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@@ -1,5 +1,5 @@
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/**
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- * Copyright (c) 2017 mol* contributors, licensed under MIT, See LICENSE file for more info.
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+ * Copyright (c) 2017-2018 mol* contributors, licensed under MIT, See LICENSE file for more info.
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*
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* @author David Sehnal <david.sehnal@gmail.com>
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* @author Alexander Rose <alexander.rose@weirdbyte.de>
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@@ -17,1428 +17,10 @@
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* furnished to do so, subject to the following conditions:
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*/
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-export interface Mat4 extends Array<number> { [d: number]: number, '@type': 'mat4', length: 16 }
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-export interface Mat3 extends Array<number> { [d: number]: number, '@type': 'mat3', length: 9 }
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-export interface Vec3 extends Array<number> { [d: number]: number, '@type': 'vec3', length: 3 }
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-export interface Vec4 extends Array<number> { [d: number]: number, '@type': 'vec4', length: 4 }
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-export interface Quat extends Array<number> { [d: number]: number, '@type': 'quat', length: 4 }
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+import Mat4 from './3d/mat4'
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+import Mat3 from './3d/mat3'
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+import Vec3 from './3d/vec3'
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+import Vec4 from './3d/vec4'
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+import Quat from './3d/quat'
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-const enum EPSILON { Value = 0.000001 }
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-
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-export function Mat4() {
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- return Mat4.zero();
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-}
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-
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-export function Quat() {
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- return Quat.zero();
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-}
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-
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-/**
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- * Stores a 4x4 matrix in a column major (j * 4 + i indexing) format.
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- */
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-export namespace Mat4 {
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- export function zero(): Mat4 {
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- // force double backing array by 0.1.
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- const ret = [0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
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- ret[0] = 0.0;
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- return ret as any;
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- }
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-
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- export function identity(): Mat4 {
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- const out = zero();
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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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- export function setIdentity(mat: Mat4): Mat4 {
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- mat[0] = 1;
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- mat[1] = 0;
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- mat[2] = 0;
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- mat[3] = 0;
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- mat[4] = 0;
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- mat[5] = 1;
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- mat[6] = 0;
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- mat[7] = 0;
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- mat[8] = 0;
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- mat[9] = 0;
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- mat[10] = 1;
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- mat[11] = 0;
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- mat[12] = 0;
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- mat[13] = 0;
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- mat[14] = 0;
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- mat[15] = 1;
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- return mat;
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- }
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-
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- export function ofRows(rows: number[][]): Mat4 {
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- const out = zero();
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- for (let i = 0; i < 4; i++) {
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- const r = rows[i];
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- for (let j = 0; j < 4; j++) {
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- out[4 * j + i] = r[j];
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- }
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- }
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- return out;
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- }
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-
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- const _id = identity();
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- export function isIdentity(m: Mat4, eps?: number) {
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- return areEqual(m, _id, typeof eps === 'undefined' ? EPSILON.Value : eps);
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- }
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-
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- export function areEqual(a: Mat4, b: Mat4, eps: number) {
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- for (let i = 0; i < 16; i++) {
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- if (Math.abs(a[i] - b[i]) > eps) return false;
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- }
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- return true;
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- }
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-
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- export function setValue(a: Mat4, i: number, j: number, value: number) {
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- a[4 * j + i] = value;
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- }
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-
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- export function toArray(a: Mat4, out: Helpers.NumberArray, offset: number) {
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- out[offset + 0] = a[0];
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- out[offset + 1] = a[1];
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- out[offset + 2] = a[2];
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- out[offset + 3] = a[3];
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- out[offset + 4] = a[4];
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- out[offset + 5] = a[5];
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- out[offset + 6] = a[6];
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- out[offset + 7] = a[7];
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- out[offset + 8] = a[8];
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- out[offset + 9] = a[9];
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- out[offset + 10] = a[10];
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- out[offset + 11] = a[11];
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- out[offset + 12] = a[12];
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- out[offset + 13] = a[13];
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- out[offset + 14] = a[14];
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- out[offset + 15] = a[15];
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- }
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-
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- export function fromArray(a: Mat4, array: Helpers.NumberArray, offset: number) {
