Maths

Maths functions and types that can be used by Lua scripts and plugins.

Classes

Type	Name
struct	vrbox A box.
struct	vrmatrix3 A matrix.
struct	vrmatrix4 A matrix.
struct	vrplane A plane.
struct	vrquaternion A quaternion.
struct	vrray A ray.
struct	vrsphere A sphere.
struct	vrvec2 A vector.
struct	vrvec3 A vector.
struct	vrvec4 A vector.

Functions

Type	Name
vrbox	vrAABox(vrvec3 min, vrvec3 max) Construct an axis aligned bounding box.
number	vrAABoxExtent(vrbox box) Returns the largest dimension of an axis aligned bounding box.
vrbox	vrAABoxMerge(Any l, vrbox r) Returns an axis aligned bounding box that contains two other bounding boxes.
vrbox	vrAABoxPosAndSize(vrvec3 pos, vrvec3 size) Construct an axis aligned bounding box, using a position and a size.
vrbox	vrAABoxTransform(Any box, vrmatrix4 matrix) Returns an axis aligned bounding box transformed by a matrix.
number	vrAngleRadians(number arcLength, number radius) Calculates the angle of an arc in radians.
vrnode	vrApplyForce(vrnode node, vrvec3 force, vrvec3 relPos, number duration) Applies a force to an object causing a dynamics response.
boolean	vrApproxEquals(Any left, Any right, number prec =0.0) Returns whether or not two items are approximately equal.
number	vrArcLength(number angleRadians, number radius) Calculates the length of an arc.
number	vrArcRadius(number arcLength, number angleRadians) Calculates the radius of an arc.
void	vrAssemblyLookAt(vrnode assembly, vrvec3 eyePos, vrvec3 lookAtPos, vrvec3 upVec) Rotates the assembly so that it is looking at the given position.
number	vrBitsToInteger(boolean ... ) Converts boolean values to an integer.
Any	vrCopy(Any c) Returns a copy of a Vector, Matrix, Ray, Sphere, AABBox, Quaternion or Plane.
vrvec3	vrCross(Any vec1, Any vec2) Returns the cross product of two vectors. Both vectors must be the same type.
number	vrDot(Any vec1, Any vec2) Returns the dot product of two vectors. Both vectors must be the same type.
vrvec3	vrGetForwardVec(vrnode viewportNode =nil) Extracts the forward vector from the inverse of the current view matrix.
vrnode	vrGetOwnerNode(Any c) Get the node that owns this Vector, Matrix, Ray, Sphere, AABBox, Quaternion or Plane.
vrvec3	vrHSV2RGB(vrvec3 hsvColour) Converts a HSV coiour (vec3f) to an RGB colour (vec3f)
boolean	vrIntegerToBits(number i) Converts an integer to a boolean value for each bit.
boolean	vrIsDoublePrecision() Returns true if the scenegraph uses double precision values for matrices etc.
number	vrLength(Any vec) Returns the length of a vector.
number	vrLengthSquared(Any vec) Returns the squared length of a vector.
vrmatrix3	vrMat3() Return an identity 3x3 Matrix.
vrmatrix4	vrMat4() Return an identity 4x4 Matrix.
vrmatrix4	vrMat4Frustum(number left, number right, number bottom, number top, number nearval, number farval, number focalval) Return a frustum projection matrix.
vrmatrix4	vrMat4Ortho(number left, number right, number bottom, number top, number nearval, number farval) Return an orthographic projection matrix.
vrmatrix4	vrMat4Ortho2D(number left, number right, number bottom, number top) Return a 2D orthographic projection matrix.
number	vrMatDeterminant(Any m) Returns the determinant of the matrix.
number	vrMatGetValue(Any m, number x, number y) Get the value of an element of a matrix.
vrmatrix4	vrMatInverse(vrmatrix4 m) Returns the inverse of a 4x4 matrix.
Any	vrMatOrthoNormalise(Any m) Returns an orthogonal matrix.
vrmatrix4	vrMatRotateEulerX(Any m, number v) Return M rotated on the X axis by angle V.
vrmatrix4	vrMatRotateEulerY(Any m, number v) Return M rotated on the Y axis by angle V.
vrmatrix4	vrMatRotateEulerZ(Any m, number v) Return M rotated on the Z axis by angle V.
vrmatrix4	vrMatScale(Any m, Any v) Return M scaled by vector V. If V is a scalar then a vector in which x=v, y=v, z=v will be used.
