import * as glMatrix from "./common.js";
/**
* 4x4 Matrix<br>Format: column-major, when typed out it looks like row-major<br>The matrices are being post multiplied.
* @module mat4
*/
/**
* Creates a new identity mat4
*
* @returns {mat4} a new 4x4 matrix
*/
export function create() {
let out = new glMatrix.ARRAY_TYPE(16);
if (glMatrix.ARRAY_TYPE != 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 {ReadonlyMat4} a matrix to clone
* @returns {mat4} a new 4x4 matrix
*/
export function clone(a) {
let out = new glMatrix.ARRAY_TYPE(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 {ReadonlyMat4} 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
) {
let out = new glMatrix.ARRAY_TYPE(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 {ReadonlyMat4} 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) {
let a01 = a[1],
a02 = a[2],
a03 = a[3];
let a12 = a[6],
a13 = a[7];
let 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 {ReadonlyMat4} a the source matrix
* @returns {mat4} out
*/
export function invert(out, a) {
let a00 = a[0],
a01 = a[1],
a02 = a[2],
a03 = a[3];
let a10 = a[4],
a11 = a[5],
a12 = a[6],
a13 = a[7];
let a20 = a[8],
a21 = a[9],
a22 = a[10],
a23 = a[11];
let a30 = a[12],
a31 = a[13],
a32 = a[14],
a33 = a[15];
let b00 = a00 * a11 - a01 * a10;
let b01 = a00 * a12 - a02 * a10;
let b02 = a00 * a13 - a03 * a10;
let b03 = a01 * a12 - a02 * a11;
let b04 = a01 * a13 - a03 * a11;
let b05 = a02 * a13 - a03 * a12;
let b06 = a20 * a31 - a21 * a30;
let b07 = a20 * a32 - a22 * a30;
let b08 = a20 * a33 - a23 * a30;
let b09 = a21 * a32 - a22 * a31;
let b10 = a21 * a33 - a23 * a31;
let 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 {ReadonlyMat4} a the source matrix
* @returns {mat4} out
*/
export function adjoint(out, a) {
let a00 = a[0],
a01 = a[1],
a02 = a[2],
a03 = a[3];
let a10 = a[4],
a11 = a[5],
a12 = a[6],
a13 = a[7];
let a20 = a[8],
a21 = a[9],
a22 = a[10],
a23 = a[11];
let a30 = a[12],
a31 = a[13],
a32 = a[14],
a33 = a[15];
out[0] =
a11 * (a22 * a33 - a23 * a32) -
a21 * (a12 * a33 - a13 * a32) +
a31 * (a12 * a23 - a13 * a22);
out[1] = -(
a01 * (a22 * a33 - a23 * a32) -
a21 * (a02 * a33 - a03 * a32) +
a31 * (a02 * a23 - a03 * a22)
);
out[2] =
a01 * (a12 * a33 - a13 * a32) -
a11 * (a02 * a33 - a03 * a32) +
a31 * (a02 * a13 - a03 * a12);
out[3] = -(
a01 * (a12 * a23 - a13 * a22) -
a11 * (a02 * a23 - a03 * a22) +
a21 * (a02 * a13 - a03 * a12)
);
out[4] = -(
a10 * (a22 * a33 - a23 * a32) -
a20 * (a12 * a33 - a13 * a32) +
a30 * (a12 * a23 - a13 * a22)
);
out[5] =
a00 * (a22 * a33 - a23 * a32) -
a20 * (a02 * a33 - a03 * a32) +
a30 * (a02 * a23 - a03 * a22);
out[6] = -(
a00 * (a12 * a33 - a13 * a32) -
a10 * (a02 * a33 - a03 * a32) +
a30 * (a02 * a13 - a03 * a12)
);
out[7] =
a00 * (a12 * a23 - a13 * a22) -
a10 * (a02 * a23 - a03 * a22) +
a20 * (a02 * a13 - a03 * a12);
out[8] =
a10 * (a21 * a33 - a23 * a31) -
a20 * (a11 * a33 - a13 * a31) +
a30 * (a11 * a23 - a13 * a21);
out[9] = -(
a00 * (a21 * a33 - a23 * a31) -
a20 * (a01 * a33 - a03 * a31) +
a30 * (a01 * a23 - a03 * a21)
);
out[10] =
a00 * (a11 * a33 - a13 * a31) -
a10 * (a01 * a33 - a03 * a31) +
a30 * (a01 * a13 - a03 * a11);
out[11] = -(
a00 * (a11 * a23 - a13 * a21) -
a10 * (a01 * a23 - a03 * a21) +
a20 * (a01 * a13 - a03 * a11)
);