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- a[0] = array[offset + 0]
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- a[1] = array[offset + 1]
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- a[2] = array[offset + 2]
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- a[3] = array[offset + 3]
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- a[4] = array[offset + 4]
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- a[5] = array[offset + 5]
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- a[6] = array[offset + 6]
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- a[7] = array[offset + 7]
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- a[8] = array[offset + 8]
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- a[9] = array[offset + 9]
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- a[10] = array[offset + 10]
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- a[11] = array[offset + 11]
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- a[12] = array[offset + 12]
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- a[13] = array[offset + 13]
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- a[14] = array[offset + 14]
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- a[15] = array[offset + 15]
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- }
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-
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- export function copy(out: Mat4, a: Mat4) {
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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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- export function clone(a: Mat4) {
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- return Mat4.copy(Mat4.zero(), a);
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- }
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-
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- export function transpose(out: Mat4, a: Mat4) {
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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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- const a01 = a[1], a02 = a[2], a03 = a[3];
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- const a12 = a[6], a13 = a[7];
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- const 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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- export function invert(out: Mat4, a: Mat4) {
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- const a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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- a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
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- a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
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- a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
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-
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- b00 = a00 * a11 - a01 * a10,
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- b01 = a00 * a12 - a02 * a10,
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- b02 = a00 * a13 - a03 * a10,
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- b03 = a01 * a12 - a02 * a11,
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- b04 = a01 * a13 - a03 * a11,
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- b05 = a02 * a13 - a03 * a12,
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- b06 = a20 * a31 - a21 * a30,
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- b07 = a20 * a32 - a22 * a30,
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- b08 = a20 * a33 - a23 * a30,
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- b09 = a21 * a32 - a22 * a31,
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- b10 = a21 * a33 - a23 * a31,
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- b11 = a22 * a33 - a23 * a32;
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-
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- // Calculate the determinant
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- let det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
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-
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- if (!det) {
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- console.warn('non-invertible matrix.', a);
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- return out;
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- }
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- det = 1.0 / det;
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-
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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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-
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- return out;
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- }
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-
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- export function mul(out: Mat4, a: Mat4, b: Mat4) {
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- const a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3],
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- a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7],
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- a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11],
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- a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
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-
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- // Cache only the current line of the second matrix
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- let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
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- out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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- out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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- out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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- out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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-
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- b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
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- out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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- out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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- out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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- out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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-
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- b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
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- out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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- out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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- out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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- out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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-
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- b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
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- out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
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- out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
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- out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
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- out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
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- return out;
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- }
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-
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- export function mul3(out: Mat4, a: Mat4, b: Mat4, c: Mat4) {
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- return mul(out, mul(out, a, b), c);
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- }
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-
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- export function translate(out: Mat4, a: Mat4, v: Vec3) {
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- const x = v[0], y = v[1], z = v[2];
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- let a00: number, a01: number, a02: number, a03: number,
