580 lines
20 KiB
JavaScript
580 lines
20 KiB
JavaScript
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import mat3 from './mat3';
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import vec3 from './vec3';
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import vec4 from './vec4';
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import { epsilon } from './constants';
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export default class mat4 {
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constructor(values) {
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this.values = new Float32Array(16);
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if (values !== undefined) {
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this.init(values);
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}
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}
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at(index) {
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return this.values[index];
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}
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init(values) {
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for (let i = 0; i < 16; i++) {
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this.values[i] = values[i];
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}
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return this;
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}
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reset() {
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for (let i = 0; i < 16; i++) {
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this.values[i] = 0;
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}
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}
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copy(dest) {
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if (!dest) {
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dest = new mat4();
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}
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for (let i = 0; i < 16; i++) {
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dest.values[i] = this.values[i];
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}
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return dest;
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}
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all() {
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const data = [];
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for (let i = 0; i < 16; i++) {
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data[i] = this.values[i];
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}
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return data;
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}
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row(index) {
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return [
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this.values[index * 4 + 0],
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this.values[index * 4 + 1],
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this.values[index * 4 + 2],
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this.values[index * 4 + 3]
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];
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}
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col(index) {
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return [
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this.values[index],
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this.values[index + 4],
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this.values[index + 8],
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this.values[index + 12]
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];
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}
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equals(matrix, threshold = epsilon) {
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for (let i = 0; i < 16; i++) {
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if (Math.abs(this.values[i] - matrix.at(i)) > threshold) {
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return false;
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}
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}
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return true;
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}
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determinant() {
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const a00 = this.values[0];
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const a01 = this.values[1];
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const a02 = this.values[2];
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const a03 = this.values[3];
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const a10 = this.values[4];
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const a11 = this.values[5];
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const a12 = this.values[6];
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const a13 = this.values[7];
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const a20 = this.values[8];
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const a21 = this.values[9];
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const a22 = this.values[10];
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const a23 = this.values[11];
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const a30 = this.values[12];
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const a31 = this.values[13];
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const a32 = this.values[14];
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const a33 = this.values[15];
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const det00 = a00 * a11 - a01 * a10;
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const det01 = a00 * a12 - a02 * a10;
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const det02 = a00 * a13 - a03 * a10;
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const det03 = a01 * a12 - a02 * a11;
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const det04 = a01 * a13 - a03 * a11;
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const det05 = a02 * a13 - a03 * a12;
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const det06 = a20 * a31 - a21 * a30;
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const det07 = a20 * a32 - a22 * a30;
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const det08 = a20 * a33 - a23 * a30;
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const det09 = a21 * a32 - a22 * a31;
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const det10 = a21 * a33 - a23 * a31;
