@lightningjs/renderer
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Lightning 3 Renderer
1,678 lines • 54.6 kB
JavaScript
/*
* If not stated otherwise in this file or this component's LICENSE file the
* following copyright and licenses apply:
*
* Copyright 2023 Comcast Cable Communications Management, LLC.
*
* Licensed under the Apache License, Version 2.0 (the License);
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
import { getMatrixArrayType, EPSILON, } from './common.js';
/**
* Creates a new identity Mat4
*
* @returns {Mat4} a new 4x4 matrix
*/
export function create() {
const out = getMatrixArrayType(16);
if (!(out instanceof Float32Array)) {
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
}
out[0] = 1;
out[5] = 1;
out[10] = 1;
out[15] = 1;
return out;
}
/**
* Creates a new Mat4 initialized with values from an existing matrix
*
* @param {Mat4} a matrix to clone
* @returns {Mat4} a new 4x4 matrix
*/
export function clone(a) {
const out = getMatrixArrayType(16);
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;
}
/**
* Copy the values from one Mat4 to another
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the source matrix
* @returns {Mat4} out
*/
export function copy(out, a) {
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;
}
/**
* Create a new Mat4 with the given values
*
* @param {Number} m00 Component in column 0, row 0 position (index 0)
* @param {Number} m01 Component in column 0, row 1 position (index 1)
* @param {Number} m02 Component in column 0, row 2 position (index 2)
* @param {Number} m03 Component in column 0, row 3 position (index 3)
* @param {Number} m10 Component in column 1, row 0 position (index 4)
* @param {Number} m11 Component in column 1, row 1 position (index 5)
* @param {Number} m12 Component in column 1, row 2 position (index 6)
* @param {Number} m13 Component in column 1, row 3 position (index 7)
* @param {Number} m20 Component in column 2, row 0 position (index 8)
* @param {Number} m21 Component in column 2, row 1 position (index 9)
* @param {Number} m22 Component in column 2, row 2 position (index 10)
* @param {Number} m23 Component in column 2, row 3 position (index 11)
* @param {Number} m30 Component in column 3, row 0 position (index 12)
* @param {Number} m31 Component in column 3, row 1 position (index 13)
* @param {Number} m32 Component in column 3, row 2 position (index 14)
* @param {Number} m33 Component in column 3, row 3 position (index 15)
* @returns {Mat4} A new Mat4
*/
export function fromValues(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
const out = getMatrixArrayType(16);
out[0] = m00;
out[1] = m01;
out[2] = m02;
out[3] = m03;
out[4] = m10;
out[5] = m11;
out[6] = m12;
out[7] = m13;
out[8] = m20;
out[9] = m21;
out[10] = m22;
out[11] = m23;
out[12] = m30;
out[13] = m31;
out[14] = m32;
out[15] = m33;
return out;
}
/**
* Set the components of a Mat4 to the given values
*
* @param {Mat4} out the receiving matrix
* @param {Number} m00 Component in column 0, row 0 position (index 0)
* @param {Number} m01 Component in column 0, row 1 position (index 1)
* @param {Number} m02 Component in column 0, row 2 position (index 2)
* @param {Number} m03 Component in column 0, row 3 position (index 3)
* @param {Number} m10 Component in column 1, row 0 position (index 4)
* @param {Number} m11 Component in column 1, row 1 position (index 5)
* @param {Number} m12 Component in column 1, row 2 position (index 6)
* @param {Number} m13 Component in column 1, row 3 position (index 7)
* @param {Number} m20 Component in column 2, row 0 position (index 8)
* @param {Number} m21 Component in column 2, row 1 position (index 9)
* @param {Number} m22 Component in column 2, row 2 position (index 10)
* @param {Number} m23 Component in column 2, row 3 position (index 11)
* @param {Number} m30 Component in column 3, row 0 position (index 12)
* @param {Number} m31 Component in column 3, row 1 position (index 13)
* @param {Number} m32 Component in column 3, row 2 position (index 14)
* @param {Number} m33 Component in column 3, row 3 position (index 15)
* @returns {Mat4} out
*/
export function set(out, m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
out[0] = m00;
out[1] = m01;
out[2] = m02;
out[3] = m03;
out[4] = m10;
out[5] = m11;
out[6] = m12;
out[7] = m13;
out[8] = m20;
out[9] = m21;
out[10] = m22;
out[11] = m23;
out[12] = m30;
out[13] = m31;
out[14] = m32;
out[15] = m33;
return out;
}
/**
* Set a Mat4 to the identity matrix
*
* @param {Mat4} out the receiving matrix
* @returns {Mat4} out
*/
export function identity(out) {
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;
}
/**
* Transpose the values of a Mat4
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the source matrix
* @returns {Mat4} out
*/
export function transpose(out, a) {
// 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;
