src/lib/math.js
// Some temporary vars to help avoid garbage collection
const doublePrecision = true;
const FloatArrayType = doublePrecision ? Float64Array : Float32Array;
const tempMat1 = new FloatArrayType(16);
const tempMat2 = new FloatArrayType(16);
const tempVec4 = new FloatArrayType(4);
/**
* @private
*/
const math = {
MIN_DOUBLE: -Number.MAX_SAFE_INTEGER,
MAX_DOUBLE: Number.MAX_SAFE_INTEGER,
/**
* The number of radiians in a degree (0.0174532925).
* @property DEGTORAD
* @type {Number}
*/
DEGTORAD: 0.0174532925,
/**
* The number of degrees in a radian.
* @property RADTODEG
* @type {Number}
*/
RADTODEG: 57.295779513,
/**
* Returns a new, uninitialized two-element vector.
* @method vec2
* @param [values] Initial values.
* @static
* @returns {Number[]}
*/
vec2(values) {
return new FloatArrayType(values || 2);
},
/**
* Returns a new, uninitialized three-element vector.
* @method vec3
* @param [values] Initial values.
* @static
* @returns {Number[]}
*/
vec3(values) {
return new FloatArrayType(values || 3);
},
/**
* Returns a new, uninitialized four-element vector.
* @method vec4
* @param [values] Initial values.
* @static
* @returns {Number[]}
*/
vec4(values) {
return new FloatArrayType(values || 4);
},
/**
* Returns a new, uninitialized 3x3 matrix.
* @method mat3
* @param [values] Initial values.
* @static
* @returns {Number[]}
*/
mat3(values) {
return new FloatArrayType(values || 9);
},
/**
* Converts a 3x3 matrix to 4x4
* @method mat3ToMat4
* @param mat3 3x3 matrix.
* @param mat4 4x4 matrix
* @static
* @returns {Number[]}
*/
mat3ToMat4(mat3, mat4 = new FloatArrayType(16)) {
mat4[0] = mat3[0];
mat4[1] = mat3[1];
mat4[2] = mat3[2];
mat4[3] = 0;
mat4[4] = mat3[3];
mat4[5] = mat3[4];
mat4[6] = mat3[5];
mat4[7] = 0;
mat4[8] = mat3[6];
mat4[9] = mat3[7];
mat4[10] = mat3[8];
mat4[11] = 0;
mat4[12] = 0;
mat4[13] = 0;
mat4[14] = 0;
mat4[15] = 1;
return mat4;
},
/**
* Returns a new, uninitialized 4x4 matrix.
* @method mat4
* @param [values] Initial values.
* @static
* @returns {Number[]}
*/
mat4(values) {
return new FloatArrayType(values || 16);
},
/**
* Converts a 4x4 matrix to 3x3
* @method mat4ToMat3
* @param mat4 4x4 matrix.
* @param mat3 3x3 matrix
* @static
* @returns {Number[]}
*/
mat4ToMat3(mat4, mat3) { // TODO
//return new FloatArrayType(values || 9);
},
/**
* Returns a new UUID.
* @method createUUID
* @static
* @return string The new UUID
*/
createUUID: ((() => {
const self = {};
const lut = [];
for (let i = 0; i < 256; i++) {
lut[i] = (i < 16 ? '0' : '') + (i).toString(16);
}
return () => {
const d0 = Math.random() * 0xffffffff | 0;
const d1 = Math.random() * 0xffffffff | 0;
const d2 = Math.random() * 0xffffffff | 0;
const d3 = Math.random() * 0xffffffff | 0;
return `${lut[d0 & 0xff] + lut[d0 >> 8 & 0xff] + lut[d0 >> 16 & 0xff] + lut[d0 >> 24 & 0xff]}-${lut[d1 & 0xff]}${lut[d1 >> 8 & 0xff]}-${lut[d1 >> 16 & 0x0f | 0x40]}${lut[d1 >> 24 & 0xff]}-${lut[d2 & 0x3f | 0x80]}${lut[d2 >> 8 & 0xff]}-${lut[d2 >> 16 & 0xff]}${lut[d2 >> 24 & 0xff]}${lut[d3 & 0xff]}${lut[d3 >> 8 & 0xff]}${lut[d3 >> 16 & 0xff]}${lut[d3 >> 24 & 0xff]}`;
};
}))(),
/**
* Clamps a value to the given range.
* @param {Number} value Value to clamp.
* @param {Number} min Lower bound.
* @param {Number} max Upper bound.
* @returns {Number} Clamped result.
*/
clamp(value, min, max) {
return Math.max(min, Math.min(max, value));
},
/**
* Floating-point modulus
* @method fmod
* @static
* @param {Number} a
* @param {Number} b
* @returns {*}
*/
fmod(a, b) {
if (a < b) {
console.error("math.fmod : Attempting to find modulus within negative range - would be infinite loop - ignoring");
return a;
}
while (b <= a) {
a -= b;
}
return a;
},
/**
* Negates a four-element vector.
* @method negateVec4
* @static
* @param {Array(Number)} v Vector to negate
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
negateVec4(v, dest) {
if (!dest) {
dest = v;
}
dest[0] = -v[0];
dest[1] = -v[1];
dest[2] = -v[2];
dest[3] = -v[3];
return dest;
},
/**
* Adds one four-element vector to another.
* @method addVec4
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
addVec4(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] + v[0];
dest[1] = u[1] + v[1];
dest[2] = u[2] + v[2];
dest[3] = u[3] + v[3];
return dest;
},
/**
* Adds a scalar value to each element of a four-element vector.
* @method addVec4Scalar
* @static
* @param {Array(Number)} v The vector
* @param {Number} s The scalar
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
addVec4Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] + s;
dest[1] = v[1] + s;
dest[2] = v[2] + s;
dest[3] = v[3] + s;
return dest;
},
/**
* Adds one three-element vector to another.
* @method addVec3
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
addVec3(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] + v[0];
dest[1] = u[1] + v[1];
dest[2] = u[2] + v[2];
return dest;
},
/**
* Adds a scalar value to each element of a three-element vector.
* @method addVec4Scalar
* @static
* @param {Array(Number)} v The vector
* @param {Number} s The scalar
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
addVec3Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] + s;
dest[1] = v[1] + s;
dest[2] = v[2] + s;
return dest;
},
/**
* Subtracts one four-element vector from another.
* @method subVec4
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Vector to subtract
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
subVec4(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] - v[0];
dest[1] = u[1] - v[1];
dest[2] = u[2] - v[2];
dest[3] = u[3] - v[3];
return dest;
},
/**
* Subtracts one three-element vector from another.
* @method subVec3
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Vector to subtract
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
subVec3(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] - v[0];
dest[1] = u[1] - v[1];
dest[2] = u[2] - v[2];
return dest;
},
/**
* Subtracts one two-element vector from another.
* @method subVec2
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Vector to subtract
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
subVec2(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] - v[0];
dest[1] = u[1] - v[1];
return dest;
},
/**
* Subtracts a scalar value from each element of a four-element vector.
* @method subVec4Scalar
* @static
* @param {Array(Number)} v The vector
* @param {Number} s The scalar
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
subVec4Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] - s;
dest[1] = v[1] - s;
dest[2] = v[2] - s;
dest[3] = v[3] - s;
return dest;
},
/**
* Sets each element of a 4-element vector to a scalar value minus the value of that element.
* @method subScalarVec4
* @static
* @param {Array(Number)} v The vector
* @param {Number} s The scalar
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
subScalarVec4(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = s - v[0];
dest[1] = s - v[1];
dest[2] = s - v[2];
dest[3] = s - v[3];
return dest;
},
/**
* Multiplies one three-element vector by another.
* @method mulVec3
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
mulVec4(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] * v[0];
dest[1] = u[1] * v[1];
dest[2] = u[2] * v[2];
dest[3] = u[3] * v[3];
return dest;
},
/**
* Multiplies each element of a four-element vector by a scalar.
* @method mulVec34calar
* @static
* @param {Array(Number)} v The vector
* @param {Number} s The scalar
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
mulVec4Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] * s;
dest[1] = v[1] * s;
dest[2] = v[2] * s;
dest[3] = v[3] * s;
return dest;
},
/**
* Multiplies each element of a three-element vector by a scalar.