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const det11 = a22 * a33 - a23 * a32;
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return (det00 * det11 -
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det01 * det10 +
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det02 * det09 +
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det03 * det08 -
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det04 * det07 +
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det05 * det06);
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}
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setIdentity() {
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this.values[0] = 1;
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this.values[1] = 0;
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this.values[2] = 0;
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this.values[3] = 0;
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this.values[4] = 0;
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this.values[5] = 1;
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this.values[6] = 0;
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this.values[7] = 0;
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this.values[8] = 0;
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this.values[9] = 0;
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this.values[10] = 1;
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this.values[11] = 0;
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this.values[12] = 0;
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this.values[13] = 0;
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this.values[14] = 0;
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this.values[15] = 1;
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return this;
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}
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transpose() {
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const temp01 = this.values[1];
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const temp02 = this.values[2];
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const temp03 = this.values[3];
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const temp12 = this.values[6];
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const temp13 = this.values[7];
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const temp23 = this.values[11];
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this.values[1] = this.values[4];
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this.values[2] = this.values[8];
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this.values[3] = this.values[12];
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this.values[4] = temp01;
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this.values[6] = this.values[9];
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this.values[7] = this.values[13];
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this.values[8] = temp02;
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this.values[9] = temp12;
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this.values[11] = this.values[14];
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this.values[12] = temp03;
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this.values[13] = temp13;
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this.values[14] = temp23;
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return this;
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}
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inverse() {
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const a00 = this.values[0];
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const a01 = this.values[1];
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const a02 = this.values[2];
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const a03 = this.values[3];
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const a10 = this.values[4];
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const a11 = this.values[5];
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const a12 = this.values[6];
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const a13 = this.values[7];
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const a20 = this.values[8];
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const a21 = this.values[9];
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const a22 = this.values[10];
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const a23 = this.values[11];
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const a30 = this.values[12];
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const a31 = this.values[13];
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const a32 = this.values[14];
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const a33 = this.values[15];
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const det00 = a00 * a11 - a01 * a10;
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const det01 = a00 * a12 - a02 * a10;
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const det02 = a00 * a13 - a03 * a10;
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const det03 = a01 * a12 - a02 * a11;
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const det04 = a01 * a13 - a03 * a11;
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const det05 = a02 * a13 - a03 * a12;
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const det06 = a20 * a31 - a21 * a30;
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const det07 = a20 * a32 - a22 * a30;
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const det08 = a20 * a33 - a23 * a30;
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const det09 = a21 * a32 - a22 * a31;
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const det10 = a21 * a33 - a23 * a31;
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const det11 = a22 * a33 - a23 * a32;
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let det = det00 * det11 -
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det01 * det10 +
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det02 * det09 +
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det03 * det08 -
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det04 * det07 +
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det05 * det06;
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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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this.values[0] = (a11 * det11 - a12 * det10 + a13 * det09) * det;
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this.values[1] = (-a01 * det11 + a02 * det10 - a03 * det09) * det;
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this.values[2] = (a31 * det05 - a32 * det04 + a33 * det03) * det;
