StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics
https://doi.org/10.1109/TVCG.2020.3030352
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1814 lines
47 KiB
1814 lines
47 KiB
4 years ago
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import * as glMatrix from "./common.js";
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/**
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* 4x4 Matrix<br>Format: column-major, when typed out it looks like row-major<br>The matrices are being post multiplied.
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* @module mat4
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*/
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/**
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* Creates a new identity mat4
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*
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* @returns {mat4} a new 4x4 matrix
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*/
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export function create() {
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var out = new glMatrix.ARRAY_TYPE(16);
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if (glMatrix.ARRAY_TYPE != Float32Array) {
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out[1] = 0;
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out[2] = 0;
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out[3] = 0;
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out[4] = 0;
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out[6] = 0;
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out[7] = 0;
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out[8] = 0;
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out[9] = 0;
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out[11] = 0;
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out[12] = 0;
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out[13] = 0;
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out[14] = 0;
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}
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out[0] = 1;
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out[5] = 1;
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out[10] = 1;
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out[15] = 1;
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return out;
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}
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/**
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* Creates a new mat4 initialized with values from an existing matrix
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*
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* @param {mat4} a matrix to clone
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* @returns {mat4} a new 4x4 matrix
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*/
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export function clone(a) {
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var out = new glMatrix.ARRAY_TYPE(16);
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out[0] = a[0];
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out[1] = a[1];
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out[2] = a[2];
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out[3] = a[3];
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out[4] = a[4];
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out[5] = a[5];
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out[6] = a[6];
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out[7] = a[7];
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out[8] = a[8];
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out[9] = a[9];
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out[10] = a[10];
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out[11] = a[11];
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out[12] = a[12];
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out[13] = a[13];
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out[14] = a[14];
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out[15] = a[15];
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return out;
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}
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/**
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* Copy the values from one mat4 to another
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*
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* @param {mat4} out the receiving matrix
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* @param {mat4} a the source matrix
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* @returns {mat4} out
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*/
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export function copy(out, a) {
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out[0] = a[0];
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out[1] = a[1];
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out[2] = a[2];
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out[3] = a[3];
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out[4] = a[4];
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out[5] = a[5];
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out[6] = a[6];
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out[7] = a[7];
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out[8] = a[8];
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out[9] = a[9];
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out[10] = a[10];
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out[11] = a[11];
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out[12] = a[12];
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out[13] = a[13];
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out[14] = a[14];
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out[15] = a[15];
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return out;
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}
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/**
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* Create a new mat4 with the given values
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*
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* @param {Number} m00 Component in column 0, row 0 position (index 0)
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* @param {Number} m01 Component in column 0, row 1 position (index 1)
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* @param {Number} m02 Component in column 0, row 2 position (index 2)
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* @param {Number} m03 Component in column 0, row 3 position (index 3)
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* @param {Number} m10 Component in column 1, row 0 position (index 4)
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* @param {Number} m11 Component in column 1, row 1 position (index 5)
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* @param {Number} m12 Component in column 1, row 2 position (index 6)
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* @param {Number} m13 Component in column 1, row 3 position (index 7)
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* @param {Number} m20 Component in column 2, row 0 position (index 8)
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* @param {Number} m21 Component in column 2, row 1 position (index 9)
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* @param {Number} m22 Component in column 2, row 2 position (index 10)
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* @param {Number} m23 Component in column 2, row 3 position (index 11)
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* @param {Number} m30 Component in column 3, row 0 position (index 12)
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* @param {Number} m31 Component in column 3, row 1 position (index 13)
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* @param {Number} m32 Component in column 3, row 2 position (index 14)
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* @param {Number} m33 Component in column 3, row 3 position (index 15)
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* @returns {mat4} A new mat4
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*/
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export function fromValues(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
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var out = new glMatrix.ARRAY_TYPE(16);
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out[0] = m00;
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out[1] = m01;
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out[2] = m02;
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out[3] = m03;
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out[4] = m10;
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out[5] = m11;
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out[6] = m12;
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out[7] = m13;
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out[8] = m20;
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out[9] = m21;
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out[10] = m22;
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out[11] = m23;
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out[12] = m30;
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out[13] = m31;
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out[14] = m32;
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out[15] = m33;
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return out;
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}
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/**
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* Set the components of a mat4 to the given values
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*
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* @param {mat4} out the receiving matrix
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* @param {Number} m00 Component in column 0, row 0 position (index 0)
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* @param {Number} m01 Component in column 0, row 1 position (index 1)
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* @param {Number} m02 Component in column 0, row 2 position (index 2)
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* @param {Number} m03 Component in column 0, row 3 position (index 3)
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* @param {Number} m10 Component in column 1, row 0 position (index 4)
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* @param {Number} m11 Component in column 1, row 1 position (index 5)
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* @param {Number} m12 Component in column 1, row 2 position (index 6)