* @method mulVec3Scalar
* @static
* @param {Array(Number)} v The vector
* @param {Number} s The scalar
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
mulVec3Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] * s;
dest[1] = v[1] * s;
dest[2] = v[2] * s;
return dest;
},
/**
* Multiplies each element of a two-element vector by a scalar.
* @method mulVec2Scalar
* @static
* @param {Array(Number)} v The vector
* @param {Number} s The scalar
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
mulVec2Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] * s;
dest[1] = v[1] * s;
return dest;
},
/**
* Divides one three-element vector by another.
* @method divVec3
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
divVec3(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] / v[0];
dest[1] = u[1] / v[1];
dest[2] = u[2] / v[2];
return dest;
},
/**
* Divides one four-element vector by another.
* @method divVec4
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, u otherwise
*/
divVec4(u, v, dest) {
if (!dest) {
dest = u;
}
dest[0] = u[0] / v[0];
dest[1] = u[1] / v[1];
dest[2] = u[2] / v[2];
dest[3] = u[3] / v[3];
return dest;
},
/**
* Divides a scalar by a three-element vector, returning a new vector.
* @method divScalarVec3
* @static
* @param v vec3
* @param s scalar
* @param dest vec3 - optional destination
* @return [] dest if specified, v otherwise
*/
divScalarVec3(s, v, dest) {
if (!dest) {
dest = v;
}
dest[0] = s / v[0];
dest[1] = s / v[1];
dest[2] = s / v[2];
return dest;
},
/**
* Divides a three-element vector by a scalar.
* @method divVec3Scalar
* @static
* @param v vec3
* @param s scalar
* @param dest vec3 - optional destination
* @return [] dest if specified, v otherwise
*/
divVec3Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] / s;
dest[1] = v[1] / s;
dest[2] = v[2] / s;
return dest;
},
/**
* Divides a four-element vector by a scalar.
* @method divVec4Scalar
* @static
* @param v vec4
* @param s scalar
* @param dest vec4 - optional destination
* @return [] dest if specified, v otherwise
*/
divVec4Scalar(v, s, dest) {
if (!dest) {
dest = v;
}
dest[0] = v[0] / s;
dest[1] = v[1] / s;
dest[2] = v[2] / s;
dest[3] = v[3] / s;
return dest;
},
/**
* Divides a scalar by a four-element vector, returning a new vector.
* @method divScalarVec4
* @static
* @param s scalar
* @param v vec4
* @param dest vec4 - optional destination
* @return [] dest if specified, v otherwise
*/
divScalarVec4(s, v, dest) {
if (!dest) {
dest = v;
}
dest[0] = s / v[0];
dest[1] = s / v[1];
dest[2] = s / v[2];
dest[3] = s / v[3];
return dest;
},
/**
* Returns the dot product of two four-element vectors.
* @method dotVec4
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @return The dot product
*/
dotVec4(u, v) {
return (u[0] * v[0] + u[1] * v[1] + u[2] * v[2] + u[3] * v[3]);
},
/**
* Returns the cross product of two four-element vectors.
* @method cross3Vec4
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @return The cross product
*/
cross3Vec4(u, v) {
const u0 = u[0];
const u1 = u[1];
const u2 = u[2];
const v0 = v[0];
const v1 = v[1];
const v2 = v[2];
return [
u1 * v2 - u2 * v1,
u2 * v0 - u0 * v2,
u0 * v1 - u1 * v0,
0.0];
},
/**
* Returns the cross product of two three-element vectors.
* @method cross3Vec3
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @return The cross product
*/
cross3Vec3(u, v, dest) {
if (!dest) {
dest = u;
}
const x = u[0];
const y = u[1];
const z = u[2];
const x2 = v[0];
const y2 = v[1];
const z2 = v[2];
dest[0] = y * z2 - z * y2;
dest[1] = z * x2 - x * z2;
dest[2] = x * y2 - y * x2;
return dest;
},
sqLenVec4(v) { // TODO
return math.dotVec4(v, v);
},
/**
* Returns the length of a four-element vector.
* @method lenVec4
* @static
* @param {Array(Number)} v The vector
* @return The length
*/
lenVec4(v) {
return Math.sqrt(math.sqLenVec4(v));
},
/**
* Returns the dot product of two three-element vectors.
* @method dotVec3
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @return The dot product
*/
dotVec3(u, v) {
return (u[0] * v[0] + u[1] * v[1] + u[2] * v[2]);
},
/**
* Returns the dot product of two two-element vectors.
* @method dotVec4
* @static
* @param {Array(Number)} u First vector
* @param {Array(Number)} v Second vector
* @return The dot product
*/
dotVec2(u, v) {
return (u[0] * v[0] + u[1] * v[1]);
},
sqLenVec3(v) {
return math.dotVec3(v, v);
},
sqLenVec2(v) {
return math.dotVec2(v, v);
},
/**
* Returns the length of a three-element vector.
* @method lenVec3
* @static
* @param {Array(Number)} v The vector
* @return The length
*/
lenVec3(v) {
return Math.sqrt(math.sqLenVec3(v));
},
distVec3: ((() => {
const vec = new FloatArrayType(3);
return (v, w) => math.lenVec3(math.subVec3(v, w, vec));
}))(),
/**
* Returns the length of a two-element vector.
* @method lenVec2
* @static
* @param {Array(Number)} v The vector
* @return The length
*/
lenVec2(v) {
return Math.sqrt(math.sqLenVec2(v));
},
distVec2: ((() => {
const vec = new FloatArrayType(2);
return (v, w) => math.lenVec2(math.subVec2(v, w, vec));
}))(),
/**
* @method rcpVec3
* @static
* @param v vec3
* @param dest vec3 - optional destination
* @return [] dest if specified, v otherwise
*
*/
rcpVec3(v, dest) {
return math.divScalarVec3(1.0, v, dest);
},
/**
* Normalizes a four-element vector
* @method normalizeVec4
* @static
* @param v vec4
* @param dest vec4 - optional destination
* @return [] dest if specified, v otherwise
*
*/
normalizeVec4(v, dest) {
const f = 1.0 / math.lenVec4(v);
return math.mulVec4Scalar(v, f, dest);
},
/**
* Normalizes a three-element vector
* @method normalizeVec4
* @static
*/
normalizeVec3(v, dest) {
const f = 1.0 / math.lenVec3(v);
return math.mulVec3Scalar(v, f, dest);
},
/**
* Normalizes a two-element vector
* @method normalizeVec2
* @static
*/
normalizeVec2(v, dest) {
const f = 1.0 / math.lenVec2(v);
return math.mulVec2Scalar(v, f, dest);
},
/**
* Gets the angle between two vectors
* @method angleVec3
* @param v
* @param w
* @returns {number}
*/
angleVec3(v, w) {
let theta = math.dotVec3(v, w) / (Math.sqrt(math.sqLenVec3(v) * math.sqLenVec3(w)));
theta = theta < -1 ? -1 : (theta > 1 ? 1 : theta); // Clamp to handle numerical problems
return Math.acos(theta);
},
/**
* Creates a three-element vector from the rotation part of a sixteen-element matrix.
* @param m
* @param dest
*/
vec3FromMat4Scale: ((() => {
const tempVec3 = new FloatArrayType(3);
return (m, dest) => {
tempVec3[0] = m[0];
tempVec3[1] = m[1];
tempVec3[2] = m[2];
dest[0] = math.lenVec3(tempVec3);
tempVec3[0] = m[4];
tempVec3[1] = m[5];
tempVec3[2] = m[6];
dest[1] = math.lenVec3(tempVec3);
tempVec3[0] = m[8];
tempVec3[1] = m[9];
tempVec3[2] = m[10];
dest[2] = math.lenVec3(tempVec3);
return dest;
};
}))(),
/**
* Converts an n-element vector to a JSON-serializable
* array with values rounded to two decimal places.
*/
vecToArray: ((() => {
function trunc(v) {
return Math.round(v * 100000) / 100000
}
return v => {
v = Array.prototype.slice.call(v);
for (let i = 0, len = v.length; i < len; i++) {
v[i] = trunc(v[i]);
}
return v;
};
}))(),
/**
* Converts a 3-element vector from an array to an object of the form ````{x:999, y:999, z:999}````.