}
/**
* Inverts a Mat4
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the source matrix
* @returns {Mat4} out
*/
export function invert(out, a) {
const a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
const a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
const a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
const a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
const b00 = a00 * a11 - a01 * a10;
const b01 = a00 * a12 - a02 * a10;
const b02 = a00 * a13 - a03 * a10;
const b03 = a01 * a12 - a02 * a11;
const b04 = a01 * a13 - a03 * a11;
const b05 = a02 * a13 - a03 * a12;
const b06 = a20 * a31 - a21 * a30;
const b07 = a20 * a32 - a22 * a30;
const b08 = a20 * a33 - a23 * a30;
const b09 = a21 * a32 - a22 * a31;
const b10 = a21 * a33 - a23 * a31;
const b11 = a22 * a33 - a23 * a32; // Calculate the determinant
let det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
if (!det) {
return null;
}
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;
}
/**
* Calculates the adjugate of a Mat4
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the source matrix
* @returns {Mat4} out
*/
export function adjoint(out, a) {
const a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
const a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
const a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
const a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
const b00 = a00 * a11 - a01 * a10;
const b01 = a00 * a12 - a02 * a10;
const b02 = a00 * a13 - a03 * a10;
const b03 = a01 * a12 - a02 * a11;
const b04 = a01 * a13 - a03 * a11;
const b05 = a02 * a13 - a03 * a12;
const b06 = a20 * a31 - a21 * a30;
const b07 = a20 * a32 - a22 * a30;
const b08 = a20 * a33 - a23 * a30;
const b09 = a21 * a32 - a22 * a31;
const b10 = a21 * a33 - a23 * a31;
const b11 = a22 * a33 - a23 * a32;
out[0] = a11 * b11 - a12 * b10 + a13 * b09;
out[1] = a02 * b10 - a01 * b11 - a03 * b09;
out[2] = a31 * b05 - a32 * b04 + a33 * b03;
out[3] = a22 * b04 - a21 * b05 - a23 * b03;
out[4] = a12 * b08 - a10 * b11 - a13 * b07;
out[5] = a00 * b11 - a02 * b08 + a03 * b07;
out[6] = a32 * b02 - a30 * b05 - a33 * b01;
out[7] = a20 * b05 - a22 * b02 + a23 * b01;
out[8] = a10 * b10 - a11 * b08 + a13 * b06;
out[9] = a01 * b08 - a00 * b10 - a03 * b06;
out[10] = a30 * b04 - a31 * b02 + a33 * b00;
out[11] = a21 * b02 - a20 * b04 - a23 * b00;
out[12] = a11 * b07 - a10 * b09 - a12 * b06;
out[13] = a00 * b09 - a01 * b07 + a02 * b06;
out[14] = a31 * b01 - a30 * b03 - a32 * b00;
out[15] = a20 * b03 - a21 * b01 + a22 * b00;
return out;
}
/**
* Calculates the determinant of a Mat4
*
* @param {Mat4} a the source matrix
* @returns {Number} determinant of a
*/
export function determinant(a) {
const a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
const a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
const a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
const a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];
const b0 = a00 * a11 - a01 * a10;
const b1 = a00 * a12 - a02 * a10;
const b2 = a01 * a12 - a02 * a11;
const b3 = a20 * a31 - a21 * a30;
const b4 = a20 * a32 - a22 * a30;
const b5 = a21 * a32 - a22 * a31;
const b6 = a00 * b5 - a01 * b4 + a02 * b3;
const b7 = a10 * b5 - a11 * b4 + a12 * b3;
const b8 = a20 * b2 - a21 * b1 + a22 * b0;
const b9 = a30 * b2 - a31 * b1 + a32 * b0; // Calculate the determinant
return a13 * b6 - a03 * b7 + a33 * b8 - a23 * b9;
}
/**
* Multiplies two Mat4s
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the first operand
* @param {Mat4} b the second operand
* @returns {Mat4} out
*/
export function multiply(out, a, b) {
const a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
const a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
const a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
const 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;
}
/**
* Translate a Mat4 by the given vector
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the matrix to translate
* @param {Vec3} v vector to translate by
* @returns {Mat4} out
*/
export function translate(out, a, v) {
const x = v[0], y = v[1], z = v[2];
let a00, a01, a02, a03;
let a10, a11, a12, a13;
let a20, a21, a22, a23;
if (a === out) {
out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
}
else {
a00 = a[0];
a01 = a[1];
a02 = a[2];
a03 = a[3];
a10 = a[4];
a11 = a[5];
a12 = a[6];
a13 = a[7];
a20 = a[8];
a21 = a[9];
a22 = a[10];
a23 = a[11];
out[0] = a00;
out[1] = a01;
out[2] = a02;
out[3] = a03;
out[4] = a10;
out[5] = a11;
out[6] = a12;
out[7] = a13;
out[8] = a20;
out[9] = a21;
out[10] = a22;
out[11] = a23;
out[12] = a00 * x + a10 * y + a20 * z + a[12];
out[13] = a01 * x + a11 * y + a21 * z + a[13];
out[14] = a02 * x + a12 * y + a22 * z + a[14];
out[15] = a03 * x + a13 * y + a23 * z + a[15];
}
return out;
}
/**
