Math3D library

Angle that a target is from the direction of an origin

Returns: float Angle in radians

Output 2D blend space weights for `inPositions` when sampled at `samplePosition`

samplePosition

[X, Y, unused] coordinate to sample the 2d space

inPositions

[X, Y, unused] positions in the 2d space

outWeights

Output weights for individual nodes 1:1 to inPositions

Returns 1, when bounding boxes intersects

mins1

vector minimum point of first bounding box

maxs1

vector maximum point of first bounding box

mins2

vector minimum point of second bounding box

maxs2

vector maximum point of second bounding box

Returns: int 1 if boundig boxes intersects, otherwise 0

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

>> 1

Calculates the points of a right 2D cone in 3D space

origin

vector Origin of cone

length

float Length of the cone

halfAngle

float Half of the angle of the cone in radians

angleOffset

float Angle offset of the cone in radians (handy for rotating it along with something in the world)

out leftPoint

vector Left point of the cone

out rightPoint

vector Right point of the cone

Computes curve

Returns: vector

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);

Creates rotation matrix from direction and up vector

dir

vector direction vector

up

vector up vector

out mat

vector[4] created rotation matrix

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>

Returns randon normalized direction

Returns: vector

Print( Math3D.GetRandomDir() );

>>vector ret =  0x0000000007c1a1c0 {<0.422565,0,-0.906333>}

Tests whether cylinder is intersecting oriented box.

mins

vector Minimums of bound box

maxs

vector Maximums of bound box

obbMat

vector Transform of box

cylMat

vector Transform of cylinder

cylinderRadius

float Radius of cylinder

cylinderHeight

float Height of cylinder

Returns: bool True when cylinder is intersecting oriented box

Tests whether ray is intersecting axis aligned box.

start

vector Start of ray

end

vector End of ray

mins

vector Minimums of bound box

maxs

vector Maximums of bound box

Returns: float -1 when not intersecting, else the fraction of ray

Tests whether ray is intersecting cylinder.

rayStart

vector Start of ray

rayEnd

vector End of ray

center

vector Center of cylinder

radius

float Radius of cylinder

height

float Height of cylinder

Returns: bool True when ray is intersecting cylinder

Tests whether ray is intersecting plane.

rayStart

vector Start of ray

rayEnd

vector End of ray

planeNormal

vector Normal of the plane

planeDist

float Length of the plane

intersection

vector Intersection point of the plane, only valid when return is 3

Returns: int 1 when behind, 2 when in front and 3 when intersecting the plane

Tests whether ray is intersecting sphere.

raybase

vector Start of ray

raycos

vector End of ray

center

vector Center of sphere

radius

float Radius of sphere

Returns: float -1 when not intersecting, else the fraction of ray

Tests whether sphere is intersecting axis aligned box.

origin

vector Origin of sphere

radius

float Radius of sphere

mins

vector Minimums of bound box

maxs

vector Maximums of bound box

Returns: bool True when intersects

Tests whether sphere is intersecting cone.

origin

vector Origin of sphere

radius

float Radius of sphere

conepos

vector Position of top of cone

axis

vector Orientation of cone in direction from top to bottom

angle

float Angle of cone in radians

Returns: bool True when sphere is intersecting cone

Tests whether sphere is fully inside cone.

origin

vector Origin of sphere

radius

float Radius of sphere

conepos

vector Position of top of cone

axis

vector Orientation of cone in direction from top to bottom

angle

float Angle of cone in radians

Returns: bool True when sphere is fully inside cone

Creates identity matrix

out mat

created identity matrix

      vector mat[3];
  	Math3D.MatrixIdentity3( mat );
  	Print( mat );

>> <1,0,0>,<0,1,0>,<0,0,1>

Creates identity matrix

out mat

created identity matrix

      vector mat[4];
  	Math3D.MatrixIdentity4( mat );
  	Print( mat );

>> <1,0,0>,<0,1,0>,<0,0,1>,<0,0,0>

Inverses a matrix

it mat

matrix which should be inversed

Inverses a matrix

it mat

matrix which should be inversed

Invert-transforms rotation matrix

mat0

vector[3] first matrix

mat1

vector[3] second matrix

out res

vector[3] result of first and second matrix multiplication

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>

Invert-transforms matrix

mat0

vector[4] first matrix

mat1

vector[4] second matrix

out res

vector[4] inverse result of first and second matrix multiplication

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>

Transforms rotation matrix

mat0

vector[3] first matrix

mat1

vector[3] second matrix

out res

vector[3] result of first and second matrix multiplication

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>

Transforms matrix

mat0

vector[4] first matrix

mat1

vector[4] second matrix

out res

vector[4] result of first and second matrix multiplication

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

>> <2,0,0>,<0,3,0>,<0,3,0>,<4,13,0>

Orthogonalizes matrix

it mat

matrix which should be orthogonalized

Orthogonalizes matrix

it mat

matrix which should be orthogonalized

Returns angles of rotation matrix

mat

vector[3] rotation matrix

Returns: vector roll, pitch, yaw angles

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

>> <70,15,-45>

Converts rotation matrix to quaternion

mat

vector[3] rotation matrix

out d

float[4] created quaternion copy

vector mat[3];
vector rot = "70 15 45";
rot.RotationMatrixFromAngles( mat );
float d[4];
Math3D.MatrixToQuat( mat, d );
Print( d );

>> {0.241626,0.566299,-0.118838,0.778973}

Point on line beg .. end nearest to pos

Returns: vector

Copies quaternion

s

float[4] quaternion to copy

out d

float[4] created quaternion copy

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

>> {2,3,4,1}

Creates identity quaternion

out q

float[4] created identity quaternion

float q[4];
Math3D.QuatIdentity( q );
Print( q );

>> {0,0,0,1}

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

out qout

float[4] result quaternion

q1

float[4] first quaternion

q2

float[4] second quaternion

frac

float interpolation weight

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}

Multiplies quaternions

out qout

float[4] result quaternion

q1

float[4] first quaternion

q2

float[4] second quaternion

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}

Creates scale matrix

scale

scale coeficient

out mat

created scale matrix

      vector mat[3];
  	Math3D.ScaleMatrix( 2.5, mat );
  	Print( mat );

>> <2.5,0,0>,<0,2.5,0>,<0,0,2.5>

Vector constructor from components

x

float x component

y

float y component

z

float z component

Returns: vector resulting vector

Print( Vector(1, 2, 3) );

>> <1,2,3>

Creates rotation matrix from angles

ang

vector which contains angles

out mat

vector created rotation matrix

vector mat[3];
YawPitchRollMatrix( "70 15 45", mat );
Print( mat );

>> <0.330366,0.0885213,-0.939693>,<0.458809,0.854988,0.241845>,<0.824835,-0.511037,0.241845>