* @param arr
* @returns {{x: *, y: *, z: *}}
*/
xyzArrayToObject(arr) {
return {"x": arr[0], "y": arr[1], "z": arr[2]};
},
/**
* Converts a 3-element vector object of the form ````{x:999, y:999, z:999}```` to an array.
* @param xyz
* @param [arry]
* @returns {*[]}
*/
xyzObjectToArray(xyz, arry) {
arry = arry || new FloatArrayType(3);
arry[0] = xyz.x;
arry[1] = xyz.y;
arry[2] = xyz.z;
return arry;
},
/**
* Duplicates a 4x4 identity matrix.
* @method dupMat4
* @static
*/
dupMat4(m) {
return m.slice(0, 16);
},
/**
* Extracts a 3x3 matrix from a 4x4 matrix.
* @method mat4To3
* @static
*/
mat4To3(m) {
return [
m[0], m[1], m[2],
m[4], m[5], m[6],
m[8], m[9], m[10]
];
},
/**
* Returns a 4x4 matrix with each element set to the given scalar value.
* @method m4s
* @static
*/
m4s(s) {
return [
s, s, s, s,
s, s, s, s,
s, s, s, s,
s, s, s, s
];
},
/**
* Returns a 4x4 matrix with each element set to zero.
* @method setMat4ToZeroes
* @static
*/
setMat4ToZeroes() {
return math.m4s(0.0);
},
/**
* Returns a 4x4 matrix with each element set to 1.0.
* @method setMat4ToOnes
* @static
*/
setMat4ToOnes() {
return math.m4s(1.0);
},
/**
* Returns a 4x4 matrix with each element set to 1.0.
* @method setMat4ToOnes
* @static
*/
diagonalMat4v(v) {
return new FloatArrayType([
v[0], 0.0, 0.0, 0.0,
0.0, v[1], 0.0, 0.0,
0.0, 0.0, v[2], 0.0,
0.0, 0.0, 0.0, v[3]
]);
},
/**
* Returns a 4x4 matrix with diagonal elements set to the given vector.
* @method diagonalMat4c
* @static
*/
diagonalMat4c(x, y, z, w) {
return math.diagonalMat4v([x, y, z, w]);
},
/**
* Returns a 4x4 matrix with diagonal elements set to the given scalar.
* @method diagonalMat4s
* @static
*/
diagonalMat4s(s) {
return math.diagonalMat4c(s, s, s, s);
},
/**
* Returns a 4x4 identity matrix.
* @method identityMat4
* @static
*/
identityMat4(mat = new FloatArrayType(16)) {
mat[0] = 1.0;
mat[1] = 0.0;
mat[2] = 0.0;
mat[3] = 0.0;
mat[4] = 0.0;
mat[5] = 1.0;
mat[6] = 0.0;
mat[7] = 0.0;
mat[8] = 0.0;
mat[9] = 0.0;
mat[10] = 1.0;
mat[11] = 0.0;
mat[12] = 0.0;
mat[13] = 0.0;
mat[14] = 0.0;
mat[15] = 1.0;
return mat;
},
/**
* Returns a 3x3 identity matrix.
* @method identityMat3
* @static
*/
identityMat3(mat = new FloatArrayType(9)) {
mat[0] = 1.0;
mat[1] = 0.0;
mat[2] = 0.0;
mat[3] = 0.0;
mat[4] = 1.0;
mat[5] = 0.0;
mat[6] = 0.0;
mat[7] = 0.0;
mat[8] = 1.0;
return mat;
},
/**
* Tests if the given 4x4 matrix is the identity matrix.
* @method isIdentityMat4
* @static
*/
isIdentityMat4(m) {
if (m[0] !== 1.0 || m[1] !== 0.0 || m[2] !== 0.0 || m[3] !== 0.0 ||
m[4] !== 0.0 || m[5] !== 1.0 || m[6] !== 0.0 || m[7] !== 0.0 ||
m[8] !== 0.0 || m[9] !== 0.0 || m[10] !== 1.0 || m[11] !== 0.0 ||
m[12] !== 0.0 || m[13] !== 0.0 || m[14] !== 0.0 || m[15] !== 1.0) {
return false;
}
return true;
},
/**
* Negates the given 4x4 matrix.
* @method negateMat4
* @static
*/
negateMat4(m, dest) {
if (!dest) {
dest = m;
}
dest[0] = -m[0];
dest[1] = -m[1];
dest[2] = -m[2];
dest[3] = -m[3];
dest[4] = -m[4];
dest[5] = -m[5];
dest[6] = -m[6];
dest[7] = -m[7];
dest[8] = -m[8];
dest[9] = -m[9];
dest[10] = -m[10];
dest[11] = -m[11];
dest[12] = -m[12];
dest[13] = -m[13];
dest[14] = -m[14];
dest[15] = -m[15];
return dest;
},
/**
* Adds the given 4x4 matrices together.
* @method addMat4
* @static
*/
addMat4(a, b, dest) {
if (!dest) {
dest = a;
}
dest[0] = a[0] + b[0];
dest[1] = a[1] + b[1];
dest[2] = a[2] + b[2];
dest[3] = a[3] + b[3];
dest[4] = a[4] + b[4];
dest[5] = a[5] + b[5];
dest[6] = a[6] + b[6];
dest[7] = a[7] + b[7];
dest[8] = a[8] + b[8];
dest[9] = a[9] + b[9];
dest[10] = a[10] + b[10];
dest[11] = a[11] + b[11];
dest[12] = a[12] + b[12];
dest[13] = a[13] + b[13];
dest[14] = a[14] + b[14];
dest[15] = a[15] + b[15];
return dest;
},
/**
* Adds the given scalar to each element of the given 4x4 matrix.
* @method addMat4Scalar
* @static
*/
addMat4Scalar(m, s, dest) {
if (!dest) {
dest = m;
}
dest[0] = m[0] + s;
dest[1] = m[1] + s;
dest[2] = m[2] + s;
dest[3] = m[3] + s;
dest[4] = m[4] + s;
dest[5] = m[5] + s;
dest[6] = m[6] + s;
dest[7] = m[7] + s;
dest[8] = m[8] + s;
dest[9] = m[9] + s;
dest[10] = m[10] + s;
dest[11] = m[11] + s;
dest[12] = m[12] + s;
dest[13] = m[13] + s;
dest[14] = m[14] + s;
dest[15] = m[15] + s;
return dest;
},
/**
* Adds the given scalar to each element of the given 4x4 matrix.
* @method addScalarMat4
* @static
*/
addScalarMat4(s, m, dest) {
return math.addMat4Scalar(m, s, dest);
},
/**
* Subtracts the second 4x4 matrix from the first.
* @method subMat4
* @static
*/
subMat4(a, b, dest) {
if (!dest) {
dest = a;
}
dest[0] = a[0] - b[0];
dest[1] = a[1] - b[1];
dest[2] = a[2] - b[2];
dest[3] = a[3] - b[3];
dest[4] = a[4] - b[4];
dest[5] = a[5] - b[5];
dest[6] = a[6] - b[6];
dest[7] = a[7] - b[7];
dest[8] = a[8] - b[8];
dest[9] = a[9] - b[9];
dest[10] = a[10] - b[10];
dest[11] = a[11] - b[11];
dest[12] = a[12] - b[12];
dest[13] = a[13] - b[13];
dest[14] = a[14] - b[14];
dest[15] = a[15] - b[15];
return dest;
},
/**
* Subtracts the given scalar from each element of the given 4x4 matrix.
* @method subMat4Scalar
* @static
*/
subMat4Scalar(m, s, dest) {
if (!dest) {
dest = m;
}
dest[0] = m[0] - s;
dest[1] = m[1] - s;
dest[2] = m[2] - s;
dest[3] = m[3] - s;
dest[4] = m[4] - s;
dest[5] = m[5] - s;
dest[6] = m[6] - s;
dest[7] = m[7] - s;
dest[8] = m[8] - s;
dest[9] = m[9] - s;
dest[10] = m[10] - s;
dest[11] = m[11] - s;
dest[12] = m[12] - s;
dest[13] = m[13] - s;
dest[14] = m[14] - s;
dest[15] = m[15] - s;
return dest;
},
/**
* Subtracts the given scalar from each element of the given 4x4 matrix.
