs.

§ QuaternionFromMatrix()

static Quaternion HoloToolkit.Unity.MathUtils.QuaternionFromMatrix ( Matrix4x4 m )

static

Creates a quaternion containing the rotation from the input matrix.

Parameters

m	Input matrix to convert to quaternion

Returns

Definition at line 100 of file MathUtils.cs.

§ Subtract()

static Matrix4x4 HoloToolkit.Unity.MathUtils.Subtract	(	Matrix4x4	a,
		Matrix4x4	b
	)

static

Element-wise subtraction of two Matrix4x4s - extension method

Parameters

a	matrix
b	matrix

Returns: element-wise (a-b)

Definition at line 305 of file MathUtils.cs.

§ TestPlanesAABB()

static bool HoloToolkit.Unity.MathUtils.TestPlanesAABB	(	Plane []	planes,
		int	planeMask,
		Bounds	bounds,
		out bool	entirelyInside
	)

static

Definition at line 214 of file MathUtils.cs.

§ ToTranslationRotation()

static void HoloToolkit.Unity.MathUtils.ToTranslationRotation	(	Matrix4x4	unityMtx,
		out Vector3	translation,
		out Quaternion	rotation
	)

static

Extract the translation and rotation components of a Unity matrix

Definition at line 119 of file MathUtils.cs.

§ TransformDirectionFromTo()

static Vector3 HoloToolkit.Unity.MathUtils.TransformDirectionFromTo	(	Transform	from,
		Transform	to,
		Vector3	dirInFrom
	)

static

Takes a direction in the coordinate space specified by the "from" transform and transforms it to be the correct direction in the coordinate space specified by the "to" transform applies rotation only, no translation or scale

Parameters

from
to
dirInFrom

Returns

Definition at line 59 of file MathUtils.cs.

§ TransformPointFromTo()

static Vector3 HoloToolkit.Unity.MathUtils.TransformPointFromTo	(	Transform	from,
		Transform	to,
		Vector3	ptInFrom
	)

static

Takes a point in the coordinate space specified by the "from" transform and transforms it to be the correct point in the coordinate space specified by the "to" transform applies rotation, scale and translation

Parameters

from
to
ptInFrom

Returns

Definition at line 44 of file MathUtils.cs.

§ TransformRayFromTo()

static Ray HoloToolkit.Unity.MathUtils.TransformRayFromTo	(	Transform	from,
		Transform	to,
		Ray	rayToConvert
	)

static

Takes a ray in the coordinate space specified by the "from" transform and transforms it to be the correct ray in the coordinate space specified by the "to" transform

Definition at line 84 of file MathUtils.cs.

§ TransformVectorFromTo()

static Vector3 HoloToolkit.Unity.MathUtils.TransformVectorFromTo	(	Transform	from,
		Transform	to,
		Vector3	vecInFrom
	)

static

Takes a vectpr in the coordinate space specified by the "from" transform and transforms it to be the correct direction in the coordinate space specified by the "to" transform applies rotation and scale, no translation

Parameters

from
to
vecInFrom

Returns

Definition at line 74 of file MathUtils.cs.

§ XYProject()

static Vector3 HoloToolkit.Unity.MathUtils.XYProject ( Vector3 v )

static

Project vector onto XY plane

Parameters

v

Returns: result of projecting v onto XY plane

Definition at line 152 of file MathUtils.cs.

§ XZProject()

static Vector3 HoloToolkit.Unity.MathUtils.XZProject ( Vector3 v )

static

Project vector onto XZ plane

Parameters

v

Returns: result of projecting v onto XZ plane

Definition at line 132 of file MathUtils.cs.

§ YZProject()

static Vector3 HoloToolkit.Unity.MathUtils.YZProject ( Vector3 v )

static

Project vector onto YZ plane

Parameters

v

Returns: result of projecting v onto YZ plane

Definition at line 142 of file MathUtils.cs.

The documentation for this class was generated from the following file:

Assets/HoloToolkit/Common/Scripts/MathUtils.cs

Static Public Member Functions

Detailed Description

Member Function Documentation

§ Add()

§ ClosestPointOnLineSegmentToPoint()

§ ClosestPointOnLineToPoint()

§ DistanceOfPointToLine() [1/2]

§ DistanceOfPointToLine() [2/2]

§ DistanceOfPointToLineSegment()

§ GetHorizontalFieldOfViewRadians()

§ InRange() [1/2]

§ InRange() [2/2]

§ IsInFOV()

§ NearestPointToLines()

§ NearestPointToLinesLeastSquares()

§ NearestPointToLinesRANSAC()

§ QuaternionFromMatrix()

§ Subtract()

§ TestPlanesAABB()

§ ToTranslationRotation()

§ TransformDirectionFromTo()

§ TransformPointFromTo()

§ TransformRayFromTo()

§ TransformVectorFromTo()

§ XYProject()

§ XZProject()

§ YZProject()