* Scales the Mat4 by the dimensions in the given Vec3 not using vectorization
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the matrix to scale
* @param {Vec3} v the Vec3 to scale the matrix by
* @returns {Mat4} out
**/
export function scale(out, a, v) {
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;
}
/**
* Rotates a Mat4 by the given angle around the given axis
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @param {Vec3} axis the axis to rotate around
* @returns {Mat4} out
*/
export function rotate(out, a, rad, axis) {
let x = axis[0], y = axis[1], z = axis[2];
let len = Math.hypot(x, y, z);
const 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
if (len < EPSILON) {
return null;
}
len = 1 / len;
x *= len;
y *= len;
z *= len;
const b00 = x * x * t + c, b01 = y * x * t + z * s, b02 = z * x * t - y * s, b10 = x * y * t - z * s, b11 = y * y * t + c, b12 = z * y * t + x * s, b20 = x * z * t + y * s, b21 = y * z * t - x * s, b22 = z * z * t + c; // Perform rotation-specific matrix multiplication
out[0] = a00 * b00 + a10 * b01 + a20 * b02;
out[1] = a01 * b00 + a11 * b01 + a21 * b02;
out[2] = a02 * b00 + a12 * b01 + a22 * b02;
out[3] = a03 * b00 + a13 * b01 + a23 * b02;
out[4] = a00 * b10 + a10 * b11 + a20 * b12;
out[5] = a01 * b10 + a11 * b11 + a21 * b12;
out[6] = a02 * b10 + a12 * b11 + a22 * b12;
out[7] = a03 * b10 + a13 * b11 + a23 * b12;
out[8] = a00 * b20 + a10 * b21 + a20 * b22;
out[9] = a01 * b20 + a11 * b21 + a21 * b22;
out[10] = a02 * b20 + a12 * b21 + a22 * b22;
out[11] = a03 * b20 + a13 * b21 + a23 * b22;
if (a !== out) {
// If the source and destination differ, copy the unchanged last row
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
}
return out;
}
/**
* Rotates a matrix by the given angle around the X axis
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {Mat4} out
*/
export function rotateX(out, a, rad) {
const s = Math.sin(rad);
const c = Math.cos(rad);
const a10 = a[4];
const a11 = a[5];
const a12 = a[6];
const a13 = a[7];
const a20 = a[8];
const a21 = a[9];
const a22 = a[10];
const a23 = a[11];
if (a !== out) {
// If the source and destination differ, copy the unchanged rows
out[0] = a[0];
out[1] = a[1];
out[2] = a[2];
out[3] = a[3];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
} // Perform axis-specific matrix multiplication
out[4] = a10 * c + a20 * s;
out[5] = a11 * c + a21 * s;
out[6] = a12 * c + a22 * s;
out[7] = a13 * c + a23 * s;
out[8] = a20 * c - a10 * s;
out[9] = a21 * c - a11 * s;
out[10] = a22 * c - a12 * s;
out[11] = a23 * c - a13 * s;
return out;
}
/**
* Rotates a matrix by the given angle around the Y axis
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {Mat4} out
*/
export function rotateY(out, a, rad) {
const s = Math.sin(rad);
const c = Math.cos(rad);
const a00 = a[0];
const a01 = a[1];
const a02 = a[2];
const a03 = a[3];
const a20 = a[8];
const a21 = a[9];
const a22 = a[10];
const a23 = a[11];
if (a !== out) {
// If the source and destination differ, copy the unchanged rows
out[4] = a[4];
out[5] = a[5];
out[6] = a[6];
out[7] = a[7];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
} // Perform axis-specific matrix multiplication
out[0] = a00 * c - a20 * s;
out[1] = a01 * c - a21 * s;
out[2] = a02 * c - a22 * s;
out[3] = a03 * c - a23 * s;
out[8] = a00 * s + a20 * c;
out[9] = a01 * s + a21 * c;
out[10] = a02 * s + a22 * c;
out[11] = a03 * s + a23 * c;
return out;
}
/**
* Rotates a matrix by the given angle around the Z axis
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {Mat4} out
*/
export function rotateZ(out, a, rad) {
const s = Math.sin(rad);
const c = Math.cos(rad);
const a00 = a[0];
const a01 = a[1];
const a02 = a[2];
const a03 = a[3];
const a10 = a[4];
const a11 = a[5];
const a12 = a[6];
const a13 = a[7];
if (a !== out) {
// If the source and destination differ, copy the unchanged last row
out[8] = a[8];
out[9] = a[9];
out[10] = a[10];
out[11] = a[11];
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
} // Perform axis-specific matrix multiplication
out[0] = a00 * c + a10 * s;
out[1] = a01 * c + a11 * s;
out[2] = a02 * c + a12 * s;
out[3] = a03 * c + a13 * s;
out[4] = a10 * c - a00 * s;
out[5] = a11 * c - a01 * s;
out[6] = a12 * c - a02 * s;
out[7] = a13 * c - a03 * s;
return out;
}
/**
* Creates a matrix from a vector translation
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.translate(dest, dest, vec);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {Vec3} v Translation vector
* @returns {Mat4} out
*/
export function fromTranslation(out, v) {
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
out[15] = 1;
return out;
}
/**
* Creates a matrix from a vector scaling
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.scale(dest, dest, vec);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {Vec3} v Scaling vector
* @returns {Mat4} out
*/
export function fromScaling(out, v) {