* @method subScalarMat4
* @static
*/
subScalarMat4(s, m, dest) {
if (!dest) {
dest = m;
}
dest[0] = s - m[0];
dest[1] = s - m[1];
dest[2] = s - m[2];
dest[3] = s - m[3];
dest[4] = s - m[4];
dest[5] = s - m[5];
dest[6] = s - m[6];
dest[7] = s - m[7];
dest[8] = s - m[8];
dest[9] = s - m[9];
dest[10] = s - m[10];
dest[11] = s - m[11];
dest[12] = s - m[12];
dest[13] = s - m[13];
dest[14] = s - m[14];
dest[15] = s - m[15];
return dest;
},
/**
* Multiplies the two given 4x4 matrix by each other.
* @method mulMat4
* @static
*/
mulMat4(a, b, dest) {
if (!dest) {
dest = a;
}
// Cache the matrix values (makes for huge speed increases!)
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];
const a20 = a[8];
const a21 = a[9];
const a22 = a[10];
const a23 = a[11];
const a30 = a[12];
const a31 = a[13];
const a32 = a[14];
const a33 = a[15];
const b00 = b[0];
const b01 = b[1];
const b02 = b[2];
const b03 = b[3];
const b10 = b[4];
const b11 = b[5];
const b12 = b[6];
const b13 = b[7];
const b20 = b[8];
const b21 = b[9];
const b22 = b[10];
const b23 = b[11];
const b30 = b[12];
const b31 = b[13];
const b32 = b[14];
const b33 = b[15];
dest[0] = b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30;
dest[1] = b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31;
dest[2] = b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32;
dest[3] = b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33;
dest[4] = b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30;
dest[5] = b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31;
dest[6] = b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32;
dest[7] = b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33;
dest[8] = b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30;
dest[9] = b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31;
dest[10] = b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32;
dest[11] = b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33;
dest[12] = b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30;
dest[13] = b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31;
dest[14] = b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32;
dest[15] = b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33;
return dest;
},
/**
* Multiplies the two given 3x3 matrices by each other.
* @method mulMat4
* @static
*/
mulMat3(a, b, dest) {
if (!dest) {
dest = new FloatArrayType(9);
}
const a11 = a[0];
const a12 = a[3];
const a13 = a[6];
const a21 = a[1];
const a22 = a[4];
const a23 = a[7];
const a31 = a[2];
const a32 = a[5];
const a33 = a[8];
const b11 = b[0];
const b12 = b[3];
const b13 = b[6];
const b21 = b[1];
const b22 = b[4];
const b23 = b[7];
const b31 = b[2];
const b32 = b[5];
const b33 = b[8];
dest[0] = a11 * b11 + a12 * b21 + a13 * b31;
dest[3] = a11 * b12 + a12 * b22 + a13 * b32;
dest[6] = a11 * b13 + a12 * b23 + a13 * b33;
dest[1] = a21 * b11 + a22 * b21 + a23 * b31;
dest[4] = a21 * b12 + a22 * b22 + a23 * b32;
dest[7] = a21 * b13 + a22 * b23 + a23 * b33;
dest[2] = a31 * b11 + a32 * b21 + a33 * b31;
dest[5] = a31 * b12 + a32 * b22 + a33 * b32;
dest[8] = a31 * b13 + a32 * b23 + a33 * b33;
return dest;
},
/**
* Multiplies each element of the given 4x4 matrix by the given scalar.
* @method mulMat4Scalar
* @static
*/
mulMat4Scalar(m, s, dest) {
if (!dest) {
dest = m;
}
dest[0] = m[0] * s;
dest[1] = m[1] * s;
dest[2] = m[2] * s;
dest[3] = m[3] * s;
dest[4] = m[4] * s;
dest[5] = m[5] * s;
dest[6] = m[6] * s;
dest[7] = m[7] * s;
dest[8] = m[8] * s;
dest[9] = m[9] * s;
dest[10] = m[10] * s;
dest[11] = m[11] * s;
dest[12] = m[12] * s;
dest[13] = m[13] * s;
dest[14] = m[14] * s;
dest[15] = m[15] * s;
return dest;
},
/**
* Multiplies the given 4x4 matrix by the given four-element vector.
* @method mulMat4v4
* @static
*/
mulMat4v4(m, v, dest = math.vec4()) {
const v0 = v[0];
const v1 = v[1];
const v2 = v[2];
const v3 = v[3];
dest[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12] * v3;
dest[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13] * v3;
dest[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14] * v3;
dest[3] = m[3] * v0 + m[7] * v1 + m[11] * v2 + m[15] * v3;
return dest;
},
/**
* Transposes the given 4x4 matrix.
* @method transposeMat4
* @static
*/
transposeMat4(mat, dest) {
// If we are transposing ourselves we can skip a few steps but have to cache some values
const m4 = mat[4];
const m14 = mat[14];
const m8 = mat[8];
const m13 = mat[13];
const m12 = mat[12];
const m9 = mat[9];
if (!dest || mat === dest) {
const a01 = mat[1];
const a02 = mat[2];
const a03 = mat[3];
const a12 = mat[6];
const a13 = mat[7];
const a23 = mat[11];
mat[1] = m4;
mat[2] = m8;
mat[3] = m12;
mat[4] = a01;
mat[6] = m9;
mat[7] = m13;
mat[8] = a02;
mat[9] = a12;
mat[11] = m14;
mat[12] = a03;
mat[13] = a13;
mat[14] = a23;
return mat;
}
dest[0] = mat[0];
dest[1] = m4;
dest[2] = m8;
dest[3] = m12;
dest[4] = mat[1];
dest[5] = mat[5];
dest[6] = m9;
dest[7] = m13;
dest[8] = mat[2];
dest[9] = mat[6];
dest[10] = mat[10];
dest[11] = m14;
dest[12] = mat[3];
dest[13] = mat[7];
dest[14] = mat[11];
dest[15] = mat[15];
return dest;
},
/**
* Transposes the given 3x3 matrix.
*
* @method transposeMat3
* @static
*/
transposeMat3(mat, dest) {
if (dest === mat) {
const a01 = mat[1];
const a02 = mat[2];
const a12 = mat[5];
dest[1] = mat[3];
dest[2] = mat[6];
dest[3] = a01;
dest[5] = mat[7];
dest[6] = a02;
dest[7] = a12;
} else {
dest[0] = mat[0];
dest[1] = mat[3];
dest[2] = mat[6];
dest[3] = mat[1];
dest[4] = mat[4];
dest[5] = mat[7];
dest[6] = mat[2];
dest[7] = mat[5];
dest[8] = mat[8];
}
return dest;
},
/**
* Returns the determinant of the given 4x4 matrix.
* @method determinantMat4
* @static
*/
determinantMat4(mat) {
// Cache the matrix values (makes for huge speed increases!)
const a00 = mat[0];
const a01 = mat[1];
const a02 = mat[2];
const a03 = mat[3];
const a10 = mat[4];
const a11 = mat[5];
const a12 = mat[6];
const a13 = mat[7];
const a20 = mat[8];
const a21 = mat[9];
const a22 = mat[10];
const a23 = mat[11];
const a30 = mat[12];
const a31 = mat[13];
const a32 = mat[14];
const a33 = mat[15];
return a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 - a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 +
a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 - a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 +
a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 - a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 +
a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 - a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 +
a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 - a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 +
a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 - a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33;
},
/**
* Returns the inverse of the given 4x4 matrix.