out[12] = -(
a10 * (a21 * a32 - a22 * a31) -
a20 * (a11 * a32 - a12 * a31) +
a30 * (a11 * a22 - a12 * a21)
);
out[13] =
a00 * (a21 * a32 - a22 * a31) -
a20 * (a01 * a32 - a02 * a31) +
a30 * (a01 * a22 - a02 * a21);
out[14] = -(
a00 * (a11 * a32 - a12 * a31) -
a10 * (a01 * a32 - a02 * a31) +
a30 * (a01 * a12 - a02 * a11)
);
out[15] =
a00 * (a11 * a22 - a12 * a21) -
a10 * (a01 * a22 - a02 * a21) +
a20 * (a01 * a12 - a02 * a11);
return out;
}
/**
* Calculates the determinant of a mat4
*
* @param {ReadonlyMat4} a the source matrix
* @returns {Number} determinant of a
*/
export function determinant(a) {
let a00 = a[0],
a01 = a[1],
a02 = a[2],
a03 = a[3];
let a10 = a[4],
a11 = a[5],
a12 = a[6],
a13 = a[7];
let a20 = a[8],
a21 = a[9],
a22 = a[10],
a23 = a[11];
let a30 = a[12],
a31 = a[13],
a32 = a[14],
a33 = a[15];
let b00 = a00 * a11 - a01 * a10;
let b01 = a00 * a12 - a02 * a10;
let b02 = a00 * a13 - a03 * a10;
let b03 = a01 * a12 - a02 * a11;
let b04 = a01 * a13 - a03 * a11;
let b05 = a02 * a13 - a03 * a12;
let b06 = a20 * a31 - a21 * a30;
let b07 = a20 * a32 - a22 * a30;
let b08 = a20 * a33 - a23 * a30;
let b09 = a21 * a32 - a22 * a31;
let b10 = a21 * a33 - a23 * a31;
let b11 = a22 * a33 - a23 * a32;
// Calculate the determinant
return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
}
/**
* Multiplies two mat4s
*
* @param {mat4} out the receiving matrix
* @param {ReadonlyMat4} a the first operand
* @param {ReadonlyMat4} b the second operand
* @returns {mat4} out
*/
export function multiply(out, a, b) {
let a00 = a[0],
a01 = a[1],
a02 = a[2],
a03 = a[3];
let a10 = a[4],
a11 = a[5],
a12 = a[6],
a13 = a[7];
let a20 = a[8],
a21 = a[9],
a22 = a[10],
a23 = a[11];
let 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 {ReadonlyMat4} a the matrix to translate
* @param {ReadonlyVec3} v vector to translate by
* @returns {mat4} out
*/
export function translate(out, a, v) {
let 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 {ReadonlyMat4} a the matrix to scale
* @param {ReadonlyVec3} v the vec3 to scale the matrix by
* @returns {mat4} out
**/
export function scale(out, a, v) {
let 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 {ReadonlyMat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @param {ReadonlyVec3} 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);
let s, c, t;
let a00, a01, a02, a03;
let a10, a11, a12, a13;
let a20, a21, a22, a23;
let b00, b01, b02;
let b10, b11, b12;
let b20, b21, b22;
if (len < glMatrix.EPSILON) {
return null;
}
len = 1 / len;
x *= len;
y *= len;
z *= len;
s = Math.sin(rad);
c = Math.cos(rad);
t = 1 - c;
a00 = a[0];
a01 = a[1];
a02 = a[2];
a03 = a[3];
a10 = a[4];
a11 = a[5];
a12 = a[6];
a13 = a[7];
a20 = a[8];
a21 = a[9];
a22 = a[10];
a23 = a[11];
// Construct the elements of the rotation matrix
b00 = x * x * t + c;
b01 = y * x * t + z * s;
b02 = z * x * t - y * s;
b10 = x * y * t - z * s;
b11 = y * y * t + c;
b12 = z * y * t + x * s;
b20 = x * z * t + y * s;
b21 = y * z * t - x * s;
b22 = z * z * t + c;
// Perform rotation-specific matrix multiplication
out[0] = a00 * b00 + a10 * b01 + a20 * b02;
out[1] = a01 * b00 + a11 * b01 + a21 * b02;
out[2] = a02 * b00 + a12 * b01 + a22 * b02;
out[3] = a03 * b00 + a13 * b01 + a23 * b02;
out[4] = a00 * b10 + a10 * b11 + a20 * b12;
