yg.math

Classes for math.

class yg.math.Trafo

Represents a 3-dimensional homogeneous transform.

constructor

yg.math.Trafo() -> yg.math.Trafo

function yg.math.Trafo.rotateLocal()

Rotates the transform around local axis ax by angle radians.

yg.math.Trafo.rotateLocal(angle, ax) -> void

Argument	Type	Info
`angle`	number	Radians to rotate
`ax`	string	Local rotation axis. Options: `"X"`, `"Y"`, `"Z"`

function yg.math.Trafo.rotateGlobal()

Rotates the transform around global axis ax by angle radians.

yg.math.Trafo.rotateGlobal(angle, ax) -> void

Argument	Type	Info
`angle`	number	Radians to rotate
`ax`	string	Global rotation axis. Options: `"X"`, `"Y"`, `"Z"`

function yg.math.Trafo.translateLocal()

Translates the transform by local vector trans.

yg.math.Trafo.translateLocal(trans) -> void

Argument	Type	Info
`trans`	{number}	Local translation vector (array of 3 numbers)

function yg.math.Trafo.translateGlobal()

Translates the transform by global vector trans.

yg.math.Trafo.translateGlobal(trans) -> void

Argument	Type	Info
`trans`	{number}	Global translation vector (array of 3 numbers)

function yg.math.Trafo.setScaleLocal()

Sets the (local) scale of the transform to scale (array of 3 numbers), {x,y,z}-component.

yg.math.Trafo.setScaleLocal(scale) -> void

Argument	Type	Info
`scale`	{number}	Scale to set (array of 3 numbers)

function yg.math.Trafo.setRotation()

Sets the rotation of the transform from a quaternion.

yg.math.Trafo.setRotation(rot) -> void

Argument	Type	Info
`rot`	{number}	Quaternion to set rotation from (array of 4 numbers)

function yg.math.Trafo.setTranslation()

Sets the translation of the transform.

yg.math.Trafo.setTranslation(trans) -> void

Argument	Type	Info
`trans`	{number}	Vector to set translation from (array of 3 numbers)

function yg.math.Trafo.pointTo()

Points the positive Z axis (Z+) of the transform to center point, with transform origin eye, respecting up vector up.

yg.math.Trafo.pointTo(eye, center, up) -> void

Argument	Type	Info
`eye`	{number}	Eye (origin) vector (array of 3 numbers)
`center`	{number}	Center vector (array of 3 numbers)
`up`	{number}	Up vector (array of 3 numbers)

function yg.math.Trafo.lookAt()

Points the negative Z axis (Z-) of the transform to center point, with transform origin eye, respecting up vector up. Typically used to create an extrinsic camera matrix to generate a view matrix during rendering.

yg.math.Trafo.lookAt(eye, center, up) -> void

Argument	Type	Info
`eye`	{number}	Eye (origin) vector (array of 3 numbers)
`center`	{number}	Center vector (array of 3 numbers)
`up`	{number}	Up vector (array of 3 numbers)

function yg.math.Trafo.lerp()

Performs linear interpolation of this transform to target transform by using interpolation factor t in [0,1].

yg.math.Trafo.lerp(t, target, dst) -> void

Argument	Type	Info
`t`	number	Interpolation factor in [0,1]
`target`	yg.math.Trafo	Target transform to interpolate to
`dst`	yg.math.Trafo	Destination (output) transform

function yg.math.Trafo.setIdentity()

Resets the transform. Resulting matrix is identity.

yg.math.Trafo.setIdentity() -> void

function yg.math.Trafo.getAxisLocal(ax)

Returns a local axis of the transform (array of 3 numbers), expressed in world system.

yg.math.Trafo.getAxisLocal(ax) -> {number}

Argument	Type	Info
`ax`	string	Desired axis. Options: `"X"`, `"Y"`, `"Z"`

function yg.math.Trafo.getAxisGlobal(ax)

Returns a global axis of the transform (array of 3 numbers).