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* @param {Number} m13 Component in column 1, row 3 position (index 7)
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* @param {Number} m20 Component in column 2, row 0 position (index 8)
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* @param {Number} m21 Component in column 2, row 1 position (index 9)
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* @param {Number} m22 Component in column 2, row 2 position (index 10)
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* @param {Number} m23 Component in column 2, row 3 position (index 11)
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* @param {Number} m30 Component in column 3, row 0 position (index 12)
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* @param {Number} m31 Component in column 3, row 1 position (index 13)
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* @param {Number} m32 Component in column 3, row 2 position (index 14)
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* @param {Number} m33 Component in column 3, row 3 position (index 15)
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* @returns {mat4} out
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*/
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export function set(out, m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
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out[0] = m00;
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out[1] = m01;
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out[2] = m02;
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out[3] = m03;
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out[4] = m10;
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out[5] = m11;
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out[6] = m12;
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out[7] = m13;
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out[8] = m20;
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out[9] = m21;
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out[10] = m22;
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out[11] = m23;
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out[12] = m30;
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out[13] = m31;
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out[14] = m32;
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out[15] = m33;
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return out;
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}
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/**
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* Set a mat4 to the identity matrix
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*
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* @param {mat4} out the receiving matrix
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* @returns {mat4} out
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*/
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export function identity(out) {
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out[0] = 1;
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out[1] = 0;
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out[2] = 0;
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out[3] = 0;
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out[4] = 0;
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out[5] = 1;
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out[6] = 0;
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out[7] = 0;
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out[8] = 0;
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out[9] = 0;
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out[10] = 1;
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out[11] = 0;
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out[12] = 0;
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out[13] = 0;
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out[14] = 0;
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out[15] = 1;
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return out;
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}
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/**
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* Transpose the values of a mat4
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*
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* @param {mat4} out the receiving matrix
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* @param {mat4} a the source matrix
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* @returns {mat4} out
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*/
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export function transpose(out, a) {
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// If we are transposing ourselves we can skip a few steps but have to cache some values
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if (out === a) {
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var a01 = a[1],
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a02 = a[2],
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a03 = a[3];
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var a12 = a[6],
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a13 = a[7];
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var a23 = a[11];
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out[1] = a[4];
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out[2] = a[8];
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out[3] = a[12];
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out[4] = a01;
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out[6] = a[9];
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out[7] = a[13];
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out[8] = a02;
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out[9] = a12;
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out[11] = a[14];
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out[12] = a03;
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out[13] = a13;
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out[14] = a23;
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} else {
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out[0] = a[0];
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out[1] = a[4];
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out[2] = a[8];
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out[3] = a[12];
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out[4] = a[1];
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out[5] = a[5];
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out[6] = a[9];
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out[7] = a[13];
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out[8] = a[2];
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out[9] = a[6];
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out[10] = a[10];
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out[11] = a[14];
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out[12] = a[3];
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out[13] = a[7];
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out[14] = a[11];
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out[15] = a[15];
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}
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return out;
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}
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/**
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* Inverts a mat4
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*
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* @param {mat4} out the receiving matrix
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* @param {mat4} a the source matrix
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* @returns {mat4} out
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*/
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export function invert(out, a) {
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var a00 = a[0],
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a01 = a[1],
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a02 = a[2],
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a03 = a[3];
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var a10 = a[4],
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a11 = a[5],
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a12 = a[6],
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a13 = a[7];
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var a20 = a[8],
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a21 = a[9],
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a22 = a[10],
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a23 = a[11];
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var a30 = a[12],
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a31 = a[13],
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a32 = a[14],
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a33 = a[15];
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var b00 = a00 * a11 - a01 * a10;
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var b01 = a00 * a12 - a02 * a10;
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var b02 = a00 * a13 - a03 * a10;
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var b03 = a01 * a12 - a02 * a11;
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var b04 = a01 * a13 - a03 * a11;
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var b05 = a02 * a13 - a03 * a12;
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var b06 = a20 * a31 - a21 * a30;
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var b07 = a20 * a32 - a22 * a30;
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var b08 = a20 * a33 - a23 * a30;
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var b09 = a21 * a32 - a22 * a31;
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var b10 = a21 * a33 - a23 * a31;
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var b11 = a22 * a33 - a23 * a32; // Calculate the determinant
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var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
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if (!det) {
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return null;
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}
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det = 1.0 / det;
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out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
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out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
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out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
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out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
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out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
