Math3D Interface Reference

Static Public Member Functions
static proto float	IntersectionRayBox (vector start, vector end, vector mins, vector maxs)
static proto float	IntersectionRaySphere (vector raybase, vector raycos, vector center, float radius)
	Tests whether intersection of ray and sphere exists and returns distance to intersection from raybase and raycos (I{01} = P + dir*t{01}).
static proto bool	IntersectionSphereCone (vector origin, float radius, vector conepos, vector axis, float angle)
	Tests whether sphere is intersecting cone.
static proto bool	IntersectionWholeSphereCone (vector origin, float radius, vector conepos, vector axis, float angle)
	Tests whether sphere is intersecting cone.
static proto bool	IntersectionPointCylinder (vector origin, vector cylinderTip, vector cylinderAxis, float cylinderRadius)
	Tests whether point is intersecting cylinder.
static proto bool	IntersectionSphereAABB (vector origin, float radius, vector mins, vector maxs)
	Tests whether sphere is intersecting AABB.
static proto bool	IntersectionBoxBox (vector mins1, vector maxs1, vector mins2, vector maxs2)
	Returns true, when bounding boxes intersect.
static proto void	DirectionAndUpMatrix (vector dir, vector up, out vector mat[4])
	Creates rotation matrix from direction and up vector.
static proto void	MatrixMultiply3 (vector mat0[3], vector mat1[3], out vector res[3])
	Transforms rotation matrix.
static proto void	MatrixMultiply4 (vector mat0[4], vector mat1[4], out vector res[4])
	Transforms matrix.
static proto void	MatrixGetInverse3 (vector mat[3], out vector res[3])
	Inverts matrix.
static proto void	MatrixGetInverse4 (vector mat[4], out vector res[4])
	Inverts matrix.
static proto void	MatrixInvMultiply3 (vector mat0[3], vector mat1[3], out vector res[3])
	Invert-transforms rotation matrix.
static proto void	MatrixInvMultiply4 (vector mat0[4], vector mat1[4], out vector res[4])
	Invert-transforms matrix.
static proto void	MatrixToQuat (vector mat[3], out float d[4])
	Converts rotation matrix to quaternion.
static proto vector	MatrixToAngles (vector mat[3])
	Returns angles of rotation matrix.
static proto float	MatrixToAnglesAndScale (vector mat[3], out vector angles)
	Returns angles and scale of rotation matrix.
static proto void	MatrixFromForwardVec (vector forwardVec, out vector mat[3])
static proto void	MatrixFromUpVec (vector upVec, out vector mat[3])
static proto void	AnglesToMatrix (vector ang, out vector mat[3])
	Creates rotation matrix from angles (yaw, pitch, roll in degrees).
static proto void	MatrixIdentity4 (out vector mat[4])
	Creates identity matrix.
static proto void	MatrixIdentity3 (out vector mat[3])
	Creates identity matrix.
static proto void	MatrixCopy (vector matSrc[], out vector matDst[])
	Copy matrixes.
static proto void	MatrixNormalize (vector mat[])
	Normalize matrix.
static proto void	MatrixScale (vector mat[], float scale)
	Scale matrix.
static proto void	QuatIdentity (out float q[4])
	Creates identity quaternion.
static proto void	QuatCopy (float s[4], out float d[4])
	Copies quaternion.
static proto void	QuatToMatrix (float q[4], out vector mat[3])
	Converts quaternion to rotation matrix.
static proto float	QuatNormalize (out float quat[4])
	Normalizes quaternion.
static proto void	QuatLerp (out float qout[4], float q1[4], float q2[4], float frac)
	Linear interpolation between q1 and q2 with weight frac (0...1).
static proto void	QuatMultiply (out float qout[4], float q1[4], float q2[4])
	Multiplies quaternions.
static proto float	QuatAngle (float q1[4], float q2[4])
	Returns a float value equal to the angle between two quaternions.
static proto float	QuatDot (float q1[4], float q2[4])
	Returns a float value equal to the dot product of two quaternions.
static proto void	QuatRotateTowards (out float qout[4], float q1[4], float q2[4], float maxDegreesDelta)
	Returns a quaternion qout that is rotated between quaternions q1 and q2.
static proto float	QuatNorm (float quat[4])
	Returns the norm of a quaternion.
static proto float	QuatLength (float quat[4])
	Returns the magnitude of a quaternion.
static proto void	QuatInverse (out float qout[4], float q[4])
	Inverse quaternion.
static proto void	QuatScale (out float qout[4], float scale)
	Multiply each part of quaternion by scalar.
static proto void	QuatConjugate (out float qout[4], float q[4])
	Conjugate quaternion.
static proto vector	QuatToAngles (float q[4])
	Returns Angles vector (yaw, pitch, roll) from quaternion.
static proto vector	Curve (ECurveType type, float param, notnull array< vector > points, array< float > knots=null)
	Computes curve.
static proto vector	Curve3 (ECurveType type, float param, notnull Curve3 points, int curveIndex, array< float > knots=null)
	Evaluates a single curve from multicurve object.
static proto void	TessellateBezierSpline (array< vector > points, array< vector > segmentPoints, float maxDistance, int maxPointsPerSegment, array< vector > outPoints)
	Generates tessellation of a cubic, C0 Bezier spline.
static proto void	TessellateHermiteSpline (array< vector > points, array< vector > tangents, float maxDistance, int maxPointsPerSegment, array< vector > outPoints)
	Generates tessellation of a cubic, C0 Hermite spline.
static proto int	PolyToTriangles (vector in[], int num, out int indices[])
	Convert polygon to triangles.
static proto float	PointLineSegmentDistanceSqr (vector point, vector v0, vector v1)
	Calculates squared distance of point to a line segment given by points v0 and v1.
static proto float	PointLineSegmentDistance (vector point, vector v0, vector v1)
	Calculates distance of point to a line segment given by points v0 and v1.
static proto float	PointLineDistance (vector point, vector pointOnLine, vector dirVector)
	Calculates distance of point to a parametric line given by a point on line and direction vector.
static proto bool	IntersectionLineSegments (vector p11, vector p12, vector p21, vector p22)
	Determines whether two line segments intersect or not.

