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webgl-lookaround-skybox/m4.js

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/*
* Copyright 2021 GFXFundamentals.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following disclaimer
* in the documentation and/or other materials provided with the
* distribution.
* * Neither the name of GFXFundamentals. nor the names of his
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* Various 3d math functions.
*
* @module webgl-3d-math
*/
(function(root, factory) { // eslint-disable-line
if (typeof define === 'function' && define.amd) {
// AMD. Register as an anonymous module.
define([], factory);
} else {
// Browser globals
root.m4 = factory();
}
}(this, function() {
"use strict";
/**
* An array or typed array with 3 values.
* @typedef {number[]|TypedArray} Vector3
* @memberOf module:webgl-3d-math
*/
/**
* An array or typed array with 4 values.
* @typedef {number[]|TypedArray} Vector4
* @memberOf module:webgl-3d-math
*/
/**
* An array or typed array with 16 values.
* @typedef {number[]|TypedArray} Matrix4
* @memberOf module:webgl-3d-math
*/
let MatType = Float32Array;
/**
* Sets the type this library creates for a Mat4
* @param {constructor} Ctor the constructor for the type. Either `Float32Array` or `Array`
* @return {constructor} previous constructor for Mat4
*/
function setDefaultType(Ctor) {
const OldType = MatType;
MatType = Ctor;
return OldType;
}
/**
* Takes two 4-by-4 matrices, a and b, and computes the product in the order
* that pre-composes b with a. In other words, the matrix returned will
* transform by b first and then a. Note this is subtly different from just
* multiplying the matrices together. For given a and b, this function returns
* the same object in both row-major and column-major mode.
* @param {Matrix4} a A matrix.
* @param {Matrix4} b A matrix.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
*/
function multiply(a, b, dst) {
dst = dst || new MatType(16);
var b00 = b[0 * 4 + 0];
var b01 = b[0 * 4 + 1];
var b02 = b[0 * 4 + 2];
var b03 = b[0 * 4 + 3];
var b10 = b[1 * 4 + 0];
var b11 = b[1 * 4 + 1];
var b12 = b[1 * 4 + 2];
var b13 = b[1 * 4 + 3];
var b20 = b[2 * 4 + 0];
var b21 = b[2 * 4 + 1];
var b22 = b[2 * 4 + 2];
var b23 = b[2 * 4 + 3];
var b30 = b[3 * 4 + 0];
var b31 = b[3 * 4 + 1];
var b32 = b[3 * 4 + 2];
var b33 = b[3 * 4 + 3];
var a00 = a[0 * 4 + 0];
var a01 = a[0 * 4 + 1];
var a02 = a[0 * 4 + 2];
var a03 = a[0 * 4 + 3];
var a10 = a[1 * 4 + 0];
var a11 = a[1 * 4 + 1];
var a12 = a[1 * 4 + 2];
var a13 = a[1 * 4 + 3];
var a20 = a[2 * 4 + 0];
var a21 = a[2 * 4 + 1];
var a22 = a[2 * 4 + 2];
var a23 = a[2 * 4 + 3];
var a30 = a[3 * 4 + 0];
var a31 = a[3 * 4 + 1];
var a32 = a[3 * 4 + 2];
var a33 = a[3 * 4 + 3];
dst[ 0] = b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30;
dst[ 1] = b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31;
dst[ 2] = b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32;
dst[ 3] = b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33;
dst[ 4] = b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30;
dst[ 5] = b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31;
dst[ 6] = b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32;
dst[ 7] = b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33;
dst[ 8] = b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30;
dst[ 9] = b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31;
dst[10] = b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32;
dst[11] = b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33;
dst[12] = b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30;
dst[13] = b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31;
dst[14] = b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32;
dst[15] = b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33;
return dst;
}
/**
* adds 2 vectors3s
* @param {Vector3} a a
* @param {Vector3} b b
* @param {Vector3} dst optional vector3 to store result
* @return {Vector3} dst or new Vector3 if not provided
* @memberOf module:webgl-3d-math
*/
function addVectors(a, b, dst) {
dst = dst || new MatType(3);
dst[0] = a[0] + b[0];
dst[1] = a[1] + b[1];
dst[2] = a[2] + b[2];
return dst;
}
/**
* subtracts 2 vectors3s
* @param {Vector3} a a
* @param {Vector3} b b
* @param {Vector3} dst optional vector3 to store result
* @return {Vector3} dst or new Vector3 if not provided
* @memberOf module:webgl-3d-math
*/
function subtractVectors(a, b, dst) {
dst = dst || new MatType(3);
dst[0] = a[0] - b[0];
dst[1] = a[1] - b[1];
dst[2] = a[2] - b[2];
return dst;
}
/**
* scale vectors3
* @param {Vector3} v vector
* @param {Number} s scale
* @param {Vector3} dst optional vector3 to store result
* @return {Vector3} dst or new Vector3 if not provided
* @memberOf module:webgl-3d-math
*/
function scaleVector(v, s, dst) {
dst = dst || new MatType(3);
dst[0] = v[0] * s;
dst[1] = v[1] * s;
dst[2] = v[2] * s;
return dst;
}
/**
* normalizes a vector.