void	vrMatSetValue(Any m, number x, number y, number v) Set the value of an element of a matrix.
string	vrMatToString(Any m) Get a string representation of a matrix.
vrmatrix4	vrMatTranslate(Any m, vrvec3 v) Return M translated by the vector V.
Any	vrMatTranspose(Any m) Returns the tranpose of a 3x3 matrix, or a 4x4 matrix with the 3x3 component transposed.
Any	vrNormalise(Any c) Returns normalised vector/matrix.
vrplane	vrPlane(vrvec3 normal, number distance) Returns a plane.
vrplane	vrPlaneFromMatrix(vrmatrix4 mat) Returns a plane created from a matrix.
vrplane	vrPlaneFromTriangle(vrvec3 point1, vrvec3 point2, vrvec3 point3) Returns a plane created from a triangle defined by 3 points.
number	vrPlaneGetPointDistance(vrplane plane, vrvec3 point) Returns the distance a point is from the plane. A negative value means that the point is behind the plane. A positive value means the point is in front. A zero means it is on the plane.
boolean	vrPlaneLineIntersect(vrplane plane, vrvec3 point1, vrvec3 point2) Returns whether or not a line made of two points will intersect a plane.
number	vrPlaneRayIntersect(vrplane plane, vrray ray) Returns how far along the ray an intersection point with this plane is.
vrplane	vrPlaneTransform(Any plane, vrmatrix4 mat) Returns a plane transformed by a matrix.
void	vrPolarToDegrees(number degrees, number minutes, number seconds) Convert polar coordinates to degrees.
number	vrPolarToRadians(number degrees, number minutes, number seconds) Convert polar coordinates to radians.
vrvec3	vrProjInvTransformVec(vrvec3 vec, vrnode viewportNode =nil) Transforms a vector by the inverse of the current projection matrix.
vrvec3	vrProjTransformVec(vrvec3 vec, vrnode viewportNode =nil) Transforms a vector by the current projection matrix.
vrquaternion	vrQuaternion() Return an identity quaternion.
number	vrQuaternionDot(vrquaternion l, vrquaternion r) Returns the dot product of two quaternions.
vrquaternion	vrQuaternionFromAxisAngle(vrvec3 axis, number angle) Return a quaternion constructed from a rotation around an axis.
vrquaternion	vrQuaternionFromEulerAngles(vrvec3 angles) Return a quaternion constructed from euler angles.
vrquaternion	vrQuaternionFromMat(Any m) Returns a quaternion constructed from a 4x4 matrix.
vrquaternion	vrQuaternionLerp(vrquaternion l, vrquaternion r, number d) Returns the linear interpolation between two quaternions.
vrquaternion	vrQuaternionSlerp(vrquaternion l, vrquaternion r, number d) Returns the spherical interpolation between two quaternions.
vrray	vrRay(vrvec3 origin, vrvec3 dir) Returns a ray.
number	vrSmoothStep(number a, number b, number x) Return a smoothly interpolated value between A and B.
vrsphere	vrSphere(vrvec3 position, number radius) Returns a sphere.
vrsphere	vrSphereMerge(Any left, vrsphere right) Returns a sphere that encapsulates two spheres.
vrsphere	vrSphereTransform(Any sphere, vrmatrix4 matrix) Returns a sphere transformed by a matrix.
void	vrSuspendDynamics(vrnode node, boolean onOff) Enables or disables dynamics.
boolean	vrTestContain(Any a, Any b) Returns whether or object A completly contains object B.
boolean	vrTestIntersection(Any a, Any b) Returns whether or not two objects are intersecting one another.
vrvec3	vrTransformVecByWorldRotation(vrnode node, vrvec3 vec) Transforms a vector by the world rotation of the node.
vec2	vrVec2(number x =0.0, number y =0.0) Returns a 2 dimensional vector.
vrvec3	vrVec3(number x =0.0, number y =0.0, number z =0.0) Returns a 3 dimensional vector.
vrvec4	vrVec4(number x =0.0, number y =0.0, number z =0.0, number w =0.0) Returns a 4 dimensional vector.
vrvec3	vrViewInvTransformVec(vrvec3 vec, vrnode viewportNode =nil) Transforms a vector by the inverse of the current view matrix.
vrvec3	vrViewTransformVec(vrvec3 vec, vrnode viewportNode =nil) Transforms a vector by the current view matrix.

