Class MathUtilities

Math Utilities class.

Inheritance

Object

MathUtilities

Inherited Members

Object.ToString()

Object.Equals(Object)

Object.Equals(Object, Object)

Object.ReferenceEquals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Namespace: Microsoft.MixedReality.Toolkit.Utilities

Assembly: cs.temp.dll.dll

Syntax

public static class MathUtilities

Methods

Add(Matrix4x4, Matrix4x4)

Element-wise addition of two Matrix4x4s - extension method

Declaration

public static Matrix4x4 Add(Matrix4x4 a, Matrix4x4 b)

Parameters

Type	Name	Description
Matrix4x4	a	matrix
Matrix4x4	b	matrix

Returns

Type	Description
Matrix4x4	element-wise (a+b)

AngularScaleFromDistance(Single, Single)

Declaration

[Obsolete("Method obsolete. Use ScaleFromAngularSizeAndDistance instead")]
public static float AngularScaleFromDistance(float angle, float distance)

Parameters

Type	Name	Description
Single	angle
Single	distance

Returns

Type	Description
Single

CLampLerp(Single, Single, Single, Single)

Clamps via a lerp for a "soft" clamp effect

Declaration

public static float CLampLerp(float pos, float min, float max, float clampFactor)

Parameters

Type	Name	Description
Single	pos	number to clamp
Single	min	if pos is less than min, then lerp clamps to this value
Single	max	if pos is more than max, lerp clamps to this value
Single	clampFactor	Range from 0.0f to 1.0f of how close to snap to min and max

Returns

Type	Description
Single	A soft clamped value

ClosestPointOnLineSegmentToPoint(Vector3, Vector3, Vector3)

Declaration

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

Parameters

Type	Name	Description
Vector3	point
Vector3	lineStart
Vector3	lineEnd

Returns

Type	Description
Vector3

ClosestPointOnLineToPoint(Vector3, Vector3, Vector3)

Declaration

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

Parameters

Type	Name	Description
Vector3	point
Vector3	linePointA
Vector3	linePointB

Returns

Type	Description
Vector3

DegreesToRadians(Double)

Convert degrees to radians.

Declaration

public static float DegreesToRadians(double degrees)

Parameters

Type	Name	Description
Double	degrees	Angle, in degrees.

Returns

Type	Description
Single	Angle, in radians.

DistanceOfPointToLine(Ray, Vector3)

find unsigned distance of 3D point to an infinite line

Declaration

public static float DistanceOfPointToLine(Ray ray, Vector3 point)

Parameters

Type	Name	Description
Ray	ray	ray that specifies an infinite line
Vector3	point	3D point

Returns

Type	Description
Single	unsigned perpendicular distance from point to line

DistanceOfPointToLine(Vector3, Vector3, Vector3)

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

Declaration

public static float DistanceOfPointToLine(Vector3 point, Vector3 linePointA, Vector3 linePointB)

Parameters

Type	Name	Description
Vector3	point
Vector3	linePointA
Vector3	linePointB

Returns

Type	Description
Single

DistanceOfPointToLineSegment(Vector3, Vector3, Vector3)

Declaration

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

Parameters

Type	Name	Description
Vector3	point
Vector3	lineStart
Vector3	lineEnd

Returns

Type	Description
Single

GetAngleBetween(Vector2, Vector2)

Calculates the angle (at pointA) between two, two-dimensional points.

Declaration

public static float GetAngleBetween(Vector2 pointA, Vector2 pointB)

Parameters

Type	Name	Description
Vector2	pointA	The first point.
Vector2	pointB	The second point.

Returns

Type	Description
Single	The angle between the two points.

GetDirection(Quaternion)

Calculates the direction vector from a rotation.

Declaration

public static Vector3 GetDirection(Quaternion rotation)

Parameters

Type	Name	Description
Quaternion	rotation	Quaternion representing the rotation of the object.

Returns

Type	Description
Vector3	Normalized Vector3 representing the direction vector.

InRange(Vector2, Vector2, Vector2)

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

Declaration

public static bool InRange(Vector2 vec, Vector2 lower, Vector2 upper)

Parameters

Type	Name	Description
Vector2	vec	The vector to test
Vector2	lower	The lower bounds
Vector2	upper	The upper bounds

Returns

Type	Description
Boolean	true if in range, otherwise false

InRange(Vector3, Vector3, Vector3)

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

Declaration

public static bool InRange(Vector3 vec, Vector3 lower, Vector3 upper)

Parameters

Type	Name	Description
Vector3	vec	The vector to test
Vector3	lower	The lower bounds
Vector3	upper	The upper bounds

Returns

Type	Description
Boolean	true if in range, otherwise false

IsInFOV(Vector3, Transform, Single, Single, Single, Single)

Returns if a point lies within a frame of reference view as defined by arguments

Declaration

public static bool IsInFOV(Vector3 testPosition, Transform frameOfReference, float verticalFOV, float horizontalFOV, float minPlaneDistance, float maxPlaneDistance)

Parameters

Type	Name	Description
Vector3	testPosition
Transform	frameOfReference
Single	verticalFOV
Single	horizontalFOV
Single	minPlaneDistance
Single	maxPlaneDistance

Returns

Type	Description
Boolean

Remarks

Field of view parameters are in degrees and plane distances are in meters

IsInFOVCone(Transform, Vector3, Single, Single, Single)

Returns true if a point lies inside the cone described with given parameters, false otherwise. The cone is inscribed to a radius equal to the vertical height of the provided FOV. The test also ensures the distance from the point to the cone lies within the given range.