* @param {Vector3} v vector to normalize
* @param {Vector3} dst optional vector3 to store result
* @return {Vector3} dst or new Vector3 if not provided
* @memberOf module:webgl-3d-math
*/
function normalize(v, dst) {
dst = dst || new MatType(3);
var length = Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
// make sure we don't divide by 0.
if (length > 0.00001) {
dst[0] = v[0] / length;
dst[1] = v[1] / length;
dst[2] = v[2] / length;
}
return dst;
}
/**
* Computes the length of a vector
* @param {Vector3} v vector to take length of
* @return {number} length of vector
*/
function length(v) {
return Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
}
/**
* Computes the length squared of a vector
* @param {Vector3} v vector to take length of
* @return {number} length sqaured of vector
*/
function lengthSq(v) {
return v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
}
/**
* Computes the cross product of 2 vectors3s
* @param {Vector3} a a
* @param {Vector3} b b
* @param {Vector3} dst optional vector3 to store result
* @return {Vector3} dst or new Vector3 if not provided
* @memberOf module:webgl-3d-math
*/
function cross(a, b, dst) {
dst = dst || new MatType(3);
dst[0] = a[1] * b[2] - a[2] * b[1];
dst[1] = a[2] * b[0] - a[0] * b[2];
dst[2] = a[0] * b[1] - a[1] * b[0];
return dst;
}
/**
* Computes the dot product of two vectors; assumes both vectors have
* three entries.
* @param {Vector3} a Operand vector.
* @param {Vector3} b Operand vector.
* @return {number} dot product
* @memberOf module:webgl-3d-math
*/
function dot(a, b) {
return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);
}
/**
* Computes the distance squared between 2 points
* @param {Vector3} a
* @param {Vector3} b
* @return {number} distance squared between a and b
*/
function distanceSq(a, b) {
const dx = a[0] - b[0];
const dy = a[1] - b[1];
const dz = a[2] - b[2];
return dx * dx + dy * dy + dz * dz;
}
/**
* Computes the distance between 2 points
* @param {Vector3} a
* @param {Vector3} b
* @return {number} distance between a and b
*/
function distance(a, b) {
return Math.sqrt(distanceSq(a, b));
}
/**
* Makes an identity matrix.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function identity(dst) {
dst = dst || new MatType(16);
dst[ 0] = 1;
dst[ 1] = 0;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = 1;
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = 0;
dst[ 9] = 0;
dst[10] = 1;
dst[11] = 0;
dst[12] = 0;
dst[13] = 0;
dst[14] = 0;
dst[15] = 1;
return dst;
}
/**
* Transposes a matrix.
* @param {Matrix4} m matrix to transpose.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function transpose(m, dst) {
dst = dst || new MatType(16);
dst[ 0] = m[0];
dst[ 1] = m[4];
dst[ 2] = m[8];
dst[ 3] = m[12];
dst[ 4] = m[1];
dst[ 5] = m[5];
dst[ 6] = m[9];
dst[ 7] = m[13];
dst[ 8] = m[2];
dst[ 9] = m[6];
dst[10] = m[10];
dst[11] = m[14];
dst[12] = m[3];
dst[13] = m[7];
dst[14] = m[11];
dst[15] = m[15];
return dst;
}
/**
* Creates a lookAt matrix.
* This is a world matrix for a camera. In other words it will transform
* from the origin to a place and orientation in the world. For a view
* matrix take the inverse of this.
* @param {Vector3} cameraPosition position of the camera
* @param {Vector3} target position of the target
* @param {Vector3} up direction
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function lookAt(cameraPosition, target, up, dst) {
dst = dst || new MatType(16);
var zAxis = normalize(
subtractVectors(cameraPosition, target));
var xAxis = normalize(cross(up, zAxis));
var yAxis = normalize(cross(zAxis, xAxis));
dst[ 0] = xAxis[0];
dst[ 1] = xAxis[1];
dst[ 2] = xAxis[2];
dst[ 3] = 0;
dst[ 4] = yAxis[0];
dst[ 5] = yAxis[1];
dst[ 6] = yAxis[2];
dst[ 7] = 0;
dst[ 8] = zAxis[0];
dst[ 9] = zAxis[1];
dst[10] = zAxis[2];
dst[11] = 0;
dst[12] = cameraPosition[0];
dst[13] = cameraPosition[1];
dst[14] = cameraPosition[2];
dst[15] = 1;
return dst;
}
/**
* Computes a 4-by-4 perspective transformation matrix given the angular height
* of the frustum, the aspect ratio, and the near and far clipping planes. The
* arguments define a frustum extending in the negative z direction. The given
* angle is the vertical angle of the frustum, and the horizontal angle is
* determined to produce the given aspect ratio. The arguments near and far are
* the distances to the near and far clipping planes. Note that near and far
* are not z coordinates, but rather they are distances along the negative
* z-axis. The matrix generated sends the viewing frustum to the unit box.
* We assume a unit box extending from -1 to 1 in the x and y dimensions and
* from -1 to 1 in the z dimension.
* @param {number} fieldOfViewInRadians field of view in y axis.