Member Function Documentation

AnglesToMatrix()

static proto void Math3D.AnglesToMatrix ( vector ang, out vector mat[3] )

static

Creates rotation matrix from angles (yaw, pitch, roll in degrees).

vector mat[3];
Math3D.AnglesToMatrix( "70 15 45", mat );
Print( mat );
 
>> <0.41382,-0.683013,-0.601869>,<0.069869,0.683013,-0.727057>,<0.907673,0.258819,0.330366>

Parameters

	ang	vector which contains angles
[out]	mat	created rotation matrix

Curve()

static proto vector Math3D.Curve ( ECurveType type, float param, notnull array< vector > points, array< float > knots = null )

static

Computes curve.

Knots array is used only for non-uniform curve types. For example, CatmullRom and CurveProperty2D.

auto points = new array<vector>();
points.Insert( Vector( 0, 0, 0) );
    points.Insert( Vector( 5, 0, 0) );
    points.Insert( Vector( 8, 3, 0) );
    points.Insert( Vector( 6, 1, 0) );
 
float t = 0.5;
vector result = Math3D.Curve(ECurveType.CatmullRom, t, points);

Curve3()

static proto vector Math3D.Curve3 ( ECurveType type, float param, notnull Curve3 points, int curveIndex, array< float > knots = null )

static

Evaluates a single curve from multicurve object.

