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Alexander Rose authoredAlexander Rose authored
mat4.ts 27.69 KiB
/**
* Copyright (c) 2017-2018 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author David Sehnal <david.sehnal@gmail.com>
* @author Alexander Rose <alexander.rose@weirdbyte.de>
*/
/*
* This code has been modified from https://github.com/toji/gl-matrix/,
* copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*/
import { EPSILON, equalEps } from './common'
import Vec3 from './vec3';
import Quat from './quat';
import { degToRad } from '../../misc';
interface Mat4 extends Array<number> { [d: number]: number, '@type': 'mat4', length: 16 }
interface ReadonlyMat4 extends Array<number> { readonly [d: number]: number, '@type': 'mat4', length: 16 }
function Mat4() {
return Mat4.zero();
}
/**
* Stores a 4x4 matrix in a column major (j * 4 + i indexing) format.
*/
namespace Mat4 {
export function zero(): Mat4 {
// force double backing array by 0.1.
const ret = [0.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
ret[0] = 0.0;
return ret as any;
}
export function identity(): Mat4 {
const out = zero();
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
export function setIdentity(mat: Mat4): Mat4 {
mat[0] = 1;
mat[1] = 0;
mat[2] = 0;
mat[3] = 0;
mat[4] = 0;
mat[5] = 1; mat[6] = 0;
mat[7] = 0;
mat[8] = 0;
mat[9] = 0;
mat[10] = 1;
mat[11] = 0;
mat[12] = 0;
mat[13] = 0;
mat[14] = 0;
mat[15] = 1;
return mat;
}
export function setZero(mat: Mat4): Mat4 {
for (let i = 0; i < 16; i++) mat[i] = 0;
return mat;
}
export function ofRows(rows: number[][]): Mat4 {
const out = zero();
for (let i = 0; i < 4; i++) {
const r = rows[i];
for (let j = 0; j < 4; j++) {
out[4 * j + i] = r[j];
}
}
return out;
}
const _id = identity();
export function isIdentity(m: Mat4, eps?: number) {
return areEqual(m, _id, typeof eps === 'undefined' ? EPSILON.Value : eps);
}
export function areEqual(a: Mat4, b: Mat4, eps: number) {
for (let i = 0; i < 16; i++) {
if (Math.abs(a[i] - b[i]) > eps) return false;
}
return true;
}
export function setValue(a: Mat4, i: number, j: number, value: number) {
a[4 * j + i] = value;
}
export function toArray(a: Mat4, out: Helpers.NumberArray, offset: number) {
out[offset + 0] = a[0];
out[offset + 1] = a[1];
out[offset + 2] = a[2];
out[offset + 3] = a[3];
out[offset + 4] = a[4];
out[offset + 5] = a[5];
out[offset + 6] = a[6];
out[offset + 7] = a[7];
out[offset + 8] = a[8];
out[offset + 9] = a[9];
out[offset + 10] = a[10];
out[offset + 11] = a[11];
out[offset + 12] = a[12];
out[offset + 13] = a[13];
out[offset + 14] = a[14];
out[offset + 15] = a[15];
}
export function fromArray(a: Mat4, array: Helpers.NumberArray, offset: number) {
a[0] = array[offset + 0]
a[1] = array[offset + 1]
a[2] = array[offset + 2]
a[3] = array[offset + 3]
a[4] = array[offset + 4] a[5] = array[offset + 5]
a[6] = array[offset + 6]
a[7] = array[offset + 7]
a[8] = array[offset + 8]
a[9] = array[offset + 9]
a[10] = array[offset + 10]
a[11] = array[offset + 11]
a[12] = array[offset + 12]
a[13] = array[offset + 13]
a[14] = array[offset + 14]
a[15] = array[offset + 15]
return a
}
export function copy(out: Mat4, a: Mat4) {
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
return out;
}
export function clone(a: Mat4) {
return Mat4.copy(Mat4.zero(), a);
}
export function transpose(out: Mat4, a: Mat4) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
if (out === a) {
const a01 = a[1], a02 = a[2], a03 = a[3];
const a12 = a[6], a13 = a[7];
const a23 = a[11];
out[1] = a[4];