Declaration

public static bool IsInFOVCone(Transform cone, Vector3 point, float fieldOfView, float minDist = 0.05F, float maxDist = 100F)

Parameters

Type	Name	Description
Transform	cone	The transform that defines the orientation and position of the cone
Vector3	point	The point to test if it lies within the cone FOV
Single	fieldOfView	Field of view for the cone which calculates its radius
Single	minDist	Point must be at least this far away (along direction forward) from the cone
Single	maxDist	Point must be at most this far away (along direction forward) from the cone.

Returns

Type	Description
Boolean

Remarks

Field of view parameter is in degrees and distances are in meters.

NearestPointToLines(Ray, Ray)

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

Declaration

public static Vector3 NearestPointToLines(Ray p, Ray q)

Parameters

Type	Name	Description
Ray	p	ray that specifies a line
Ray	q	ray that specifies a line

Returns

Type	Description
Vector3	point nearest to the lines

NearestPointToLinesLeastSquares(IEnumerable<Ray>)

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

Declaration

public static Vector3 NearestPointToLinesLeastSquares(IEnumerable<Ray> rays)

Parameters

Type	Name	Description
IEnumerable<Ray>	rays	each ray specifies an infinite line

Returns

Type	Description
Vector3	point nearest to the set of lines

NearestPointToLinesRANSAC(List<Ray>, Int32, Single, out Int32)

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

Declaration

public static Vector3 NearestPointToLinesRANSAC(List<Ray> rays, int ransac_iterations, float ransac_threshold, out int numActualInliers)

Parameters

Type	Name	Description
List<Ray>	rays	list of rays, each specifying a line, must have at least 1
Int32	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
Single	ransac_threshold	minimum distance from point to line for a line to be considered an inlier
Int32	numActualInliers	return number of inliers: lines that are within ransac_threshold of nearest point

Returns

Type	Description
Vector3	point nearest to the set of lines, ignoring outliers

QuaternionFromMatrix(Matrix4x4)

Creates a quaternion containing the rotation from the input matrix.

Declaration

public static Quaternion QuaternionFromMatrix(Matrix4x4 m)

Parameters

Type	Name	Description
Matrix4x4	m	Input matrix to convert to quaternion

Returns

Type	Description
Quaternion

RadiansToDegrees(Single)

Convert radians to degrees.

Declaration

public static float RadiansToDegrees(float radians)

Parameters

Type	Name	Description
Single	radians	Angle, in radians.

Returns

Type	Description
Single	Angle, in degrees.

ScaleFromAngularSizeAndDistance(Single, Single)

Retrieve angular measurement describing how large a sphere or circle appears from a given point of view. Takes an angle (at given point of view) and a distance and returns the actual diameter of the object.

Declaration

public static float ScaleFromAngularSizeAndDistance(float angle, float distance)

Parameters

Type	Name	Description
Single	angle
Single	distance

Returns

Type	Description
Single

Subtract(Matrix4x4, Matrix4x4)

Element-wise subtraction of two Matrix4x4s - extension method

Declaration

public static Matrix4x4 Subtract(Matrix4x4 a, Matrix4x4 b)

Parameters

Type	Name	Description
Matrix4x4	a	matrix
Matrix4x4	b	matrix

Returns

Type	Description
Matrix4x4	element-wise (a-b)

TestPlanesAABB(Plane[], Int32, Bounds, out Boolean)

Declaration

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

Parameters

Type	Name	Description
Plane[]	planes
Int32	planeMask
Bounds	bounds
Boolean	entirelyInside

Returns

Type	Description
Boolean

ToTranslationRotation(Matrix4x4, out Vector3, out Quaternion)

Extract the translation and rotation components of a Unity matrix

Declaration

public static void ToTranslationRotation(Matrix4x4 unityMtx, out Vector3 translation, out Quaternion rotation)

Parameters

Type	Name	Description
Matrix4x4	unityMtx
Vector3	translation
Quaternion	rotation

TransformDirectionFromTo(Transform, Transform, Vector3)

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

Declaration

public static Vector3 TransformDirectionFromTo(Transform from, Transform to, Vector3 fromDirection)

Parameters

Type	Name	Description
Transform	from
Transform	to
Vector3	fromDirection

Returns

Type	Description
Vector3	Direction to.

TransformPointFromTo(Transform, Transform, Vector3)

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.

Declaration

public static Vector3 TransformPointFromTo(Transform from, Transform to, Vector3 fromPoint)

Parameters

Type	Name	Description
Transform	from
Transform	to
Vector3	fromPoint

Returns

Type	Description
Vector3	Point to.

TransformRayFromTo(Transform, Transform, Ray)

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

Declaration

public static Ray TransformRayFromTo(Transform from, Transform to, Ray rayToConvert)

Parameters

Type	Name	Description
Transform	from
Transform	to
Ray	rayToConvert

Returns

Type	Description
Ray

TransformVectorFromTo(Transform, Transform, Vector3)

Takes a vector 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

Declaration

public static Vector3 TransformVectorFromTo(Transform from, Transform to, Vector3 vecInFrom)

Parameters

Type	Name	Description
Transform	from
Transform	to
Vector3	vecInFrom

Returns

Type	Description
Vector3

XYProject(Vector3)

Project vector onto XY plane

Declaration

public static Vector3 XYProject(Vector3 v)

Parameters

Type	Name	Description
Vector3	v

Returns

Type	Description
Vector3	result of projecting v onto XY plane

XZProject(Vector3)

Project vector onto XZ plane

Declaration

public static Vector3 XZProject(Vector3 v)

Parameters

Type	Name	Description
Vector3	v

Returns

Type	Description
Vector3	result of projecting v onto XZ plane

YZProject(Vector3)

Project vector onto YZ plane

Declaration

public static Vector3 YZProject(Vector3 v)

Parameters

Type	Name	Description
Vector3	v

Returns

Type	Description
Vector3	result of projecting v onto YZ plane