out[0] = v[0];
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = v[1];
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = v[2];
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
/**
* Creates a matrix from a given angle around a given axis
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.rotate(dest, dest, rad, axis);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @param {Vec3} axis the axis to rotate around
* @returns {Mat4} out
*/
export function fromRotation(out, rad, axis) {
let x = axis[0], y = axis[1], z = axis[2];
let len = Math.hypot(x, y, z);
const s = Math.sin(rad), c = Math.cos(rad), t = 1 - c; // Perform rotation-specific matrix multiplication
if (len < EPSILON) {
return null;
}
len = 1 / len;
x *= len;
y *= len;
z *= len;
out[0] = x * x * t + c;
out[1] = y * x * t + z * s;
out[2] = z * x * t - y * s;
out[3] = 0;
out[4] = x * y * t - z * s;
out[5] = y * y * t + c;
out[6] = z * y * t + x * s;
out[7] = 0;
out[8] = x * z * t + y * s;
out[9] = y * z * t - x * s;
out[10] = z * z * t + c;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
/**
* Creates a matrix from the given angle around the X axis
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.rotateX(dest, dest, rad);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @returns {Mat4} out
*/
export function fromXRotation(out, rad) {
const s = Math.sin(rad);
const c = Math.cos(rad); // Perform axis-specific matrix multiplication
out[0] = 1;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = c;
out[6] = s;
out[7] = 0;
out[8] = 0;
out[9] = -s;
out[10] = c;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
/**
* Creates a matrix from the given angle around the Y axis
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.rotateY(dest, dest, rad);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @returns {Mat4} out
*/
export function fromYRotation(out, rad) {
const s = Math.sin(rad);
const c = Math.cos(rad); // Perform axis-specific matrix multiplication
out[0] = c;
out[1] = 0;
out[2] = -s;
out[3] = 0;
out[4] = 0;
out[5] = 1;
out[6] = 0;
out[7] = 0;
out[8] = s;
out[9] = 0;
out[10] = c;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
/**
* Creates a matrix from the given angle around the Z axis
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.rotateZ(dest, dest, rad);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @returns {Mat4} out
*/
export function fromZRotation(out, rad) {
const s = Math.sin(rad);
const c = Math.cos(rad); // Perform axis-specific matrix multiplication
out[0] = c;
out[1] = s;
out[2] = 0;
out[3] = 0;
out[4] = -s;
out[5] = c;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[10] = 1;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
/**
* Creates a matrix from a quaternion rotation and vector translation
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.translate(dest, vec);
* let quatMat = Mat4.create();
* quat4.toMat4(quat, quatMat);
* Mat4.multiply(dest, quatMat);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {quat4} q Rotation quaternion
* @param {Vec3} v Translation vector
* @returns {Mat4} out
*/
export function fromRotationTranslation(out, q, v) {
// Quaternion math
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 xy = x * y2;
const xz = x * z2;
const yy = y * y2;
const yz = y * z2;
const zz = z * z2;
const wx = w * x2;
const wy = w * y2;
const wz = w * z2;
out[0] = 1 - (yy + zz);
out[1] = xy + wz;
out[2] = xz - wy;
out[3] = 0;
out[4] = xy - wz;
out[5] = 1 - (xx + zz);
out[6] = yz + wx;
out[7] = 0;
out[8] = xz + wy;
out[9] = yz - wx;
out[10] = 1 - (xx + yy);
out[11] = 0;
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
out[15] = 1;
return out;
}
/**
* Creates a new Mat4 from a dual quat.
*
* @param {Mat4} out Matrix
* @param {Quat2} a Dual Quaternion
* @returns {Mat4} Mat4 receiving operation result
*/
export function fromQuat2(out, a) {
const translation = getMatrixArrayType(3);
const bx = -a[0], by = -a[1], bz = -a[2], bw = a[3], ax = a[4], ay = a[5], az = a[6], aw = a[7];
const magnitude = bx * bx + by * by + bz * bz + bw * bw; //Only scale if it makes sense
if (magnitude > 0) {
translation[0] = ((ax * bw + aw * bx + ay * bz - az * by) * 2) / magnitude;
translation[1] = ((ay * bw + aw * by + az * bx - ax * bz) * 2) / magnitude;
translation[2] = ((az * bw + aw * bz + ax * by - ay * bx) * 2) / magnitude;
}
else {
translation[0] = (ax * bw + aw * bx + ay * bz - az * by) * 2;
translation[1] = (ay * bw + aw * by + az * bx - ax * bz) * 2;
translation[2] = (az * bw + aw * bz + ax * by - ay * bx) * 2;
}
fromRotationTranslation(out, a, translation);
return out;
}
/**
* Returns the translation vector component of a transformation
* matrix. If a matrix is built with fromRotationTranslation,
* the returned vector will be the same as the translation vector
* originally supplied.