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this.values[3] = (-a21 * det05 + a22 * det04 - a23 * det03) * det;
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this.values[4] = (-a10 * det11 + a12 * det08 - a13 * det07) * det;
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this.values[5] = (a00 * det11 - a02 * det08 + a03 * det07) * det;
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this.values[6] = (-a30 * det05 + a32 * det02 - a33 * det01) * det;
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this.values[7] = (a20 * det05 - a22 * det02 + a23 * det01) * det;
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this.values[8] = (a10 * det10 - a11 * det08 + a13 * det06) * det;
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this.values[9] = (-a00 * det10 + a01 * det08 - a03 * det06) * det;
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this.values[10] = (a30 * det04 - a31 * det02 + a33 * det00) * det;
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this.values[11] = (-a20 * det04 + a21 * det02 - a23 * det00) * det;
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this.values[12] = (-a10 * det09 + a11 * det07 - a12 * det06) * det;
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this.values[13] = (a00 * det09 - a01 * det07 + a02 * det06) * det;
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this.values[14] = (-a30 * det03 + a31 * det01 - a32 * det00) * det;
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this.values[15] = (a20 * det03 - a21 * det01 + a22 * det00) * det;
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return this;
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}
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multiply(matrix) {
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const a00 = this.values[0];
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const a01 = this.values[1];
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const a02 = this.values[2];
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const a03 = this.values[3];
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const a10 = this.values[4];
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const a11 = this.values[5];
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const a12 = this.values[6];
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const a13 = this.values[7];
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const a20 = this.values[8];
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const a21 = this.values[9];
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const a22 = this.values[10];
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const a23 = this.values[11];
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const a30 = this.values[12];
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const a31 = this.values[13];
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const a32 = this.values[14];
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const a33 = this.values[15];
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let b0 = matrix.at(0);
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let b1 = matrix.at(1);
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let b2 = matrix.at(2);
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let b3 = matrix.at(3);
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this.values[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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this.values[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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this.values[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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this.values[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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b0 = matrix.at(4);
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b1 = matrix.at(5);
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b2 = matrix.at(6);
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b3 = matrix.at(7);
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this.values[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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this.values[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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this.values[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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this.values[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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b0 = matrix.at(8);
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b1 = matrix.at(9);
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b2 = matrix.at(10);
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b3 = matrix.at(11);
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this.values[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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this.values[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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this.values[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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this.values[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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b0 = matrix.at(12);
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b1 = matrix.at(13);
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b2 = matrix.at(14);
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b3 = matrix.at(15);
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this.values[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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this.values[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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this.values[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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this.values[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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return this;
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}
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multiplyVec3(vector) {
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const x = vector.x;
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const y = vector.y;
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const z = vector.z;
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return new vec3([
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this.values[0] * x +
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this.values[4] * y +
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this.values[8] * z +
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this.values[12],
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this.values[1] * x +