* @method inverseMat4
* @static
*/
inverseMat4(mat, dest) {
if (!dest) {
dest = mat;
}
// Cache the matrix values (makes for huge speed increases!)
const a00 = mat[0];
const a01 = mat[1];
const a02 = mat[2];
const a03 = mat[3];
const a10 = mat[4];
const a11 = mat[5];
const a12 = mat[6];
const a13 = mat[7];
const a20 = mat[8];
const a21 = mat[9];
const a22 = mat[10];
const a23 = mat[11];
const a30 = mat[12];
const a31 = mat[13];
const a32 = mat[14];
const a33 = mat[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 (inlined to avoid double-caching)
const invDet = 1 / (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06);
dest[0] = (a11 * b11 - a12 * b10 + a13 * b09) * invDet;
dest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * invDet;
dest[2] = (a31 * b05 - a32 * b04 + a33 * b03) * invDet;
dest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * invDet;
dest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * invDet;
dest[5] = (a00 * b11 - a02 * b08 + a03 * b07) * invDet;
dest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * invDet;
dest[7] = (a20 * b05 - a22 * b02 + a23 * b01) * invDet;
dest[8] = (a10 * b10 - a11 * b08 + a13 * b06) * invDet;
dest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * invDet;
dest[10] = (a30 * b04 - a31 * b02 + a33 * b00) * invDet;
dest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * invDet;
dest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * invDet;
dest[13] = (a00 * b09 - a01 * b07 + a02 * b06) * invDet;
dest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * invDet;
dest[15] = (a20 * b03 - a21 * b01 + a22 * b00) * invDet;
return dest;
},
/**
* Returns the trace of the given 4x4 matrix.
* @method traceMat4
* @static
*/
traceMat4(m) {
return (m[0] + m[5] + m[10] + m[15]);
},
/**
* Returns 4x4 translation matrix.
* @method translationMat4
* @static
*/
translationMat4v(v, dest) {
const m = dest || math.identityMat4();
m[12] = v[0];
m[13] = v[1];
m[14] = v[2];
return m;
},
/**
* Returns 3x3 translation matrix.
* @method translationMat3
* @static
*/
translationMat3v(v, dest) {
const m = dest || math.identityMat3();
m[6] = v[0];
m[7] = v[1];
return m;
},
/**
* Returns 4x4 translation matrix.
* @method translationMat4c
* @static
*/
translationMat4c: ((() => {
const xyz = new FloatArrayType(3);
return (x, y, z, dest) => {
xyz[0] = x;
xyz[1] = y;
xyz[2] = z;
return math.translationMat4v(xyz, dest);
};
}))(),
/**
* Returns 4x4 translation matrix.
* @method translationMat4s
* @static
*/
translationMat4s(s, dest) {
return math.translationMat4c(s, s, s, dest);
},
/**
* Efficiently post-concatenates a translation to the given matrix.
* @param v
* @param m
*/
translateMat4v(xyz, m) {
return math.translateMat4c(xyz[0], xyz[1], xyz[2], m);
},
/**
* Efficiently post-concatenates a translation to the given matrix.
* @param x
* @param y
* @param z
* @param m
*/
OLDtranslateMat4c(x, y, z, m) {
const m12 = m[12];
m[0] += m12 * x;
m[4] += m12 * y;
m[8] += m12 * z;
const m13 = m[13];
m[1] += m13 * x;
m[5] += m13 * y;
m[9] += m13 * z;
const m14 = m[14];
m[2] += m14 * x;
m[6] += m14 * y;
m[10] += m14 * z;
const m15 = m[15];
m[3] += m15 * x;
m[7] += m15 * y;
m[11] += m15 * z;
return m;
},
translateMat4c(x, y, z, m) {
const m3 = m[3];
m[0] += m3 * x;
m[1] += m3 * y;
m[2] += m3 * z;
const m7 = m[7];
m[4] += m7 * x;
m[5] += m7 * y;
m[6] += m7 * z;
const m11 = m[11];
m[8] += m11 * x;
m[9] += m11 * y;
m[10] += m11 * z;
const m15 = m[15];
m[12] += m15 * x;
m[13] += m15 * y;
m[14] += m15 * z;
return m;
},
/**
* Returns 4x4 rotation matrix.
* @method rotationMat4v
* @static
*/
rotationMat4v(anglerad, axis, m) {
const ax = math.normalizeVec4([axis[0], axis[1], axis[2], 0.0], []);
const s = Math.sin(anglerad);
const c = Math.cos(anglerad);
const q = 1.0 - c;
const x = ax[0];
const y = ax[1];
const z = ax[2];
let xy;
let yz;
let zx;
let xs;
let ys;
let zs;
//xx = x * x; used once
//yy = y * y; used once
//zz = z * z; used once
xy = x * y;
yz = y * z;
zx = z * x;
xs = x * s;
ys = y * s;
zs = z * s;
m = m || math.mat4();
m[0] = (q * x * x) + c;
m[1] = (q * xy) + zs;
m[2] = (q * zx) - ys;
m[3] = 0.0;
m[4] = (q * xy) - zs;
m[5] = (q * y * y) + c;
m[6] = (q * yz) + xs;
m[7] = 0.0;
m[8] = (q * zx) + ys;
m[9] = (q * yz) - xs;
m[10] = (q * z * z) + c;
m[11] = 0.0;
m[12] = 0.0;
m[13] = 0.0;
m[14] = 0.0;
m[15] = 1.0;
return m;
},
/**
* Returns 4x4 rotation matrix.
* @method rotationMat4c
* @static
*/
rotationMat4c(anglerad, x, y, z, mat) {
return math.rotationMat4v(anglerad, [x, y, z], mat);
},
/**
* Returns 4x4 scale matrix.
* @method scalingMat4v
* @static
*/
scalingMat4v(v, m = math.identityMat4()) {
m[0] = v[0];
m[5] = v[1];
m[10] = v[2];
return m;
},
/**
* Returns 3x3 scale matrix.
* @method scalingMat3v
* @static
*/
scalingMat3v(v, m = math.identityMat3()) {
m[0] = v[0];
m[4] = v[1];
return m;
},
/**
* Returns 4x4 scale matrix.
* @method scalingMat4c
* @static
*/
scalingMat4c: ((() => {
const xyz = new FloatArrayType(3);
return (x, y, z, dest) => {
xyz[0] = x;
xyz[1] = y;
xyz[2] = z;
return math.scalingMat4v(xyz, dest);
};
}))(),
/**
* Efficiently post-concatenates a scaling to the given matrix.
* @method scaleMat4c
* @param x
* @param y
* @param z
* @param m
*/
scaleMat4c(x, y, z, m) {
m[0] *= x;
m[4] *= y;
m[8] *= z;
m[1] *= x;
m[5] *= y;
m[9] *= z;
m[2] *= x;
m[6] *= y;
m[10] *= z;
m[3] *= x;
m[7] *= y;
m[11] *= z;
return m;
},
/**
* Efficiently post-concatenates a scaling to the given matrix.
* @method scaleMat4c
* @param xyz
* @param m
*/
scaleMat4v(xyz, m) {
const x = xyz[0];
const y = xyz[1];
const z = xyz[2];
m[0] *= x;
m[4] *= y;
m[8] *= z;
m[1] *= x;
m[5] *= y;
m[9] *= z;
m[2] *= x;
m[6] *= y;
m[10] *= z;
m[3] *= x;
m[7] *= y;
m[11] *= z;
return m;
},
/**
* Returns 4x4 scale matrix.
* @method scalingMat4s
* @static
*/
scalingMat4s(s) {
return math.scalingMat4c(s, s, s);
},
/**
* Creates a matrix from a quaternion rotation and vector translation
*
* @param {Number[]} q Rotation quaternion
* @param {Number[]} v Translation vector
* @param {Number[]} dest Destination matrix
* @returns {Number[]} dest
*/
rotationTranslationMat4(q, v, dest = math.mat4()) {
const x = q[0];
const y = q[1];
const z = q[2];
const 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;
dest[0] = 1 - (yy + zz);
dest[1] = xy + wz;
dest[2] = xz - wy;
dest[3] = 0;
dest[4] = xy - wz;
dest[5] = 1 - (xx + zz);
dest[6] = yz + wx;
dest[7] = 0;
dest[8] = xz + wy;
dest[9] = yz - wx;
dest[10] = 1 - (xx + yy);
dest[11] = 0;
dest[12] = v[0];
dest[13] = v[1];
dest[14] = v[2];
dest[15] = 1;
return dest;
},
/**
* Gets Euler angles from a 4x4 matrix.
*
* @param {Number[]} mat The 4x4 matrix.
* @param {String} order Desired Euler angle order: "XYZ", "YXZ", "ZXY" etc.
* @param {Number[]} [dest] Destination Euler angles, created by default.
* @returns {Number[]} The Euler angles.