* @param {Vec3} out Vector to receive translation component
* @param {Mat4} mat Matrix to be decomposed (input)
* @return {Vec3} out
*/
export function getTranslation(out, mat) {
out[0] = mat[12];
out[1] = mat[13];
out[2] = mat[14];
return out;
}
/**
* Returns the scaling factor component of a transformation
* matrix. If a matrix is built with fromRotationTranslationScale
* with a normalized Quaternion paramter, the returned vector will be
* the same as the scaling vector
* originally supplied.
* @param {Vec3} out Vector to receive scaling factor component
* @param {Mat4} mat Matrix to be decomposed (input)
* @return {Vec3} out
*/
export function getScaling(out, mat) {
const m11 = mat[0];
const m12 = mat[1];
const m13 = mat[2];
const m21 = mat[4];
const m22 = mat[5];
const m23 = mat[6];
const m31 = mat[8];
const m32 = mat[9];
const m33 = mat[10];
out[0] = Math.hypot(m11, m12, m13);
out[1] = Math.hypot(m21, m22, m23);
out[2] = Math.hypot(m31, m32, m33);
return out;
}
/**
* Returns a quaternion representing the rotational component
* of a transformation matrix. If a matrix is built with
* fromRotationTranslation, the returned quaternion will be the
* same as the quaternion originally supplied.
* @param {quat} out Quaternion to receive the rotation component
* @param {Mat4} mat Matrix to be decomposed (input)
* @return {quat} out
*/
export function getRotation(out, mat) {
const scaling = getMatrixArrayType(3);
getScaling(scaling, mat);
const is1 = 1 / scaling[0];
const is2 = 1 / scaling[1];
const is3 = 1 / scaling[2];
const sm11 = mat[0] * is1;
const sm12 = mat[1] * is2;
const sm13 = mat[2] * is3;
const sm21 = mat[4] * is1;
const sm22 = mat[5] * is2;
const sm23 = mat[6] * is3;
const sm31 = mat[8] * is1;
const sm32 = mat[9] * is2;
const sm33 = mat[10] * is3;
const trace = sm11 + sm22 + sm33;
let S = 0;
if (trace > 0) {
S = Math.sqrt(trace + 1.0) * 2;
out[3] = 0.25 * S;
out[0] = (sm23 - sm32) / S;
out[1] = (sm31 - sm13) / S;
out[2] = (sm12 - sm21) / S;
}
else if (sm11 > sm22 && sm11 > sm33) {
S = Math.sqrt(1.0 + sm11 - sm22 - sm33) * 2;
out[3] = (sm23 - sm32) / S;
out[0] = 0.25 * S;
out[1] = (sm12 + sm21) / S;
out[2] = (sm31 + sm13) / S;
}
else if (sm22 > sm33) {
S = Math.sqrt(1.0 + sm22 - sm11 - sm33) * 2;
out[3] = (sm31 - sm13) / S;
out[0] = (sm12 + sm21) / S;
out[1] = 0.25 * S;
out[2] = (sm23 + sm32) / S;
}
else {
S = Math.sqrt(1.0 + sm33 - sm11 - sm22) * 2;
out[3] = (sm12 - sm21) / S;
out[0] = (sm31 + sm13) / S;
out[1] = (sm23 + sm32) / S;
out[2] = 0.25 * S;
}
return out;
}
/**
* Decomposes a transformation matrix into its rotation, translation
* and scale components. Returns only the rotation component
* @param {quat} out_r Quaternion to receive the rotation component
* @param {Vec3} out_t Vector to receive the translation vector
* @param {Vec3} out_s Vector to receive the scaling factor
* @param {Mat4} mat Matrix to be decomposed (input)
* @returns {quat} out_r
*/
export function decompose(out_r, out_t, out_s, mat) {
out_t[0] = mat[12];
out_t[1] = mat[13];
out_t[2] = mat[14];
const m11 = mat[0];
const m12 = mat[1];
const m13 = mat[2];
const m21 = mat[4];
const m22 = mat[5];
const m23 = mat[6];
const m31 = mat[8];
const m32 = mat[9];
const m33 = mat[10];
out_s[0] = Math.hypot(m11, m12, m13);
out_s[1] = Math.hypot(m21, m22, m23);
out_s[2] = Math.hypot(m31, m32, m33);
const is1 = 1 / out_s[0];
const is2 = 1 / out_s[1];
const is3 = 1 / out_s[2];
const sm11 = m11 * is1;
const sm12 = m12 * is2;
const sm13 = m13 * is3;
const sm21 = m21 * is1;
const sm22 = m22 * is2;
const sm23 = m23 * is3;
const sm31 = m31 * is1;
const sm32 = m32 * is2;
const sm33 = m33 * is3;
const trace = sm11 + sm22 + sm33;
let S = 0;
if (trace > 0) {
S = Math.sqrt(trace + 1.0) * 2;
out_r[3] = 0.25 * S;
out_r[0] = (sm23 - sm32) / S;
out_r[1] = (sm31 - sm13) / S;
out_r[2] = (sm12 - sm21) / S;
}
else if (sm11 > sm22 && sm11 > sm33) {
S = Math.sqrt(1.0 + sm11 - sm22 - sm33) * 2;
out_r[3] = (sm23 - sm32) / S;
out_r[0] = 0.25 * S;
out_r[1] = (sm12 + sm21) / S;
out_r[2] = (sm31 + sm13) / S;
}
else if (sm22 > sm33) {