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out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
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out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
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out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
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out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
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out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
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out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
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out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
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out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
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out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
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out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
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out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
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return out;
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}
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/**
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* Calculates the adjugate of a mat4
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*
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* @param {mat4} out the receiving matrix
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* @param {mat4} a the source matrix
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* @returns {mat4} out
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*/
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export function adjoint(out, a) {
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var a00 = a[0],
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a01 = a[1],
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a02 = a[2],
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a03 = a[3];
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var a10 = a[4],
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a11 = a[5],
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a12 = a[6],
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a13 = a[7];
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var a20 = a[8],
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a21 = a[9],
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a22 = a[10],
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a23 = a[11];
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var a30 = a[12],
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a31 = a[13],
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a32 = a[14],
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a33 = a[15];
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out[0] = a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22);
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|
|
out[1] = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
|
||
|
|
out[2] = a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12);
|
||
|
|
out[3] = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
|
||
|
|
out[4] = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
|
||
|
|
out[5] = a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22);
|
||
|
|
out[6] = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
|
||
|
|
out[7] = a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12);
|
||
|
|
out[8] = a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21);
|
||
|
|
out[9] = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
|
||
|
|
out[10] = a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11);
|
||
|
|
out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
|
||
|
|
out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
|
||
|
|
out[13] = a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21);
|
||
|
|
out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
|
||
|
|
out[15] = a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11);
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Calculates the determinant of a mat4
|
||
|
|
*
|
||
|
|
* @param {mat4} a the source matrix
|
||
|
|
* @returns {Number} determinant of a
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function determinant(a) {
|
||
|
|
var a00 = a[0],
|
||
|
|
a01 = a[1],
|
||
|
|
a02 = a[2],
|
||
|
|
a03 = a[3];
|
||
|
|
var a10 = a[4],
|
||
|
|
a11 = a[5],
|
||
|
|
a12 = a[6],
|
||
|
|
a13 = a[7];
|
||
|
|
var a20 = a[8],
|
||
|
|
a21 = a[9],
|
||
|
|
a22 = a[10],
|
||
|
|
a23 = a[11];
|
||
|
|
var a30 = a[12],
|
||
|
|
a31 = a[13],
|
||
|
|
a32 = a[14],
|
||
|
|
a33 = a[15];
|
||
|
|
var b00 = a00 * a11 - a01 * a10;
|
||
|
|
var b01 = a00 * a12 - a02 * a10;
|
||
|
|
var b02 = a00 * a13 - a03 * a10;
|
||
|
|
var b03 = a01 * a12 - a02 * a11;
|
||
|
|
var b04 = a01 * a13 - a03 * a11;
|
||
|
|
var b05 = a02 * a13 - a03 * a12;
|
||
|
|
var b06 = a20 * a31 - a21 * a30;
|
||
|
|
var b07 = a20 * a32 - a22 * a30;
|
||
|
|
var b08 = a20 * a33 - a23 * a30;
|
||
|
|
var b09 = a21 * a32 - a22 * a31;
|
||
|
|
var b10 = a21 * a33 - a23 * a31;
|
||
|
|
var b11 = a22 * a33 - a23 * a32; // Calculate the determinant
|
||
|
|
|
||
|
|
return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Multiplies two mat4s
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the first operand
|
||
|
|
* @param {mat4} b the second operand
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function multiply(out, a, b) {
|
||
|
|
var a00 = a[0],
|
||
|
|
a01 = a[1],
|
||
|
|
a02 = a[2],
|
||
|
|
a03 = a[3];
|
||
|
|
var a10 = a[4],
|
||
|
|
a11 = a[5],
|
||
|
|
a12 = a[6],
|
||
|
|
a13 = a[7];
|
||
|
|
var a20 = a[8],
|
||
|
|
a21 = a[9],
|
||
|
|
a22 = a[10],
|
||
|
|
a23 = a[11];
|
||
|
|
var a30 = a[12],
|
||
|
|
a31 = a[13],
|
||
|
|
a32 = a[14],
|
||
|
|
a33 = a[15]; // Cache only the current line of the second matrix
|
||
|
|
|
||
|
|
var b0 = b[0],
|
||
|
|
b1 = b[1],
|
||
|
|
b2 = b[2],
|
||
|
|
b3 = b[3];
|
||
|
|
out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
|
||
|
|
out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
|
||
|
|
out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
|
||
|
|
out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
|
||
|
|
b0 = b[4];
|
||
|
|
b1 = b[5];
|
||
|
|
b2 = b[6];
|
||
|
|
b3 = b[7];
|
||
|
|
out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
|
||
|
|
out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
|
||
|
|
out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
|
||
|
|
out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
|
||
|
|
b0 = b[8];
|
||
|
|
b1 = b[9];
|
||
|
|
b2 = b[10];
|
||
|
|
b3 = b[11];
|
||
|
|
out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
|
||
|
|
out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
|
||
|
|
out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
|
||
|
|
out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
|
||
|
|
b0 = b[12];
|
||
|
|
b1 = b[13];
|
||
|
|
b2 = b[14];
|
||
|
|
b3 = b[15];
|
||
|
|
out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
|
||
|
|
out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
|
||
|
|
out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
|
||
|
|
out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Translate a mat4 by the given vector
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the matrix to translate
|
||
|
|
* @param {vec3} v vector to translate by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function translate(out, a, v) {
|
||
|
|
var x = v[0],
|
||
|
|
y = v[1],
|
||
|
|
z = v[2];
|
||
|
|
var a00, a01, a02, a03;
|
||
|
|
var a10, a11, a12, a13;
|
||
|
|
var a20, a21, a22, a23;
|
||
|
|
|
||
|
|
if (a === out) {
|
||
|
|
out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
|
||
|
|
out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
|
||
|
|
out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
|
||
|
|
out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
|
||
|
|
} else {
|
||
|
|
a00 = a[0];
|
||
|
|
a01 = a[1];
|
||
|
|
a02 = a[2];
|
||
|
|
a03 = a[3];
|
||
|
|
a10 = a[4];
|
||
|
|
a11 = a[5];
|
||
|
|
a12 = a[6];
|
||
|
|
a13 = a[7];
|
||
|
|
a20 = a[8];
|
||
|
|
a21 = a[9];
|
||
|
|
a22 = a[10];
|
||
|
|
a23 = a[11];
|
||
|
|
out[0] = a00;
|
||
|
|
out[1] = a01;
|
||
|
|
out[2] = a02;
|
||
|
|
out[3] = a03;
|
||
|
|
out[4] = a10;
|
||
|
|
out[5] = a11;
|
||
|
|
out[6] = a12;
|
||
|
|
out[7] = a13;
|
||
|
|
out[8] = a20;
|
||
|
|
out[9] = a21;
|
||
|
|
out[10] = a22;
|
||
|
|
out[11] = a23;
|
||
|
|
out[12] = a00 * x + a10 * y + a20 * z + a[12];
|
||
|
|
out[13] = a01 * x + a11 * y + a21 * z + a[13];
|
||
|
|
out[14] = a02 * x + a12 * y + a22 * z + a[14];
|
||
|
|
out[15] = a03 * x + a13 * y + a23 * z + a[15];
|
||
|
|
}
|
||
|
|
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Scales the mat4 by the dimensions in the given vec3 not using vectorization
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the matrix to scale
|
||
|
|
* @param {vec3} v the vec3 to scale the matrix by
|
||
|
|
* @returns {mat4} out
|
||
|
|
**/
|
||
|
|
|
||
|
|
export function scale(out, a, v) {
|
||
|
|
var x = v[0],
|
||
|
|
y = v[1],
|
||
|
|
z = v[2];
|
||
|
|
out[0] = a[0] * x;
|
||
|
|
out[1] = a[1] * x;
|
||
|
|
out[2] = a[2] * x;
|
||
|
|
out[3] = a[3] * x;
|
||
|
|
out[4] = a[4] * y;
|
||
|
|
out[5] = a[5] * y;
|
||
|
|
out[6] = a[6] * y;
|
||
|
|
out[7] = a[7] * y;
|
||
|
|
out[8] = a[8] * z;
|
||
|
|
out[9] = a[9] * z;
|
||
|
|
out[10] = a[10] * z;
|
||
|
|
out[11] = a[11] * z;
|
||
|
|
out[12] = a[12];
|
||
|
|
out[13] = a[13];
|
||
|
|
out[14] = a[14];
|
||
|
|
out[15] = a[15];
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Rotates a mat4 by the given angle around the given axis
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the matrix to rotate
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @param {vec3} axis the axis to rotate around
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function rotate(out, a, rad, axis) {
|
||
|
|
var x = axis[0],
|
||
|
|
y = axis[1],
|
||
|
|
z = axis[2];
|
||
|
|
var len = Math.hypot(x, y, z);
|
||
|
|
var s, c, t;
|
||
|
|
var a00, a01, a02, a03;
|
||
|
|
var a10, a11, a12, a13;
|
||
|
|
var a20, a21, a22, a23;
|
||
|
|
var b00, b01, b02;
|
||
|
|
var b10, b11, b12;
|
||
|
|
var b20, b21, b22;
|
||
|
|
|
||
|
|
if (len < glMatrix.EPSILON) {
|
||
|
|
return null;
|
||
|
|
}
|
||
|
|
|
||
|
|
len = 1 / len;
|
||
|
|
x *= len;
|
||
|
|
y *= len;
|
||
|
|
z *= len;
|
||
|
|
s = Math.sin(rad);
|
||
|
|
c = Math.cos(rad);
|
||
|
|
t = 1 - c;
|
||
|
|
a00 = a[0];
|
||
|
|
a01 = a[1];
|
||
|
|
a02 = a[2];
|
||
|
|
a03 = a[3];
|
||
|
|
a10 = a[4];
|
||
|
|
a11 = a[5];
|
||
|
|
a12 = a[6];
|
||
|
|
a13 = a[7];
|
||
|
|
a20 = a[8];
|
||
|
|
a21 = a[9];
|
||
|
|
a22 = a[10];
|
||
|
|