See also

Curve

DirectionAndUpMatrix()

static proto void Math3D.DirectionAndUpMatrix ( vector dir, vector up, out vector mat[4] )

static

Creates rotation matrix from direction and up vector.

vector mat[4];
vector dir = "1 0 1";
vector up = "0 1 0";
DirectionAndUpMatrix( dir, up, mat );
Print( mat );
 
>> <0.707107,0,-0.707107>,<0,1,0>,<0.707107,0,0.707107>,<0,0,0>

Parameters

	dir	direction vector
	up	up vector
[out]	mat	created rotation matrix

IntersectionBoxBox()

static proto bool Math3D.IntersectionBoxBox ( vector mins1, vector maxs1, vector mins2, vector maxs2 )

static

Returns true, when bounding boxes intersect.

vector mins1 = "1 1 1";
vector maxs1 = "3 3 3";
vector mins2 = "2 2 2";
vector maxs2 = "4 4 4";
Print( Math3D.IntersectionBoxBox(mins1, maxs1, mins2, maxs2) );
 
>> 1

Parameters

mins1	Minimum point of first bounding box.
maxs1	Maximum point of first bounding box.
mins2	Minimum point of second bounding box.
maxs2	Maximum point of second bounding box.

Returns

true when bounding boxes intersect, otherwise false.

IntersectionLineSegments()

static proto bool Math3D.IntersectionLineSegments ( vector p11, vector p12, vector p21, vector p22 )

static

Determines whether two line segments intersect or not.

Parameters

p11	First point of the first segment
p12	Second point of the first segment
p21	First point of the second segment
p22	Second point of the second segment

Returns

true if the segments intersect, false otherwise.

IntersectionPointCylinder()

static proto bool Math3D.IntersectionPointCylinder ( vector origin, vector cylinderTip, vector cylinderAxis, float cylinderRadius )

static

Tests whether point is intersecting cylinder.

Parameters

origin	Origin of point
cylinderTip	Tip of cylinder
cylinderAxis	Axis of cylinder
cylinderRadius	Radius of cylinder

Returns

true when intersects

IntersectionRayBox()

static proto float Math3D.IntersectionRayBox ( vector start, vector end, vector mins, vector maxs )

static

IntersectionRaySphere()

static proto float Math3D.IntersectionRaySphere ( vector raybase, vector raycos, vector center, float radius )

static

Tests whether intersection of ray and sphere exists and returns distance to intersection from raybase and raycos (I{01} = P + dir*t{01}).

Parameters

raybase	start point of ray
raycos	direction of ray
center	sphere center
radius	radius of sphere

IntersectionSphereAABB()

static proto bool Math3D.IntersectionSphereAABB ( vector origin, float radius, vector mins, vector maxs )

static

Tests whether sphere is intersecting AABB.

Parameters

origin	Origin of sphere
radius	Radius of sphere
mins	minimum point of bounding box
maxs	maximum point of bounding box

Returns

true when intersects

IntersectionSphereCone()

static proto bool Math3D.IntersectionSphereCone ( vector origin, float radius, vector conepos, vector axis, float angle )

static

Tests whether sphere is intersecting cone.

Parameters

origin	Origin of sphere
radius	Radius of sphere
conepos	Position of top of cone
axis	Orientation of cone in direction from top to bottom
angle	Angle of cone in radians

Returns

true when intersects

IntersectionWholeSphereCone()

static proto bool Math3D.IntersectionWholeSphereCone ( vector origin, float radius, vector conepos, vector axis, float angle )

static

Tests whether sphere is intersecting cone.

Parameters

origin	Origin of sphere
radius	Radius of sphere
conepos	Position of top of cone
axis	Orientation of cone in direction from top to bottom
angle	Angle of cone in radians

Returns

true when intersects

MatrixCopy()

static proto void Math3D.MatrixCopy ( vector matSrc[], out vector matDst[] )

static

Copy matrixes.

Parameters

	matSrc	vector[3] or vector[4]
[out]	matDst	vector[3] or vector[4]

MatrixFromForwardVec()

static proto void Math3D.MatrixFromForwardVec ( vector forwardVec, out vector mat[3] )

static

MatrixFromUpVec()

static proto void Math3D.MatrixFromUpVec ( vector upVec, out vector mat[3] )

static

MatrixGetInverse3()

static proto void Math3D.MatrixGetInverse3 ( vector mat[3], out vector res[3] )

static

Inverts matrix.

vector mat[3] = { "2 0 0", "0 3 0", "0 0 1" }; // rotation matrix
vector res[3];
Math3D.MatrixGetInverse3(mat, res);
Print( res );
 