* @param {number} aspect aspect of viewport (width / height)
* @param {number} near near Z clipping plane
* @param {number} far far Z clipping plane
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function perspective(fieldOfViewInRadians, aspect, near, far, dst) {
dst = dst || new MatType(16);
var f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewInRadians);
var rangeInv = 1.0 / (near - far);
dst[ 0] = f / aspect;
dst[ 1] = 0;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = f;
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = 0;
dst[ 9] = 0;
dst[10] = (near + far) * rangeInv;
dst[11] = -1;
dst[12] = 0;
dst[13] = 0;
dst[14] = near * far * rangeInv * 2;
dst[15] = 0;
return dst;
}
/**
* Computes a 4-by-4 orthographic projection matrix given the coordinates of the
* planes defining the axis-aligned, box-shaped viewing volume. The matrix
* generated sends that box to the unit box. Note that although left and right
* are x coordinates and bottom and top are y coordinates, near and far
* are not z coordinates, but rather they are distances along the negative
* z-axis. We assume a unit box extending from -1 to 1 in the x and y
* dimensions and from -1 to 1 in the z dimension.
* @param {number} left The x coordinate of the left plane of the box.
* @param {number} right The x coordinate of the right plane of the box.
* @param {number} bottom The y coordinate of the bottom plane of the box.
* @param {number} top The y coordinate of the right plane of the box.
* @param {number} near The negative z coordinate of the near plane of the box.
* @param {number} far The negative z coordinate of the far plane of the box.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function orthographic(left, right, bottom, top, near, far, dst) {
dst = dst || new MatType(16);
dst[ 0] = 2 / (right - left);
dst[ 1] = 0;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = 2 / (top - bottom);
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = 0;
dst[ 9] = 0;
dst[10] = 2 / (near - far);
dst[11] = 0;
dst[12] = (left + right) / (left - right);
dst[13] = (bottom + top) / (bottom - top);
dst[14] = (near + far) / (near - far);
dst[15] = 1;
return dst;
}
/**
* Computes a 4-by-4 perspective transformation matrix given the left, right,
* top, bottom, near and far clipping planes. The arguments define a frustum
* extending in the negative z direction. The arguments near and far are the
* distances to the near and far clipping planes. Note that near and far are not
* z coordinates, but rather they are distances along the negative z-axis. The
* matrix generated sends the viewing frustum to the unit box. We assume a unit
* box extending from -1 to 1 in the x and y dimensions and from -1 to 1 in the z
* dimension.
* @param {number} left The x coordinate of the left plane of the box.
* @param {number} right The x coordinate of the right plane of the box.
* @param {number} bottom The y coordinate of the bottom plane of the box.
* @param {number} top The y coordinate of the right plane of the box.
* @param {number} near The negative z coordinate of the near plane of the box.
* @param {number} far The negative z coordinate of the far plane of the box.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function frustum(left, right, bottom, top, near, far, dst) {
dst = dst || new MatType(16);
var dx = right - left;
var dy = top - bottom;
var dz = far - near;
dst[ 0] = 2 * near / dx;
dst[ 1] = 0;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = 2 * near / dy;
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = (left + right) / dx;
dst[ 9] = (top + bottom) / dy;
dst[10] = -(far + near) / dz;
dst[11] = -1;
dst[12] = 0;
dst[13] = 0;
dst[14] = -2 * near * far / dz;
dst[15] = 0;
return dst;
}
/**
* Makes a translation matrix
* @param {number} tx x translation.
* @param {number} ty y translation.
* @param {number} tz z translation.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function translation(tx, ty, tz, dst) {
dst = dst || new MatType(16);
dst[ 0] = 1;
dst[ 1] = 0;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = 1;
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = 0;
dst[ 9] = 0;
dst[10] = 1;
dst[11] = 0;
dst[12] = tx;
dst[13] = ty;
dst[14] = tz;
dst[15] = 1;
return dst;
}
/**
* Multiply by translation matrix.
* @param {Matrix4} m matrix to multiply
* @param {number} tx x translation.
* @param {number} ty y translation.