Functions Documentation

vrAABox

vrbox vrAABox(
    vrvec3 min,
    vrvec3 max
)

Construct an axis aligned bounding box.

Parameters:

• min The minimum value of the bounding box.
• max The maximum value of the bounding box.

Return: A new box enclosing the min/max points

vrAABoxExtent

number vrAABoxExtent(
    vrbox box
)

Returns the largest dimension of an axis aligned bounding box.

vrAABoxMerge

vrbox vrAABoxMerge(
    Any l,
    vrbox r
)

Returns an axis aligned bounding box that contains two other bounding boxes.

vrAABoxPosAndSize

vrbox vrAABoxPosAndSize(
    vrvec3 pos,
    vrvec3 size
)

Construct an axis aligned bounding box, using a position and a size.

Parameters:

• pos The position of the bounding box.
• size The size of the bounding box.

Return: A new box enclosing the pos/size points

vrAABoxTransform

vrbox vrAABoxTransform(
    Any box,
    vrmatrix4 matrix
)

Returns an axis aligned bounding box transformed by a matrix.

vrAngleRadians

number vrAngleRadians(
    number arcLength,
    number radius
)

Calculates the angle of an arc in radians.

Parameters:

• arcLength The length of the arc
• radius The radius of the circle

Return: The angle

vrApplyForce

vrnode vrApplyForce(
    vrnode node,
    vrvec3 force,
    vrvec3 relPos,
    number duration
)

Applies a force to an object causing a dynamics response.

vrApproxEquals

boolean vrApproxEquals(
    Any left,
    Any right,
    number prec =0.0
)

Returns whether or not two items are approximately equal.

Parameters:

• prec Override the default epsilon value used for comparing floating point values

vrArcLength

number vrArcLength(
    number angleRadians,
    number radius
)

Calculates the length of an arc.

Parameters:

• angleRadians The angle to measure
• radius The radius of the circle

Return: The length

vrArcRadius

number vrArcRadius(
    number arcLength,
    number angleRadians
)

Calculates the radius of an arc.

Parameters:

• arcLength The length of the arc
• angleRadians The angle of the arc

Return: The radius

vrAssemblyLookAt

void vrAssemblyLookAt(
    vrnode assembly,
    vrvec3 eyePos,
    vrvec3 lookAtPos,
    vrvec3 upVec
)

Rotates the assembly so that it is looking at the given position.

Parameters:

• eyePos New position for the assembly
• lookAtPos Position the assembly is looking at along it's Z axis
• upVec World up vector

vrBitsToInteger

number vrBitsToInteger(
    boolean ... 
)

Converts boolean values to an integer.

Parameters:

• ... Values (1 or 0, or true or false) that make up the bit field.

Return: Integer composed of the individual bits provided

vrCopy

Any vrCopy(
    Any c
)

Returns a copy of a Vector, Matrix, Ray, Sphere, AABBox, Quaternion or Plane.

vrCross

vrvec3 vrCross(
    Any vec1,
    Any vec2
)

Returns the cross product of two vectors. Both vectors must be the same type.

Parameters:

• vec1 Vector 1 {x, y} or {x, y, z}.
• vec2 Vector 2 {x, y} or {x, y, z}.

vrDot

number vrDot(
    Any vec1,
    Any vec2
)

Returns the dot product of two vectors. Both vectors must be the same type.