a23 = a[11]; // Construct the elements of the rotation matrix
|
||
|
|
|
||
|
|
b00 = x * x * t + c;
|
||
|
|
b01 = y * x * t + z * s;
|
||
|
|
b02 = z * x * t - y * s;
|
||
|
|
b10 = x * y * t - z * s;
|
||
|
|
b11 = y * y * t + c;
|
||
|
|
b12 = z * y * t + x * s;
|
||
|
|
b20 = x * z * t + y * s;
|
||
|
|
b21 = y * z * t - x * s;
|
||
|
|
b22 = z * z * t + c; // Perform rotation-specific matrix multiplication
|
||
|
|
|
||
|
|
out[0] = a00 * b00 + a10 * b01 + a20 * b02;
|
||
|
|
out[1] = a01 * b00 + a11 * b01 + a21 * b02;
|
||
|
|
out[2] = a02 * b00 + a12 * b01 + a22 * b02;
|
||
|
|
out[3] = a03 * b00 + a13 * b01 + a23 * b02;
|
||
|
|
out[4] = a00 * b10 + a10 * b11 + a20 * b12;
|
||
|
|
out[5] = a01 * b10 + a11 * b11 + a21 * b12;
|
||
|
|
out[6] = a02 * b10 + a12 * b11 + a22 * b12;
|
||
|
|
out[7] = a03 * b10 + a13 * b11 + a23 * b12;
|
||
|
|
out[8] = a00 * b20 + a10 * b21 + a20 * b22;
|
||
|
|
out[9] = a01 * b20 + a11 * b21 + a21 * b22;
|
||
|
|
out[10] = a02 * b20 + a12 * b21 + a22 * b22;
|
||
|
|
out[11] = a03 * b20 + a13 * b21 + a23 * b22;
|
||
|
|
|
||
|
|
if (a !== out) {
|
||
|
|
// If the source and destination differ, copy the unchanged last row
|
||
|
|
out[12] = a[12];
|
||
|
|
out[13] = a[13];
|
||
|
|
out[14] = a[14];
|
||
|
|
out[15] = a[15];
|
||
|
|
}
|
||
|
|
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Rotates a matrix by the given angle around the X axis
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the matrix to rotate
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function rotateX(out, a, rad) {
|
||
|
|
var s = Math.sin(rad);
|
||
|
|
var c = Math.cos(rad);
|
||
|
|
var a10 = a[4];
|
||
|
|
var a11 = a[5];
|
||
|
|
var a12 = a[6];
|
||
|
|
var a13 = a[7];
|
||
|
|
var a20 = a[8];
|
||
|
|
var a21 = a[9];
|
||
|
|
var a22 = a[10];
|
||
|
|
var a23 = a[11];
|
||
|
|
|
||
|
|
if (a !== out) {
|
||
|
|
// If the source and destination differ, copy the unchanged rows
|
||
|
|
out[0] = a[0];
|
||
|
|
out[1] = a[1];
|
||
|
|
out[2] = a[2];
|
||
|
|
out[3] = a[3];
|
||
|
|
out[12] = a[12];
|
||
|
|
out[13] = a[13];
|
||
|
|
out[14] = a[14];
|
||
|
|
out[15] = a[15];
|
||
|
|
} // Perform axis-specific matrix multiplication
|
||
|
|
|
||
|
|
|
||
|
|
out[4] = a10 * c + a20 * s;
|
||
|
|
out[5] = a11 * c + a21 * s;
|
||
|
|
out[6] = a12 * c + a22 * s;
|
||
|
|
out[7] = a13 * c + a23 * s;
|
||
|
|
out[8] = a20 * c - a10 * s;
|
||
|
|
out[9] = a21 * c - a11 * s;
|
||
|
|
out[10] = a22 * c - a12 * s;
|
||
|
|
out[11] = a23 * c - a13 * s;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Rotates a matrix by the given angle around the Y axis
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the matrix to rotate
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function rotateY(out, a, rad) {
|
||
|
|
var s = Math.sin(rad);
|
||
|
|
var c = Math.cos(rad);
|
||
|
|
var a00 = a[0];
|
||
|
|
var a01 = a[1];
|
||
|
|
var a02 = a[2];
|
||
|
|
var a03 = a[3];
|
||
|
|
var a20 = a[8];
|
||
|
|
var a21 = a[9];
|
||
|
|
var a22 = a[10];
|
||
|
|
var a23 = a[11];
|
||
|
|
|
||
|
|
if (a !== out) {
|
||
|
|
// If the source and destination differ, copy the unchanged rows
|
||
|
|
out[4] = a[4];
|
||
|
|
out[5] = a[5];
|
||
|
|
out[6] = a[6];
|
||
|
|
out[7] = a[7];
|
||
|
|
out[12] = a[12];
|
||
|
|
out[13] = a[13];
|
||
|
|
out[14] = a[14];
|
||
|
|
out[15] = a[15];
|
||
|
|
} // Perform axis-specific matrix multiplication
|
||
|
|
|
||
|
|
|
||
|
|
out[0] = a00 * c - a20 * s;
|
||
|
|
out[1] = a01 * c - a21 * s;
|
||
|
|
out[2] = a02 * c - a22 * s;
|
||
|
|
out[3] = a03 * c - a23 * s;
|
||
|
|
out[8] = a00 * s + a20 * c;
|
||
|
|
out[9] = a01 * s + a21 * c;
|
||
|
|
out[10] = a02 * s + a22 * c;
|
||
|
|
out[11] = a03 * s + a23 * c;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Rotates a matrix by the given angle around the Z axis
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the matrix to rotate
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function rotateZ(out, a, rad) {
|
||
|
|
var s = Math.sin(rad);
|
||
|
|
var c = Math.cos(rad);
|
||
|
|
var a00 = a[0];
|
||
|
|
var a01 = a[1];
|
||
|
|
var a02 = a[2];
|
||
|
|
var a03 = a[3];
|
||
|
|
var a10 = a[4];
|
||
|
|
var a11 = a[5];
|
||
|
|
var a12 = a[6];
|
||
|
|
var a13 = a[7];
|
||
|
|
|
||
|
|
if (a !== out) {
|
||
|
|
// If the source and destination differ, copy the unchanged last row
|
||
|
|
out[8] = a[8];
|
||
|
|
out[9] = a[9];
|
||
|
|
out[10] = a[10];
|
||
|
|
out[11] = a[11];
|
||
|
|
out[12] = a[12];
|
||
|
|
out[13] = a[13];
|
||
|
|
out[14] = a[14];
|
||
|
|
out[15] = a[15];
|
||
|
|
} // Perform axis-specific matrix multiplication
|
||
|
|
|
||
|
|
|
||
|
|
out[0] = a00 * c + a10 * s;
|
||
|
|
out[1] = a01 * c + a11 * s;
|
||
|
|
out[2] = a02 * c + a12 * s;
|
||
|
|
out[3] = a03 * c + a13 * s;
|
||
|
|
out[4] = a10 * c - a00 * s;
|
||
|
|
out[5] = a11 * c - a01 * s;
|
||
|
|
out[6] = a12 * c - a02 * s;
|
||
|
|
out[7] = a13 * c - a03 * s;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from a vector translation
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.translate(dest, dest, vec);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {vec3} v Translation vector
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromTranslation(out, v) {
|
||
|
|
out[0] = 1;
|
||
|
|
out[1] = 0;
|
||
|
|
out[2] = 0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = 0;
|
||
|
|
out[5] = 1;
|
||
|
|
out[6] = 0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = 0;
|
||
|
|
out[9] = 0;
|
||
|
|
out[10] = 1;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = v[0];
|
||
|
|
out[13] = v[1];
|
||
|
|
out[14] = v[2];
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from a vector scaling
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.scale(dest, dest, vec);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {vec3} v Scaling vector
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromScaling(out, v) {
|
||
|
|
out[0] = v[0];
|
||
|
|
out[1] = 0;
|
||
|
|
out[2] = 0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = 0;
|
||
|
|
out[5] = v[1];
|
||
|
|
out[6] = 0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = 0;
|
||
|
|
out[9] = 0;
|
||
|
|
out[10] = v[2];
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[14] = 0;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from a given angle around a given axis
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.rotate(dest, dest, rad, axis);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @param {vec3} axis the axis to rotate around
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromRotation(out, rad, axis) {
|
||
|
|
var x = axis[0],
|
||
|
|
y = axis[1],
|
||
|
|
z = axis[2];
|
||
|
|
var len = Math.hypot(x, y, z);
|
||
|
|
var s, c, t;
|
||
|
|
|
||
|
|
if (len < glMatrix.EPSILON) {
|
||
|
|
return null;
|
||
|
|
}
|
||
|
|
|
||
|
|
len = 1 / len;
|
||
|
|
x *= len;
|
||
|
|
y *= len;
|
||
|
|
z *= len;
|
||
|
|
s = Math.sin(rad);
|
||
|
|
c = Math.cos(rad);
|
||
|
|
t = 1 - c; // Perform rotation-specific matrix multiplication
|
||
|
|
|
||
|
|
out[0] = x * x * t + c;
|
||
|
|
out[1] = y * x * t + z * s;
|
||
|
|
out[2] = z * x * t - y * s;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = x * y * t - z * s;
|
||
|
|
out[5] = y * y * t + c;
|
||
|
|
out[6] = z * y * t + x * s;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = x * z * t + y * s;
|
||
|
|
out[9] = y * z * t - x * s;
|
||
|
|
out[10] = z * z * t + c;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[14] = 0;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from the given angle around the X axis
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.rotateX(dest, dest, rad);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromXRotation(out, rad) {
|
||
|
|
var s = Math.sin(rad);
|
||
|
|
var c = Math.cos(rad); // Perform axis-specific matrix multiplication
|
||
|
|
|
||
|
|
out[0] = 1;
|
||
|
|
out[1] = 0;
|
||
|
|
out[2] = 0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = 0;
|
||
|
|
out[5] = c;
|
||
|
|
out[6] = s;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = 0;
|
||
|
|
out[9] = -s;
|
||
|
|
out[10] = c;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[14] = 0;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from the given angle around the Y axis
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.rotateY(dest, dest, rad);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromYRotation(out, rad) {
|
||
|
|
var s = Math.sin(rad);
|
||
|
|
var c = Math.cos(rad); // Perform axis-specific matrix multiplication
|
||
|
|
|
||
|
|
out[0] = c;
|
||
|
|
out[1] = 0;
|
||
|
|
out[2] = -s;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = 0;
|
||
|
|
out[5] = 1;
|
||
|
|
out[6] = 0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = s;
|
||
|
|
out[9] = 0;
|
||
|
|
out[10] = c;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[14] = 0;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from the given angle around the Z axis
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.rotateZ(dest, dest, rad);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {Number} rad the angle to rotate the matrix by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromZRotation(out, rad) {
|
||
|
|
var s = Math.sin(rad);
|
||
|
|
var c = Math.cos(rad); // Perform axis-specific matrix multiplication
|
||
|
|
|
||
|
|
out[0] = c;
|
||
|
|
out[1] = s;
|
||
|
|
out[2] = 0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = -s;
|
||
|
|
out[5] = c;
|
||
|
|
out[6] = 0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = 0;
|
||
|
|
out[9] = 0;
|
||
|
|
out[10] = 1;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[14] = 0;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from a quaternion rotation and vector translation
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.translate(dest, vec);
|
||
|
|
* let quatMat = mat4.create();
|
||
|
|
* quat4.toMat4(quat, quatMat);
|
||
|
|
* mat4.multiply(dest, quatMat);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {quat4} q Rotation quaternion
|
||
|
|
* @param {vec3} v Translation vector
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromRotationTranslation(out, q, v) {
|
||
|
|
// Quaternion math
|
||
|
|
var x = q[0],
|
||
|
|
y = q[1],
|
||
|
|
z = q[2],
|
||
|
|
w = q[3];
|
||
|
|
var x2 = x + x;
|
||
|
|
var y2 = y + y;
|
||
|
|
var z2 = z + z;
|
||
|
|
var xx = x * x2;
|
||
|
|
var xy = x * y2;
|
||
|
|
var xz = x * z2;
|
||
|
|
var yy = y * y2;
|
||
|
|
var yz = y * z2;
|
||
|
|
var zz = z * z2;
|
||
|
|
var wx = w * x2;
|
||
|
|
var wy = w * y2;
|
||
|
|
var wz = w * z2;
|
||
|
|
out[0] = 1 - (yy + zz);
|
||
|
|
out[1] = xy + wz;
|
||
|
|
out[2] = xz - wy;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = xy - wz;
|
||
|
|
out[5] = 1 - (xx + zz);
|
||
|
|
out[6] = yz + wx;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = xz + wy;
|
||
|
|
out[9] = yz - wx;
|
||
|
|
out[10] = 1 - (xx + yy);
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = v[0];
|
||
|
|
out[13] = v[1];
|
||
|
|
out[14] = v[2];
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a new mat4 from a dual quat.