* @param {number} tz z translation.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function translate(m, tx, ty, tz, dst) {
// This is the optimized version of
// return multiply(m, translation(tx, ty, tz), dst);
dst = dst || new MatType(16);
var m00 = m[0];
var m01 = m[1];
var m02 = m[2];
var m03 = m[3];
var m10 = m[1 * 4 + 0];
var m11 = m[1 * 4 + 1];
var m12 = m[1 * 4 + 2];
var m13 = m[1 * 4 + 3];
var m20 = m[2 * 4 + 0];
var m21 = m[2 * 4 + 1];
var m22 = m[2 * 4 + 2];
var m23 = m[2 * 4 + 3];
var m30 = m[3 * 4 + 0];
var m31 = m[3 * 4 + 1];
var m32 = m[3 * 4 + 2];
var m33 = m[3 * 4 + 3];
if (m !== dst) {
dst[ 0] = m00;
dst[ 1] = m01;
dst[ 2] = m02;
dst[ 3] = m03;
dst[ 4] = m10;
dst[ 5] = m11;
dst[ 6] = m12;
dst[ 7] = m13;
dst[ 8] = m20;
dst[ 9] = m21;
dst[10] = m22;
dst[11] = m23;
}
dst[12] = m00 * tx + m10 * ty + m20 * tz + m30;
dst[13] = m01 * tx + m11 * ty + m21 * tz + m31;
dst[14] = m02 * tx + m12 * ty + m22 * tz + m32;
dst[15] = m03 * tx + m13 * ty + m23 * tz + m33;
return dst;
}
/**
* Makes an x rotation matrix
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function xRotation(angleInRadians, dst) {
dst = dst || new MatType(16);
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
dst[ 0] = 1;
dst[ 1] = 0;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = c;
dst[ 6] = s;
dst[ 7] = 0;
dst[ 8] = 0;
dst[ 9] = -s;
dst[10] = c;
dst[11] = 0;
dst[12] = 0;
dst[13] = 0;
dst[14] = 0;
dst[15] = 1;
return dst;
}
/**
* Multiply by an x rotation matrix
* @param {Matrix4} m matrix to multiply
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function xRotate(m, angleInRadians, dst) {
// this is the optimized version of
// return multiply(m, xRotation(angleInRadians), dst);
dst = dst || new MatType(16);
var m10 = m[4];
var m11 = m[5];
var m12 = m[6];
var m13 = m[7];
var m20 = m[8];
var m21 = m[9];
var m22 = m[10];
var m23 = m[11];
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
dst[4] = c * m10 + s * m20;
dst[5] = c * m11 + s * m21;
dst[6] = c * m12 + s * m22;
dst[7] = c * m13 + s * m23;
dst[8] = c * m20 - s * m10;
dst[9] = c * m21 - s * m11;
dst[10] = c * m22 - s * m12;
dst[11] = c * m23 - s * m13;
if (m !== dst) {
dst[ 0] = m[ 0];
dst[ 1] = m[ 1];
dst[ 2] = m[ 2];
dst[ 3] = m[ 3];
dst[12] = m[12];
dst[13] = m[13];
dst[14] = m[14];
dst[15] = m[15];
}
return dst;
}
/**
* Makes an y rotation matrix
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function yRotation(angleInRadians, dst) {
dst = dst || new MatType(16);
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
dst[ 0] = c;
dst[ 1] = 0;
dst[ 2] = -s;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = 1;
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = s;
dst[ 9] = 0;
dst[10] = c;
dst[11] = 0;
dst[12] = 0;
dst[13] = 0;
dst[14] = 0;
dst[15] = 1;
return dst;
}
/**
* Multiply by an y rotation matrix
* @param {Matrix4} m matrix to multiply
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function yRotate(m, angleInRadians, dst) {
// this is the optimized version of
// return multiply(m, yRotation(angleInRadians), dst);
dst = dst || new MatType(16);
var m00 = m[0 * 4 + 0];
var m01 = m[0 * 4 + 1];
var m02 = m[0 * 4 + 2];
var m03 = m[0 * 4 + 3];
var m20 = m[2 * 4 + 0];
var m21 = m[2 * 4 + 1];
var m22 = m[2 * 4 + 2];
var m23 = m[2 * 4 + 3];
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
dst[ 0] = c * m00 - s * m20;
dst[ 1] = c * m01 - s * m21;
dst[ 2] = c * m02 - s * m22;
dst[ 3] = c * m03 - s * m23;
dst[ 8] = c * m20 + s * m00;
dst[ 9] = c * m21 + s * m01;
dst[10] = c * m22 + s * m02;
dst[11] = c * m23 + s * m03;
if (m !== dst) {
dst[ 4] = m[ 4];
dst[ 5] = m[ 5];
dst[ 6] = m[ 6];
dst[ 7] = m[ 7];
dst[12] = m[12];
dst[13] = m[13];
dst[14] = m[14];
dst[15] = m[15];
}
return dst;
}
/**
* Makes an z rotation matrix
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function zRotation(angleInRadians, dst) {
dst = dst || new MatType(16);
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
dst[ 0] = c;
dst[ 1] = s;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = -s;
dst[ 5] = c;
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = 0;
dst[ 9] = 0;
dst[10] = 1;
dst[11] = 0;
dst[12] = 0;
dst[13] = 0;
dst[14] = 0;
dst[15] = 1;
return dst;
}
/**
* Multiply by an z rotation matrix
* @param {Matrix4} m matrix to multiply
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function zRotate(m, angleInRadians, dst) {