Parameters:

• vec1 Vector 1 {x, y} or {x, y, z}.
• vec2 Vector 2 {x, y} or {x, y, z}.

vrGetForwardVec

vrvec3 vrGetForwardVec(
    vrnode viewportNode =nil
)

Extracts the forward vector from the inverse of the current view matrix.

Parameters:

• viewportNode Viewport to get the view matrix from (defaults to local user's default viewport)

vrGetOwnerNode

vrnode vrGetOwnerNode(
    Any c
)

Get the node that owns this Vector, Matrix, Ray, Sphere, AABBox, Quaternion or Plane.

Return: The owner of this data (the node that will be affected by changes to its data)

vrHSV2RGB

vrvec3 vrHSV2RGB(
    vrvec3 hsvColour
)

Converts a HSV coiour (vec3f) to an RGB colour (vec3f)

Parameters:

• hsvColour The input colour in HSV

vrIntegerToBits

boolean vrIntegerToBits(
    number i
)

Converts an integer to a boolean value for each bit.

Parameters:

• i The integer to split into bits

Return: 32 bools, one for each bit in the number

vrIsDoublePrecision

boolean vrIsDoublePrecision()

Returns true if the scenegraph uses double precision values for matrices etc.

vrLength

number vrLength(
    Any vec
)

Returns the length of a vector.

Parameters:

• vec Vector {x, y} or {x, y, z}.

vrLengthSquared

number vrLengthSquared(
    Any vec
)

Returns the squared length of a vector.

Parameters:

• vec Vector {x, y} or {x, y, z}.

vrMat3

vrmatrix3 vrMat3()

Return an identity 3x3 Matrix.

vrMat4

vrmatrix4 vrMat4()

Return an identity 4x4 Matrix.

vrMat4Frustum

vrmatrix4 vrMat4Frustum(
    number left,
    number right,
    number bottom,
    number top,
    number nearval,
    number farval,
    number focalval
)

Return a frustum projection matrix.

vrMat4Ortho

vrmatrix4 vrMat4Ortho(
    number left,
    number right,
    number bottom,
    number top,
    number nearval,
    number farval
)

Return an orthographic projection matrix.

vrMat4Ortho2D

vrmatrix4 vrMat4Ortho2D(
    number left,
    number right,
    number bottom,
    number top
)

Return a 2D orthographic projection matrix.

vrMatDeterminant

number vrMatDeterminant(
    Any m
)

Returns the determinant of the matrix.

Parameters:

• m The matrix to get the determinant of.

vrMatGetValue

number vrMatGetValue(
    Any m,
    number x,
    number y
)

Get the value of an element of a matrix.

Parameters:

• m The matrix to select the element from
• x The column of the element to select.
• y The row of the element to select.

vrMatInverse

vrmatrix4 vrMatInverse(
    vrmatrix4 m
)

Returns the inverse of a 4x4 matrix.

Parameters:

• m The matrix to take the inverse of.

vrMatOrthoNormalise

Any vrMatOrthoNormalise(
    Any m
)

Returns an orthogonal matrix.

Parameters:

• m The matrix to orthonormalise.

Return: Orthogonal mat3 or mat4 depending on the type passed in

vrMatRotateEulerX

vrmatrix4 vrMatRotateEulerX(
    Any m,
    number v
)

Return M rotated on the X axis by angle V.

Parameters:

• m The matrix to rotate.
• v The angle to rotate M by.

vrMatRotateEulerY

vrmatrix4 vrMatRotateEulerY(
    Any m,
    number v
)

Return M rotated on the Y axis by angle V.

Parameters:

• m The matrix to rotate.
• v The angle to rotate M by.

vrMatRotateEulerZ

vrmatrix4 vrMatRotateEulerZ(
    Any m,
    number v
)

Return M rotated on the Z axis by angle V.

Parameters:

• m The matrix to rotate.
• v The angle to rotate M by.

vrMatScale

vrmatrix4 vrMatScale(
    Any m,
    Any v
)

Return M scaled by vector V. If V is a scalar then a vector in which x=v, y=v, z=v will be used.