out[5] = a01 * b10 + a11 * b11 + a21 * b12;
out[6] = a02 * b10 + a12 * b11 + a22 * b12;
out[7] = a03 * b10 + a13 * b11 + a23 * b12;
out[8] = a00 * b20 + a10 * b21 + a20 * b22;
out[9] = a01 * b20 + a11 * b21 + a21 * b22;
out[10] = a02 * b20 + a12 * b21 + a22 * b22;
out[11] = a03 * b20 + a13 * b21 + a23 * b22;
if (a !== out) {
// If the source and destination differ, copy the unchanged last row
out[12] = a[12];
out[13] = a[13];
out[14] = a[14];
out[15] = a[15];
}
return out;
}
/**
* Rotates a matrix by the given angle around the X axis
*
* @param {mat4} out the receiving matrix
* @param {ReadonlyMat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
export function rotateX(out, a, rad) {
let s = Math.sin(rad);
let c = Math.cos(rad);
let a10 = a[4];
let a11 = a[5];
let a12 = a[6];
let a13 = a[7];
let a20 = a[8];
let a21 = a[9];
let a22 = a[10];
let 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 {ReadonlyMat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
export function rotateY(out, a, rad) {
let s = Math.sin(rad);
let c = Math.cos(rad);
let a00 = a[0];
let a01 = a[1];
let a02 = a[2];
let a03 = a[3];
let a20 = a[8];
let a21 = a[9];
let a22 = a[10];
let 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 {ReadonlyMat4} a the matrix to rotate
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
export function rotateZ(out, a, rad) {
let s = Math.sin(rad);
let c = Math.cos(rad);
let a00 = a[0];
let a01 = a[1];
let a02 = a[2];
let a03 = a[3];
let a10 = a[4];
let a11 = a[5];
let a12 = a[6];
let 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 {ReadonlyVec3} 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 {ReadonlyVec3} 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 {ReadonlyVec3} 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);
let s, c, t;
if (len < glMatrix.EPSILON) {
return null;
}
len = 1 / len;
x *= len;
y *= len;
z *= len;
s = Math.sin(rad);
c = Math.cos(rad);
t = 1 - c;
// Perform rotation-specific matrix multiplication
out[0] = x * x * t + c;
out[1] = y * x * t + z * s;
out[2] = z * x * t - y * s;
out[3] = 0;
out[4] = x * y * t - z * s;
out[5] = y * y * t + c;
out[6] = z * y * t + x * s;
out[7] = 0;
out[8] = x * z * t + y * s;
out[9] = y * z * t - x * s;
out[10] = z * z * t + c;
out[11] = 0;
out[12] = 0;
out[13] = 0;
out[14] = 0;
out[15] = 1;
return out;
}
/**
* Creates a matrix from the given angle around the X axis
* This is equivalent to (but much faster than):
*
* mat4.identity(dest);
* mat4.rotateX(dest, dest, rad);
*
* @param {mat4} out mat4 receiving operation result
* @param {Number} rad the angle to rotate the matrix by
* @returns {mat4} out
*/
export function fromXRotation(out, rad) {
let s = Math.sin(rad);
let 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) {
let s = Math.sin(rad);
let 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) {
let s = Math.sin(rad);
let 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 {ReadonlyVec3} v Translation vector
* @returns {mat4} out
*/
export function fromRotationTranslation(out, q, v) {
// Quaternion math
let x = q[0],
y = q[1],
z = q[2],
w = q[3];
let x2 = x + x;
let y2 = y + y;
let z2 = z + z;
let xx = x * x2;
let xy = x * y2;
let xz = x * z2;
let yy = y * y2;
let yz = y * z2;
let zz = z * z2;