// This is the optimized version of
// return multiply(m, zRotation(angleInRadians), dst);
dst = dst || new MatType(16);
var m00 = m[0 * 4 + 0];
var m01 = m[0 * 4 + 1];
var m02 = m[0 * 4 + 2];
var m03 = m[0 * 4 + 3];
var m10 = m[1 * 4 + 0];
var m11 = m[1 * 4 + 1];
var m12 = m[1 * 4 + 2];
var m13 = m[1 * 4 + 3];
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
dst[ 0] = c * m00 + s * m10;
dst[ 1] = c * m01 + s * m11;
dst[ 2] = c * m02 + s * m12;
dst[ 3] = c * m03 + s * m13;
dst[ 4] = c * m10 - s * m00;
dst[ 5] = c * m11 - s * m01;
dst[ 6] = c * m12 - s * m02;
dst[ 7] = c * m13 - s * m03;
if (m !== dst) {
dst[ 8] = m[ 8];
dst[ 9] = m[ 9];
dst[10] = m[10];
dst[11] = m[11];
dst[12] = m[12];
dst[13] = m[13];
dst[14] = m[14];
dst[15] = m[15];
}
return dst;
}
/**
* Makes an rotation matrix around an arbitrary axis
* @param {Vector3} axis axis to rotate around
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function axisRotation(axis, angleInRadians, dst) {
dst = dst || new MatType(16);
var x = axis[0];
var y = axis[1];
var z = axis[2];
var n = Math.sqrt(x * x + y * y + z * z);
x /= n;
y /= n;
z /= n;
var xx = x * x;
var yy = y * y;
var zz = z * z;
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
var oneMinusCosine = 1 - c;
dst[ 0] = xx + (1 - xx) * c;
dst[ 1] = x * y * oneMinusCosine + z * s;
dst[ 2] = x * z * oneMinusCosine - y * s;
dst[ 3] = 0;
dst[ 4] = x * y * oneMinusCosine - z * s;
dst[ 5] = yy + (1 - yy) * c;
dst[ 6] = y * z * oneMinusCosine + x * s;
dst[ 7] = 0;
dst[ 8] = x * z * oneMinusCosine + y * s;
dst[ 9] = y * z * oneMinusCosine - x * s;
dst[10] = zz + (1 - zz) * c;
dst[11] = 0;
dst[12] = 0;
dst[13] = 0;
dst[14] = 0;
dst[15] = 1;
return dst;
}
/**
* Multiply by an axis rotation matrix
* @param {Matrix4} m matrix to multiply
* @param {Vector3} axis axis to rotate around
* @param {number} angleInRadians amount to rotate
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function axisRotate(m, axis, angleInRadians, dst) {
// This is the optimized version of
// return multiply(m, axisRotation(axis, angleInRadians), dst);
dst = dst || new MatType(16);
var x = axis[0];
var y = axis[1];
var z = axis[2];
var n = Math.sqrt(x * x + y * y + z * z);
x /= n;
y /= n;
z /= n;
var xx = x * x;
var yy = y * y;
var zz = z * z;
var c = Math.cos(angleInRadians);
var s = Math.sin(angleInRadians);
var oneMinusCosine = 1 - c;
var r00 = xx + (1 - xx) * c;
var r01 = x * y * oneMinusCosine + z * s;
var r02 = x * z * oneMinusCosine - y * s;
var r10 = x * y * oneMinusCosine - z * s;
var r11 = yy + (1 - yy) * c;
var r12 = y * z * oneMinusCosine + x * s;
var r20 = x * z * oneMinusCosine + y * s;
var r21 = y * z * oneMinusCosine - x * s;
var r22 = zz + (1 - zz) * c;
var m00 = m[0];
var m01 = m[1];
var m02 = m[2];
var m03 = m[3];
var m10 = m[4];
var m11 = m[5];
var m12 = m[6];
var m13 = m[7];
var m20 = m[8];
var m21 = m[9];
var m22 = m[10];
var m23 = m[11];
dst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;
dst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;
dst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;
dst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;
dst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;
dst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;
dst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;
dst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;
dst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;
dst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;
dst[10] = r20 * m02 + r21 * m12 + r22 * m22;
dst[11] = r20 * m03 + r21 * m13 + r22 * m23;
if (m !== dst) {
dst[12] = m[12];
dst[13] = m[13];
dst[14] = m[14];
dst[15] = m[15];
}
return dst;
}
/**
* Makes a scale matrix
* @param {number} sx x scale.
* @param {number} sy y scale.
* @param {number} sz z scale.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function scaling(sx, sy, sz, dst) {
dst = dst || new MatType(16);
dst[ 0] = sx;
dst[ 1] = 0;
dst[ 2] = 0;
dst[ 3] = 0;
dst[ 4] = 0;
dst[ 5] = sy;
dst[ 6] = 0;
dst[ 7] = 0;
dst[ 8] = 0;
dst[ 9] = 0;
dst[10] = sz;
dst[11] = 0;
dst[12] = 0;
dst[13] = 0;
dst[14] = 0;
dst[15] = 1;
return dst;
}
/**
* Multiply by a scaling matrix
* @param {Matrix4} m matrix to multiply
* @param {number} sx x scale.
* @param {number} sy y scale.
* @param {number} sz z scale.