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- a10: number, a11: number, a12: number, a13: number,
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- a20: number, a21: number, a22: number, a23: number;
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-
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- if (a === out) {
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- out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
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- out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
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- out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
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- out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
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- } else {
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- a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
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- a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
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- a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
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-
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- out[0] = a00; out[1] = a01; out[2] = a02; out[3] = a03;
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- out[4] = a10; out[5] = a11; out[6] = a12; out[7] = a13;
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- out[8] = a20; out[9] = a21; out[10] = a22; out[11] = a23;
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-
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- out[12] = a00 * x + a10 * y + a20 * z + a[12];
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- out[13] = a01 * x + a11 * y + a21 * z + a[13];
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- out[14] = a02 * x + a12 * y + a22 * z + a[14];
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- out[15] = a03 * x + a13 * y + a23 * z + a[15];
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- }
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-
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- return out;
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- }
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-
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- export function fromTranslation(out: Mat4, v: Vec3) {
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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] = v[0];
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- out[13] = v[1];
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- out[14] = v[2];
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- out[15] = 1;
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- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function setTranslation(out: Mat4, v: Vec3) {
|
|
|
- out[12] = v[0];
|
|
|
- out[13] = v[1];
|
|
|
- out[14] = v[2];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function rotate(out: Mat4, a: Mat4, rad: number, axis: Mat4) {
|
|
|
- let x = axis[0], y = axis[1], z = axis[2],
|
|
|
- len = Math.sqrt(x * x + y * y + z * z),
|
|
|
- s, c, t,
|
|
|
- a00, a01, a02, a03,
|
|
|
- a10, a11, a12, a13,
|
|
|
- a20, a21, a22, a23,
|
|
|
- b00, b01, b02,
|
|
|
- b10, b11, b12,
|
|
|
- b20, b21, b22;
|
|
|
-
|
|
|
- if (Math.abs(len) < EPSILON.Value) {
|
|
|
- return Mat4.identity();
|
|
|
- }
|
|
|
-
|
|
|
- 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;
|
|
|
- }
|
|
|
-
|
|
|
- export function fromRotation(out: Mat4, rad: number, axis: Vec3) {
|
|
|
- let x = axis[0], y = axis[1], z = axis[2],
|
|
|
- len = Math.sqrt(x * x + y * y + z * z),
|
|
|
- s, c, t;
|
|
|
-
|
|
|
- if (Math.abs(len) < EPSILON.Value) { return setIdentity(out); }
|
|
|
-
|
|
|
- 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;
|
|
|
- }
|
|
|
-
|
|
|
- export function scale(out: Mat4, a: Mat4, v: Vec3) {
|
|
|
- const 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;
|
|
|
- }
|
|
|
-
|
|
|
- export function fromScaling(out: Mat4, v: Vec3) {
|
|
|
- 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;
|
|
|
- }
|
|
|
-
|
|
|
- export function makeTable(m: Mat4) {
|
|
|
- let ret = '';
|
|
|
- for (let i = 0; i < 4; i++) {
|
|
|
- for (let j = 0; j < 4; j++) {
|
|
|
- ret += m[4 * j + i].toString();
|
|
|
- if (j < 3) ret += ' ';
|
|
|
- }
|
|
|
- if (i < 3) ret += '\n';
|
|
|
- }
|
|
|
- return ret;
|
|
|
- }
|
|
|
-
|
|
|
- export function determinant(a: Mat4) {
|
|
|
- const 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],
|
|
|
- a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15],
|
|
|
-
|
|
|
- b00 = a00 * a11 - a01 * a10,
|
|
|
- b01 = a00 * a12 - a02 * a10,
|
|
|
- b02 = a00 * a13 - a03 * a10,
|
|
|
- b03 = a01 * a12 - a02 * a11,
|
|
|
- b04 = a01 * a13 - a03 * a11,
|
|
|
- b05 = a02 * a13 - a03 * a12,
|
|
|
- b06 = a20 * a31 - a21 * a30,
|
|
|
- b07 = a20 * a32 - a22 * a30,
|
|
|
- b08 = a20 * a33 - a23 * a30,
|
|
|
- b09 = a21 * a32 - a22 * a31,
|
|
|
- b10 = a21 * a33 - a23 * a31,
|
|
|
- b11 = a22 * a33 - a23 * a32;
|
|
|
-
|
|
|
- // Calculate the determinant
|
|
|
- return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Check if the matrix has the form
|
|
|
- * [ Rotation Translation ]
|
|
|
- * [ 0 1 ]
|
|
|
- */
|
|
|
- export function isRotationAndTranslation(a: Mat4, eps?: number) {
|
|
|
- return _isRotationAndTranslation(a, typeof eps !== 'undefined' ? eps : EPSILON.Value)
|
|
|
- }
|
|
|
-
|
|
|
- function _isRotationAndTranslation(a: Mat4, eps: number) {
|
|
|
- const 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],
|
|
|
- /* a30 = a[12], a31 = a[13], a32 = a[14],*/ a33 = a[15];
|
|
|
-
|
|
|
- if (a33 !== 1 || a03 !== 0 || a13 !== 0 || a23 !== 0) {
|
|
|
- return false;
|
|
|
- }
|
|
|
- const det3x3 = a00 * (a11 * a22 - a12 * a21) - a01 * (a10 * a22 - a12 * a20) + a02 * (a10 * a21 - a11 * a20);
|
|
|
- if (det3x3 < 1 - eps || det3x3 > 1 + eps) {
|
|
|
- return false;
|
|
|
- }
|
|
|
- return true;
|
|
|
- }
|
|
|
-
|
|
|
- export function fromQuat(out: Mat4, q: Quat) {
|
|
|
- const x = q[0], y = q[1], z = q[2], w = q[3];
|
|
|
- const x2 = x + x;
|
|
|
- const y2 = y + y;
|
|
|
- const z2 = z + z;
|
|
|
-
|
|
|
- const xx = x * x2;
|
|
|
- const yx = y * x2;
|
|
|
- const yy = y * y2;
|
|
|
- const zx = z * x2;
|
|
|
- const zy = z * y2;
|
|
|
- const zz = z * z2;
|
|
|
- const wx = w * x2;
|
|
|
- const wy = w * y2;
|
|
|
- const 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
|
|
|
- */
|
|
|
- export function frustum(out: Mat4, left: number, right: number, bottom: number, top: number, near: number, far: number) {
|
|
|
- let rl = 1 / (right - left);
|
|
|
- let tb = 1 / (top - bottom);
|
|
|
- let 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
|
|
|
- */
|
|
|
- export function perspective(out: Mat4, fovy: number, aspect: number, near: number, far: number) {
|
|
|
- let f = 1.0 / Math.tan(fovy / 2);
|
|
|
- let nf = 1 / (near - far);
|
|
|
- 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[10] = (far + near) * nf;
|
|
|
- out[11] = -1;
|
|
|
- out[12] = 0;
|
|
|
- out[13] = 0;
|
|
|
- out[14] = (2 * far * near) * nf;
|
|
|
- out[15] = 0;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Generates a orthogonal projection matrix with the given bounds
|
|
|
- */
|
|
|
- export function ortho(out: Mat4, left: number, right: number, bottom: number, top: number, near: number, far: number) {
|
|
|
- let lr = 1 / (left - right);
|
|
|
- let bt = 1 / (bottom - top);
|
|
|
- let 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
|
|
|
- */
|
|
|
- export function lookAt(out: Mat4, eye: Vec3, center: Vec3, up: Vec3) {
|
|
|
- let x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
|
|
|
- let eyex = eye[0];
|
|
|
- let eyey = eye[1];
|
|
|
- let eyez = eye[2];
|
|
|
- let upx = up[0];
|
|
|
- let upy = up[1];
|
|
|
- let upz = up[2];
|
|
|
- let centerx = center[0];
|
|
|
- let centery = center[1];
|
|
|
- let centerz = center[2];
|
|
|
-
|
|
|
- if (Math.abs(eyex - centerx) < EPSILON.Value &&
|
|
|
- Math.abs(eyey - centery) < EPSILON.Value &&
|
|
|
- Math.abs(eyez - centerz) < EPSILON.Value
|
|
|
- ) {
|
|
|
- return setIdentity(out);
|
|
|
- }
|
|
|
-
|
|
|
- z0 = eyex - centerx;
|
|
|
- z1 = eyey - centery;
|
|
|
- z2 = eyez - centerz;
|
|
|
-
|
|
|
- len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
|
|
|
- z0 *= len;
|
|
|
- z1 *= len;
|
|
|
- z2 *= len;
|
|
|
-
|
|
|
- x0 = upy * z2 - upz * z1;
|
|
|
- x1 = upz * z0 - upx * z2;
|
|
|
- x2 = upx * z1 - upy * z0;
|
|
|
- len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * 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.sqrt(y0 * y0 + y1 * y1 + y2 * 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;
|
|
|
- }
|
|
|
-}
|
|
|
-
|
|
|
-export namespace Mat3 {
|
|
|
- export function zero(): Mat3 {
|
|
|
- // force double backing array by 0.1.
