Array-based vector, quaternion and matrix math for PEX
// require any of the modules
var mat4 = require('pex-math/mat4')
// all of them are namespaces of functions
var identityMatrix = mat4.create()
// => [1, 0, 0, 0,
// 0, 1, 0, 0,
// 0, 0, 1, 0,
// 0, 0, 0, 1]
var vec2 = require('pex-math/vec2')
vec2.create()Returns a new vec2 at 0, 0, 0.
vec2.set(v, w)Sets a vector to another vector.
v: vec2 - the vector being setw: vec2 - the vector used as templateReturns v.
vec2.copy(v)Returns a copy of a vector.
v: vec2Returns a new instance of v.
vec2.equals(v, w)Compares two vectors.
v: vec2w: vec2Returns a bool.
vec2.add(v, w)Add a vector with another.
v: vec2w: vec2Returns v after addition.
vec2.sub(v, w)Subtracts a vector with another.
v: vec2w: vec2Returns v after subtraction.
vec2.scale(v, s)Scales a vector by a number.
v: vec2s: NumberReturns v scaled.
vec2.dot(v, w)Calculates the dot product of two vectors.
v: vec2w: vec2Returns v after calculation.
vec2.length(v)Calculates the length of a vector.
v: vec2Returns the length of v.
vec2.lengthSq(v)Calculates the squared length of a vector.
v: vec2Returns the squared length of v.
vec2.normalize(v)Normalises a vector.
v: vec2Returns v normalised.
vec2.distance(v, w)Calculates the distance between two vectors.
v: vec2w: vec2Returns the distance between v and w.
vec2.distanceSq(v, w)Calculates the squared distance between two vectors.
v: vec2w: vec2Returns the squared distance between v and w.
vec2.limit(v, s)Limits a vector to a length.
v: vec2s: NumberReturns v scaled.
vec2.lerp(v, w, t)Linearly interpolates between two vectors.
v: vec2w: vec2t: Number - lerp valueReturns v lerped.
vec2.toString(v, precision)Prints a vector to a string.
v: vec2precision: numberReturns a String.
var vec3 = require('pex-math/vec3')
vec3.create()Returns a new vec3 at 0, 0, 0.
vec3.set(v, w)Sets a vector to another vector.
v: vec3 - the vector being setw: vec3 - the vector used as templateReturns v.
vec3.copy(v)Returns a copy of a vector.
v: vec3Returns a new instance of v.
vec3.equals(v, w)Compares two vectors.
v: vec3w: vec3Returns a bool.
vec3.add(v, w)Add a vector with another.
v: vec3w: vec3Returns v after addition.
vec3.addScaled(v, w, s)Add a vector with another scaled vector.
v: vec3w: vec3s: NumberReturns v after addition.
vec3.sub(v, w)Subtracts a vector with another.
v: vec3w: vec3Returns v after subtraction.
vec3.scale(v, s)Scales a vector by a number.
v: vec3s: NumberReturns v scaled.
vec3.multMat4(v, m)Multiplies a vector by a matrix.
v: vec3m: mat4Returns v after multiplication.
vec3.multQuat(v, q)Multiplies a vector by a quaternion.
v: vec3q: quatReturns v after multiplication.
vec3.dot(v, w)Calculates the dot product of two vectors.
v: vec3w: vec3Returns v after calculation.
vec3.cross(v, w)Calculates the cross product of two vectors.
v: vec3w: vec3Returns v after calculation.
vec3.length(v)Calculates the length of a vector.
v: vec3Returns the length of v.
vec3.lengthSq(v)Calculates the squared length of a vector.
v: vec3Returns the squared length of v.
vec3.normalize(v)Normalises a vector.
v: vec3Returns v normalised.
vec3.distance(v, w)Calculates the distance between two vectors.
v: vec3w: vec3Returns the distance between v and w.
vec3.distanceSq(v, w)Calculates the squared distance between two vectors.
v: vec3w: vec3Returns the squared distance between v and w.
vec3.limit(v, s)Limits a vector to a length.
v: vec3s: NumberReturns v scaled.
vec3.lerp(v, w, t)Linearly interpolates between two vectors.
v: vec3w: vec3t: Number - lerp valueReturns v lerped.
vec3.toString(v, p)Prints a vector to a string.
v: vec3p: Number - precisionReturns a String.
var vec4 = require('pex-math/vec4')
vec4.create()Returns a new vec4 at 0, 0, 0.
vec4.equals(v, w)Compares two vectors.
v: vec4w: vec4Returns a bool.
vec4.set(v, w)Sets a vector to another vector.
v: vec4 - the vector being setw: vec4 - the vector used as templateReturns v.
vec4.fromVec3(v, v3)Create a vec4 from vec3.
v: vec4v3: vec3Returns v4.
vec4.multMat4(v, m)Multiplies a vector with a matrix.
v: vec4m: mat4Returns v.
vec4.copy(v)Returns a copy of a vector.
v: vec4Returns a new instance of v.
vec4.scale(v, s)Scales a vector by a number.
v: vec4s: NumberReturns v scaled.
var mat2x3 = require('pex-math/mat2x3')
mat2x3.create()Returns a 2x3 identity matrix, a short form for a 3x3 matrix with the last row ignored.
