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  • License MIT

Array based vector, qaternion and matrix math for the pex library

Package Exports

  • pex-math
  • pex-math/euler
  • pex-math/mat3
  • pex-math/mat4
  • pex-math/quat
  • pex-math/utils
  • pex-math/utils.js
  • pex-math/vec2
  • pex-math/vec2.js
  • pex-math/vec3
  • pex-math/vec3.js
  • pex-math/vec4

This package does not declare an exports field, so the exports above have been automatically detected and optimized by JSPM instead. If any package subpath is missing, it is recommended to post an issue to the original package (pex-math) to support the "exports" field. If that is not possible, create a JSPM override to customize the exports field for this package.

Readme

pex-math

js-standard-style

Array-based vector, quaternion and matrix math for PEX

Usage

// 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]

API

vec2

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 set
  • w: vec2 - the vector used as template

Returns v.

vec2.copy(v)

Returns a copy of a vector.

  • v: vec2

Returns a new instance of v.

vec2.equals(v, w)

Compares two vectors.

  • v: vec2
  • w: vec2

Returns a bool.

vec2.add(v, w)

Add a vector with another.

  • v: vec2
  • w: vec2

Returns v after addition.

vec2.sub(v, w)

Subtracts a vector with another.

  • v: vec2
  • w: vec2

Returns v after subtraction.

vec2.scale(v, s)

Scales a vector by a number.

  • v: vec2
  • s: Number

Returns v scaled.

vec2.dot(v, w)

Calculates the dot product of two vectors.

  • v: vec2
  • w: vec2

Returns v after calculation.

vec2.length(v)

Calculates the length of a vector.

  • v: vec2

Returns the length of v.

vec2.lengthSq(v)

Calculates the squared length of a vector.

  • v: vec2

Returns the squared length of v.

vec2.normalize(v)

Normalises a vector.

  • v: vec2

Returns v normalised.

vec2.distance(v, w)

Calculates the distance between two vectors.

  • v: vec2
  • w: vec2

Returns the distance between v and w.

vec2.distanceSq(v, w)

Calculates the squared distance between two vectors.

  • v: vec2
  • w: vec2

Returns the squared distance between v and w.

vec2.limit(v, s)

Limits a vector to a length.

  • v: vec2
  • s: Number

Returns v scaled.

vec2.lerp(v, w, t)

Linearly interpolates between two vectors.

  • v: vec2
  • w: vec2
  • t: Number - lerp value

Returns v lerped.

vec2.toString(v, precision)

Prints a vector to a string.

  • v: vec2
  • precision: number

Returns a String.

vec3

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 set
  • w: vec3 - the vector used as template

Returns v.

vec3.copy(v)

Returns a copy of a vector.

  • v: vec3

Returns a new instance of v.

vec3.equals(v, w)

Compares two vectors.

  • v: vec3
  • w: vec3

Returns a bool.

vec3.add(v, w)

Add a vector with another.

  • v: vec3
  • w: vec3

Returns v after addition.

vec3.addScaled(v, w, s)

Add a vector with another scaled vector.

  • v: vec3
  • w: vec3
  • s: Number

Returns v after addition.

vec3.sub(v, w)

Subtracts a vector with another.

  • v: vec3
  • w: vec3

Returns v after subtraction.

vec3.scale(v, s)

Scales a vector by a number.

  • v: vec3
  • s: Number

Returns v scaled.

vec3.multMat4(v, m)

Multiplies a vector by a matrix.

  • v: vec3
  • m: mat4

Returns v after multiplication.

vec3.multQuat(v, q)

Multiplies a vector by a quaternion.

  • v: vec3
  • q: quat

Returns v after multiplication.

vec3.dot(v, w)

Calculates the dot product of two vectors.

  • v: vec3
  • w: vec3

Returns v after calculation.

vec3.cross(v, w)

Calculates the cross product of two vectors.

  • v: vec3
  • w: vec3

Returns v after calculation.

vec3.length(v)

Calculates the length of a vector.

  • v: vec3

Returns the length of v.

vec3.lengthSq(v)

Calculates the squared length of a vector.

  • v: vec3

Returns the squared length of v.

vec3.normalize(v)

Normalises a vector.

  • v: vec3

Returns v normalised.

vec3.distance(v, w)

Calculates the distance between two vectors.

  • v: vec3
  • w: vec3

Returns the distance between v and w.

vec3.distanceSq(v, w)

Calculates the squared distance between two vectors.

  • v: vec3
  • w: vec3

Returns the squared distance between v and w.

vec3.limit(v, s)

Limits a vector to a length.