|
|
|
- const ret = [0.1, 0, 0, 0, 0, 0, 0, 0, 0];
|
|
|
- ret[0] = 0.0;
|
|
|
- return ret as any;
|
|
|
- }
|
|
|
-}
|
|
|
-
|
|
|
-export namespace Vec3 {
|
|
|
- export function zero(): Vec3 {
|
|
|
- const out = [0.1, 0.0, 0.0];
|
|
|
- out[0] = 0;
|
|
|
- return out as any;
|
|
|
- }
|
|
|
-
|
|
|
- export function clone(a: Vec3): Vec3 {
|
|
|
- const out = zero();
|
|
|
- out[0] = a[0];
|
|
|
- out[1] = a[1];
|
|
|
- out[2] = a[2];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function fromObj(v: { x: number, y: number, z: number }): Vec3 {
|
|
|
- return create(v.x, v.y, v.z);
|
|
|
- }
|
|
|
-
|
|
|
- export function toObj(v: Vec3) {
|
|
|
- return { x: v[0], y: v[1], z: v[2] };
|
|
|
- }
|
|
|
-
|
|
|
- export function fromArray(v: Vec3, array: Helpers.NumberArray, offset: number) {
|
|
|
- v[0] = array[offset + 0]
|
|
|
- v[1] = array[offset + 1]
|
|
|
- v[2] = array[offset + 2]
|
|
|
- }
|
|
|
-
|
|
|
- export function toArray(v: Vec3, out: Helpers.NumberArray, offset: number) {
|
|
|
- out[offset + 0] = v[0]
|
|
|
- out[offset + 1] = v[1]
|
|
|
- out[offset + 2] = v[2]
|
|
|
- }
|
|
|
-
|
|
|
- export function create(x: number, y: number, z: number): Vec3 {
|
|
|
- const out = zero();
|
|
|
- out[0] = x;
|
|
|
- out[1] = y;
|
|
|
- out[2] = z;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function set(out: Vec3, x: number, y: number, z: number): Vec3 {
|
|
|
- out[0] = x;
|
|
|
- out[1] = y;
|
|
|
- out[2] = z;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function copy(out: Vec3, a: Vec3) {
|
|
|
- out[0] = a[0];
|
|
|
- out[1] = a[1];
|
|
|
- out[2] = a[2];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function add(out: Vec3, a: Vec3, b: Vec3) {
|
|
|
- out[0] = a[0] + b[0];
|
|
|
- out[1] = a[1] + b[1];
|
|
|
- out[2] = a[2] + b[2];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function sub(out: Vec3, a: Vec3, b: Vec3) {
|
|
|
- out[0] = a[0] - b[0];
|
|
|
- out[1] = a[1] - b[1];
|
|
|
- out[2] = a[2] - b[2];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function scale(out: Vec3, a: Vec3, b: number) {
|
|
|
- out[0] = a[0] * b;
|
|
|
- out[1] = a[1] * b;
|
|
|
- out[2] = a[2] * b;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function scaleAndAdd(out: Vec3, a: Vec3, b: Vec3, scale: number) {
|
|
|
- out[0] = a[0] + (b[0] * scale);
|
|
|
- out[1] = a[1] + (b[1] * scale);
|
|
|
- out[2] = a[2] + (b[2] * scale);
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function distance(a: Vec3, b: Vec3) {
|
|
|
- const x = b[0] - a[0],
|
|
|
- y = b[1] - a[1],
|
|
|
- z = b[2] - a[2];
|
|
|
- return Math.sqrt(x * x + y * y + z * z);
|
|
|
- }
|
|
|
-
|
|
|
- export function squaredDistance(a: Vec3, b: Vec3) {
|
|
|
- const x = b[0] - a[0],
|
|
|
- y = b[1] - a[1],
|
|
|
- z = b[2] - a[2];
|
|
|
- return x * x + y * y + z * z;
|
|
|
- }
|
|
|
-
|
|
|
- export function magnitude(a: Vec3) {
|
|
|
- const x = a[0],
|
|
|
- y = a[1],
|
|
|
- z = a[2];
|
|
|
- return Math.sqrt(x * x + y * y + z * z);
|
|
|
- }
|
|
|
-
|
|
|
- export function squaredMagnitude(a: Vec3) {
|
|
|
- const x = a[0],
|
|
|
- y = a[1],
|
|
|
- z = a[2];
|
|
|
- return x * x + y * y + z * z;
|
|
|
- }
|
|
|
-
|
|
|
- export function normalize(out: Vec3, a: Vec3) {
|
|
|
- const x = a[0],
|
|
|
- y = a[1],
|
|
|
- z = a[2];
|
|
|
- let len = x * x + y * y + z * z;
|
|
|
- if (len > 0) {
|
|
|
- len = 1 / Math.sqrt(len);
|
|
|
- out[0] = a[0] * len;
|
|
|
- out[1] = a[1] * len;
|
|
|
- out[2] = a[2] * len;
|
|
|
- }
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function dot(a: Vec3, b: Vec3) {
|
|
|
- return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
|
|
|
- }
|
|
|
-
|
|
|
- export function cross(out: Vec3, a: Vec3, b: Vec3) {
|
|
|
- const ax = a[0], ay = a[1], az = a[2],
|
|
|
- bx = b[0], by = b[1], bz = b[2];
|
|
|
-
|
|
|
- out[0] = ay * bz - az * by;
|
|
|
- out[1] = az * bx - ax * bz;