Row major memory layout:
0 1 2
3 4 5
Equivalent to the column major OpenGL spec:
0 3
1 4
2 5
m00 m10
m01 m11
m02 m12
Returns a new mat2x3.
mat2x3.set(m, n)Sets a matrix from another matrix.
m: mat2x3 - the matrix being setn: mat2x3 - the matrix used as templateReturns m.
mat2x3.identity(m)Sets a matrix to the identity matrix.
m: mat2x3Returns m as its identity.
mat2x3.mult(m, n)Multiplies two matrices.
m: mat2x3n: mat2x3Returns m multiplied by n.
mat2x3.translate(m, v)Translates a matrix by a vector.
m: mat2x3v: vec2Returns m translated.
mat2x3.rotate(m, r)Rotates a matrix by an angle.
m: mat2x3r: Number - the angle of rotationReturns m rotated.
mat2x3.scale(m, v)Scales a matrix by a vector.
m: mat2x3v: vec2Returns m scaled.
var mat3 = require('pex-math/mat3')
mat3.create()Returns a 3x3 identity matrix.
Row major memory layout:
0 1 2
3 4 5
6 7 8
Equivalent to the column major OpenGL spec:
0 3 6
1 4 7
2 5 8
m00 m10 m20
m01 m11 m21
m02 m12 m22
Returns a new mat3.
mat3.set(m, n)Sets a matrix from another matrix.
m: mat3 - the matrix being setn: mat3 - the matrix used as templateReturns m.
mat3.identity(m)Sets a matrix to the identity matrix.
m: mat3Returns m as its identity.
mat3.mult(m, n)Multiplies two matrices.
m: mat3n: mat3Returns m multiplied by n.
mat3.equals(m, n)Compares two matrices.
m: mat3n: mat3Returns a bool.
mat3.fromMat2x3(m, m2x3)Sets a 3x3 matrix from a 2x3 matrix.
m: mat3m2x3: mat2x3Returns m3.
mat3.fromMat4(m, m4)Sets a 3x3 matrix to a 4x4 matrix.
m: mat3m4: mat4Returns m3.
mat3.fromQuat(m, q)Sets matrix to a quaternion.
m: mat3q: quatReturns m.
var mat4 = require('pex-math/mat4')
mat4.create()Returns a 4x4 identity matrix.
Row major memory layout:
0 1 2 3
4 5 6 7
8 9 10 11
12 13 14 15
Equivalent to the column major OpenGL spec:
0 4 8 12
1 5 9 13
2 6 10 14
3 7 11 15
m00 m10 m20 m30
m01 m11 m21 m31
m02 m12 m22 m32
m03 m13 m23 m33
Returns a new mat4.
mat4.set(m, n)Sets a matrix from another matrix.
m: mat4 - the matrix being setn: mat4 - the matrix used as templateReturns the newly set a.
mat4.equals(m, n)Compares two matrices.
m: mat4n: mat4Returns a bool.
mat4.copy(m)Returns a copy of a matrix.
m: mat4Returns a new instance of m.
mat4.mult(m, n)Multiplies two matrices.
m: mat4n: mat4Returns m multiplied by n.
mat4.invert(m)Inverts a matrix.
m: mat4Returns m inverted.
mat4.tranpose(m)Transposes a matrix.
m: mat4Returns m transposed.
mat4.identity(m)Sets a matrix to the identity matrix.
m: mat4Returns m as its identity.
mat4.scale(m, v)Scales a matrix by a vector.
m: mat4v: vec3Returns m scaled.
mat4.translate(m, v)Translates a matrix by a vector.
m: mat4v: vec3Returns m translated.
mat4.rotate(m, r, v)Rotates a matrix by an angle at an axis.
m: mat4r: Number - the angle of rotationv: vec3 - the axis of rotationReturns m rotated.
mat4.frustum(m, left, right, bottom, top, near, far)Create a frustum matrix.
m: mat4left: Number - left boundright: Number - right boundbottom: Number - bottom boundtop: Number - top boundnear: Number - near clipping planefar: Number - far clipping planeReturns m.