|
||
|
|
*
|
||
|
|
* @param {mat4} out Matrix
|
||
|
|
* @param {quat2} a Dual Quaternion
|
||
|
|
* @returns {mat4} mat4 receiving operation result
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromQuat2(out, a) {
|
||
|
|
var translation = new glMatrix.ARRAY_TYPE(3);
|
||
|
|
var bx = -a[0],
|
||
|
|
by = -a[1],
|
||
|
|
bz = -a[2],
|
||
|
|
bw = a[3],
|
||
|
|
ax = a[4],
|
||
|
|
ay = a[5],
|
||
|
|
az = a[6],
|
||
|
|
aw = a[7];
|
||
|
|
var magnitude = bx * bx + by * by + bz * bz + bw * bw; //Only scale if it makes sense
|
||
|
|
|
||
|
|
if (magnitude > 0) {
|
||
|
|
translation[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2 / magnitude;
|
||
|
|
translation[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2 / magnitude;
|
||
|
|
translation[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2 / magnitude;
|
||
|
|
} else {
|
||
|
|
translation[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2;
|
||
|
|
translation[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2;
|
||
|
|
translation[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2;
|
||
|
|
}
|
||
|
|
|
||
|
|
fromRotationTranslation(out, a, translation);
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Returns the translation vector component of a transformation
|
||
|
|
* matrix. If a matrix is built with fromRotationTranslation,
|
||
|
|
* the returned vector will be the same as the translation vector
|
||
|
|
* originally supplied.
|
||
|
|
* @param {vec3} out Vector to receive translation component
|
||
|
|
* @param {mat4} mat Matrix to be decomposed (input)
|
||
|
|
* @return {vec3} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function getTranslation(out, mat) {
|
||
|
|
out[0] = mat[12];
|
||
|
|
out[1] = mat[13];
|
||
|
|
out[2] = mat[14];
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Returns the scaling factor component of a transformation
|
||
|
|
* matrix. If a matrix is built with fromRotationTranslationScale
|
||
|
|
* with a normalized Quaternion paramter, the returned vector will be
|
||
|
|
* the same as the scaling vector
|
||
|
|
* originally supplied.
|
||
|
|
* @param {vec3} out Vector to receive scaling factor component
|
||
|
|
* @param {mat4} mat Matrix to be decomposed (input)
|
||
|
|
* @return {vec3} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function getScaling(out, mat) {
|
||
|
|
var m11 = mat[0];
|
||
|
|
var m12 = mat[1];
|
||
|
|
var m13 = mat[2];
|
||
|
|
var m21 = mat[4];
|
||
|
|
var m22 = mat[5];
|
||
|
|
var m23 = mat[6];
|
||
|
|
var m31 = mat[8];
|
||
|
|
var m32 = mat[9];
|
||
|
|
var m33 = mat[10];
|
||
|
|
out[0] = Math.hypot(m11, m12, m13);
|
||
|
|
out[1] = Math.hypot(m21, m22, m23);
|
||
|
|
out[2] = Math.hypot(m31, m32, m33);
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Returns a quaternion representing the rotational component
|
||
|
|
* of a transformation matrix. If a matrix is built with
|
||
|
|
* fromRotationTranslation, the returned quaternion will be the
|
||
|
|
* same as the quaternion originally supplied.
|
||
|
|
* @param {quat} out Quaternion to receive the rotation component
|
||
|
|
* @param {mat4} mat Matrix to be decomposed (input)
|
||
|
|
* @return {quat} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function getRotation(out, mat) {
|
||
|
|
var scaling = new glMatrix.ARRAY_TYPE(3);
|
||
|
|
getScaling(scaling, mat);
|
||
|
|
var is1 = 1 / scaling[0];
|
||
|
|
var is2 = 1 / scaling[1];
|
||
|
|
var is3 = 1 / scaling[2];
|
||
|
|
var sm11 = mat[0] * is1;
|
||
|
|
var sm12 = mat[1] * is2;
|
||
|
|
var sm13 = mat[2] * is3;
|
||
|
|
var sm21 = mat[4] * is1;
|
||
|
|
var sm22 = mat[5] * is2;
|
||
|
|
var sm23 = mat[6] * is3;
|
||
|
|
var sm31 = mat[8] * is1;
|
||
|
|
var sm32 = mat[9] * is2;
|
||
|
|
var sm33 = mat[10] * is3;
|
||
|
|
var trace = sm11 + sm22 + sm33;
|
||
|
|
var S = 0;
|
||
|
|
|
||
|
|
if (trace > 0) {
|
||
|
|
S = Math.sqrt(trace + 1.0) * 2;
|
||
|
|
out[3] = 0.25 * S;
|
||
|
|
out[0] = (sm23 - sm32) / S;
|
||
|
|
out[1] = (sm31 - sm13) / S;
|
||
|
|
out[2] = (sm12 - sm21) / S;
|
||
|
|
} else if (sm11 > sm22 && sm11 > sm33) {
|
||
|
|
S = Math.sqrt(1.0 + sm11 - sm22 - sm33) * 2;
|
||
|
|
out[3] = (sm23 - sm32) / S;
|
||
|
|
out[0] = 0.25 * S;
|
||
|
|
out[1] = (sm12 + sm21) / S;
|
||
|
|
out[2] = (sm31 + sm13) / S;
|
||
|
|
} else if (sm22 > sm33) {
|
||
|
|
S = Math.sqrt(1.0 + sm22 - sm11 - sm33) * 2;
|
||
|
|
out[3] = (sm31 - sm13) / S;
|
||
|
|
out[0] = (sm12 + sm21) / S;
|
||
|
|
out[1] = 0.25 * S;
|
||
|
|
out[2] = (sm23 + sm32) / S;
|
||
|
|
} else {
|
||
|
|
S = Math.sqrt(1.0 + sm33 - sm11 - sm22) * 2;
|
||
|
|
out[3] = (sm12 - sm21) / S;
|
||
|
|
out[0] = (sm31 + sm13) / S;
|
||
|
|
out[1] = (sm23 + sm32) / S;
|
||
|
|
out[2] = 0.25 * S;
|
||
|
|
}
|
||
|
|
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from a quaternion rotation, vector translation and vector scale
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.translate(dest, vec);
|
||
|
|
* let quatMat = mat4.create();
|
||
|
|
* quat4.toMat4(quat, quatMat);
|
||
|
|
* mat4.multiply(dest, quatMat);
|
||
|
|
* mat4.scale(dest, scale)
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {quat4} q Rotation quaternion
|
||
|
|
* @param {vec3} v Translation vector
|
||
|
|
* @param {vec3} s Scaling vector
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromRotationTranslationScale(out, q, v, s) {
|
||
|
|
// Quaternion math
|
||
|
|
var x = q[0],
|
||
|
|
y = q[1],
|
||
|
|
z = q[2],
|
||
|
|
w = q[3];
|
||
|
|
var x2 = x + x;
|
||
|
|
var y2 = y + y;
|
||
|
|
var z2 = z + z;
|
||
|
|
var xx = x * x2;
|
||
|
|
var xy = x * y2;
|
||
|
|
var xz = x * z2;
|
||
|
|
var yy = y * y2;
|
||
|
|
var yz = y * z2;
|
||
|
|
var zz = z * z2;
|
||
|
|
var wx = w * x2;
|
||
|
|
var wy = w * y2;
|
||
|
|
var wz = w * z2;
|
||
|
|
var sx = s[0];
|
||
|
|
var sy = s[1];
|
||
|
|
var sz = s[2];
|
||
|
|
out[0] = (1 - (yy + zz)) * sx;
|
||
|
|
out[1] = (xy + wz) * sx;
|
||
|
|
out[2] = (xz - wy) * sx;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = (xy - wz) * sy;
|
||
|
|
out[5] = (1 - (xx + zz)) * sy;
|
||
|
|
out[6] = (yz + wx) * sy;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = (xz + wy) * sz;
|
||
|
|
out[9] = (yz - wx) * sz;
|
||
|
|
out[10] = (1 - (xx + yy)) * sz;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = v[0];
|
||
|
|
out[13] = v[1];
|
||
|
|
out[14] = v[2];
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Creates a matrix from a quaternion rotation, vector translation and vector scale, rotating and scaling around the given origin
|
||
|
|
* This is equivalent to (but much faster than):
|
||
|
|
*
|
||
|
|
* mat4.identity(dest);
|
||
|
|
* mat4.translate(dest, vec);
|
||
|
|
* mat4.translate(dest, origin);
|
||
|
|
* let quatMat = mat4.create();
|
||
|
|
* quat4.toMat4(quat, quatMat);
|
||
|
|
* mat4.multiply(dest, quatMat);
|
||
|
|
* mat4.scale(dest, scale)
|
||
|
|
* mat4.translate(dest, negativeOrigin);
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {quat4} q Rotation quaternion
|
||
|
|
* @param {vec3} v Translation vector
|
||
|
|
* @param {vec3} s Scaling vector
|
||
|
|
* @param {vec3} o The origin vector around which to scale and rotate
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromRotationTranslationScaleOrigin(out, q, v, s, o) {
|
||
|
|
// Quaternion math
|
||
|
|
var x = q[0],
|
||
|
|
y = q[1],
|
||
|
|
z = q[2],
|
||
|
|
w = q[3];
|
||
|
|
var x2 = x + x;
|
||
|
|
var y2 = y + y;
|
||
|
|
var z2 = z + z;
|
||
|
|
var xx = x * x2;
|
||
|
|
var xy = x * y2;
|
||
|
|
var xz = x * z2;
|
||
|
|
var yy = y * y2;
|
||
|
|
var yz = y * z2;
|
||
|
|
var zz = z * z2;