let wx = w * x2;
let wy = w * y2;
let 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 {ReadonlyQuat2} a Dual Quaternion
* @returns {mat4} mat4 receiving operation result
*/
export function fromQuat2(out, a) {
let translation = new glMatrix.ARRAY_TYPE(3);
let bx = -a[0],
by = -a[1],
bz = -a[2],
bw = a[3],
ax = a[4],
ay = a[5],
az = a[6],
aw = a[7];
let 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 {ReadonlyMat4} 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 {ReadonlyMat4} mat Matrix to be decomposed (input)
* @return {vec3} out
*/
export function getScaling(out, mat) {
let m11 = mat[0];
let m12 = mat[1];
let m13 = mat[2];
let m21 = mat[4];
let m22 = mat[5];
let m23 = mat[6];
let m31 = mat[8];
let m32 = mat[9];
let 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 {ReadonlyMat4} mat Matrix to be decomposed (input)
* @return {quat} out
*/
export function getRotation(out, mat) {
let scaling = new glMatrix.ARRAY_TYPE(3);
getScaling(scaling, mat);
let is1 = 1 / scaling[0];
let is2 = 1 / scaling[1];
let is3 = 1 / scaling[2];
let sm11 = mat[0] * is1;
let sm12 = mat[1] * is2;
let sm13 = mat[2] * is3;
let sm21 = mat[4] * is1;
let sm22 = mat[5] * is2;
let sm23 = mat[6] * is3;
let sm31 = mat[8] * is1;
let sm32 = mat[9] * is2;
let sm33 = mat[10] * is3;
let 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;
}
/**
* 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 {ReadonlyVec3} v Translation vector
* @param {ReadonlyVec3} s Scaling vector
* @returns {mat4} out
*/
export function fromRotationTranslationScale(out, q, v, s) {
// Quaternion math
let x = q[0],
y = q[1],
z = q[2],
w = q[3];
let x2 = x + x;
let y2 = y + y;
let z2 = z + z;
let xx = x * x2;
let xy = x * y2;
let xz = x * z2;
let yy = y * y2;
let yz = y * z2;
let zz = z * z2;
let wx = w * x2;
let wy = w * y2;
let wz = w * z2;
let sx = s[0];
let sy = s[1];
let 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 {ReadonlyVec3} v Translation vector
* @param {ReadonlyVec3} s Scaling vector
* @param {ReadonlyVec3} o The origin vector around which to scale and rotate
* @returns {mat4} out
*/
export function fromRotationTranslationScaleOrigin(out, q, v, s, o) {
// Quaternion math
let x = q[0],
y = q[1],
z = q[2],
w = q[3];
let x2 = x + x;
let y2 = y + y;
let z2 = z + z;
let xx = x * x2;
let xy = x * y2;
let xz = x * z2;
let yy = y * y2;
let yz = y * z2;
let zz = z * z2;
let wx = w * x2;
let wy = w * y2;
let wz = w * z2;
let sx = s[0];
let sy = s[1];
let sz = s[2];
let ox = o[0];
let oy = o[1];
let oz = o[2];
let out0 = (1 - (yy + zz)) * sx;
let out1 = (xy + wz) * sx;
let out2 = (xz - wy) * sx;
let out4 = (xy - wz) * sy;
let out5 = (1 - (xx + zz)) * sy;
let out6 = (yz + wx) * sy;
let out8 = (xz + wy) * sz;
let out9 = (yz - wx) * sz;
let 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 {ReadonlyQuat} q Quaternion to create matrix from
*
* @returns {mat4} out
*/
export function fromQuat(out, q) {
let x = q[0],
y = q[1],
z = q[2],
w = q[3];
let x2 = x + x;
let y2 = y + y;
let z2 = z + z;
let xx = x * x2;
let yx = y * x2;
let yy = y * y2;
let zx = z * x2;
let zy = z * y2;
let zz = z * z2;
let wx = w * x2;
let wy = w * y2;
let 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) {
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.