S = Math.sqrt(1.0 + sm22 - sm11 - sm33) * 2;
out_r[3] = (sm31 - sm13) / S;
out_r[0] = (sm12 + sm21) / S;
out_r[1] = 0.25 * S;
out_r[2] = (sm23 + sm32) / S;
}
else {
S = Math.sqrt(1.0 + sm33 - sm11 - sm22) * 2;
out_r[3] = (sm12 - sm21) / S;
out_r[0] = (sm31 + sm13) / S;
out_r[1] = (sm23 + sm32) / S;
out_r[2] = 0.25 * S;
}
return out_r;
}
/**
* Creates a matrix from a quaternion rotation, vector translation and vector scale
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.translate(dest, vec);
* let quatMat = Mat4.create();
* quat4.toMat4(quat, quatMat);
* Mat4.multiply(dest, quatMat);
* Mat4.scale(dest, scale)
*
* @param {Mat4} out Mat4 receiving operation result
* @param {quat4} q Rotation quaternion
* @param {Vec3} v Translation vector
* @param {Vec3} s Scaling vector
* @returns {Mat4} out
*/
export function fromRotationTranslationScale(out, q, v, s) {
// Quaternion math
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 xy = x * y2;
const xz = x * z2;
const yy = y * y2;
const yz = y * z2;
const zz = z * z2;
const wx = w * x2;
const wy = w * y2;
const wz = w * z2;
const sx = s[0];
const sy = s[1];
const sz = s[2];
out[0] = (1 - (yy + zz)) * sx;
out[1] = (xy + wz) * sx;
out[2] = (xz - wy) * sx;
out[3] = 0;
out[4] = (xy - wz) * sy;
out[5] = (1 - (xx + zz)) * sy;
out[6] = (yz + wx) * sy;
out[7] = 0;
out[8] = (xz + wy) * sz;
out[9] = (yz - wx) * sz;
out[10] = (1 - (xx + yy)) * sz;
out[11] = 0;
out[12] = v[0];
out[13] = v[1];
out[14] = v[2];
out[15] = 1;
return out;
}
/**
* Creates a matrix from a quaternion rotation, vector translation and vector scale, rotating and scaling around the given origin
* This is equivalent to (but much faster than):
*
* Mat4.identity(dest);
* Mat4.translate(dest, vec);
* Mat4.translate(dest, origin);
* let quatMat = Mat4.create();
* quat4.toMat4(quat, quatMat);
* Mat4.multiply(dest, quatMat);
* Mat4.scale(dest, scale)
* Mat4.translate(dest, negativeOrigin);
*
* @param {Mat4} out Mat4 receiving operation result
* @param {quat4} q Rotation quaternion
* @param {Vec3} v Translation vector
* @param {Vec3} s Scaling vector
* @param {Vec3} o The origin vector around which to scale and rotate
* @returns {Mat4} out
*/
export function fromRotationTranslationScaleOrigin(out, q, v, s, o) {
// Quaternion math
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 xy = x * y2;
const xz = x * z2;
const yy = y * y2;
const yz = y * z2;
const zz = z * z2;
const wx = w * x2;
const wy = w * y2;
const wz = w * z2;
const sx = s[0];
const sy = s[1];
const sz = s[2];
const ox = o[0];
const oy = o[1];
const oz = o[2];
const out0 = (1 - (yy + zz)) * sx;
const out1 = (xy + wz) * sx;
const out2 = (xz - wy) * sx;
const out4 = (xy - wz) * sy;
const out5 = (1 - (xx + zz)) * sy;
const out6 = (yz + wx) * sy;
const out8 = (xz + wy) * sz;
const out9 = (yz - wx) * sz;
const out10 = (1 - (xx + yy)) * sz;
out[0] = out0;
out[1] = out1;
out[2] = out2;
out[3] = 0;
out[4] = out4;
out[5] = out5;
out[6] = out6;
out[7] = 0;
out[8] = out8;
out[9] = out9;
out[10] = out10;
out[11] = 0;
out[12] = v[0] + ox - (out0 * ox + out4 * oy + out8 * oz);
out[13] = v[1] + oy - (out1 * ox + out5 * oy + out9 * oz);
out[14] = v[2] + oz - (out2 * ox + out6 * oy + out10 * oz);
out[15] = 1;
return out;
}
/**
* Calculates a 4x4 matrix from the given quaternion
*
* @param {Mat4} out Mat4 receiving operation result
* @param {Quat} q Quaternion to create matrix from
*
* @returns {Mat4} out
*/
export function fromQuat(out, q) {
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
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {Number} left Left bound of the frustum
* @param {Number} right Right bound of the frustum
* @param {Number} bottom Bottom bound of the frustum
* @param {Number} top Top bound of the frustum
* @param {Number} near Near bound of the frustum
* @param {Number} far Far bound of the frustum
* @returns {Mat4} out
*/
export function frustum(out, left, right, bottom, top, near, far) {
const rl = 1 / (right - left);
const tb = 1 / (top - bottom);
const 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.