mat4.perspective(m, fovy, aspectRatio, near, far)Create a perspective matrix.
m: mat4 - out matrixfovy: Number - field of view in radiansaspectRatio: Number - aspect rationear: Number - near clipping planefar: Number - far clipping planeReturns m.
mat4.ortho(m, left, right, bottom, top, near, far)Create a orthographic matrix.
m: mat4left: Number - left boundright: Number - right boundbottom: Number - bottom boundtop: Number - top boundnear: Number - near clipping planefar: Number - far clipping planeReturns m.
mat4.lookAt(m, from, to, up)Calculates a lookAt matrix from a position, target and up vectors.
m: mat4from: vec3 - position vectorto: vec3 - target vectorup: vec3 - up vectorReturns m.
mat4.fromQuat(m, q)Sets matrix to a quaternion.
m: mat4q: quatReturns m.
mat4.fromMat3(m, m3)Sets a 4x4 matrix to a 3x3 matrix.
m: mat4m3: mat3Returns m.
mat4.fromTranslationRotationScale(m, t, r, s)Sets matrix to the TRS matrix.
m: mat4t: vec3r: quats: vec3Returns m.
var quat = require('pex-math/quat')
quat.create()Create a new quaternion.
quat.equals(q, p)Compares two quaternions.
q: quatp: quatReturns bool.
quat.identity(q)Sets a quaternion to the identity quaternion.
q: quatReturns q.
quat.copy(q)Returns a copy of a quaternion.
q: quatReturns a new instance of q.
quat.set(q, p)Sets one quaternion to another.
q: quatp: quatReturns q.
quat.mult(q, p)Multiplies one quaternion by another.
q: quatp: quatReturns q after multiplication.
quat.invert(q)Inverts a quaternion.
q: quatReturns q inverted.
quat.conjugate(q)Conjugates a quaternion.
q: quatReturns q conjugates.
quat.length(q)Calculates the length of a quaternion.
q: quatReturns the length of q.
quat.normalize(q)Normalizes a quaternion.
q: quatReturns q normalized.
quat.dot(q, p)Calculates the dot product of two quaternions.
q: quatp: quatReturns the dot product of q and p.
quat.fromEuler(q, euler)Set euler angles to a quaternion. Assumes XYZ rotation order.
q: quateuler: vec3/euler [x/yaw, y/pitch, z/roll]Returns q.
quat.fromAxisAngle(q, axis, angle)Set the angle at an axis of a quaternion.
q: quataxis: vec3angle: NumberReturns q.
quat.fromAxes(q, xAxis, yAxis, zAxis)Sets quaternion from orthonormal base xyz.
q: quatxAxis: vec3zAxis: vec3yAxis: vec3Returns q.
quat.fromMat3(q, m)Sets a quaternion to a 3x3 matrix.
q: quatm: mat3Returns q.
quat.fromMat4(q, m)Sets a quaternion to a 4x4 matrix.
q: quatm: mat4Returns q.
quat.slerp(q, p, t)Spherical linear interpolation between two quaternions.
q: quatp: quatt: NumberReturns q.
quat.fromTo(q, from, to, up)TODO
Returns q.
vec3 array of [x, y, z] rotation [yaw, pitch, roll] in radians.
var euler = require('pex-math/euler')
euler.create()Create a new euler angles [0, 0, 0].
euler.fromQuat(e, q)Creates euler angles from quaterion. Assumes XYZ order of rotations.
e: euler/vec3q: quatReturns e.
utils.lerp(a, b, t)Linear interpolation between two numbers.
a: Numberb: Numbert: NumberReturns a Number.
utils.clamp(a, min, max)Clamps a number between two numbers.
a: Numbermin: Numbermax: NumberReturns a Number.
utils.smoothstep(a, min, max)a: Numbermin: Numbermax: NumberReturns a Number.
utils.map(a, inStart, inEnd, outStart, outEnd)Maps a number from one range to another.
a: NumberinStart: NumberinEnd: NumberoutStart: NumberoutEnd: NumberReturns a Number.
toRadians(degrees)Transforms degrees into radians.
degrees - NumberReturns a Number.
toDegrees(radians)Transforms radians into degrees.
radians - NumberReturns a Number.
fraction(a)Returns the fractional part of a number.
a - NumberReturns a Number.
sign(a)Returns the sign of a number.
a - NumberReturns a Number.
sign(a)Returns the sign of a number.
a - NumberReturns a Number.
isPowerOfTwo(a)Returns the sign of a number.
a - NumberReturns a Number.
nextPowerOfTwo(a)Returns the sign of a number.
a - NumberReturns a Number.