>> <0.5,0,0>,<0,0.333,0>,<0,0,1>

Parameters

	mat	input matrix
[out]	res	inverted matrix

MatrixGetInverse4()

static proto void Math3D.MatrixGetInverse4 ( vector mat[4], out vector res[4] )

static

Inverts matrix.

vector mat[4] = { "2 0 0 0", "0 3 0 0", "0 0 1 0", "0 0 0 5" }; // rotation matrix
vector res[4];
Math3D.MatrixGetInverse4(mat, res);
Print( res );
 
>> <0.5,0,0,0>,<0,0.333,0,0>,<0,0,1,0>,<0,0,0,0.2>

Parameters

	mat	input matrix
[out]	res	inverted matrix

MatrixIdentity3()

static proto void Math3D.MatrixIdentity3 ( out vector mat[3] )

static

Creates identity matrix.

vector mat[3];
Math3D.MatrixIdentity3( mat );
Print( mat );
 
>> <1,0,0>,<0,1,0>,<0,0,1>

Parameters

[out]

mat

created identity matrix

MatrixIdentity4()

static proto void Math3D.MatrixIdentity4 ( out vector mat[4] )

static

Creates identity matrix.

vector mat[4];
Math3D.MatrixIdentity4( mat );
Print( mat );
 
>> <1,0,0>,<0,1,0>,<0,0,1>,<0,0,0>

Parameters

[out]

mat

created identity matrix

MatrixInvMultiply3()

static proto void Math3D.MatrixInvMultiply3 ( vector mat0[3], vector mat1[3], out vector res[3] )

static

Invert-transforms rotation matrix.

vector mat0[3] = { "1.5 2.5 0", "0.1 1.3 0", "0 0 1" }; // rotation matrix
vector mat1[3] = { "1 0.4 0", "0 1 0", "0 1.3 2.7" }; // rotation matrix
vector res[3];
Math3D.MatrixInvMultiply3(mat0, mat1, res);
Print( res );
 
>> <2.5,0.62,0>,<2.5,1.3,0>,<3.25,1.69,2.7>

Parameters

	mat0	first matrix
	mat1	second matrix
[out]	res	result of first and second matrix multiplication

MatrixInvMultiply4()

static proto void Math3D.MatrixInvMultiply4 ( vector mat0[4], vector mat1[4], out vector res[4] )

static

Invert-transforms matrix.

vector mat0[4] = { "2 0 0", "0 3 0", "0 0 1", "0 0 0" }; // scale matrix
vector mat1[4] = { "1 0 0", "0 1 0", "0 0 1", "2 4 1" }; // translation matrix
vector res[4];
Math3D.MatrixInvMultiply4(mat0, mat1, res);
Print( res );
 
>> <2,0,0>,<0,3,1>,<0,3,1>,<4,12,4>

Parameters

	mat0	first matrix
	mat1	second matrix
[out]	res	inverse result of first and second matrix multiplication

MatrixMultiply3()

static proto void Math3D.MatrixMultiply3 ( vector mat0[3], vector mat1[3], out vector res[3] )

static

Transforms rotation matrix.

vector mat0[3] = { "1.5 2.5 0", "0.1 1.3 0", "0 0 1" }; // rotation matrix
vector mat1[3] = { "1 0.4 0", "0 1 0", "0 1.3 2.7" }; // rotation matrix
vector res[3];
Math3D.MatrixMultiply3(mat0, mat1, res);
Print( res );
 
>> <1.54,3.02,0>,<0.1,1.3,0>,<0.13,1.69,2.7>

Parameters

	mat0	first matrix
	mat1	second matrix
[out]	res	result of first and second matrix multiplication

MatrixMultiply4()

static proto void Math3D.MatrixMultiply4 ( vector mat0[4], vector mat1[4], out vector res[4] )

static

Transforms matrix.

vector mat0[4] = { "2 0 0", "0 3 0", "0 1 0", "0 0 0" }; // scale matrix
vector mat1[4] = { "1 0 0", "0 1 0", "0 1 0", "2 4 1" }; // translation matrix
vector res[4];
Math3D.MatrixMultiply4(mat0, mat1, res);
Print( res );
 
>> <2,0,0>,<0,3,0>,<0,3,0>,<4,13,0>

Parameters

	mat0	first matrix
	mat1	second matrix
[out]	res	result of first and second matrix multiplication

MatrixNormalize()

static proto void Math3D.MatrixNormalize ( vector mat[] )

static

Normalize matrix.