* The near/far clip planes correspond to a normalized device coordinate Z range of [-1, 1],
* which matches WebGL/OpenGL's clip volume.
* Passing null/undefined/no value for far will generate infinite projection matrix.
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {number} fovy Vertical field of view in radians
* @param {number} aspect Aspect ratio. typically viewport width/height
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum, can be null or Infinity
* @returns {Mat4} out
*/
export function perspectiveNO(out, fovy, aspect, near, far) {
const f = 1.0 / Math.tan(fovy / 2);
out[0] = f / aspect;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = f;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[15] = 0;
if (far != null && far !== Infinity) {
const nf = 1 / (near - far);
out[10] = (far + near) * nf;
out[14] = 2 * far * near * nf;
}
else {
out[10] = -1;
out[14] = -2 * near;
}
return out;
}
/**
* Alias for {@link perspectiveNO}
* @function
*/
export const perspective = perspectiveNO;
/**
* Generates a perspective projection matrix suitable for WebGPU with the given bounds.
* The near/far clip planes correspond to a normalized device coordinate Z range of [0, 1],
* which matches WebGPU/Vulkan/DirectX/Metal's clip volume.
* Passing null/undefined/no value for far will generate infinite projection matrix.
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {number} fovy Vertical field of view in radians
* @param {number} aspect Aspect ratio. typically viewport width/height
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum, can be null or Infinity
* @returns {Mat4} out
*/
export function perspectiveZO(out, fovy, aspect, near, far) {
const f = 1.0 / Math.tan(fovy / 2);
out[0] = f / aspect;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = f;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[15] = 0;
if (far != null && far !== Infinity) {
const nf = 1 / (near - far);
out[10] = far * nf;
out[14] = far * near * nf;
}
else {
out[10] = -1;
out[14] = -near;
}
return out;
}
/**
* Generates a perspective projection matrix with the given field of view.
* This is primarily useful for generating projection matrices to be used
* with the still experiemental WebVR API.
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {Object} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {Mat4} out
*/
export function perspectiveFromFieldOfView(out, fov, near, far) {
const upTan = Math.tan((fov.upDegrees * Math.PI) / 180.0);
const downTan = Math.tan((fov.downDegrees * Math.PI) / 180.0);
const leftTan = Math.tan((fov.leftDegrees * Math.PI) / 180.0);
const rightTan = Math.tan((fov.rightDegrees * Math.PI) / 180.0);
const xScale = 2.0 / (leftTan + rightTan);
const yScale = 2.0 / (upTan + downTan);
out[0] = xScale;
out[1] = 0.0;
out[2] = 0.0;
out[3] = 0.0;
out[4] = 0.0;
out[5] = yScale;
out[6] = 0.0;
out[7] = 0.0;
out[8] = -((leftTan - rightTan) * xScale * 0.5);
out[9] = (upTan - downTan) * yScale * 0.5;
out[10] = far / (near - far);
out[11] = -1.0;
out[12] = 0.0;
out[13] = 0.0;
out[14] = (far * near) / (near - far);
out[15] = 0.0;
return out;
}
/**
* Generates a orthogonal projection matrix with the given bounds.
* The near/far clip planes correspond to a normalized device coordinate Z range of [-1, 1],
* which matches WebGL/OpenGL's clip volume.
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {number} left Left bound of the frustum
* @param {number} right Right bound of the frustum
* @param {number} bottom Bottom bound of the frustum
* @param {number} top Top bound of the frustum
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {Mat4} out
*/
export function orthoNO(out, left, right, bottom, top, near, far) {
const lr = 1 / (left - right);
const bt = 1 / (bottom - top);
const 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;
}
/**
* Alias for {@link orthoNO}
* @function
*/
export const ortho = orthoNO;
/**
* Generates a orthogonal projection matrix with the given bounds.
* The near/far clip planes correspond to a normalized device coordinate Z range of [0, 1],
* which matches WebGPU/Vulkan/DirectX/Metal's clip volume.
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {number} left Left bound of the frustum
* @param {number} right Right bound of the frustum
* @param {number} bottom Bottom bound of the frustum
* @param {number} top Top bound of the frustum
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {Mat4} out
*/
export function orthoZO(out, left, right, bottom, top, near, far) {
const lr = 1 / (left - right);
const bt = 1 / (bottom - top);
const 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] = nf;
out[11] = 0;
out[12] = (left + right) * lr;
out[13] = (top + bottom) * bt;
out[14] = near * nf;
out[15] = 1;
return out;
}
/**
* Generates a look-at matrix with the given eye position, focal point, and up axis.