|
|
|
- out[2] = ax * by - ay * bx;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Performs a linear interpolation between two Vec3's
|
|
|
- */
|
|
|
- export function lerp(out: Vec3, a: Vec3, b: Vec3, t: number) {
|
|
|
- const ax = a[0],
|
|
|
- ay = a[1],
|
|
|
- az = a[2];
|
|
|
- out[0] = ax + t * (b[0] - ax);
|
|
|
- out[1] = ay + t * (b[1] - ay);
|
|
|
- out[2] = az + t * (b[2] - az);
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Performs a hermite interpolation with two control points
|
|
|
- */
|
|
|
- export function hermite(out: Vec3, a: Vec3, b: Vec3, c: Vec3, d: Vec3, t: number) {
|
|
|
- const factorTimes2 = t * t;
|
|
|
- const factor1 = factorTimes2 * (2 * t - 3) + 1;
|
|
|
- const factor2 = factorTimes2 * (t - 2) + t;
|
|
|
- const factor3 = factorTimes2 * (t - 1);
|
|
|
- const factor4 = factorTimes2 * (3 - 2 * t);
|
|
|
-
|
|
|
- out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
|
|
|
- out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
|
|
|
- out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;
|
|
|
-
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Performs a bezier interpolation with two control points
|
|
|
- */
|
|
|
- export function bezier(out: Vec3, a: Vec3, b: Vec3, c: Vec3, d: Vec3, t: number) {
|
|
|
- const inverseFactor = 1 - t;
|
|
|
- const inverseFactorTimesTwo = inverseFactor * inverseFactor;
|
|
|
- const factorTimes2 = t * t;
|
|
|
- const factor1 = inverseFactorTimesTwo * inverseFactor;
|
|
|
- const factor2 = 3 * t * inverseFactorTimesTwo;
|
|
|
- const factor3 = 3 * factorTimes2 * inverseFactor;
|
|
|
- const factor4 = factorTimes2 * t;
|
|
|
-
|
|
|
- out[0] = a[0] * factor1 + b[0] * factor2 + c[0] * factor3 + d[0] * factor4;
|
|
|
- out[1] = a[1] * factor1 + b[1] * factor2 + c[1] * factor3 + d[1] * factor4;
|
|
|
- out[2] = a[2] * factor1 + b[2] * factor2 + c[2] * factor3 + d[2] * factor4;
|
|
|
-
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Generates a random vector with the given scale
|
|
|
- */
|
|
|
- export function random(out: Vec3, scale: number) {
|
|
|
- const r = Math.random() * 2.0 * Math.PI;
|
|
|
- const z = (Math.random() * 2.0) - 1.0;
|
|
|
- const zScale = Math.sqrt(1.0-z*z) * scale;
|
|
|
-
|
|
|
- out[0] = Math.cos(r) * zScale;
|
|
|
- out[1] = Math.sin(r) * zScale;
|
|
|
- out[2] = z * scale;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Transforms the Vec3 with a Mat4. 4th vector component is implicitly '1'
|
|
|
- */
|
|
|
- export function transformMat4(out: Vec3, a: Vec3, m: Mat4) {
|
|
|
- const x = a[0], y = a[1], z = a[2],
|
|
|
- w = 1 / ((m[3] * x + m[7] * y + m[11] * z + m[15]) || 1.0);
|
|
|
- out[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) * w;
|
|
|
- out[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) * w;
|
|
|
- out[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) * w;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- const angleTempA = zero(), angleTempB = zero();
|
|
|
- export function angle(a: Vec3, b: Vec3) {
|
|
|
- copy(angleTempA, a);
|
|
|
- copy(angleTempB, b);
|
|
|
-
|
|
|
- normalize(angleTempA, angleTempA);
|
|
|
- normalize(angleTempB, angleTempB);
|
|
|
-
|
|
|
- const cosine = dot(angleTempA, angleTempB);
|
|
|
-
|
|
|
- if (cosine > 1.0) {
|
|
|
- return 0;
|
|
|
- }
|
|
|
- else if (cosine < -1.0) {
|
|
|
- return Math.PI;
|
|
|
- } else {
|
|
|
- return Math.acos(cosine);
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- const rotTemp = zero();
|
|
|
- export function makeRotation(mat: Mat4, a: Vec3, b: Vec3): Mat4 {
|
|
|
- const by = angle(a, b);
|
|
|
- if (Math.abs(by) < 0.0001) return Mat4.setIdentity(mat);
|
|
|
- const axis = cross(rotTemp, a, b);
|
|
|
- return Mat4.fromRotation(mat, by, axis);
|
|
|
- }
|
|
|
-}
|
|
|
-
|
|
|
-export namespace Vec4 {
|
|
|
- export function zero(): Vec4 {
|
|
|
- // force double backing array by 0.1.