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function scale(m, sx, sy, sz, dst) {
// This is the optimized version of
// return multiply(m, scaling(sx, sy, sz), dst);
dst = dst || new MatType(16);
dst[ 0] = sx * m[0 * 4 + 0];
dst[ 1] = sx * m[0 * 4 + 1];
dst[ 2] = sx * m[0 * 4 + 2];
dst[ 3] = sx * m[0 * 4 + 3];
dst[ 4] = sy * m[1 * 4 + 0];
dst[ 5] = sy * m[1 * 4 + 1];
dst[ 6] = sy * m[1 * 4 + 2];
dst[ 7] = sy * m[1 * 4 + 3];
dst[ 8] = sz * m[2 * 4 + 0];
dst[ 9] = sz * m[2 * 4 + 1];
dst[10] = sz * m[2 * 4 + 2];
dst[11] = sz * m[2 * 4 + 3];
if (m !== dst) {
dst[12] = m[12];
dst[13] = m[13];
dst[14] = m[14];
dst[15] = m[15];
}
return dst;
}
/**
* creates a matrix from translation, quaternion, scale
* @param {Number[]} translation [x, y, z] translation
* @param {Number[]} quaternion [x, y, z, z] quaternion rotation
* @param {Number[]} scale [x, y, z] scale
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
*/
function compose(translation, quaternion, scale, dst) {
dst = dst || new MatType(16);
const x = quaternion[0];
const y = quaternion[1];
const z = quaternion[2];
const w = quaternion[3];
const x2 = x + x;
const y2 = y + y;
const z2 = z + z;
const xx = x * x2;
const xy = x * y2;
const xz = x * z2;
const yy = y * y2;
const yz = y * z2;
const zz = z * z2;
const wx = w * x2;
const wy = w * y2;
const wz = w * z2;
const sx = scale[0];
const sy = scale[1];
const sz = scale[2];
dst[0] = (1 - (yy + zz)) * sx;
dst[1] = (xy + wz) * sx;
dst[2] = (xz - wy) * sx;
dst[3] = 0;
dst[4] = (xy - wz) * sy;
dst[5] = (1 - (xx + zz)) * sy;
dst[6] = (yz + wx) * sy;
dst[7] = 0;
dst[ 8] = (xz + wy) * sz;
dst[ 9] = (yz - wx) * sz;
dst[10] = (1 - (xx + yy)) * sz;
dst[11] = 0;
dst[12] = translation[0];
dst[13] = translation[1];
dst[14] = translation[2];
dst[15] = 1;
return dst;
}
function quatFromRotationMatrix(m, dst) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
// assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
const m11 = m[0];
const m12 = m[4];
const m13 = m[8];
const m21 = m[1];
const m22 = m[5];
const m23 = m[9];
const m31 = m[2];
const m32 = m[6];
const m33 = m[10];
const trace = m11 + m22 + m33;
if (trace > 0) {
const s = 0.5 / Math.sqrt(trace + 1);
dst[3] = 0.25 / s;
dst[0] = (m32 - m23) * s;
dst[1] = (m13 - m31) * s;
dst[2] = (m21 - m12) * s;
} else if (m11 > m22 && m11 > m33) {
const s = 2 * Math.sqrt(1 + m11 - m22 - m33);
dst[3] = (m32 - m23) / s;
dst[0] = 0.25 * s;
dst[1] = (m12 + m21) / s;
dst[2] = (m13 + m31) / s;
} else if (m22 > m33) {
const s = 2 * Math.sqrt(1 + m22 - m11 - m33);
dst[3] = (m13 - m31) / s;
dst[0] = (m12 + m21) / s;
dst[1] = 0.25 * s;
dst[2] = (m23 + m32) / s;
} else {
const s = 2 * Math.sqrt(1 + m33 - m11 - m22);
dst[3] = (m21 - m12) / s;
dst[0] = (m13 + m31) / s;
dst[1] = (m23 + m32) / s;
dst[2] = 0.25 * s;
}
}
function decompose(mat, translation, quaternion, scale) {
let sx = m4.length(mat.slice(0, 3));
const sy = m4.length(mat.slice(4, 7));
const sz = m4.length(mat.slice(8, 11));
// if determinate is negative, we need to invert one scale
const det = determinate(mat);
if (det < 0) {
sx = -sx;
}
translation[0] = mat[12];
translation[1] = mat[13];
translation[2] = mat[14];
// scale the rotation part
const matrix = m4.copy(mat);
const invSX = 1 / sx;
const invSY = 1 / sy;
const invSZ = 1 / sz;
matrix[0] *= invSX;
matrix[1] *= invSX;
matrix[2] *= invSX;
matrix[4] *= invSY;
matrix[5] *= invSY;
matrix[6] *= invSY;
matrix[8] *= invSZ;
matrix[9] *= invSZ;
matrix[10] *= invSZ;
quatFromRotationMatrix(matrix, quaternion);
scale[0] = sx;
scale[1] = sy;
scale[2] = sz;
}
function determinate(m) {
var m00 = m[0 * 4 + 0];
var m01 = m[0 * 4 + 1];
var m02 = m[0 * 4 + 2];
var m03 = m[0 * 4 + 3];
var m10 = m[1 * 4 + 0];
var m11 = m[1 * 4 + 1];
var m12 = m[1 * 4 + 2];
var m13 = m[1 * 4 + 3];
var m20 = m[2 * 4 + 0];
var m21 = m[2 * 4 + 1];
var m22 = m[2 * 4 + 2];
var m23 = m[2 * 4 + 3];
var m30 = m[3 * 4 + 0];
var m31 = m[3 * 4 + 1];
var m32 = m[3 * 4 + 2];
var m33 = m[3 * 4 + 3];
var tmp_0 = m22 * m33;
var tmp_1 = m32 * m23;
var tmp_2 = m12 * m33;
var tmp_3 = m32 * m13;
var tmp_4 = m12 * m23;
var tmp_5 = m22 * m13;
var tmp_6 = m02 * m33;
var tmp_7 = m32 * m03;
var tmp_8 = m02 * m23;
var tmp_9 = m22 * m03;
var tmp_10 = m02 * m13;
var tmp_11 = m12 * m03;
var t0 = (tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31) -
(tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31);
var t1 = (tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31) -
(tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31);
var t2 = (tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31) -
(tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31);
var t3 = (tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21) -
(tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21);
return 1.0 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);
}
/**
* Computes the inverse of a matrix.