out[2] = a[8];
out[3] = a[12];
out[4] = a01;
out[6] = a[9];
out[7] = a[13];
out[8] = a02;
out[9] = a12;
out[11] = a[14];
out[12] = a03;
out[13] = a13;
out[14] = a23;
} else {
out[0] = a[0];
out[1] = a[4];
out[2] = a[8];
out[3] = a[12];
out[4] = a[1];
out[5] = a[5];
out[6] = a[9];
out[7] = a[13];
out[8] = a[2];
out[9] = a[6];
out[10] = a[10];
out[11] = a[14];
out[12] = a[3]; out[13] = a[7];
out[14] = a[11];
out[15] = a[15];
}
return out;
}
export function invert(out: Mat4, 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
let det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
if (!det) {
console.warn('non-invertible matrix.', a);
return out;
}
det = 1.0 / det;
out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;
return out;
}
export function mul(out: Mat4, a: Mat4, b: 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];
// Cache only the current line of the second matrix
let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30; out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
return out;
}
export function mul3(out: Mat4, a: Mat4, b: Mat4, c: Mat4) {
return mul(out, mul(out, a, b), c);
}
/** Translate a Mat4 by the given Vec3 */
export function translate(out: Mat4, a: Mat4, v: Vec3) {
const x = v[0], y = v[1], z = v[2];
let a00: number, a01: number, a02: number, a03: number,
a10: number, a11: number, a12: number, a13: number,
a20: number, a21: number, a22: number, a23: number;
if (a === out) {
out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
} else {
a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];
out[0] = a00; out[1] = a01; out[2] = a02; out[3] = a03;
out[4] = a10; out[5] = a11; out[6] = a12; out[7] = a13;
out[8] = a20; out[9] = a21; out[10] = a22; out[11] = a23;
out[12] = a00 * x + a10 * y + a20 * z + a[12];
out[13] = a01 * x + a11 * y + a21 * z + a[13];
out[14] = a02 * x + a12 * y + a22 * z + a[14];
out[15] = a03 * x + a13 * y + a23 * z + a[15];
}
return out;
}
export function fromTranslation(out: Mat4, v: Vec3) {
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
out[15] = 1;
return out; }
export function setTranslation(out: Mat4, v: Vec3) {
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
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.
*/
export function setAxes(out: Mat4, view: Vec3, right: Vec3, up: Vec3) {
out[0] = right[0];
out[4] = right[1];
out[8] = right[2];
out[1] = up[0];
out[5] = up[1];
out[9] = up[2];
out[2] = view[0];
out[6] = view[1];
out[10] = view[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 scaleUniformly(out: Mat4, a: Mat4, scale: number) {
out[0] = a[0] * scale;
out[1] = a[1] * scale;
out[2] = a[2] * scale;
out[3] = a[3] * scale;
out[4] = a[4] * scale;
out[5] = a[5] * scale;
out[6] = a[6] * scale;
out[7] = a[7] * scale;
out[8] = a[8] * scale;
out[9] = a[9] * scale;
out[10] = a[10] * scale;
out[11] = a[11] * scale;
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 fromUniformScaling(out: Mat4, scale: number) {
out[0] = scale;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = scale;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = scale;
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 (!equalEps(a33, 1, eps) || !equalEps(a03, 0, eps) || !equalEps(a13, 0, eps) || !equalEps(a23, 0, eps)) {
return false;
}
const det3x3 = a00 * (a11 * a22 - a12 * a21) - a01 * (a10 * a22 - a12 * a20) + a02 * (a10 * a21 - a11 * a20);
if (!equalEps(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;
}
/**
* Generates a matrix that makes something look at something else.