|
|
|
- const ret = [0.1, 0, 0, 0];
|
|
|
- ret[0] = 0.0;
|
|
|
- return ret as any;
|
|
|
- }
|
|
|
-
|
|
|
- export function clone(a: Vec4) {
|
|
|
- const out = zero();
|
|
|
- out[0] = a[0];
|
|
|
- out[1] = a[1];
|
|
|
- out[2] = a[2];
|
|
|
- out[3] = a[3];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function create(x: number, y: number, z: number, w: number) {
|
|
|
- const out = zero();
|
|
|
- out[0] = x;
|
|
|
- out[1] = y;
|
|
|
- out[2] = z;
|
|
|
- out[3] = w;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function copy(out: Vec4, a: Vec4) {
|
|
|
- out[0] = a[0];
|
|
|
- out[1] = a[1];
|
|
|
- out[2] = a[2];
|
|
|
- out[3] = a[3];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function set(out: Vec4, x: number, y: number, z: number, w: number) {
|
|
|
- out[0] = x;
|
|
|
- out[1] = y;
|
|
|
- out[2] = z;
|
|
|
- out[3] = w;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function add(out: Quat, a: Quat, b: Quat) {
|
|
|
- out[0] = a[0] + b[0];
|
|
|
- out[1] = a[1] + b[1];
|
|
|
- out[2] = a[2] + b[2];
|
|
|
- out[3] = a[3] + b[3];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function distance(a: Vec4, b: Vec4) {
|
|
|
- const x = b[0] - a[0],
|
|
|
- y = b[1] - a[1],
|
|
|
- z = b[2] - a[2],
|
|
|
- w = b[3] - a[3];
|
|
|
- return Math.sqrt(x * x + y * y + z * z + w * w);
|
|
|
- }
|
|
|
-
|
|
|
- export function squaredDistance(a: Vec4, b: Vec4) {
|
|
|
- const x = b[0] - a[0],
|
|
|
- y = b[1] - a[1],
|
|
|
- z = b[2] - a[2],
|
|
|
- w = b[3] - a[3];
|
|
|
- return x * x + y * y + z * z + w * w;
|
|
|
- }
|
|
|
-
|
|
|
- export function norm(a: Vec4) {
|
|
|
- const x = a[0],
|
|
|
- y = a[1],
|
|
|
- z = a[2],
|
|
|
- w = a[3];
|
|
|
- return Math.sqrt(x * x + y * y + z * z + w * w);
|
|
|
- }
|
|
|
-
|
|
|
- export function squaredNorm(a: Vec4) {
|
|
|
- const x = a[0],
|
|
|
- y = a[1],
|
|
|
- z = a[2],
|
|
|
- w = a[3];
|
|
|
- return x * x + y * y + z * z + w * w;
|
|
|
- }
|
|
|
-
|
|
|
- export function transform(out: Vec4, a: Vec4, m: Mat4) {
|
|
|
- const x = a[0], y = a[1], z = a[2], w = a[3];
|
|
|
- out[0] = m[0] * x + m[4] * y + m[8] * z + m[12] * w;
|
|
|
- out[1] = m[1] * x + m[5] * y + m[9] * z + m[13] * w;
|
|
|
- out[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;
|
|
|
- out[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;
|
|
|
- return out;
|
|
|
- }
|
|
|
-}
|
|
|
-
|
|
|
-export namespace Quat {
|
|
|
- export function zero(): Quat {
|
|
|
- // force double backing array by 0.1.
|
|
|
- const ret = [0.1, 0, 0, 0];
|
|
|
- ret[0] = 0.0;
|
|
|
- return ret as any;
|
|
|
- }
|
|
|
-
|
|
|
- export function identity(): Quat {
|
|
|
- const out = zero();
|
|
|
- out[3] = 1;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function create(x: number, y: number, z: number, w: number) {
|
|
|
- const out = identity();
|
|
|
- out[0] = x;
|
|
|
- out[1] = y;
|
|
|
- out[2] = z;
|
|
|
- out[3] = w;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function setAxisAngle(out: Quat, axis: Vec3, rad: number) {
|
|
|
- rad = rad * 0.5;
|
|
|
- let s = Math.sin(rad);
|
|
|
- out[0] = s * axis[0];
|
|
|
- out[1] = s * axis[1];
|
|
|
- out[2] = s * axis[2];
|
|
|
- out[3] = Math.cos(rad);
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Gets the rotation axis and angle for a given
|
|
|
- * quaternion. If a quaternion is created with
|
|
|
- * setAxisAngle, this method will return the same
|
|
|
- * values as providied in the original parameter list
|
|
|
- * OR functionally equivalent values.
|
|
|
- * Example: The quaternion formed by axis [0, 0, 1] and
|
|
|
- * angle -90 is the same as the quaternion formed by
|
|
|
- * [0, 0, 1] and 270. This method favors the latter.
|
|
|
- */
|
|
|
- export function getAxisAngle(out_axis: Vec3, q: Quat) {
|
|
|
- let rad = Math.acos(q[3]) * 2.0;
|
|
|
- let s = Math.sin(rad / 2.0);
|
|
|
- if (s !== 0.0) {
|
|
|
- out_axis[0] = q[0] / s;
|
|
|
- out_axis[1] = q[1] / s;
|
|
|
- out_axis[2] = q[2] / s;
|
|
|
- } else {
|
|
|
- // If s is zero, return any axis (no rotation - axis does not matter)
|
|
|
- out_axis[0] = 1;
|
|
|
- out_axis[1] = 0;
|
|
|
- out_axis[2] = 0;
|
|
|
- }
|
|
|
- return rad;
|
|
|
- }
|
|
|
-
|
|
|
- export function multiply(out: Quat, a: Quat, b: Quat) {
|
|
|
- let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
- let bx = b[0], by = b[1], bz = b[2], bw = b[3];
|
|
|
-
|
|
|
- out[0] = ax * bw + aw * bx + ay * bz - az * by;
|
|
|
- out[1] = ay * bw + aw * by + az * bx - ax * bz;
|
|
|
- out[2] = az * bw + aw * bz + ax * by - ay * bx;
|
|
|
- out[3] = aw * bw - ax * bx - ay * by - az * bz;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function rotateX(out: Quat, a: Quat, rad: number) {
|
|
|
- rad *= 0.5;
|
|
|
-
|
|
|
- let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
- let bx = Math.sin(rad), bw = Math.cos(rad);
|
|
|
-
|
|
|
- out[0] = ax * bw + aw * bx;
|
|
|
- out[1] = ay * bw + az * bx;
|
|
|
- out[2] = az * bw - ay * bx;
|
|
|
- out[3] = aw * bw - ax * bx;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function rotateY(out: Quat, a: Quat, rad: number) {
|
|
|
- rad *= 0.5;
|
|
|
-
|
|
|
- let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
- let by = Math.sin(rad), bw = Math.cos(rad);
|
|
|
-
|
|
|
- out[0] = ax * bw - az * by;
|
|
|
- out[1] = ay * bw + aw * by;
|
|
|
- out[2] = az * bw + ax * by;
|
|
|
- out[3] = aw * bw - ay * by;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function rotateZ(out: Quat, a: Quat, rad: number) {
|
|
|
- rad *= 0.5;
|
|
|
-
|
|
|
- let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
- let bz = Math.sin(rad), bw = Math.cos(rad);
|
|
|
-
|
|
|
- out[0] = ax * bw + ay * bz;
|
|
|
- out[1] = ay * bw - ax * bz;
|
|
|
- out[2] = az * bw + aw * bz;
|
|
|
- out[3] = aw * bw - az * bz;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Calculates the W component of a quat from the X, Y, and Z components.