*/
mat4ToEuler(mat, order, dest = math.vec4()) {
const clamp = math.clamp;
// Assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
const m11 = mat[0];
const m12 = mat[4];
const m13 = mat[8];
const m21 = mat[1];
const m22 = mat[5];
const m23 = mat[9];
const m31 = mat[2];
const m32 = mat[6];
const m33 = mat[10];
if (order === 'XYZ') {
dest[1] = Math.asin(clamp(m13, -1, 1));
if (Math.abs(m13) < 0.99999) {
dest[0] = Math.atan2(-m23, m33);
dest[2] = Math.atan2(-m12, m11);
} else {
dest[0] = Math.atan2(m32, m22);
dest[2] = 0;
}
} else if (order === 'YXZ') {
dest[0] = Math.asin(-clamp(m23, -1, 1));
if (Math.abs(m23) < 0.99999) {
dest[1] = Math.atan2(m13, m33);
dest[2] = Math.atan2(m21, m22);
} else {
dest[1] = Math.atan2(-m31, m11);
dest[2] = 0;
}
} else if (order === 'ZXY') {
dest[0] = Math.asin(clamp(m32, -1, 1));
if (Math.abs(m32) < 0.99999) {
dest[1] = Math.atan2(-m31, m33);
dest[2] = Math.atan2(-m12, m22);
} else {
dest[1] = 0;
dest[2] = Math.atan2(m21, m11);
}
} else if (order === 'ZYX') {
dest[1] = Math.asin(-clamp(m31, -1, 1));
if (Math.abs(m31) < 0.99999) {
dest[0] = Math.atan2(m32, m33);
dest[2] = Math.atan2(m21, m11);
} else {
dest[0] = 0;
dest[2] = Math.atan2(-m12, m22);
}
} else if (order === 'YZX') {
dest[2] = Math.asin(clamp(m21, -1, 1));
if (Math.abs(m21) < 0.99999) {
dest[0] = Math.atan2(-m23, m22);
dest[1] = Math.atan2(-m31, m11);
} else {
dest[0] = 0;
dest[1] = Math.atan2(m13, m33);
}
} else if (order === 'XZY') {
dest[2] = Math.asin(-clamp(m12, -1, 1));
if (Math.abs(m12) < 0.99999) {
dest[0] = Math.atan2(m32, m22);
dest[1] = Math.atan2(m13, m11);
} else {
dest[0] = Math.atan2(-m23, m33);
dest[1] = 0;
}
}
return dest;
},
composeMat4(position, quaternion, scale, mat = math.mat4()) {
math.quaternionToRotationMat4(quaternion, mat);
math.scaleMat4v(scale, mat);
math.translateMat4v(position, mat);
return mat;
},
decomposeMat4: (() => {
const vec = new FloatArrayType(3);
const matrix = new FloatArrayType(16);
return function decompose(mat, position, quaternion, scale) {
vec[0] = mat[0];
vec[1] = mat[1];
vec[2] = mat[2];
let sx = math.lenVec3(vec);
vec[0] = mat[4];
vec[1] = mat[5];
vec[2] = mat[6];
const sy = math.lenVec3(vec);
vec[8] = mat[8];
vec[9] = mat[9];
vec[10] = mat[10];
const sz = math.lenVec3(vec);
// if determine is negative, we need to invert one scale
const det = math.determinantMat4(mat);
if (det < 0) {
sx = -sx;
}
position[0] = mat[12];
position[1] = mat[13];
position[2] = mat[14];
// scale the rotation part
matrix.set(mat);
const invSX = 1 / sx;
const invSY = 1 / sy;
const invSZ = 1 / sz;
matrix[0] *= invSX;
matrix[1] *= invSX;
matrix[2] *= invSX;
matrix[4] *= invSY;
matrix[5] *= invSY;
matrix[6] *= invSY;
matrix[8] *= invSZ;
matrix[9] *= invSZ;
matrix[10] *= invSZ;
math.mat4ToQuaternion(matrix, quaternion);
scale[0] = sx;
scale[1] = sy;
scale[2] = sz;
return this;
};
})(),
/**
* Returns a 4x4 'lookat' viewing transform matrix.
* @method lookAtMat4v
* @param pos vec3 position of the viewer
* @param target vec3 point the viewer is looking at
* @param up vec3 pointing "up"
* @param dest mat4 Optional, mat4 matrix will be written into
*
* @return {mat4} dest if specified, a new mat4 otherwise
*/
lookAtMat4v(pos, target, up, dest) {
if (!dest) {
dest = math.mat4();
}
const posx = pos[0];
const posy = pos[1];
const posz = pos[2];
const upx = up[0];
const upy = up[1];
const upz = up[2];
const targetx = target[0];
const targety = target[1];
const targetz = target[2];
if (posx === targetx && posy === targety && posz === targetz) {
return math.identityMat4();
}
let z0;
let z1;
let z2;
let x0;
let x1;
let x2;
let y0;
let y1;
let y2;
let len;
//vec3.direction(eye, center, z);
z0 = posx - targetx;
z1 = posy - targety;
z2 = posz - targetz;
// normalize (no check needed for 0 because of early return)
len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
z0 *= len;
z1 *= len;
z2 *= len;
//vec3.normalize(vec3.cross(up, z, x));
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;
}
//vec3.normalize(vec3.cross(z, x, y));
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;
}
dest[0] = x0;
dest[1] = y0;
dest[2] = z0;
dest[3] = 0;
dest[4] = x1;
dest[5] = y1;
dest[6] = z1;
dest[7] = 0;
dest[8] = x2;
dest[9] = y2;
dest[10] = z2;
dest[11] = 0;
dest[12] = -(x0 * posx + x1 * posy + x2 * posz);
dest[13] = -(y0 * posx + y1 * posy + y2 * posz);
dest[14] = -(z0 * posx + z1 * posy + z2 * posz);
dest[15] = 1;
return dest;
},
/**
* Returns a 4x4 'lookat' viewing transform matrix.
* @method lookAtMat4c
* @static
*/
lookAtMat4c(posx, posy, posz, targetx, targety, targetz, upx, upy, upz) {
return math.lookAtMat4v([posx, posy, posz], [targetx, targety, targetz], [upx, upy, upz], []);
},
/**
* Returns a 4x4 orthographic projection matrix.
* @method orthoMat4c
* @static
*/
orthoMat4c(left, right, bottom, top, near, far, dest) {
if (!dest) {
dest = math.mat4();
}
const rl = (right - left);
const tb = (top - bottom);
const fn = (far - near);
dest[0] = 2.0 / rl;
dest[1] = 0.0;
dest[2] = 0.0;
dest[3] = 0.0;
dest[4] = 0.0;
dest[5] = 2.0 / tb;
dest[6] = 0.0;
dest[7] = 0.0;
dest[8] = 0.0;
dest[9] = 0.0;
dest[10] = -2.0 / fn;
dest[11] = 0.0;
dest[12] = -(left + right) / rl;
dest[13] = -(top + bottom) / tb;
dest[14] = -(far + near) / fn;
dest[15] = 1.0;
return dest;
},
/**
* Returns a 4x4 perspective projection matrix.
* @method frustumMat4v
* @static
*/
frustumMat4v(fmin, fmax, m) {
if (!m) {
m = math.mat4();
}
const fmin4 = [fmin[0], fmin[1], fmin[2], 0.0];
const fmax4 = [fmax[0], fmax[1], fmax[2], 0.0];
math.addVec4(fmax4, fmin4, tempMat1);
math.subVec4(fmax4, fmin4, tempMat2);
const t = 2.0 * fmin4[2];
const tempMat20 = tempMat2[0];
const tempMat21 = tempMat2[1];
const tempMat22 = tempMat2[2];
m[0] = t / tempMat20;
m[1] = 0.0;
m[2] = 0.0;
m[3] = 0.0;
m[4] = 0.0;
m[5] = t / tempMat21;
m[6] = 0.0;
m[7] = 0.0;
m[8] = tempMat1[0] / tempMat20;
m[9] = tempMat1[1] / tempMat21;
m[10] = -tempMat1[2] / tempMat22;
m[11] = -1.0;
m[12] = 0.0;
m[13] = 0.0;
m[14] = -t * fmax4[2] / tempMat22;
m[15] = 0.0;
return m;
},
/**
* Returns a 4x4 perspective projection matrix.