"X" -> {1, 0, 0}
"Y" -> {0, 1, 0}
"Z" -> {0, 0, 1}

yg.math.Trafo.getAxisGlobal(ax) -> {number}

Argument	Type	Info
`ax`	string	Desired axis. Options: `"X"`, `"Y"`, `"Z"`

function yg.math.Trafo.getEye()

Returns the eye (origin) of the transform (array of 3 numbers).

yg.math.Trafo.getEye() -> {number}

function yg.math.Trafo.getRotation()

Returns the rotation of the transform as a quaternion (array of 4 numbers).

yg.math.Trafo.getRotation() -> {number}

function yg.math.Trafo.getScale()

Returns the scale of the transform (array of 3 numbers).

yg.math.Trafo.getScale() -> {number}

class yg.math.Camera

Represents a camera with extrinsics (pose in world) and intrinsics (projection) in 3-dimensional space.

constructor

yg.math.Camera() -> yg.math.Camera

function yg.math.Camera.setPerspective()

Sets the camera to PERSPECTIVE projection mode.

yg.math.Camera.setPerspective(fovy, aspect, zNear, zFar) -> void

Argument	Type	Info
`fovy`	number	Vertical (Y) field of view [degrees]
`aspect`	number	Aspect ratio (width/height = X/Y)
`zNear`	number	Distance of near clipping plane
`zFar`	number	Distance of far clipping plane

function yg.math.Camera.setOrthographic()

Sets the camera to ORTHOGRAPHIC projection mode.

yg.math.Camera.setOrthographic(height, aspect, zNear, zFar) -> void

Argument	Type	Info
`height`	number	Height of the view cuboid
`aspect`	number	Aspect ratio (width/height = X/Y)
`zNear`	number	Distance of near clipping plane
`zFar`	number	Distance of far clipping plane

function yg.math.Camera.setFovy()

Sets the vertical (Y) field of view. Always set but only valid during PERSPECTIVE projection mode.

yg.math.Camera.setFovy(fovy) -> void

Argument	Type	Info
`fovy`	number	Vertical (Y) field of view [degrees]

function yg.math.Camera.setHeight()

Sets the height of the view cuboid. Always set but only valid during ORTHOGRAPHIC projection mode.

yg.math.Camera.setHeight(height) -> void

Argument	Type	Info
`height`	number	Height of the view cuboid

function yg.math.Camera.setAspect()

Sets the projection aspect ratio. Valid for both PERSPECTIVE and ORTHOGRAPHIC projection modes.

yg.math.Camera.setAspect(aspect) -> void

Argument	Type	Info
`aspect`	number	Aspect ratio (width/height = X/Y)

function yg.math.Camera.setZNear()

Sets the distance of the near clipping plane. Valid for both PERSPECTIVE and ORTHOGRAPHIC projection modes.

yg.math.Camera.setZNear(zNear) -> void

Argument	Type	Info
`zNear`	number	Distance of near clipping plane

function yg.math.Camera.setZFar()

Sets the distance of the far clipping plane. Valid for both PERSPECTIVE and ORTHOGRAPHIC projection modes.

yg.math.Camera.setZFar(zFar) -> void

Argument	Type	Info
`zFar`	number	Distance of far clipping plane

function yg.math.Camera.rotateFirstPerson()

Rotates yaw and pitch angles of camera transform. Pitch is locked to [-pi/2, +pi/2].

yg.math.Camera.rotateFirstPerson(yaw, pitch) -> void

Argument	Type	Info
`yaw`	number	Yaw angle to rotate (add) [Rad]
`pitch`	number	Pitch angle to rotate (add) [Rad]

function yg.math.Camera.trafo()

Returns (a reference to) the transform of the camera (extrinsics).

yg.math.Camera.trafo() -> yg.math.Trafo

function yg.math.Camera.castRay()

Casts a ray into the scene through viewport coordinates and returns it as an array of 6 numbers, representing the origin and direction of the ray: {org.x, org.y, org.z, dir.x, dir.y, dir.z}.

yg.math.Camera.castRay(viewportX, viewportY) -> {number}

Argument	Type	Info
`viewportX`	number	X-component of viewport coordinates to cast a ray through
`viewportY`	number	Y-component of viewport coordinates to cast a ray through