MatrixScale()

static proto void Math3D.MatrixScale ( vector mat[], float scale )

static

Scale matrix.

MatrixToAngles()

static proto vector Math3D.MatrixToAngles ( vector mat[3] )

static

Returns angles of rotation matrix.

vector mat[3];
Math3D.AnglesToMatrix( "70 15 45", mat );
vector ang = Math3D.MatrixToAngles( mat );
Print( ang );
 
>> <70,15,45>

Parameters

mat	rotation matrix

Returns

yaw, pitch, roll angles in degrees

MatrixToAnglesAndScale()

static proto float Math3D.MatrixToAnglesAndScale ( vector mat[3], out vector angles )

static

Returns angles and scale of rotation matrix.

Parameters

mat	rotation matrix
angles	yaw, pitch, roll angles in degrees

Returns

scale of matrix

MatrixToQuat()

static proto void Math3D.MatrixToQuat ( vector mat[3], out float d[4] )

static

Converts rotation matrix to quaternion.

vector mat[3];
vector rot = "70 15 45";
Math3D.AnglesToMatrix(rot, mat);
float d[4];
Math3D.MatrixToQuat( mat, d );
Print( d );
 
>> {0.241626,0.566299,-0.118838,0.778973}

Parameters

	mat	rotation matrix
[out]	d	created quaternion copy

PointLineDistance()

static proto float Math3D.PointLineDistance ( vector point, vector pointOnLine, vector dirVector )

static

Calculates distance of point to a parametric line given by a point on line and direction vector.

PointLineSegmentDistance()

static proto float Math3D.PointLineSegmentDistance ( vector point, vector v0, vector v1 )

static

Calculates distance of point to a line segment given by points v0 and v1.

PointLineSegmentDistanceSqr()

static proto float Math3D.PointLineSegmentDistanceSqr ( vector point, vector v0, vector v1 )

static

Calculates squared distance of point to a line segment given by points v0 and v1.

PolyToTriangles()

static proto int Math3D.PolyToTriangles ( vector in[], int num, out int indices[] )

static

Convert polygon to triangles.

Returns

number of generated vertices

QuatAngle()

static proto float Math3D.QuatAngle ( float q1[4], float q2[4] )

static

Returns a float value equal to the angle between two quaternions.

QuatConjugate()

static proto void Math3D.QuatConjugate ( out float qout[4], float q[4] )

static

Conjugate quaternion.

QuatCopy()

static proto void Math3D.QuatCopy ( float s[4], out float d[4] )

static

Copies quaternion.

float s[4] = { 2, 3, 4, 1 };
float d[4];
Math3D.QuatCopy( s, d );
Print( d );
 
>> {2,3,4,1}

Parameters

	s	quaternion to copy
[out]	d	created quaternion copy

QuatDot()

static proto float Math3D.QuatDot ( float q1[4], float q2[4] )

static

Returns a float value equal to the dot product of two quaternions.

QuatIdentity()

static proto void Math3D.QuatIdentity ( out float q[4] )

static

Creates identity quaternion.

float q[4];
Math3D.QuatIdentity( q );
Print( q );
 
>> {0,0,0,1}

Parameters

[out]

q

created identity quaternion

QuatInverse()

static proto void Math3D.QuatInverse ( out float qout[4], float q[4] )

static

Inverse quaternion.

QuatLength()

static proto float Math3D.QuatLength ( float quat[4] )

static

Returns the magnitude of a quaternion.