* @param {Matrix4} m matrix to compute inverse of
* @param {Matrix4} [dst] optional matrix to store result
* @return {Matrix4} dst or a new matrix if none provided
* @memberOf module:webgl-3d-math
*/
function inverse(m, dst) {
dst = dst || new MatType(16);
var m00 = m[0 * 4 + 0];
var m01 = m[0 * 4 + 1];
var m02 = m[0 * 4 + 2];
var m03 = m[0 * 4 + 3];
var m10 = m[1 * 4 + 0];
var m11 = m[1 * 4 + 1];
var m12 = m[1 * 4 + 2];
var m13 = m[1 * 4 + 3];
var m20 = m[2 * 4 + 0];
var m21 = m[2 * 4 + 1];
var m22 = m[2 * 4 + 2];
var m23 = m[2 * 4 + 3];
var m30 = m[3 * 4 + 0];
var m31 = m[3 * 4 + 1];
var m32 = m[3 * 4 + 2];
var m33 = m[3 * 4 + 3];
var tmp_0 = m22 * m33;
var tmp_1 = m32 * m23;
var tmp_2 = m12 * m33;
var tmp_3 = m32 * m13;
var tmp_4 = m12 * m23;
var tmp_5 = m22 * m13;
var tmp_6 = m02 * m33;
var tmp_7 = m32 * m03;
var tmp_8 = m02 * m23;
var tmp_9 = m22 * m03;
var tmp_10 = m02 * m13;
var tmp_11 = m12 * m03;
var tmp_12 = m20 * m31;
var tmp_13 = m30 * m21;
var tmp_14 = m10 * m31;
var tmp_15 = m30 * m11;
var tmp_16 = m10 * m21;
var tmp_17 = m20 * m11;
var tmp_18 = m00 * m31;
var tmp_19 = m30 * m01;
var tmp_20 = m00 * m21;
var tmp_21 = m20 * m01;
var tmp_22 = m00 * m11;
var tmp_23 = m10 * m01;
var t0 = (tmp_0 * m11 + tmp_3 * m21 + tmp_4 * m31) -
(tmp_1 * m11 + tmp_2 * m21 + tmp_5 * m31);
var t1 = (tmp_1 * m01 + tmp_6 * m21 + tmp_9 * m31) -
(tmp_0 * m01 + tmp_7 * m21 + tmp_8 * m31);
var t2 = (tmp_2 * m01 + tmp_7 * m11 + tmp_10 * m31) -
(tmp_3 * m01 + tmp_6 * m11 + tmp_11 * m31);
var t3 = (tmp_5 * m01 + tmp_8 * m11 + tmp_11 * m21) -
(tmp_4 * m01 + tmp_9 * m11 + tmp_10 * m21);
var d = 1.0 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);
dst[0] = d * t0;
dst[1] = d * t1;
dst[2] = d * t2;
dst[3] = d * t3;
dst[4] = d * ((tmp_1 * m10 + tmp_2 * m20 + tmp_5 * m30) -
(tmp_0 * m10 + tmp_3 * m20 + tmp_4 * m30));
dst[5] = d * ((tmp_0 * m00 + tmp_7 * m20 + tmp_8 * m30) -
(tmp_1 * m00 + tmp_6 * m20 + tmp_9 * m30));
dst[6] = d * ((tmp_3 * m00 + tmp_6 * m10 + tmp_11 * m30) -
(tmp_2 * m00 + tmp_7 * m10 + tmp_10 * m30));
dst[7] = d * ((tmp_4 * m00 + tmp_9 * m10 + tmp_10 * m20) -
(tmp_5 * m00 + tmp_8 * m10 + tmp_11 * m20));
dst[8] = d * ((tmp_12 * m13 + tmp_15 * m23 + tmp_16 * m33) -
(tmp_13 * m13 + tmp_14 * m23 + tmp_17 * m33));
dst[9] = d * ((tmp_13 * m03 + tmp_18 * m23 + tmp_21 * m33) -
(tmp_12 * m03 + tmp_19 * m23 + tmp_20 * m33));
dst[10] = d * ((tmp_14 * m03 + tmp_19 * m13 + tmp_22 * m33) -
(tmp_15 * m03 + tmp_18 * m13 + tmp_23 * m33));
dst[11] = d * ((tmp_17 * m03 + tmp_20 * m13 + tmp_23 * m23) -
(tmp_16 * m03 + tmp_21 * m13 + tmp_22 * m23));
dst[12] = d * ((tmp_14 * m22 + tmp_17 * m32 + tmp_13 * m12) -
(tmp_16 * m32 + tmp_12 * m12 + tmp_15 * m22));
dst[13] = d * ((tmp_20 * m32 + tmp_12 * m02 + tmp_19 * m22) -
(tmp_18 * m22 + tmp_21 * m32 + tmp_13 * m02));
dst[14] = d * ((tmp_18 * m12 + tmp_23 * m32 + tmp_15 * m02) -
(tmp_22 * m32 + tmp_14 * m02 + tmp_19 * m12));
dst[15] = d * ((tmp_22 * m22 + tmp_16 * m02 + tmp_21 * m12) -
(tmp_20 * m12 + tmp_23 * m22 + tmp_17 * m02));
return dst;
}
/**
* Takes a matrix and a vector with 4 entries, transforms that vector by
* the matrix, and returns the result as a vector with 4 entries.