|
||
|
|
var wx = w * x2;
|
||
|
|
var wy = w * y2;
|
||
|
|
var wz = w * z2;
|
||
|
|
var sx = s[0];
|
||
|
|
var sy = s[1];
|
||
|
|
var sz = s[2];
|
||
|
|
var ox = o[0];
|
||
|
|
var oy = o[1];
|
||
|
|
var oz = o[2];
|
||
|
|
var out0 = (1 - (yy + zz)) * sx;
|
||
|
|
var out1 = (xy + wz) * sx;
|
||
|
|
var out2 = (xz - wy) * sx;
|
||
|
|
var out4 = (xy - wz) * sy;
|
||
|
|
var out5 = (1 - (xx + zz)) * sy;
|
||
|
|
var out6 = (yz + wx) * sy;
|
||
|
|
var out8 = (xz + wy) * sz;
|
||
|
|
var out9 = (yz - wx) * sz;
|
||
|
|
var out10 = (1 - (xx + yy)) * sz;
|
||
|
|
out[0] = out0;
|
||
|
|
out[1] = out1;
|
||
|
|
out[2] = out2;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = out4;
|
||
|
|
out[5] = out5;
|
||
|
|
out[6] = out6;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = out8;
|
||
|
|
out[9] = out9;
|
||
|
|
out[10] = out10;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = v[0] + ox - (out0 * ox + out4 * oy + out8 * oz);
|
||
|
|
out[13] = v[1] + oy - (out1 * ox + out5 * oy + out9 * oz);
|
||
|
|
out[14] = v[2] + oz - (out2 * ox + out6 * oy + out10 * oz);
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Calculates a 4x4 matrix from the given quaternion
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 receiving operation result
|
||
|
|
* @param {quat} q Quaternion to create matrix from
|
||
|
|
*
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function fromQuat(out, q) {
|
||
|
|
var x = q[0],
|
||
|
|
y = q[1],
|
||
|
|
z = q[2],
|
||
|
|
w = q[3];
|
||
|
|
var x2 = x + x;
|
||
|
|
var y2 = y + y;
|
||
|
|
var z2 = z + z;
|
||
|
|
var xx = x * x2;
|
||
|
|
var yx = y * x2;
|
||
|
|
var yy = y * y2;
|
||
|
|
var zx = z * x2;
|
||
|
|
var zy = z * y2;
|
||
|
|
var zz = z * z2;
|
||
|
|
var wx = w * x2;
|
||
|
|
var wy = w * y2;
|
||
|
|
var wz = w * z2;
|
||
|
|
out[0] = 1 - yy - zz;
|
||
|
|
out[1] = yx + wz;
|
||
|
|
out[2] = zx - wy;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = yx - wz;
|
||
|
|
out[5] = 1 - xx - zz;
|
||
|
|
out[6] = zy + wx;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = zx + wy;
|
||
|
|
out[9] = zy - wx;
|
||
|
|
out[10] = 1 - xx - yy;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[14] = 0;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Generates a frustum matrix with the given bounds
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 frustum matrix will be written into
|
||
|
|
* @param {Number} left Left bound of the frustum
|
||
|
|
* @param {Number} right Right bound of the frustum
|
||
|
|
* @param {Number} bottom Bottom bound of the frustum
|
||
|
|
* @param {Number} top Top bound of the frustum
|
||
|
|
* @param {Number} near Near bound of the frustum
|
||
|
|
* @param {Number} far Far bound of the frustum
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function frustum(out, left, right, bottom, top, near, far) {
|
||
|
|
var rl = 1 / (right - left);
|
||
|
|
var tb = 1 / (top - bottom);
|
||
|
|
var nf = 1 / (near - far);
|
||
|
|
out[0] = near * 2 * rl;
|
||
|
|
out[1] = 0;
|
||
|
|
out[2] = 0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = 0;
|
||
|
|
out[5] = near * 2 * tb;
|
||
|
|
out[6] = 0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = (right + left) * rl;
|
||
|
|
out[9] = (top + bottom) * tb;
|
||
|
|
out[10] = (far + near) * nf;
|
||
|
|
out[11] = -1;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[14] = far * near * 2 * nf;
|
||
|
|
out[15] = 0;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Generates a perspective projection matrix with the given bounds.
|
||
|
|
* Passing null/undefined/no value for far will generate infinite projection matrix.
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 frustum matrix will be written into
|
||
|
|
* @param {number} fovy Vertical field of view in radians
|
||
|
|
* @param {number} aspect Aspect ratio. typically viewport width/height
|
||
|
|
* @param {number} near Near bound of the frustum
|
||
|
|
* @param {number} far Far bound of the frustum, can be null or Infinity
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function perspective(out, fovy, aspect, near, far) {
|
||
|
|
var f = 1.0 / Math.tan(fovy / 2),
|
||
|
|
nf;
|
||
|
|
out[0] = f / aspect;
|
||
|
|
out[1] = 0;
|
||
|
|
out[2] = 0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = 0;
|
||
|
|
out[5] = f;
|
||
|
|
out[6] = 0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = 0;
|
||
|
|
out[9] = 0;
|
||
|
|
out[11] = -1;
|
||
|
|
out[12] = 0;
|
||
|
|
out[13] = 0;
|
||
|
|
out[15] = 0;
|
||
|
|
|
||
|
|
if (far != null && far !== Infinity) {
|
||
|
|
nf = 1 / (near - far);
|
||
|
|
out[10] = (far + near) * nf;
|
||
|
|
out[14] = 2 * far * near * nf;
|
||
|
|
} else {
|
||
|
|
out[10] = -1;
|
||
|
|
out[14] = -2 * near;
|
||
|
|
}
|
||
|
|
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Generates a perspective projection matrix with the given field of view.
|
||
|
|
* This is primarily useful for generating projection matrices to be used
|
||
|
|
* with the still experiemental WebVR API.
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 frustum matrix will be written into
|
||
|
|
* @param {Object} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
|
||
|
|
* @param {number} near Near bound of the frustum
|
||
|
|
* @param {number} far Far bound of the frustum
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function perspectiveFromFieldOfView(out, fov, near, far) {
|
||
|
|
var upTan = Math.tan(fov.upDegrees * Math.PI / 180.0);
|
||
|
|
var downTan = Math.tan(fov.downDegrees * Math.PI / 180.0);
|
||
|
|
var leftTan = Math.tan(fov.leftDegrees * Math.PI / 180.0);
|
||
|
|
var rightTan = Math.tan(fov.rightDegrees * Math.PI / 180.0);
|
||
|
|
var xScale = 2.0 / (leftTan + rightTan);
|
||
|
|
var yScale = 2.0 / (upTan + downTan);
|
||
|
|
out[0] = xScale;
|
||
|
|
out[1] = 0.0;
|
||
|
|
out[2] = 0.0;
|
||
|
|
out[3] = 0.0;
|
||
|
|
out[4] = 0.0;
|
||
|
|
out[5] = yScale;
|
||
|
|
out[6] = 0.0;
|
||
|
|
out[7] = 0.0;
|
||
|
|
out[8] = -((leftTan - rightTan) * xScale * 0.5);
|
||
|
|
out[9] = (upTan - downTan) * yScale * 0.5;
|
||
|
|
out[10] = far / (near - far);
|
||
|
|
out[11] = -1.0;
|
||
|
|
out[12] = 0.0;
|
||
|
|
out[13] = 0.0;
|
||
|
|
out[14] = far * near / (near - far);
|
||
|
|
out[15] = 0.0;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Generates a orthogonal projection matrix with the given bounds
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 frustum matrix will be written into
|
||
|
|
* @param {number} left Left bound of the frustum
|
||
|
|
* @param {number} right Right bound of the frustum
|
||
|
|
* @param {number} bottom Bottom bound of the frustum
|
||
|
|
* @param {number} top Top bound of the frustum
|
||
|
|
* @param {number} near Near bound of the frustum
|
||
|
|
* @param {number} far Far bound of the frustum
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function ortho(out, left, right, bottom, top, near, far) {
|
||
|
|
var lr = 1 / (left - right);
|
||
|
|
var bt = 1 / (bottom - top);
|
||
|
|
var nf = 1 / (near - far);
|
||
|
|
out[0] = -2 * lr;
|
||
|
|
out[1] = 0;
|
||
|
|
out[2] = 0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = 0;
|
||
|
|
out[5] = -2 * bt;
|
||
|
|
out[6] = 0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = 0;
|
||
|
|
out[9] = 0;
|
||
|
|
out[10] = 2 * nf;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = (left + right) * lr;
|
||
|
|
out[13] = (top + bottom) * bt;
|
||
|
|
out[14] = (far + near) * nf;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Generates a look-at matrix with the given eye position, focal point, and up axis.