* Passing null/undefined/no value for far will generate infinite projection matrix.
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {number} fovy Vertical field of view in radians
* @param {number} aspect Aspect ratio. typically viewport width/height
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum, can be null or Infinity
* @returns {mat4} out
*/
export function perspective(out, fovy, aspect, near, far) {
let f = 1.0 / Math.tan(fovy / 2),
nf;
out[0] = f / aspect;
out[1] = 0;
out[2] = 0;
out[3] = 0;
out[4] = 0;
out[5] = f;
out[6] = 0;
out[7] = 0;
out[8] = 0;
out[9] = 0;
out[11] = -1;
out[12] = 0;
out[13] = 0;
out[15] = 0;
if (far != null && far !== Infinity) {
nf = 1 / (near - far);
out[10] = (far + near) * nf;
out[14] = 2 * far * near * nf;
} else {
out[10] = -1;
out[14] = -2 * near;
}
return out;
}
/**
* Generates a perspective projection matrix with the given field of view.
* This is primarily useful for generating projection matrices to be used
* with the still experiemental WebVR API.
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {Object} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {mat4} out
*/
export function perspectiveFromFieldOfView(out, fov, near, far) {
let upTan = Math.tan((fov.upDegrees * Math.PI) / 180.0);
let downTan = Math.tan((fov.downDegrees * Math.PI) / 180.0);
let leftTan = Math.tan((fov.leftDegrees * Math.PI) / 180.0);
let rightTan = Math.tan((fov.rightDegrees * Math.PI) / 180.0);
let xScale = 2.0 / (leftTan + rightTan);
let yScale = 2.0 / (upTan + downTan);
out[0] = xScale;
out[1] = 0.0;
out[2] = 0.0;
out[3] = 0.0;
out[4] = 0.0;
out[5] = yScale;
out[6] = 0.0;
out[7] = 0.0;
out[8] = -((leftTan - rightTan) * xScale * 0.5);
out[9] = (upTan - downTan) * yScale * 0.5;
out[10] = far / (near - far);
out[11] = -1.0;
out[12] = 0.0;
out[13] = 0.0;
out[14] = (far * near) / (near - far);
out[15] = 0.0;
return out;
}
/**
* Generates a orthogonal projection matrix with the given bounds
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {number} left Left bound of the frustum
* @param {number} right Right bound of the frustum
* @param {number} bottom Bottom bound of the frustum
* @param {number} top Top bound of the frustum
* @param {number} near Near bound of the frustum
* @param {number} far Far bound of the frustum
* @returns {mat4} out
*/
export function ortho(out, left, right, bottom, top, near, far) {
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.