|
|
|
- * Assumes that quaternion is 1 unit in length.
|
|
|
- * Any existing W component will be ignored.
|
|
|
- */
|
|
|
- export function calculateW(out: Quat, a: Quat) {
|
|
|
- let x = a[0], y = a[1], z = a[2];
|
|
|
-
|
|
|
- out[0] = x;
|
|
|
- out[1] = y;
|
|
|
- out[2] = z;
|
|
|
- out[3] = Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Performs a spherical linear interpolation between two quat
|
|
|
- */
|
|
|
- export function slerp(out: Quat, a: Quat, b: Quat, t: number) {
|
|
|
- // benchmarks:
|
|
|
- // http://jsperf.com/quaternion-slerp-implementations
|
|
|
- let ax = a[0], ay = a[1], az = a[2], aw = a[3];
|
|
|
- let bx = b[0], by = b[1], bz = b[2], bw = b[3];
|
|
|
-
|
|
|
- let omega, cosom, sinom, scale0, scale1;
|
|
|
-
|
|
|
- // calc cosine
|
|
|
- cosom = ax * bx + ay * by + az * bz + aw * bw;
|
|
|
- // adjust signs (if necessary)
|
|
|
- if ( cosom < 0.0 ) {
|
|
|
- cosom = -cosom;
|
|
|
- bx = - bx;
|
|
|
- by = - by;
|
|
|
- bz = - bz;
|
|
|
- bw = - bw;
|
|
|
- }
|
|
|
- // calculate coefficients
|
|
|
- if ( (1.0 - cosom) > 0.000001 ) {
|
|
|
- // standard case (slerp)
|
|
|
- omega = Math.acos(cosom);
|
|
|
- sinom = Math.sin(omega);
|
|
|
- scale0 = Math.sin((1.0 - t) * omega) / sinom;
|
|
|
- scale1 = Math.sin(t * omega) / sinom;
|
|
|
- } else {
|
|
|
- // "from" and "to" quaternions are very close
|
|
|
- // ... so we can do a linear interpolation
|
|
|
- scale0 = 1.0 - t;
|
|
|
- scale1 = t;
|
|
|
- }
|
|
|
- // calculate final values
|
|
|
- out[0] = scale0 * ax + scale1 * bx;
|
|
|
- out[1] = scale0 * ay + scale1 * by;
|
|
|
- out[2] = scale0 * az + scale1 * bz;
|
|
|
- out[3] = scale0 * aw + scale1 * bw;
|
|
|
-
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function invert(out: Quat, a: Quat) {
|
|
|
- let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
|
|
|
- let dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;
|
|
|
- let invDot = dot ? 1.0/dot : 0;
|
|
|
-
|
|
|
- // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0
|
|
|
-
|
|
|
- out[0] = -a0 * invDot;
|
|
|
- out[1] = -a1 * invDot;
|
|
|
- out[2] = -a2 * invDot;
|
|
|
- out[3] = a3 * invDot;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Calculates the conjugate of a quat
|
|
|
- * If the quaternion is normalized, this function is faster than quat.inverse and produces the same result.
|
|
|
- */
|
|
|
- export function conjugate(out: Quat, a: Quat) {
|
|
|
- out[0] = -a[0];
|
|
|
- out[1] = -a[1];
|
|
|
- out[2] = -a[2];
|
|
|
- out[3] = a[3];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Creates a quaternion from the given 3x3 rotation matrix.
|
|
|
- *
|
|
|
- * NOTE: The resultant quaternion is not normalized, so you should be sure
|
|
|
- * to renormalize the quaternion yourself where necessary.
|
|
|
- */
|
|
|
- export function fromMat3(out: Quat, m: Mat3) {
|
|
|
- // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
|
|
|
- // article "Quaternion Calculus and Fast Animation".