Parameters:

• m The matrix to scale.
• v The vector or scalar to scale M by.

vrMatSetValue

void vrMatSetValue(
    Any m,
    number x,
    number y,
    number v
)

Set the value of an element of a matrix.

Parameters:

• m The matrix of whose elements to set.
• x The column of the element to select.
• y The row of the element to select.
• v The value to set the element.

vrMatToString

string vrMatToString(
    Any m
)

Get a string representation of a matrix.

Parameters:

• m The matrix to stringify

vrMatTranslate

vrmatrix4 vrMatTranslate(
    Any m,
    vrvec3 v
)

Return M translated by the vector V.

Parameters:

• m The matrix to translate.
• v The vector to translate the matrix by.

vrMatTranspose

Any vrMatTranspose(
    Any m
)

Returns the tranpose of a 3x3 matrix, or a 4x4 matrix with the 3x3 component transposed.

Parameters:

• m The matrix to take the transpose of.

Return: vrmat3 or vrmat4 depending on the type passed in

vrNormalise

Any vrNormalise(
    Any c
)

Returns normalised vector/matrix.

Parameters:

• c Vector2 or Vector3 or Mat3 or Mat4

Return: Normalised vector or matrix depending on the type passed in

vrPlane

vrplane vrPlane(
    vrvec3 normal,
    number distance
)

Returns a plane.

Parameters:

• normal The normal of the plane.
• distance The distance from origin.

vrPlaneFromMatrix

vrplane vrPlaneFromMatrix(
    vrmatrix4 mat
)

Returns a plane created from a matrix.

vrPlaneFromTriangle

vrplane vrPlaneFromTriangle(
    vrvec3 point1,
    vrvec3 point2,
    vrvec3 point3
)

Returns a plane created from a triangle defined by 3 points.

vrPlaneGetPointDistance

number vrPlaneGetPointDistance(
    vrplane plane,
    vrvec3 point
)

Returns the distance a point is from the plane. A negative value means that the point is behind the plane. A positive value means the point is in front. A zero means it is on the plane.

vrPlaneLineIntersect

boolean vrPlaneLineIntersect(
    vrplane plane,
    vrvec3 point1,
    vrvec3 point2
)

Returns whether or not a line made of two points will intersect a plane.

Return: true if the line intersects the plane

vrPlaneRayIntersect

number vrPlaneRayIntersect(
    vrplane plane,
    vrray ray
)

Returns how far along the ray an intersection point with this plane is.

vrPlaneTransform

vrplane vrPlaneTransform(
    Any plane,
    vrmatrix4 mat
)

Returns a plane transformed by a matrix.

vrPolarToDegrees

void vrPolarToDegrees(
    number degrees,
    number minutes,
    number seconds
)

Convert polar coordinates to degrees.

vrPolarToRadians

number vrPolarToRadians(
    number degrees,
    number minutes,
    number seconds
)

Convert polar coordinates to radians.

vrProjInvTransformVec

vrvec3 vrProjInvTransformVec(
    vrvec3 vec,
    vrnode viewportNode =nil
)

Transforms a vector by the inverse of the current projection matrix.

Parameters:

• viewportNode Viewport to get the projection matrix from (defaults to local user's default viewport)

vrProjTransformVec

vrvec3 vrProjTransformVec(
    vrvec3 vec,
    vrnode viewportNode =nil
)

Transforms a vector by the current projection matrix.

Parameters:

• viewportNode Viewport to get the projection matrix from (defaults to local user's default viewport)

vrQuaternion

vrquaternion vrQuaternion()

Return an identity quaternion.

vrQuaternionDot

number vrQuaternionDot(
    vrquaternion l,
    vrquaternion r
)

Returns the dot product of two quaternions.

vrQuaternionFromAxisAngle

vrquaternion vrQuaternionFromAxisAngle(
    vrvec3 axis,
    number angle
)

Return a quaternion constructed from a rotation around an axis.