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this.values[5] * y +
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this.values[9] * z +
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this.values[13],
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this.values[2] * x +
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this.values[6] * y +
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this.values[10] * z +
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this.values[14]
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]);
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}
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multiplyVec4(vector, dest) {
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if (!dest) {
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dest = new vec4();
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}
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const x = vector.x;
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const y = vector.y;
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const z = vector.z;
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const w = vector.w;
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dest.x =
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this.values[0] * x +
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this.values[4] * y +
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this.values[8] * z +
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this.values[12] * w;
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dest.y =
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this.values[1] * x +
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this.values[5] * y +
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this.values[9] * z +
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this.values[13] * w;
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dest.z =
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this.values[2] * x +
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this.values[6] * y +
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this.values[10] * z +
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this.values[14] * w;
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dest.w =
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this.values[3] * x +
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this.values[7] * y +
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this.values[11] * z +
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this.values[15] * w;
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return dest;
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}
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toMat3() {
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return new mat3([
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this.values[0],
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this.values[1],
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this.values[2],
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this.values[4],
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this.values[5],
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this.values[6],
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this.values[8],
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this.values[9],
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this.values[10]
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]);
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}
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toInverseMat3() {
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const a00 = this.values[0];
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const a01 = this.values[1];
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const a02 = this.values[2];
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const a10 = this.values[4];
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const a11 = this.values[5];
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const a12 = this.values[6];
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const a20 = this.values[8];
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const a21 = this.values[9];
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const a22 = this.values[10];
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const det01 = a22 * a11 - a12 * a21;
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const det11 = -a22 * a10 + a12 * a20;
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const det21 = a21 * a10 - a11 * a20;
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let det = a00 * det01 + a01 * det11 + a02 * det21;
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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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return new mat3([
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det01 * det,
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(-a22 * a01 + a02 * a21) * det,
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(a12 * a01 - a02 * a11) * det,
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det11 * det,
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(a22 * a00 - a02 * a20) * det,
|
||
|
|
(-a12 * a00 + a02 * a10) * det,
|
||
|
|
det21 * det,
|
||
|
|
(-a21 * a00 + a01 * a20) * det,
|
||
|
|
(a11 * a00 - a01 * a10) * det
|
||
|
|
]);
|
||
|
|
}
|
||
|
|
translate(vector) {
|
||
|
|
const x = vector.x;
|
||
|
|
const y = vector.y;
|
||
|
|
const z = vector.z;
|
||
|
|
this.values[12] +=
|
||
|
|
this.values[0] * x + this.values[4] * y + this.values[8] * z;
|
||
|
|
this.values[13] +=
|
||
|
|
this.values[1] * x + this.values[5] * y + this.values[9] * z;
|
||
|
|
this.values[14] +=
|
||
|
|
this.values[2] * x + this.values[6] * y + this.values[10] * z;
|
||
|
|
this.values[15] +=
|
||
|
|
this.values[3] * x + this.values[7] * y + this.values[11] * z;
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
scale(vector) {
|
||
|
|
const x = vector.x;
|
||
|
|
const y = vector.y;
|
||
|
|
const z = vector.z;
|
||
|
|
this.values[0] *= x;
|
||
|
|
this.values[1] *= x;
|
||
|
|
this.values[2] *= x;
|
||
|
|
this.values[3] *= x;
|
||
|
|
this.values[4] *= y;
|
||
|
|
this.values[5] *= y;
|
||
|
|
this.values[6] *= y;
|
||
|
|
this.values[7] *= y;
|
||
|
|
this.values[8] *= z;
|
||
|
|
this.values[9] *= z;
|
||
|
|
this.values[10] *= z;
|
||
|
|
this.values[11] *= z;
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
rotate(angle, axis) {
|
||
|
|
let x = axis.x;
|
||
|
|
let y = axis.y;
|
||
|
|
let z = axis.z;
|
||
|
|
let length = Math.sqrt(x * x + y * y + z * z);
|
||
|
|
if (!length) {
|
||
|
|
return null;
|
||
|
|
}
|
||
|
|
if (length !== 1) {
|
||
|
|
length = 1 / length;
|
||
|
|
x *= length;
|
||
|
|
y *= length;
|
||
|
|
z *= length;
|
||
|
|
}
|
||
|
|