|
||
|
|
* If you want a matrix that actually makes an object look at another object, you should use targetTo instead.
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 frustum matrix will be written into
|
||
|
|
* @param {vec3} eye Position of the viewer
|
||
|
|
* @param {vec3} center Point the viewer is looking at
|
||
|
|
* @param {vec3} up vec3 pointing up
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function lookAt(out, eye, center, up) {
|
||
|
|
var x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
|
||
|
|
var eyex = eye[0];
|
||
|
|
var eyey = eye[1];
|
||
|
|
var eyez = eye[2];
|
||
|
|
var upx = up[0];
|
||
|
|
var upy = up[1];
|
||
|
|
var upz = up[2];
|
||
|
|
var centerx = center[0];
|
||
|
|
var centery = center[1];
|
||
|
|
var centerz = center[2];
|
||
|
|
|
||
|
|
if (Math.abs(eyex - centerx) < glMatrix.EPSILON && Math.abs(eyey - centery) < glMatrix.EPSILON && Math.abs(eyez - centerz) < glMatrix.EPSILON) {
|
||
|
|
return identity(out);
|
||
|
|
}
|
||
|
|
|
||
|
|
z0 = eyex - centerx;
|
||
|
|
z1 = eyey - centery;
|
||
|
|
z2 = eyez - centerz;
|
||
|
|
len = 1 / Math.hypot(z0, z1, z2);
|
||
|
|
z0 *= len;
|
||
|
|
z1 *= len;
|
||
|
|
z2 *= len;
|
||
|
|
x0 = upy * z2 - upz * z1;
|
||
|
|
x1 = upz * z0 - upx * z2;
|
||
|
|
x2 = upx * z1 - upy * z0;
|
||
|
|
len = Math.hypot(x0, x1, x2);
|
||
|
|
|
||
|
|
if (!len) {
|
||
|
|
x0 = 0;
|
||
|
|
x1 = 0;
|
||
|
|
x2 = 0;
|
||
|
|
} else {
|
||
|
|
len = 1 / len;
|
||
|
|
x0 *= len;
|
||
|
|
x1 *= len;
|
||
|
|
x2 *= len;
|
||
|
|
}
|
||
|
|
|
||
|
|
y0 = z1 * x2 - z2 * x1;
|
||
|
|
y1 = z2 * x0 - z0 * x2;
|
||
|
|
y2 = z0 * x1 - z1 * x0;
|
||
|
|
len = Math.hypot(y0, y1, y2);
|
||
|
|
|
||
|
|
if (!len) {
|
||
|
|
y0 = 0;
|
||
|
|
y1 = 0;
|
||
|
|
y2 = 0;
|
||
|
|
} else {
|
||
|
|
len = 1 / len;
|
||
|
|
y0 *= len;
|
||
|
|
y1 *= len;
|
||
|
|
y2 *= len;
|
||
|
|
}
|
||
|
|
|
||
|
|
out[0] = x0;
|
||
|
|
out[1] = y0;
|
||
|
|
out[2] = z0;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = x1;
|
||
|
|
out[5] = y1;
|
||
|
|
out[6] = z1;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = x2;
|
||
|
|
out[9] = y2;
|
||
|
|
out[10] = z2;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
|
||
|
|
out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
|
||
|
|
out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Generates a matrix that makes something look at something else.
|
||
|
|
*
|
||
|
|
* @param {mat4} out mat4 frustum matrix will be written into
|
||
|
|
* @param {vec3} eye Position of the viewer
|
||
|
|
* @param {vec3} center Point the viewer is looking at
|
||
|
|
* @param {vec3} up vec3 pointing up
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function targetTo(out, eye, target, up) {
|
||
|
|
var eyex = eye[0],
|
||
|
|
eyey = eye[1],
|
||
|
|
eyez = eye[2],
|
||
|
|
upx = up[0],
|
||
|
|
upy = up[1],
|
||
|
|
upz = up[2];
|
||
|
|
var z0 = eyex - target[0],
|
||
|
|
z1 = eyey - target[1],
|
||
|
|
z2 = eyez - target[2];
|
||
|
|
var len = z0 * z0 + z1 * z1 + z2 * z2;
|
||
|
|
|
||
|
|
if (len > 0) {
|
||
|
|
len = 1 / Math.sqrt(len);
|
||
|
|
z0 *= len;
|
||
|
|
z1 *= len;
|
||
|
|
z2 *= len;
|
||
|
|
}
|
||
|
|
|
||
|
|
var x0 = upy * z2 - upz * z1,
|
||
|
|
x1 = upz * z0 - upx * z2,
|
||
|
|
x2 = upx * z1 - upy * z0;
|
||
|
|
len = x0 * x0 + x1 * x1 + x2 * x2;
|
||
|
|
|
||
|
|
if (len > 0) {
|
||
|
|
len = 1 / Math.sqrt(len);
|
||
|
|
x0 *= len;
|
||
|
|
x1 *= len;
|
||
|
|
x2 *= len;
|
||
|
|
}
|
||
|
|
|
||
|
|
out[0] = x0;
|
||
|
|
out[1] = x1;
|
||
|
|
out[2] = x2;
|
||
|
|
out[3] = 0;
|
||
|
|
out[4] = z1 * x2 - z2 * x1;
|
||
|
|
out[5] = z2 * x0 - z0 * x2;
|
||
|
|
out[6] = z0 * x1 - z1 * x0;
|
||
|
|
out[7] = 0;
|
||
|
|
out[8] = z0;
|
||
|
|
out[9] = z1;
|
||
|
|
out[10] = z2;
|
||
|
|
out[11] = 0;
|
||
|
|
out[12] = eyex;
|
||
|
|
out[13] = eyey;
|
||
|
|
out[14] = eyez;
|
||
|
|
out[15] = 1;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Returns a string representation of a mat4
|
||
|
|
*
|
||
|
|
* @param {mat4} a matrix to represent as a string
|
||
|
|
* @returns {String} string representation of the matrix
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function str(a) {
|
||
|
|
return "mat4(" + a[0] + ", " + a[1] + ", " + a[2] + ", " + a[3] + ", " + a[4] + ", " + a[5] + ", " + a[6] + ", " + a[7] + ", " + a[8] + ", " + a[9] + ", " + a[10] + ", " + a[11] + ", " + a[12] + ", " + a[13] + ", " + a[14] + ", " + a[15] + ")";
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Returns Frobenius norm of a mat4
|
||
|
|
*
|
||
|
|
* @param {mat4} a the matrix to calculate Frobenius norm of
|
||
|
|
* @returns {Number} Frobenius norm
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function frob(a) {
|
||
|
|
return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], a[11], a[12], a[13], a[14], a[15]);
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Adds two mat4's
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the first operand
|
||
|
|
* @param {mat4} b the second operand
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function add(out, a, b) {
|
||
|
|
out[0] = a[0] + b[0];
|
||
|
|
out[1] = a[1] + b[1];
|
||
|
|
out[2] = a[2] + b[2];
|
||
|
|
out[3] = a[3] + b[3];
|
||
|
|
out[4] = a[4] + b[4];
|
||
|
|
out[5] = a[5] + b[5];
|
||
|
|
out[6] = a[6] + b[6];
|
||
|
|
out[7] = a[7] + b[7];
|
||
|
|
out[8] = a[8] + b[8];
|
||
|
|
out[9] = a[9] + b[9];
|
||
|
|
out[10] = a[10] + b[10];
|
||
|
|
out[11] = a[11] + b[11];
|
||
|
|
out[12] = a[12] + b[12];
|
||
|
|
out[13] = a[13] + b[13];
|
||
|
|
out[14] = a[14] + b[14];
|
||
|
|
out[15] = a[15] + b[15];
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Subtracts matrix b from matrix a
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the first operand
|
||
|
|
* @param {mat4} b the second operand
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function subtract(out, a, b) {
|
||
|
|
out[0] = a[0] - b[0];
|
||
|
|
out[1] = a[1] - b[1];
|
||
|
|
out[2] = a[2] - b[2];
|
||
|
|
out[3] = a[3] - b[3];
|
||
|
|
out[4] = a[4] - b[4];
|
||
|
|
out[5] = a[5] - b[5];
|
||
|
|
out[6] = a[6] - b[6];
|
||
|
|
out[7] = a[7] - b[7];
|
||
|
|
out[8] = a[8] - b[8];
|
||
|
|
out[9] = a[9] - b[9];
|
||
|
|
out[10] = a[10] - b[10];
|
||
|
|
out[11] = a[11] - b[11];
|
||
|
|
out[12] = a[12] - b[12];
|
||
|
|
out[13] = a[13] - b[13];
|
||
|
|
out[14] = a[14] - b[14];
|
||
|
|
out[15] = a[15] - b[15];
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Multiply each element of the matrix by a scalar.