Parameters:

• axis The axis to rotate around.
• angle The angle to rotate by.

vrQuaternionFromEulerAngles

vrquaternion vrQuaternionFromEulerAngles(
    vrvec3 angles
)

Return a quaternion constructed from euler angles.

Parameters:

• angles The X, Y and Z angles to construct the quaternion from.

vrQuaternionFromMat

vrquaternion vrQuaternionFromMat(
    Any m
)

Returns a quaternion constructed from a 4x4 matrix.

Parameters:

• m The matrix to construct with (mat3 or mat4).

vrQuaternionLerp

vrquaternion vrQuaternionLerp(
    vrquaternion l,
    vrquaternion r,
    number d
)

Returns the linear interpolation between two quaternions.

vrQuaternionSlerp

vrquaternion vrQuaternionSlerp(
    vrquaternion l,
    vrquaternion r,
    number d
)

Returns the spherical interpolation between two quaternions.

vrRay

vrray vrRay(
    vrvec3 origin,
    vrvec3 dir
)

Returns a ray.

Parameters:

• origin The origin of the ray.
• dir The direction the ray is pointing.

vrSmoothStep

number vrSmoothStep(
    number a,
    number b,
    number x
)

Return a smoothly interpolated value between A and B.

Parameters:

• a The lowest value.
• b The highest value.
• x How much to interpolate.

vrSphere

vrsphere vrSphere(
    vrvec3 position,
    number radius
)

Returns a sphere.

Parameters:

• position The center of the sphere.
• radius The radius of the sphere.

vrSphereMerge

vrsphere vrSphereMerge(
    Any left,
    vrsphere right
)

Returns a sphere that encapsulates two spheres.

vrSphereTransform

vrsphere vrSphereTransform(
    Any sphere,
    vrmatrix4 matrix
)

Returns a sphere transformed by a matrix.

vrSuspendDynamics

void vrSuspendDynamics(
    vrnode node,
    boolean onOff
)

Enables or disables dynamics.

vrTestContain

boolean vrTestContain(
    Any a,
    Any b
)

Returns whether or object A completly contains object B.

Parameters:

• a A sphere or AABB
• b A sphere, AABB, or vec3

Return: true if b is inside a

vrTestIntersection

boolean vrTestIntersection(
    Any a,
    Any b
)

Returns whether or not two objects are intersecting one another.

Parameters:

• a A sphere or AABB
• b A sphere or AABB

Return: True if the objects are intersecting

vrTransformVecByWorldRotation

vrvec3 vrTransformVecByWorldRotation(
    vrnode node,
    vrvec3 vec
)

Transforms a vector by the world rotation of the node.

vrVec2

vec2 vrVec2(
    number x =0.0,
    number y =0.0
)

Returns a 2 dimensional vector.

Parameters:

• x The X component of the resulting vector
• y The Y component of the resulting vector

vrVec3

vrvec3 vrVec3(
    number x =0.0,
    number y =0.0,
    number z =0.0
)

Returns a 3 dimensional vector.

Parameters:

• x The X component of the resulting vector
• y The Y component of the resulting vector
• z The Z component of the resulting vector

vrVec4

vrvec4 vrVec4(
    number x =0.0,
    number y =0.0,
    number z =0.0,
    number w =0.0
)

Returns a 4 dimensional vector.

Parameters:

• x The X component of the resulting vector
• y The Y component of the resulting vector
• z The Z component of the resulting vector
• w The W component of the resulting vector

vrViewInvTransformVec

vrvec3 vrViewInvTransformVec(
    vrvec3 vec,
    vrnode viewportNode =nil
)

Transforms a vector by the inverse of the current view matrix.

Parameters:

• viewportNode Viewport to get the view matrix from (defaults to local user's default viewport)

vrViewTransformVec

vrvec3 vrViewTransformVec(
    vrvec3 vec,
    vrnode viewportNode =nil
)

Transforms a vector by the current view matrix.

Parameters:

• viewportNode Viewport to get the view matrix from (defaults to local user's default viewport)