* @param {Matrix4} m The matrix.
* @param {Vector4} v The point in homogenous coordinates.
* @param {Vector4} dst optional vector4 to store result
* @return {Vector4} dst or new Vector4 if not provided
* @memberOf module:webgl-3d-math
*/
function transformVector(m, v, dst) {
dst = dst || new MatType(4);
for (var i = 0; i < 4; ++i) {
dst[i] = 0.0;
for (var j = 0; j < 4; ++j) {
dst[i] += v[j] * m[j * 4 + i];
}
}
return dst;
}
/**
* Takes a 4-by-4 matrix and a vector with 3 entries,
* interprets the vector as a point, transforms that point by the matrix, and
* returns the result as a vector with 3 entries.
* @param {Matrix4} m The matrix.
* @param {Vector3} v The point.
* @param {Vector4} dst optional vector4 to store result
* @return {Vector4} dst or new Vector4 if not provided
* @memberOf module:webgl-3d-math
*/
function transformPoint(m, v, dst) {
dst = dst || new MatType(3);
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
var d = v0 * m[0 * 4 + 3] + v1 * m[1 * 4 + 3] + v2 * m[2 * 4 + 3] + m[3 * 4 + 3];
dst[0] = (v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0] + m[3 * 4 + 0]) / d;
dst[1] = (v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1] + m[3 * 4 + 1]) / d;
dst[2] = (v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2] + m[3 * 4 + 2]) / d;
return dst;
}
/**
* Takes a 4-by-4 matrix and a vector with 3 entries, interprets the vector as a
* direction, transforms that direction by the matrix, and returns the result;
* assumes the transformation of 3-dimensional space represented by the matrix
* is parallel-preserving, i.e. any combination of rotation, scaling and
* translation, but not a perspective distortion. Returns a vector with 3
* entries.
* @param {Matrix4} m The matrix.
* @param {Vector3} v The direction.
* @param {Vector4} dst optional vector4 to store result
* @return {Vector4} dst or new Vector4 if not provided
* @memberOf module:webgl-3d-math
*/
function transformDirection(m, v, dst) {
dst = dst || new MatType(3);
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
dst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];
dst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];
dst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];
return dst;
}
/**
* Takes a 4-by-4 matrix m and a vector v with 3 entries, interprets the vector
* as a normal to a surface, and computes a vector which is normal upon
* transforming that surface by the matrix. The effect of this function is the
* same as transforming v (as a direction) by the inverse-transpose of m. This
* function assumes the transformation of 3-dimensional space represented by the
* matrix is parallel-preserving, i.e. any combination of rotation, scaling and
* translation, but not a perspective distortion. Returns a vector with 3
* entries.
* @param {Matrix4} m The matrix.
* @param {Vector3} v The normal.
* @param {Vector3} [dst] The direction.
* @return {Vector3} The transformed direction.
* @memberOf module:webgl-3d-math
*/
function transformNormal(m, v, dst) {
dst = dst || new MatType(3);
var mi = inverse(m);
var v0 = v[0];
var v1 = v[1];
var v2 = v[2];
dst[0] = v0 * mi[0 * 4 + 0] + v1 * mi[0 * 4 + 1] + v2 * mi[0 * 4 + 2];
dst[1] = v0 * mi[1 * 4 + 0] + v1 * mi[1 * 4 + 1] + v2 * mi[1 * 4 + 2];
dst[2] = v0 * mi[2 * 4 + 0] + v1 * mi[2 * 4 + 1] + v2 * mi[2 * 4 + 2];
return dst;
}
function copy(src, dst) {
dst = dst || new MatType(16);
dst[ 0] = src[ 0];
dst[ 1] = src[ 1];
dst[ 2] = src[ 2];
dst[ 3] = src[ 3];
dst[ 4] = src[ 4];
dst[ 5] = src[ 5];
dst[ 6] = src[ 6];
dst[ 7] = src[ 7];
dst[ 8] = src[ 8];
dst[ 9] = src[ 9];
dst[10] = src[10];
dst[11] = src[11];
dst[12] = src[12];
dst[13] = src[13];
dst[14] = src[14];
dst[15] = src[15];
return dst;
}
return {
copy: copy,
lookAt: lookAt,
addVectors: addVectors,
subtractVectors: subtractVectors,
scaleVector: scaleVector,
distance: distance,
distanceSq: distanceSq,
normalize: normalize,
compose: compose,
cross: cross,
decompose: decompose,
dot: dot,
identity: identity,
transpose: transpose,
length: length,
lengthSq: lengthSq,
orthographic: orthographic,
frustum: frustum,
perspective: perspective,
translation: translation,
translate: translate,
xRotation: xRotation,
yRotation: yRotation,
zRotation: zRotation,
xRotate: xRotate,
yRotate: yRotate,
zRotate: zRotate,
axisRotation: axisRotation,
axisRotate: axisRotate,
scaling: scaling,
scale: scale,
multiply: multiply,
inverse: inverse,
transformVector: transformVector,
transformPoint: transformPoint,
transformDirection: transformDirection,
transformNormal: transformNormal,
setDefaultType: setDefaultType,
};
}));