* @method frustumMat4v
* @static
*/
frustumMat4(left, right, bottom, top, near, far, dest) {
if (!dest) {
dest = math.mat4();
}
const rl = (right - left);
const tb = (top - bottom);
const fn = (far - near);
dest[0] = (near * 2) / rl;
dest[1] = 0;
dest[2] = 0;
dest[3] = 0;
dest[4] = 0;
dest[5] = (near * 2) / tb;
dest[6] = 0;
dest[7] = 0;
dest[8] = (right + left) / rl;
dest[9] = (top + bottom) / tb;
dest[10] = -(far + near) / fn;
dest[11] = -1;
dest[12] = 0;
dest[13] = 0;
dest[14] = -(far * near * 2) / fn;
dest[15] = 0;
return dest;
},
/**
* Returns a 4x4 perspective projection matrix.
* @method perspectiveMat4v
* @static
*/
perspectiveMat4(fovyrad, aspectratio, znear, zfar, m) {
const pmin = [];
const pmax = [];
pmin[2] = znear;
pmax[2] = zfar;
pmax[1] = pmin[2] * Math.tan(fovyrad / 2.0);
pmin[1] = -pmax[1];
pmax[0] = pmax[1] * aspectratio;
pmin[0] = -pmax[0];
return math.frustumMat4v(pmin, pmax, m);
},
/**
* Transforms a three-element position by a 4x4 matrix.
* @method transformPoint3
* @static
*/
transformPoint3(m, p, dest = math.vec3()) {
const x = p[0];
const y = p[1];
const z = p[2];
dest[0] = (m[0] * x) + (m[4] * y) + (m[8] * z) + m[12];
dest[1] = (m[1] * x) + (m[5] * y) + (m[9] * z) + m[13];
dest[2] = (m[2] * x) + (m[6] * y) + (m[10] * z) + m[14];
return dest;
},
/**
* Transforms a homogeneous coordinate by a 4x4 matrix.
* @method transformPoint3
* @static
*/
transformPoint4(m, v, dest = math.vec4()) {
dest[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12] * v[3];
dest[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13] * v[3];
dest[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14] * v[3];
dest[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3];
return dest;
},
/**
* Transforms an array of three-element positions by a 4x4 matrix.
* @method transformPoints3
* @static
*/
transformPoints3(m, points, points2) {
const result = points2 || [];
const len = points.length;
let p0;
let p1;
let p2;
let pi;
// cache values
const m0 = m[0];
const m1 = m[1];
const m2 = m[2];
const m3 = m[3];
const m4 = m[4];
const m5 = m[5];
const m6 = m[6];
const m7 = m[7];
const m8 = m[8];
const m9 = m[9];
const m10 = m[10];
const m11 = m[11];
const m12 = m[12];
const m13 = m[13];
const m14 = m[14];
const m15 = m[15];
let r;
for (let i = 0; i < len; ++i) {
// cache values
pi = points[i];
p0 = pi[0];
p1 = pi[1];
p2 = pi[2];
r = result[i] || (result[i] = [0, 0, 0]);
r[0] = (m0 * p0) + (m4 * p1) + (m8 * p2) + m12;
r[1] = (m1 * p0) + (m5 * p1) + (m9 * p2) + m13;
r[2] = (m2 * p0) + (m6 * p1) + (m10 * p2) + m14;
r[3] = (m3 * p0) + (m7 * p1) + (m11 * p2) + m15;
}
result.length = len;
return result;
},
/**
* Transforms an array of positions by a 4x4 matrix.
* @method transformPositions3
* @static
*/
transformPositions3(m, p, p2 = p) {
let i;
const len = p.length;
let x;
let y;
let z;
const m0 = m[0];
const m1 = m[1];
const m2 = m[2];
const m3 = m[3];
const m4 = m[4];
const m5 = m[5];
const m6 = m[6];
const m7 = m[7];
const m8 = m[8];
const m9 = m[9];
const m10 = m[10];
const m11 = m[11];
const m12 = m[12];
const m13 = m[13];
const m14 = m[14];
const m15 = m[15];
for (i = 0; i < len; i += 3) {
x = p[i + 0];
y = p[i + 1];
z = p[i + 2];
p2[i + 0] = (m0 * x) + (m4 * y) + (m8 * z) + m12;
p2[i + 1] = (m1 * x) + (m5 * y) + (m9 * z) + m13;
p2[i + 2] = (m2 * x) + (m6 * y) + (m10 * z) + m14;
p2[i + 3] = (m3 * x) + (m7 * y) + (m11 * z) + m15;
}
return p2;
},
/**
* Transforms an array of positions by a 4x4 matrix.
* @method transformPositions4
* @static
*/
transformPositions4(m, p, p2 = p) {
let i;
const len = p.length;
let x;
let y;
let z;
const m0 = m[0];
const m1 = m[1];
const m2 = m[2];
const m3 = m[3];
const m4 = m[4];
const m5 = m[5];
const m6 = m[6];
const m7 = m[7];
const m8 = m[8];
const m9 = m[9];
const m10 = m[10];
const m11 = m[11];
const m12 = m[12];
const m13 = m[13];
const m14 = m[14];
const m15 = m[15];
for (i = 0; i < len; i += 4) {
x = p[i + 0];
y = p[i + 1];
z = p[i + 2];
p2[i + 0] = (m0 * x) + (m4 * y) + (m8 * z) + m12;
p2[i + 1] = (m1 * x) + (m5 * y) + (m9 * z) + m13;
p2[i + 2] = (m2 * x) + (m6 * y) + (m10 * z) + m14;
p2[i + 3] = (m3 * x) + (m7 * y) + (m11 * z) + m15;
}
return p2;
},
/**
* Transforms a three-element vector by a 4x4 matrix.
* @method transformVec3
* @static
*/
transformVec3(m, v, dest) {
const v0 = v[0];
const v1 = v[1];
const v2 = v[2];
dest = dest || this.vec3();
dest[0] = (m[0] * v0) + (m[4] * v1) + (m[8] * v2);
dest[1] = (m[1] * v0) + (m[5] * v1) + (m[9] * v2);
dest[2] = (m[2] * v0) + (m[6] * v1) + (m[10] * v2);
return dest;
},
/**
* Transforms a four-element vector by a 4x4 matrix.
* @method transformVec4
* @static
*/
transformVec4(m, v, dest) {
const v0 = v[0];
const v1 = v[1];
const v2 = v[2];
const v3 = v[3];
dest = dest || math.vec4();
dest[0] = m[0] * v0 + m[4] * v1 + m[8] * v2 + m[12] * v3;
dest[1] = m[1] * v0 + m[5] * v1 + m[9] * v2 + m[13] * v3;
dest[2] = m[2] * v0 + m[6] * v1 + m[10] * v2 + m[14] * v3;
dest[3] = m[3] * v0 + m[7] * v1 + m[11] * v2 + m[15] * v3;
return dest;
},
/**
* Rotate a 3D vector around the x-axis
*
* @method rotateVec3X
* @param {Number[]} a The vec3 point to rotate
* @param {Number[]} b The origin of the rotation
* @param {Number} c The angle of rotation
* @param {Number[]} dest The receiving vec3
* @returns {Number[]} dest
* @static
*/
rotateVec3X(a, b, c, dest) {
const p = [];
const r = [];
//Translate point to the origin
p[0] = a[0] - b[0];
p[1] = a[1] - b[1];
p[2] = a[2] - b[2];
//perform rotation
r[0] = p[0];
r[1] = p[1] * Math.cos(c) - p[2] * Math.sin(c);
r[2] = p[1] * Math.sin(c) + p[2] * Math.cos(c);
//translate to correct position
dest[0] = r[0] + b[0];
dest[1] = r[1] + b[1];
dest[2] = r[2] + b[2];
return dest;
},
/**
* Rotate a 3D vector around the y-axis
*
* @method rotateVec3Y
* @param {Number[]} a The vec3 point to rotate
* @param {Number[]} b The origin of the rotation
* @param {Number} c The angle of rotation
* @param {Number[]} dest The receiving vec3
* @returns {Number[]} dest
* @static
*/
rotateVec3Y(a, b, c, dest) {
const p = [];
const r = [];
//Translate point to the origin
p[0] = a[0] - b[0];
p[1] = a[1] - b[1];
p[2] = a[2] - b[2];
//perform rotation
r[0] = p[2] * Math.sin(c) + p[0] * Math.cos(c);
r[1] = p[1];
r[2] = p[2] * Math.cos(c) - p[0] * Math.sin(c);
//translate to correct position
dest[0] = r[0] + b[0];
dest[1] = r[1] + b[1];
dest[2] = r[2] + b[2];
return dest;
},
/**
* Rotate a 3D vector around the z-axis
*
* @method rotateVec3Z
* @param {Number[]} a The vec3 point to rotate
* @param {Number[]} b The origin of the rotation
* @param {Number} c The angle of rotation
* @param {Number[]} dest The receiving vec3
* @returns {Number[]} dest
* @static
*/
rotateVec3Z(a, b, c, dest) {
const p = [];
const r = [];
//Translate point to the origin
p[0] = a[0] - b[0];
p[1] = a[1] - b[1];
p[2] = a[2] - b[2];
//perform rotation
r[0] = p[0] * Math.cos(c) - p[1] * Math.sin(c);
r[1] = p[0] * Math.sin(c) + p[1] * Math.cos(c);
r[2] = p[2];
//translate to correct position
dest[0] = r[0] + b[0];
dest[1] = r[1] + b[1];
dest[2] = r[2] + b[2];
return dest;
},
/**
* Transforms a four-element vector by a 4x4 projection matrix.