  • v: vec3
  • s: Number

Returns v scaled.

vec3.lerp(v, w, t)

Linearly interpolates between two vectors.

  • v: vec3
  • w: vec3
  • t: Number - lerp value

Returns v lerped.

vec3.toString(v, p)

Prints a vector to a string.

  • v: vec3
  • p: Number - precision

Returns a String.

vec4

var vec4 = require('pex-math/vec4')

vec4.create()

Returns a new vec4 at 0, 0, 0.

vec4.equals(v, w)

Compares two vectors.

  • v: vec4
  • w: vec4

Returns a bool.

vec4.set(v, w)

Sets a vector to another vector.

  • v: vec4 - the vector being set
  • w: vec4 - the vector used as template

Returns v.

vec4.fromVec3(v, v3)

Create a vec4 from vec3.

  • v: vec4
  • v3: vec3

Returns v4.

vec4.multMat4(v, m)

Multiplies a vector with a matrix.

  • v: vec4
  • m: mat4

Returns v.

vec4.copy(v)

Returns a copy of a vector.

  • v: vec4

Returns a new instance of v.

vec4.scale(v, s)

Scales a vector by a number.

  • v: vec4
  • s: Number

Returns v scaled.

mat2x3

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 set
  • n: mat2x3 - the matrix used as template

Returns m.

mat2x3.identity(m)

Sets a matrix to the identity matrix.

  • m: mat2x3

Returns m as its identity.

mat2x3.mult(m, n)

Multiplies two matrices.

  • m: mat2x3
  • n: mat2x3

Returns m multiplied by n.

mat2x3.translate(m, v)

Translates a matrix by a vector.

  • m: mat2x3
  • v: vec2

Returns m translated.

mat2x3.rotate(m, r)

Rotates a matrix by an angle.

  • m: mat2x3
  • r: Number - the angle of rotation

Returns m rotated.

mat2x3.scale(m, v)

Scales a matrix by a vector.

  • m: mat2x3
  • v: vec2

Returns m scaled.

mat3

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 set
  • n: mat3 - the matrix used as template

Returns m.

mat3.identity(m)

Sets a matrix to the identity matrix.

  • m: mat3

Returns m as its identity.

mat3.mult(m, n)

Multiplies two matrices.

  • m: mat3
  • n: mat3

Returns m multiplied by n.

mat3.equals(m, n)

Compares two matrices.

  • m: mat3
  • n: mat3

Returns a bool.

mat3.fromMat2x3(m, m2x3)

Sets a 3x3 matrix from a 2x3 matrix.

  • m: mat3
  • m2x3: mat2x3

Returns m3.

mat3.fromMat4(m, m4)

Sets a 3x3 matrix to a 4x4 matrix.

  • m: mat3
  • m4: mat4

Returns m3.

mat3.fromQuat(m, q)

Sets matrix to a quaternion.

  • m: mat3
  • q: quat

Returns m.

mat4

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 set
  • n: mat4 - the matrix used as template

Returns the newly set a.

mat4.equals(m, n)

Compares two matrices.

  • m: mat4
  • n: mat4

Returns a bool.

mat4.copy(m)

Returns a copy of a matrix.

  • m: mat4

Returns a new instance of m.

mat4.mult(m, n)

Multiplies two matrices.

  • m: mat4
  • n: mat4

Returns m multiplied by n.

mat4.invert(m)

Inverts a matrix.

  • m: mat4

Returns m inverted.

mat4.tranpose(m)

Transposes a matrix.

  • m: mat4

Returns m transposed.

mat4.identity(m)

Sets a matrix to the identity matrix.

  • m: mat4

Returns m as its identity.

mat4.scale(m, v)

Scales a matrix by a vector.

  • m: mat4
  • v: vec3

Returns m scaled.

mat4.translate(m, v)

Translates a matrix by a vector.

  • m: mat4
  • v: vec3

Returns m translated.

mat4.rotate(m, r, v)

Rotates a matrix by an angle at an axis.

  • m: mat4
  • r: Number - the angle of rotation
  • v: vec3 - the axis of rotation

Returns m rotated.

mat4.frustum(m, left, right, bottom, top, near, far)

Create a frustum matrix.

  • m: mat4
  • left: Number - left bound
  • right: Number - right bound
  • bottom: Number - bottom bound
  • top: Number - top bound
  • near: Number - near clipping plane
  • far: Number - far clipping plane

Returns m.

mat4.perspective(m, fovy, aspectRatio, near, far)

Create a perspective matrix.