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving matrix
|
||
|
|
* @param {mat4} a the matrix to scale
|
||
|
|
* @param {Number} b amount to scale the matrix's elements by
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function multiplyScalar(out, a, b) {
|
||
|
|
out[0] = a[0] * b;
|
||
|
|
out[1] = a[1] * b;
|
||
|
|
out[2] = a[2] * b;
|
||
|
|
out[3] = a[3] * b;
|
||
|
|
out[4] = a[4] * b;
|
||
|
|
out[5] = a[5] * b;
|
||
|
|
out[6] = a[6] * b;
|
||
|
|
out[7] = a[7] * b;
|
||
|
|
out[8] = a[8] * b;
|
||
|
|
out[9] = a[9] * b;
|
||
|
|
out[10] = a[10] * b;
|
||
|
|
out[11] = a[11] * b;
|
||
|
|
out[12] = a[12] * b;
|
||
|
|
out[13] = a[13] * b;
|
||
|
|
out[14] = a[14] * b;
|
||
|
|
out[15] = a[15] * b;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Adds two mat4's after multiplying each element of the second operand by a scalar value.
|
||
|
|
*
|
||
|
|
* @param {mat4} out the receiving vector
|
||
|
|
* @param {mat4} a the first operand
|
||
|
|
* @param {mat4} b the second operand
|
||
|
|
* @param {Number} scale the amount to scale b's elements by before adding
|
||
|
|
* @returns {mat4} out
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function multiplyScalarAndAdd(out, a, b, scale) {
|
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|
|
out[0] = a[0] + b[0] * scale;
|
||
|
|
out[1] = a[1] + b[1] * scale;
|
||
|
|
out[2] = a[2] + b[2] * scale;
|
||
|
|
out[3] = a[3] + b[3] * scale;
|
||
|
|
out[4] = a[4] + b[4] * scale;
|
||
|
|
out[5] = a[5] + b[5] * scale;
|
||
|
|
out[6] = a[6] + b[6] * scale;
|
||
|
|
out[7] = a[7] + b[7] * scale;
|
||
|
|
out[8] = a[8] + b[8] * scale;
|
||
|
|
out[9] = a[9] + b[9] * scale;
|
||
|
|
out[10] = a[10] + b[10] * scale;
|
||
|
|
out[11] = a[11] + b[11] * scale;
|
||
|
|
out[12] = a[12] + b[12] * scale;
|
||
|
|
out[13] = a[13] + b[13] * scale;
|
||
|
|
out[14] = a[14] + b[14] * scale;
|
||
|
|
out[15] = a[15] + b[15] * scale;
|
||
|
|
return out;
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
|
||
|
|
*
|
||
|
|
* @param {mat4} a The first matrix.
|
||
|
|
* @param {mat4} b The second matrix.
|
||
|
|
* @returns {Boolean} True if the matrices are equal, false otherwise.
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function exactEquals(a, b) {
|
||
|
|
return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3] && a[4] === b[4] && a[5] === b[5] && a[6] === b[6] && a[7] === b[7] && a[8] === b[8] && a[9] === b[9] && a[10] === b[10] && a[11] === b[11] && a[12] === b[12] && a[13] === b[13] && a[14] === b[14] && a[15] === b[15];
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Returns whether or not the matrices have approximately the same elements in the same position.
|
||
|
|
*
|
||
|
|
* @param {mat4} a The first matrix.
|
||
|
|
* @param {mat4} b The second matrix.
|
||
|
|
* @returns {Boolean} True if the matrices are equal, false otherwise.
|
||
|
|
*/
|
||
|
|
|
||
|
|
export function equals(a, b) {
|
||
|
|
var a0 = a[0],
|
||
|
|
a1 = a[1],
|
||
|
|
a2 = a[2],
|
||
|
|
a3 = a[3];
|
||
|
|
var a4 = a[4],
|
||
|
|
a5 = a[5],
|
||
|
|
a6 = a[6],
|
||
|
|
a7 = a[7];
|
||
|
|
var a8 = a[8],
|
||
|
|
a9 = a[9],
|
||
|
|
a10 = a[10],
|
||
|
|
a11 = a[11];
|
||
|
|
var a12 = a[12],
|
||
|
|
a13 = a[13],
|
||
|
|
a14 = a[14],
|
||
|
|
a15 = a[15];
|
||
|
|
var b0 = b[0],
|
||
|
|
b1 = b[1],
|
||
|
|
b2 = b[2],
|
||
|
|
b3 = b[3];
|
||
|
|
var b4 = b[4],
|
||
|
|
b5 = b[5],
|
||
|
|
b6 = b[6],
|
||
|
|
b7 = b[7];
|
||
|
|
var b8 = b[8],
|
||
|
|
b9 = b[9],
|
||
|
|
b10 = b[10],
|
||
|
|
b11 = b[11];
|
||
|
|
var b12 = b[12],
|
||
|
|
b13 = b[13],
|
||
|
|
b14 = b[14],
|
||
|
|
b15 = b[15];
|
||
|
|
return Math.abs(a0 - b0) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) && Math.abs(a1 - b1) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) && Math.abs(a2 - b2) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) && Math.abs(a3 - b3) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) && Math.abs(a4 - b4) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) && Math.abs(a5 - b5) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) && Math.abs(a6 - b6) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) && Math.abs(a7 - b7) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) && Math.abs(a8 - b8) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)) && Math.abs(a9 - b9) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a9), Math.abs(b9)) && Math.abs(a10 - b10) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a10), Math.abs(b10)) && Math.abs(a11 - b11) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a11), Math.abs(b11)) && Math.abs(a12 - b12) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a12), Math.abs(b12)) && Math.abs(a13 - b13) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a13), Math.abs(b13)) && Math.abs(a14 - b14) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a14), Math.abs(b14)) && Math.abs(a15 - b15) <= glMatrix.EPSILON * Math.max(1.0, Math.abs(a15), Math.abs(b15));
|
||
|
|
}
|
||
|
|
/**
|
||
|
|
* Alias for {@link mat4.multiply}
|
||
|
|
* @function
|
||
|
|
*/
|
||
|
|
|
||
|
|
export var mul = multiply;
|
||
|
|
/**
|
||
|
|
* Alias for {@link mat4.subtract}
|
||
|
|
* @function
|
||
|
|
*/
|
||
|
|
|
||
|
|
export var sub = subtract;
|