QuatLerp()

static proto void Math3D.QuatLerp ( out float qout[4], float q1[4], float q2[4], float frac )

static

Linear interpolation between q1 and q2 with weight frac (0...1).

float q1[4] = { 1, 1, 1, 1 };
float q2[4] = { 2, 2, 2, 1 };
float qout[4];
Math3D.QuatLerp( qout, q1, q2, 0.5 );
Print( qout );
 
>> {1.5,1.5,1.5,1}

Parameters

[out]	qout	result quaternion
	q1	first quaternion
	q2	second quaternion
	frac	interpolation weight

QuatMultiply()

static proto void Math3D.QuatMultiply ( out float qout[4], float q1[4], float q2[4] )

static

Multiplies quaternions.

float q1[4] = { 1, 2, 3, 1 };
float q2[4] = { 2, 2, 2, 1 };
float qout[4];
Math3D.QuatMultiply( qout, q1, q2 );
Print( qout );
 
>> {2,4,6,1}

Parameters

[out]	qout	result quaternion
	q1	first quaternion
	q2	second quaternion

QuatNorm()

static proto float Math3D.QuatNorm ( float quat[4] )

static

Returns the norm of a quaternion.

QuatNormalize()

static proto float Math3D.QuatNormalize ( out float quat[4] )

static

Normalizes quaternion.

float quat[4] = {1, 1, 1, 1};
float length = QuatNormalize(quat);
Print(length);
>> {2}
Print(quat);
>> {0.5,0.5,0.5,0.5}

Parameters

quat	in/out quaternion

Returns

length

QuatRotateTowards()

static proto void Math3D.QuatRotateTowards ( out float qout[4], float q1[4], float q2[4], float maxDegreesDelta )

static

Returns a quaternion qout that is rotated between quaternions q1 and q2.

QuatScale()

static proto void Math3D.QuatScale ( out float qout[4], float scale )

static

Multiply each part of quaternion by scalar.

QuatToAngles()

static proto vector Math3D.QuatToAngles ( float q[4] )

static

Returns Angles vector (yaw, pitch, roll) from quaternion.

QuatToMatrix()

static proto void Math3D.QuatToMatrix ( float q[4], out vector mat[3] )

static

Converts quaternion to rotation matrix.

TessellateBezierSpline()

static proto void Math3D.TessellateBezierSpline ( array< vector > points, array< vector > segmentPoints, float maxDistance, int maxPointsPerSegment, array< vector > outPoints )

static

Generates tessellation of a cubic, C0 Bezier spline.

auto points = new array<vector>();
points.Insert(Vector(0, 0, -0.5));
points.Insert(Vector(1, 0, 1.5));
 
auto segmentPoints = new array<vector>();
segmentPoints.Insert(Vector(1, 0, -1));
segmentPoints.Insert(Vector(1, 0, 1));
 
array<vector> outPoints = new array<vector>();
Math3D.TesselateBezierSpline(points, segmentPoints, 0.05, 20, outPoints);

Parameters

points	End points for each segment.
segmentPoints	Points between end points.
maxDistance	Maximum distance between two consecutive generated points.
maxPointsPerSegment	Maximum number of points to generate for each segment of the spline.
outPoints	Points of the resulting rasterization. Size of the array is changed.

TessellateHermiteSpline()

static proto void Math3D.TessellateHermiteSpline ( array< vector > points, array< vector > tangents, float maxDistance, int maxPointsPerSegment, array< vector > outPoints )

static

Generates tessellation of a cubic, C0 Hermite spline.

auto points = new array<vector>();
points.Insert(Vector(0, 0, -0.5));
points.Insert(Vector(1, 0, 1.5));
 
auto tangents = new array<vector>();
tangents.Insert(Vector(1, 0, -1));
tangents.Insert(Vector(1, 0, 1));
 
array<vector> outPoints = new array<vector>();
Math3D.TesselateHermiteSpline(points, tangents, 0.05, 20, outPoints);

Parameters

points	End points for each segment.
tangents	Tangent vectors in respective points.
maxDistance	Maximum distance between two consecutive generated points.
maxPointsPerSegment	Maximum number of points to generate for each segment of the spline.
outPoints	Points of the resulting rasterization. Size of the array is changed.

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

• Core/generated/Math/Math3D.c