*/
export function targetTo(out: Mat4, eye: Vec3, target: Vec3, up: Vec3) {
const eyex = eye[0],
eyey = eye[1],
eyez = eye[2],
upx = up[0],
upy = up[1],
upz = up[2];
let z0 = eyex - target[0],
z1 = eyey - target[1],
z2 = eyez - target[2];
let len = z0*z0 + z1*z1 + z2*z2;
if (len > 0) {
len = 1 / Math.sqrt(len);
z0 *= len;
z1 *= len;
z2 *= len;
}
let x0 = upy * z2 - upz * z1,
x1 = upz * z0 - upx * z2,
x2 = upx * z1 - upy * z0;
len = x0*x0 + x1*x1 + x2*x2;
if (len > 0) {
len = 1 / Math.sqrt(len);
x0 *= len; x1 *= len;
x2 *= len;
}
out[0] = x0;
out[1] = x1;
out[2] = x2;
out[3] = 0;
out[4] = z1 * x2 - z2 * x1;
out[5] = z2 * x0 - z0 * x2;
out[6] = z0 * x1 - z1 * x0;
out[7] = 0;
out[8] = z0;
out[9] = z1;
out[10] = z2;
out[11] = 0;
out[12] = eyex;
out[13] = eyey;
out[14] = eyez;
out[15] = 1;
return out;
}
/**
* Perm is 0-indexed permutation
*/
export function fromPermutation(out: Mat4, perm: number[]) {
setZero(out);
for (let i = 0; i < 4; i++) {
const p = perm[i];
setValue(out, i, p, 1);
}
return out;
}
export function getMaxScaleOnAxis(m: Mat4) {
const scaleXSq = m[0] * m[0] + m[1] * m[1] + m[2] * m[2]
const scaleYSq = m[4] * m[4] + m[5] * m[5] + m[6] * m[6]
const scaleZSq = m[8] * m[8] + m[9] * m[9] + m[10] * m[10]
return Math.sqrt(Math.max(scaleXSq, scaleYSq, scaleZSq))
}
/** Rotation matrix for 90deg around x-axis */
export const rotX90: ReadonlyMat4 = Mat4.fromRotation(Mat4.identity(), degToRad(90), Vec3.create(1, 0, 0))
/** Rotation matrix for 180deg around x-axis */
export const rotX180: ReadonlyMat4 = Mat4.fromRotation(Mat4.identity(), degToRad(180), Vec3.create(1, 0, 0))
/** Rotation matrix for 90deg around y-axis */
export const rotY90: ReadonlyMat4 = Mat4.fromRotation(Mat4.identity(), degToRad(90), Vec3.create(0, 1, 0))
/** Rotation matrix for 180deg around y-axis */
export const rotY180: ReadonlyMat4 = Mat4.fromRotation(Mat4.identity(), degToRad(180), Vec3.create(0, 1, 0))
/** Rotation matrix for 90deg around z-axis */
export const rotZ90: ReadonlyMat4 = Mat4.fromRotation(Mat4.identity(), degToRad(90), Vec3.create(0, 0, 1))
/** Rotation matrix for 180deg around z-axis */
export const rotZ180: ReadonlyMat4 = Mat4.fromRotation(Mat4.identity(), degToRad(180), Vec3.create(0, 0, 1))
/** Rotation matrix for 90deg around first x-axis and then y-axis */
export const rotXY90: ReadonlyMat4 = Mat4.mul(Mat4.identity(), rotX90, rotY90)
/** Rotation matrix for 90deg around first z-axis and then y-axis */
export const rotZY90: ReadonlyMat4 = Mat4.mul(Mat4.identity(), rotZ90, rotY90)
/** Rotation matrix for 90deg around first z-axis and then y-axis and then z-axis */
export const rotZYZ90: ReadonlyMat4 = Mat4.mul(Mat4.identity(), rotZY90, rotZ90)
/** Rotation matrix for 90deg around first z-axis and then 180deg around x-axis */
export const rotZ90X180: ReadonlyMat4 = Mat4.mul(Mat4.identity(), rotZ90, rotX180)
/** Rotation matrix for 90deg around first y-axis and then 180deg around z-axis */
export const rotY90Z180: ReadonlyMat4 = Mat4.mul(Mat4.identity(), rotY90, rotZ180)
}
export default Mat4