const s = Math.sin(angle);
|
||
|
|
const c = Math.cos(angle);
|
||
|
|
const t = 1.0 - c;
|
||
|
|
const a00 = this.values[0];
|
||
|
|
const a01 = this.values[1];
|
||
|
|
const a02 = this.values[2];
|
||
|
|
const a03 = this.values[3];
|
||
|
|
const a10 = this.values[4];
|
||
|
|
const a11 = this.values[5];
|
||
|
|
const a12 = this.values[6];
|
||
|
|
const a13 = this.values[7];
|
||
|
|
const a20 = this.values[8];
|
||
|
|
const a21 = this.values[9];
|
||
|
|
const a22 = this.values[10];
|
||
|
|
const a23 = this.values[11];
|
||
|
|
const b00 = x * x * t + c;
|
||
|
|
const b01 = y * x * t + z * s;
|
||
|
|
const b02 = z * x * t - y * s;
|
||
|
|
const b10 = x * y * t - z * s;
|
||
|
|
const b11 = y * y * t + c;
|
||
|
|
const b12 = z * y * t + x * s;
|
||
|
|
const b20 = x * z * t + y * s;
|
||
|
|
const b21 = y * z * t - x * s;
|
||
|
|
const b22 = z * z * t + c;
|
||
|
|
this.values[0] = a00 * b00 + a10 * b01 + a20 * b02;
|
||
|
|
this.values[1] = a01 * b00 + a11 * b01 + a21 * b02;
|
||
|
|
this.values[2] = a02 * b00 + a12 * b01 + a22 * b02;
|
||
|
|
this.values[3] = a03 * b00 + a13 * b01 + a23 * b02;
|
||
|
|
this.values[4] = a00 * b10 + a10 * b11 + a20 * b12;
|
||
|
|
this.values[5] = a01 * b10 + a11 * b11 + a21 * b12;
|
||
|
|
this.values[6] = a02 * b10 + a12 * b11 + a22 * b12;
|
||
|
|
this.values[7] = a03 * b10 + a13 * b11 + a23 * b12;
|
||
|
|
this.values[8] = a00 * b20 + a10 * b21 + a20 * b22;
|
||
|
|
this.values[9] = a01 * b20 + a11 * b21 + a21 * b22;
|
||
|
|
this.values[10] = a02 * b20 + a12 * b21 + a22 * b22;
|
||
|
|
this.values[11] = a03 * b20 + a13 * b21 + a23 * b22;
|
||
|
|
return this;
|
||
|
|
}
|
||
|
|
static frustum(left, right, bottom, top, near, far) {
|
||
|
|
const rl = right - left;
|
||
|
|
const tb = top - bottom;
|
||
|
|
const fn = far - near;
|
||
|
|
return new mat4([
|
||
|
|
(near * 2) / rl,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
(near * 2) / tb,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
(right + left) / rl,
|
||
|
|
(top + bottom) / tb,
|
||
|
|
-(far + near) / fn,
|
||
|
|
-1,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
-(far * near * 2) / fn,
|
||
|
|
0
|
||
|
|
]);
|
||
|
|
}
|
||
|
|
static perspective(fov, aspect, near, far) {
|
||
|
|
const top = near * Math.tan((fov * Math.PI) / 360.0);
|
||
|
|
const right = top * aspect;
|
||
|
|
return mat4.frustum(-right, right, -top, top, near, far);
|
||
|
|
}
|
||
|
|
static orthographic(left, right, bottom, top, near, far) {
|
||
|
|
const rl = right - left;
|
||
|
|
const tb = top - bottom;
|
||
|
|
const fn = far - near;
|
||
|
|
return new mat4([
|
||
|
|
2 / rl,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
2 / tb,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
0,
|
||
|
|
-2 / fn,
|
||
|
|
0,
|
||
|
|
-(left + right) / rl,
|
||
|
|
-(top + bottom) / tb,
|
||
|
|
-(far + near) / fn,
|
||
|
|
1
|
||
|
|
]);
|
||
|
|
}
|
||
|
|
static lookAt(position, target, up = vec3.up) {
|
||
|
|
if (position.equals(target)) {
|
||
|
|
return this.identity;
|
||
|
|
}
|
||
|
|
const z = vec3.difference(position, target).normalize();
|
||
|
|
const x = vec3.cross(up, z).normalize();
|
||
|
|
const y = vec3.cross(z, x).normalize();
|
||
|
|
return new mat4([
|
||
|
|
x.x,
|
||
|
|
y.x,
|
||
|
|
z.x,
|
||
|
|
0,
|
||
|
|
x.y,
|
||
|
|
y.y,
|
||
|
|
z.y,
|
||
|
|
0,
|
||
|
|
x.z,
|
||
|
|
y.z,
|
||
|
|
z.z,
|
||
|
|
0,
|
||
|
|
-vec3.dot(x, position),
|
||
|
|
-vec3.dot(y, position),
|
||
|
|
-vec3.dot(z, position),
|
||
|
|
1
|
||
|
|
]);
|
||
|
|
}
|
||
|
|
static product(m1, m2, result) {
|
||
|
|
const a00 = m1.at(0);
|
||
|
|
const a01 = m1.at(1);
|
||
|
|
const a02 = m1.at(2);
|
||
|
|
const a03 = m1.at(3);
|
||
|
|
const a10 = m1.at(4);
|
||
|
|
const a11 = m1.at(5);
|
||
|
|
const a12 = m1.at(6);
|
||
|
|
const a13 = m1.at(7);
|
||
|
|
const a20 = m1.at(8);
|
||
|
|
const a21 = m1.at(9);
|
||
|
|
const a22 = m1.at(10);
|
||
|
|
const a23 = m1.at(11);
|
||
|
|
const a30 = m1.at(12);
|
||
|
|
const a31 = m1.at(13);
|
||
|
|
const a32 = m1.at(14);
|
||
|
|
const a33 = m1.at(15);
|
||
|
|
const b00 = m2.at(0);
|
||
|
|
const b01 = m2.at(1);
|
||
|
|
const b02 = m2.at(2);
|
||
|
|
const b03 = m2.at(3);
|
||
|
|
const b10 = m2.at(4);
|
||
|
|
const b11 = m2.at(5);
|
||
|
|
const b12 = m2.at(6);
|
||
|
|
const b13 = m2.at(7);
|
||
|
|
const b20 = m2.at(8);
|
||
|
|
const b21 = m2.at(9);
|
||
|
|
const b22 = m2.at(10);
|
||
|
|
const b23 = m2.at(11);
|
||
|
|
const b30 = m2.at(12);
|
||
|
|
const b31 = m2.at(13);
|
||
|
|
const b32 = m2.at(14);
|
||
|
|
const b33 = m2.at(15);
|
||
|
|
if (result) {
|
||
|
|
result.init([
|
||
|
|
b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30,
|
||
|
|
b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31,
|
||
|
|
b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32,
|
||
|
|
b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33,
|
||
|
|
b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30,
|
||
|
|
b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31,
|
||
|
|
b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32,
|
||
|
|
b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33,
|
||
|
|
b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30,
|
||
|
|
b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31,
|
||
|
|
b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32,
|
||
|
|
b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33,
|
||
|
|
b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30,
|
||
|
|
b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31,
|
||
|
|
b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32,
|
||
|
|
b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33
|
||
|
|
]);
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
return new mat4([
|
||
|
|
b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30,
|
||
|
|
b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31,
|
||
|
|
b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32,
|
||
|
|
b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33,
|
||
|
|
b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30,
|
||
|
|
b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31,
|
||
|
|
b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32,
|
||
|
|
b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33,
|
||
|
|
b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30,
|
||
|
|
b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31,
|
||
|
|
b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32,
|
||
|
|
b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33,
|
||
|
|
b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30,
|
||
|
|
b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31,
|
||
|
|
b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32,
|
||
|
|
b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33
|
||
|
|
]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
mat4.identity = new mat4().setIdentity();
|