* 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 {ReadonlyVec3} eye Position of the viewer
* @param {ReadonlyVec3} center Point the viewer is looking at
* @param {ReadonlyVec3} 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;
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) < glMatrix.EPSILON &&
Math.abs(eyey - centery) < glMatrix.EPSILON &&
Math.abs(eyez - centerz) < glMatrix.EPSILON
) {
return identity(out);
}
z0 = eyex - centerx;
z1 = eyey - centery;
z2 = eyez - centerz;
len = 1 / Math.hypot(z0, z1, z2);
z0 *= len;
z1 *= len;
z2 *= len;
x0 = upy * z2 - upz * z1;
x1 = upz * z0 - upx * z2;
x2 = upx * z1 - upy * z0;
len = Math.hypot(x0, x1, x2);
if (!len) {
x0 = 0;
x1 = 0;
x2 = 0;
} else {
len = 1 / len;
x0 *= len;
x1 *= len;
x2 *= len;
}
y0 = z1 * x2 - z2 * x1;
y1 = z2 * x0 - z0 * x2;
y2 = z0 * x1 - z1 * x0;
len = Math.hypot(y0, y1, y2);
if (!len) {
y0 = 0;
y1 = 0;
y2 = 0;
} else {
len = 1 / len;
y0 *= len;
y1 *= len;
y2 *= len;
}
out[0] = x0;
out[1] = y0;
out[2] = z0;
out[3] = 0;
out[4] = x1;
out[5] = y1;
out[6] = z1;
out[7] = 0;
out[8] = x2;
out[9] = y2;
out[10] = z2;
out[11] = 0;
out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
out[15] = 1;
return out;
}
/**
* Generates a matrix that makes something look at something else.
*
* @param {mat4} out mat4 frustum matrix will be written into
* @param {ReadonlyVec3} eye Position of the viewer
* @param {ReadonlyVec3} center Point the viewer is looking at
* @param {ReadonlyVec3} up vec3 pointing up
* @returns {mat4} out
*/
export function targetTo(out, eye, target, up) {
let 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 {ReadonlyMat4} 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 {ReadonlyMat4} 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 {ReadonlyMat4} a the first operand
* @param {ReadonlyMat4} 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 {ReadonlyMat4} a the first operand
* @param {ReadonlyMat4} b the second operand
* @returns {mat4} out
*/
export function subtract(out, a, b) {
out[0] = a[0] - b[0];
out[1] = a[1] - b[1];
out[2] = a[2] - b[2];
out[3] = a[3] - b[3];
out[4] = a[4] - b[4];
out[5] = a[5] - b[5];
out[6] = a[6] - b[6];
out[7] = a[7] - b[7];
out[8] = a[8] - b[8];
out[9] = a[9] - b[9];
out[10] = a[10] - b[10];
out[11] = a[11] - b[11];
out[12] = a[12] - b[12];
out[13] = a[13] - b[13];
out[14] = a[14] - b[14];
out[15] = a[15] - b[15];
return out;
}
/**
* Multiply each element of the matrix by a scalar.
*
* @param {mat4} out the receiving matrix
* @param {ReadonlyMat4} a the matrix to scale
* @param {Number} b amount to scale the matrix's elements by
* @returns {mat4} out
*/
export function multiplyScalar(out, a, b) {
out[0] = a[0] * b;
out[1] = a[1] * b;
out[2] = a[2] * b;
out[3] = a[3] * b;
out[4] = a[4] * b;
out[5] = a[5] * b;
out[6] = a[6] * b;
out[7] = a[7] * b;
out[8] = a[8] * b;
out[9] = a[9] * b;
out[10] = a[10] * b;
out[11] = a[11] * b;
out[12] = a[12] * b;
out[13] = a[13] * b;
out[14] = a[14] * b;
out[15] = a[15] * b;
return out;
}
/**
* Adds two mat4's after multiplying each element of the second operand by a scalar value.