  • m: mat4 - out matrix
  • fovy: Number - field of view in radians
  • aspectRatio: Number - aspect ratio
  • near: Number - near clipping plane
  • far: Number - far clipping plane

Returns m.

mat4.ortho(m, left, right, bottom, top, near, far)

Create a orthographic matrix.

  • m: mat4
  • left: Number - left bound
  • right: Number - right bound
  • bottom: Number - bottom bound
  • top: Number - top bound
  • near: Number - near clipping plane
  • far: Number - far clipping plane

Returns m.

mat4.lookAt(m, from, to, up)

Calculates a lookAt matrix from a position, target and up vectors.

  • m: mat4
  • from: vec3 - position vector
  • to: vec3 - target vector
  • up: vec3 - up vector

Returns m.

mat4.fromQuat(m, q)

Sets matrix to a quaternion.

  • m: mat4
  • q: quat

Returns m.

mat4.fromMat3(m, m3)

Sets a 4x4 matrix to a 3x3 matrix.

  • m: mat4
  • m3: mat3

Returns m.

mat4.fromTranslationRotationScale(m, t, r, s)

Sets matrix to the TRS matrix.

  • m: mat4
  • t: vec3
  • r: quat
  • s: vec3

Returns m.

quat

var quat = require('pex-math/quat')

quat.create()

Create a new quaternion.

quat.equals(q, p)

Compares two quaternions.

  • q: quat
  • p: quat

Returns bool.

quat.identity(q)

Sets a quaternion to the identity quaternion.

  • q: quat

Returns q.

quat.copy(q)

Returns a copy of a quaternion.

  • q: quat

Returns a new instance of q.

quat.set(q, p)

Sets one quaternion to another.

  • q: quat
  • p: quat

Returns q.

quat.mult(q, p)

Multiplies one quaternion by another.

  • q: quat
  • p: quat

Returns q after multiplication.

quat.invert(q)

Inverts a quaternion.

  • q: quat

Returns q inverted.

quat.conjugate(q)

Conjugates a quaternion.

  • q: quat

Returns q conjugates.

quat.length(q)

Calculates the length of a quaternion.

  • q: quat

Returns the length of q.

quat.normalize(q)

Normalizes a quaternion.

  • q: quat

Returns q normalized.

quat.dot(q, p)

Calculates the dot product of two quaternions.

  • q: quat
  • p: quat

Returns the dot product of q and p.

quat.fromEuler(q, euler)

Set euler angles to a quaternion. Assumes XYZ rotation order.

  • q: quat
  • euler: 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: quat
  • axis: vec3
  • angle: Number

Returns q.

quat.fromAxes(q, xAxis, yAxis, zAxis)

Sets quaternion from orthonormal base xyz.

  • q: quat
  • xAxis: vec3
  • zAxis: vec3
  • yAxis: vec3

Returns q.

quat.fromMat3(q, m)

Sets a quaternion to a 3x3 matrix.

  • q: quat
  • m: mat3

Returns q.

quat.fromMat4(q, m)

Sets a quaternion to a 4x4 matrix.

  • q: quat
  • m: mat4

Returns q.

quat.slerp(q, p, t)

Spherical linear interpolation between two quaternions.

  • q: quat
  • p: quat
  • t: Number

Returns q.

quat.fromTo(q, from, to, up)

TODO

Returns q.

euler

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/vec3
  • q: quat

Returns e.

utils

utils.lerp(a, b, t)

Linear interpolation between two numbers.

  • a: Number
  • b: Number
  • t: Number

Returns a Number.

utils.clamp(a, min, max)

Clamps a number between two numbers.

  • a: Number
  • min: Number
  • max: Number

Returns a Number.

utils.smoothstep(a, min, max)

  • a: Number
  • min: Number
  • max: Number

Returns a Number.

utils.map(a, inStart, inEnd, outStart, outEnd)

Maps a number from one range to another.

  • a: Number
  • inStart: Number
  • inEnd: Number
  • outStart: Number
  • outEnd: Number

Returns a Number.

toRadians(degrees)

Transforms degrees into radians.

  • degrees - Number

Returns a Number.

toDegrees(radians)

Transforms radians into degrees.

  • radians - Number

Returns a Number.

fraction(a)

Returns the fractional part of a number.

  • a - Number

Returns a Number.

sign(a)

Returns the sign of a number.

  • a - Number

Returns a Number.

sign(a)

Returns the sign of a number.

  • a - Number

Returns a Number.

isPowerOfTwo(a)

Returns the sign of a number.

  • a - Number

Returns a Number.

nextPowerOfTwo(a)

Returns the sign of a number.

  • a - Number

Returns a Number.