|
|
|
- const fTrace = m[0] + m[4] + m[8];
|
|
|
- let fRoot;
|
|
|
-
|
|
|
- if ( fTrace > 0.0 ) {
|
|
|
- // |w| > 1/2, may as well choose w > 1/2
|
|
|
- fRoot = Math.sqrt(fTrace + 1.0); // 2w
|
|
|
- out[3] = 0.5 * fRoot;
|
|
|
- fRoot = 0.5/fRoot; // 1/(4w)
|
|
|
- out[0] = (m[5]-m[7])*fRoot;
|
|
|
- out[1] = (m[6]-m[2])*fRoot;
|
|
|
- out[2] = (m[1]-m[3])*fRoot;
|
|
|
- } else {
|
|
|
- // |w| <= 1/2
|
|
|
- let i = 0;
|
|
|
- if ( m[4] > m[0] ) i = 1;
|
|
|
- if ( m[8] > m[i*3+i] ) i = 2;
|
|
|
- let j = (i+1)%3;
|
|
|
- let k = (i+2)%3;
|
|
|
-
|
|
|
- fRoot = Math.sqrt(m[i*3+i]-m[j*3+j]-m[k*3+k] + 1.0);
|
|
|
- out[i] = 0.5 * fRoot;
|
|
|
- fRoot = 0.5 / fRoot;
|
|
|
- out[3] = (m[j*3+k] - m[k*3+j]) * fRoot;
|
|
|
- out[j] = (m[j*3+i] + m[i*3+j]) * fRoot;
|
|
|
- out[k] = (m[k*3+i] + m[i*3+k]) * fRoot;
|
|
|
- }
|
|
|
-
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function clone(a: Quat) {
|
|
|
- const out = zero();
|
|
|
- out[0] = a[0];
|
|
|
- out[1] = a[1];
|
|
|
- out[2] = a[2];
|
|
|
- out[3] = a[3];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function copy(out: Quat, a: Quat) {
|
|
|
- out[0] = a[0];
|
|
|
- out[1] = a[1];
|
|
|
- out[2] = a[2];
|
|
|
- out[3] = a[3];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function set(out: Quat, x: number, y: number, z: number, w: number) {
|
|
|
- out[0] = x;
|
|
|
- out[1] = y;
|
|
|
- out[2] = z;
|
|
|
- out[3] = w;
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function add(out: Quat, a: Quat, b: Quat) {
|
|
|
- out[0] = a[0] + b[0];
|
|
|
- out[1] = a[1] + b[1];
|
|
|
- out[2] = a[2] + b[2];
|
|
|
- out[3] = a[3] + b[3];
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- export function normalize(out: Quat, a: Quat) {
|
|
|
- let x = a[0];
|
|
|
- let y = a[1];
|
|
|
- let z = a[2];
|
|
|
- let w = a[3];
|
|
|
- let len = x*x + y*y + z*z + w*w;
|
|
|
- if (len > 0) {
|
|
|
- len = 1 / Math.sqrt(len);
|
|
|
- out[0] = x * len;
|
|
|
- out[1] = y * len;
|
|
|
- out[2] = z * len;
|
|
|
- out[3] = w * len;
|
|
|
- }
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Sets a quaternion to represent the shortest rotation from one
|
|
|
- * vector to another.
|
|
|
- *
|
|
|
- * Both vectors are assumed to be unit length.
|
|
|
- */
|
|
|
- const rotTmpVec3 = Vec3.zero();
|
|
|
- const rotTmpVec3UnitX = Vec3.create(1, 0, 0);
|
|
|
- const rotTmpVec3UnitY = Vec3.create(0, 1, 0);
|
|
|
- export function rotationTo(out: Quat, a: Vec3, b: Vec3) {
|
|
|
- let dot = Vec3.dot(a, b);
|
|
|
- if (dot < -0.999999) {
|
|
|
- Vec3.cross(rotTmpVec3, rotTmpVec3UnitX, a);
|
|
|
- if (Vec3.magnitude(rotTmpVec3) < 0.000001)
|
|
|
- Vec3.cross(rotTmpVec3, rotTmpVec3UnitY, a);
|
|
|
- Vec3.normalize(rotTmpVec3, rotTmpVec3);
|
|
|
- setAxisAngle(out, rotTmpVec3, Math.PI);
|
|
|
- return out;
|
|
|
- } else if (dot > 0.999999) {
|
|
|
- out[0] = 0;
|
|
|
- out[1] = 0;
|
|
|
- out[2] = 0;
|
|
|
- out[3] = 1;
|
|
|
- return out;
|
|
|
- } else {
|
|
|
- Vec3.cross(rotTmpVec3, a, b);
|
|
|
- out[0] = rotTmpVec3[0];
|
|
|
- out[1] = rotTmpVec3[1];
|
|
|
- out[2] = rotTmpVec3[2];
|
|
|
- out[3] = 1 + dot;
|
|
|
- return normalize(out, out);
|
|
|
- }
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Performs a spherical linear interpolation with two control points
|
|
|
- */
|
|
|
- let sqlerpTemp1 = Quat.zero();
|
|
|
- let sqlerpTemp2 = Quat.zero();
|
|
|
- export function sqlerp(out: Quat, a: Quat, b: Quat, c: Quat, d: Quat, t: number) {
|
|
|
- slerp(sqlerpTemp1, a, d, t);
|
|
|
- slerp(sqlerpTemp2, b, c, t);
|
|
|
- slerp(out, sqlerpTemp1, sqlerpTemp2, 2 * t * (1 - t));
|
|
|
- return out;
|
|
|
- }
|
|
|
-
|
|
|
- /**
|
|
|
- * Sets the specified quaternion with values corresponding to the given
|
|
|
- * axes. Each axis is a vec3 and is expected to be unit length and
|
|
|
- * perpendicular to all other specified axes.
|
|
|
- */
|
|
|
- const axesTmpMat = Mat3.zero();
|
|
|
- export function setAxes(out: Quat, view: Vec3, right: Vec3, up: Vec3) {
|
|
|
- axesTmpMat[0] = right[0];
|
|
|
- axesTmpMat[3] = right[1];
|
|
|
- axesTmpMat[6] = right[2];
|
|
|
-
|
|
|
- axesTmpMat[1] = up[0];
|
|
|
- axesTmpMat[4] = up[1];
|
|
|
- axesTmpMat[7] = up[2];
|
|
|
-
|
|
|
- axesTmpMat[2] = -view[0];
|
|
|
- axesTmpMat[5] = -view[1];
|
|
|
- axesTmpMat[8] = -view[2];
|
|
|
-
|
|
|
- return normalize(out, Quat.fromMat3(out, axesTmpMat));
|
|
|
- }
|
|
|
-}
|
|
|
+export { Mat4, Mat3, Vec3, Vec4, Quat }
|
Alexander Rose