*
* @param {mat4} out the receiving vector
* @param {ReadonlyMat4} a the first operand
* @param {ReadonlyMat4} b the second operand
* @param {Number} scale the amount to scale b's elements by before adding
* @returns {mat4} out
*/
export function multiplyScalarAndAdd(out, a, b, scale) {
out[0] = a[0] + b[0] * scale;
out[1] = a[1] + b[1] * scale;
out[2] = a[2] + b[2] * scale;
out[3] = a[3] + b[3] * scale;
out[4] = a[4] + b[4] * scale;
out[5] = a[5] + b[5] * scale;
out[6] = a[6] + b[6] * scale;
out[7] = a[7] + b[7] * scale;
out[8] = a[8] + b[8] * scale;
out[9] = a[9] + b[9] * scale;
out[10] = a[10] + b[10] * scale;
out[11] = a[11] + b[11] * scale;
out[12] = a[12] + b[12] * scale;
out[13] = a[13] + b[13] * scale;
out[14] = a[14] + b[14] * scale;
out[15] = a[15] + b[15] * scale;
return out;
}
/**
* Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
*
* @param {ReadonlyMat4} a The first matrix.
* @param {ReadonlyMat4} b The second matrix.
* @returns {Boolean} True if the matrices are equal, false otherwise.
*/
export function exactEquals(a, b) {
return (
a[0] === b[0] &&
a[1] === b[1] &&
a[2] === b[2] &&
a[3] === b[3] &&
a[4] === b[4] &&
a[5] === b[5] &&
a[6] === b[6] &&
a[7] === b[7] &&
a[8] === b[8] &&
a[9] === b[9] &&
a[10] === b[10] &&
a[11] === b[11] &&
a[12] === b[12] &&
a[13] === b[13] &&
a[14] === b[14] &&
a[15] === b[15]
);
}
/**
* Returns whether or not the matrices have approximately the same elements in the same position.
*
* @param {ReadonlyMat4} a The first matrix.
* @param {ReadonlyMat4} b The second matrix.
* @returns {Boolean} True if the matrices are equal, false otherwise.
*/
export function equals(a, b) {
let a0 = a[0],
a1 = a[1],
a2 = a[2],
a3 = a[3];
let a4 = a[4],
a5 = a[5],
a6 = a[6],
a7 = a[7];
let a8 = a[8],
a9 = a[9],
a10 = a[10],
a11 = a[11];
let a12 = a[12],
a13 = a[13],
a14 = a[14],
a15 = a[15];
let b0 = b[0],
b1 = b[1],
b2 = b[2],
b3 = b[3];
let b4 = b[4],
b5 = b[5],
b6 = b[6],
b7 = b[7];
let b8 = b[8],
b9 = b[9],
b10 = b[10],
b11 = b[11];
let b12 = b[12],
b13 = b[13],
b14 = b[14],
b15 = b[15];
return (
Math.abs(a0 - b0) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
Math.abs(a1 - b1) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
Math.abs(a2 - b2) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a2), Math.abs(b2)) &&
Math.abs(a3 - b3) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a3), Math.abs(b3)) &&
Math.abs(a4 - b4) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a4), Math.abs(b4)) &&
Math.abs(a5 - b5) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a5), Math.abs(b5)) &&
Math.abs(a6 - b6) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a6), Math.abs(b6)) &&
Math.abs(a7 - b7) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a7), Math.abs(b7)) &&
Math.abs(a8 - b8) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a8), Math.abs(b8)) &&
Math.abs(a9 - b9) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a9), Math.abs(b9)) &&
Math.abs(a10 - b10) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a10), Math.abs(b10)) &&
Math.abs(a11 - b11) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a11), Math.abs(b11)) &&
Math.abs(a12 - b12) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a12), Math.abs(b12)) &&
Math.abs(a13 - b13) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a13), Math.abs(b13)) &&
Math.abs(a14 - b14) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a14), Math.abs(b14)) &&
Math.abs(a15 - b15) <=
glMatrix.EPSILON * Math.max(1.0, Math.abs(a15), Math.abs(b15))
);
}
/**
* Alias for {@link mat4.multiply}
* @function
*/
export const mul = multiply;
/**
* Alias for {@link mat4.subtract}
* @function
*/
export const sub = subtract;