* If you want a matrix that actually makes an object look at another object, you should use targetTo instead.
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {Vec3} eye Position of the viewer
* @param {Vec3} center Point the viewer is looking at
* @param {Vec3} up Vec3 pointing up
* @returns {Mat4} out
*/
export function lookAt(out, eye, center, up) {
let x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
const eyex = eye[0];
const eyey = eye[1];
const eyez = eye[2];
const upx = up[0];
const upy = up[1];
const upz = up[2];
const centerx = center[0];
const centery = center[1];
const centerz = center[2];
if (Math.abs(eyex - centerx) < EPSILON &&
Math.abs(eyey - centery) < EPSILON &&
Math.abs(eyez - centerz) < EPSILON) {
return identity(out);
}
z0 = eyex - centerx;
z1 = eyey - centery;
z2 = eyez - centerz;
len = 1 / Math.hypot(z0, z1, z2);
z0 *= len;
z1 *= len;
z2 *= len;
x0 = upy * z2 - upz * z1;
x1 = upz * z0 - upx * z2;
x2 = upx * z1 - upy * z0;
len = Math.hypot(x0, x1, x2);
if (!len) {
x0 = 0;
x1 = 0;
x2 = 0;
}
else {
len = 1 / len;
x0 *= len;
x1 *= len;
x2 *= len;
}
y0 = z1 * x2 - z2 * x1;
y1 = z2 * x0 - z0 * x2;
y2 = z0 * x1 - z1 * x0;
len = Math.hypot(y0, y1, y2);
if (!len) {
y0 = 0;
y1 = 0;
y2 = 0;
}
else {
len = 1 / len;
y0 *= len;
y1 *= len;
y2 *= len;
}
out[0] = x0;
out[1] = y0;
out[2] = z0;
out[3] = 0;
out[4] = x1;
out[5] = y1;
out[6] = z1;
out[7] = 0;
out[8] = x2;
out[9] = y2;
out[10] = z2;
out[11] = 0;
out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
out[15] = 1;
return out;
}
/**
* Generates a matrix that makes something look at something else.
*
* @param {Mat4} out Mat4 frustum matrix will be written into
* @param {Vec3} eye Position of the viewer
* @param {Vec3} center Point the viewer is looking at
* @param {Vec3} up Vec3 pointing up
* @returns {Mat4} out
*/
export function targetTo(out, eye, target, up) {
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;
}
/**
* Returns a string representation of a Mat4
*
* @param {Mat4} a matrix to represent as a string
* @returns {String} string representation of the matrix
*/
export function str(a) {
return `Mat4(${a[0]}, ${a[1]}, ${a[2]}, ${a[3]}, ${a[4]}, ${a[5]}, ${a[6]}, ${a[7]}, ${a[8]}, ${a[9]}, ${a[10]}, ${a[11]}, ${a[12]}, ${a[13]}, ${a[14]}, ${a[15]})`;
}
/**
* Returns Frobenius norm of a Mat4
*
* @param {Mat4} a the matrix to calculate Frobenius norm of
* @returns {Number} Frobenius norm
*/
export function frob(a) {
return Math.hypot(a[0], a[1], a[2], a[3], a[4], a[5], a[6], a[7], a[8], a[9], a[10], a[11], a[12], a[13], a[14], a[15]);
}
/**
* Adds two Mat4's
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the first operand
* @param {Mat4} b the second operand
* @returns {Mat4} out
*/
export function add(out, a, b) {
out[0] = a[0] + b[0];
out[1] = a[1] + b[1];
out[2] = a[2] + b[2];
out[3] = a[3] + b[3];
out[4] = a[4] + b[4];
out[5] = a[5] + b[5];
out[6] = a[6] + b[6];
out[7] = a[7] + b[7];
out[8] = a[8] + b[8];
out[9] = a[9] + b[9];
out[10] = a[10] + b[10];
out[11] = a[11] + b[11];
out[12] = a[12] + b[12];
out[13] = a[13] + b[13];
out[14] = a[14] + b[14];
out[15] = a[15] + b[15];
return out;
}
/**
* Subtracts matrix b from matrix a
*
* @param {Mat4} out the receiving matrix
* @param {Mat4} a the first operand
* @param {Mat4} b the second operand
* @returns {Mat4} out
*/
export function subtract(out, a, b) {
out[0] = a[0] - b[0];
out[1] = a[1] - b[1];
out[2] = a[2] - b[2];
out[3] = a[3] - b[3];
out[4] = a[4] - b[4];
out[5] = a[5] - b[5];
out[6] = a[6] - b[6];
out[7] = a[7] - b[7];
out[8] = a[8] - b[8];
out[9] = a[9] - b[9];
out[10] = a[10] - b[10];
out[11] = a[11] - b[11];
out[12] = a[12] - b[12];
out[13] = a[13] - b[13];
out[14] = a[14] - b[14];
out[15] = a[15] - b[15];
return out;
}
/**
* Multiply each element of the matrix by a scalar.
*
* @param {Mat4} out the receiving matrix
* @pa