*
* @method projectVec4
* @param {Number[]} p 3D View-space coordinate
* @param {Number[]} q 2D Projected coordinate
* @returns {Number[]} 2D Projected coordinate
* @static
*/
projectVec4(p, q) {
const f = 1.0 / p[3];
q = q || math.vec2();
q[0] = v[0] * f;
q[1] = v[1] * f;
return q;
},
/**
* Unprojects a three-element vector.
*
* @method unprojectVec3
* @param {Number[]} p 3D Projected coordinate
* @param {Number[]} viewMat View matrix
* @returns {Number[]} projMat Projection matrix
* @static
*/
unprojectVec3: ((() => {
const mat = new FloatArrayType(16);
const mat2 = new FloatArrayType(16);
const mat3 = new FloatArrayType(16);
return function (p, viewMat, projMat, q) {
return this.transformVec3(this.mulMat4(this.inverseMat4(viewMat, mat), this.inverseMat4(projMat, mat2), mat3), p, q)
};
}))(),
/**
* Linearly interpolates between two 3D vectors.
* @method lerpVec3
* @static
*/
lerpVec3(t, t1, t2, p1, p2, dest) {
const result = dest || math.vec3();
const f = (t - t1) / (t2 - t1);
result[0] = p1[0] + (f * (p2[0] - p1[0]));
result[1] = p1[1] + (f * (p2[1] - p1[1]));
result[2] = p1[2] + (f * (p2[2] - p1[2]));
return result;
},
/**
* Flattens a two-dimensional array into a one-dimensional array.
*
* @method flatten
* @static
* @param {Array of Arrays} a A 2D array
* @returns Flattened 1D array
*/
flatten(a) {
const result = [];
let i;
let leni;
let j;
let lenj;
let item;
for (i = 0, leni = a.length; i < leni; i++) {
item = a[i];
for (j = 0, lenj = item.length; j < lenj; j++) {
result.push(item[j]);
}
}
return result;
},
identityQuaternion(dest = math.vec4()) {
dest[0] = 0.0;
dest[1] = 0.0;
dest[2] = 0.0;
dest[3] = 1.0;
return dest;
},
/**
* Initializes a quaternion from Euler angles.
*
* @param {Number[]} euler The Euler angles.
* @param {String} order Euler angle order: "XYZ", "YXZ", "ZXY" etc.
* @param {Number[]} [dest] Destination quaternion, created by default.
* @returns {Number[]} The quaternion.
*/
eulerToQuaternion(euler, order, dest = math.vec4()) {
// http://www.mathworks.com/matlabcentral/fileexchange/
// 20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/
// content/SpinCalc.m
const a = (euler[0] * math.DEGTORAD) / 2;
const b = (euler[1] * math.DEGTORAD) / 2;
const c = (euler[2] * math.DEGTORAD) / 2;
const c1 = Math.cos(a);
const c2 = Math.cos(b);
const c3 = Math.cos(c);
const s1 = Math.sin(a);
const s2 = Math.sin(b);
const s3 = Math.sin(c);
if (order === 'XYZ') {
dest[0] = s1 * c2 * c3 + c1 * s2 * s3;
dest[1] = c1 * s2 * c3 - s1 * c2 * s3;
dest[2] = c1 * c2 * s3 + s1 * s2 * c3;
dest[3] = c1 * c2 * c3 - s1 * s2 * s3;
} else if (order === 'YXZ') {
dest[0] = s1 * c2 * c3 + c1 * s2 * s3;
dest[1] = c1 * s2 * c3 - s1 * c2 * s3;
dest[2] = c1 * c2 * s3 - s1 * s2 * c3;
dest[3] = c1 * c2 * c3 + s1 * s2 * s3;
} else if (order === 'ZXY') {
dest[0] = s1 * c2 * c3 - c1 * s2 * s3;
dest[1] = c1 * s2 * c3 + s1 * c2 * s3;
dest[2] = c1 * c2 * s3 + s1 * s2 * c3;
dest[3] = c1 * c2 * c3 - s1 * s2 * s3;
} else if (order === 'ZYX') {
dest[0] = s1 * c2 * c3 - c1 * s2 * s3;
dest[1] = c1 * s2 * c3 + s1 * c2 * s3;
dest[2] = c1 * c2 * s3 - s1 * s2 * c3;
dest[3] = c1 * c2 * c3 + s1 * s2 * s3;
} else if (order === 'YZX') {
dest[0] = s1 * c2 * c3 + c1 * s2 * s3;
dest[1] = c1 * s2 * c3 + s1 * c2 * s3;
dest[2] = c1 * c2 * s3 - s1 * s2 * c3;
dest[3] = c1 * c2 * c3 - s1 * s2 * s3;
} else if (order === 'XZY') {
dest[0] = s1 * c2 * c3 - c1 * s2 * s3;
dest[1] = c1 * s2 * c3 - s1 * c2 * s3;
dest[2] = c1 * c2 * s3 + s1 * s2 * c3;
dest[3] = c1 * c2 * c3 + s1 * s2 * s3;
}
return dest;
},
mat4ToQuaternion(m, dest = math.vec4()) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
// Assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
const m11 = m[0];
const m12 = m[4];
const m13 = m[8];
const m21 = m[1];
const m22 = m[5];
const m23 = m[9];
const m31 = m[2];
const m32 = m[6];
const m33 = m[10];
let s;
const trace = m11 + m22 + m33;
if (trace > 0) {
s = 0.5 / Math.sqrt(trace + 1.0);
dest[3] = 0.25 / s;
dest[0] = (m32 - m23) * s;
dest[1] = (m13 - m31) * s;
dest[2] = (m21 - m12) * s;
} else if (m11 > m22 && m11 > m33) {
s = 2.0 * Math.sqrt(1.0 + m11 - m22 - m33);
dest[3] = (m32 - m23) / s;
dest[0] = 0.25 * s;
dest[1] = (m12 + m21) / s;
dest[2] = (m13 + m31) / s;
} else if (m22 > m33) {
s = 2.0 * Math.sqrt(1.0 + m22 - m11 - m33);
dest[3] = (m13 - m31) / s;
dest[0] = (m12 + m21) / s;
dest[1] = 0.25 * s;
dest[2] = (m23 + m32) / s;
} else {
s = 2.0 * Math.sqrt(1.0 + m33 - m11 - m22);
dest[3] = (m21 - m12) / s;
dest[0] = (m13 + m31) / s;
dest[1] = (m23 + m32) / s;
dest[2] = 0.25 * s;
}
return dest;
},
vec3PairToQuaternion(u, v, dest = math.vec4()) {
const norm_u_norm_v = Math.sqrt(math.dotVec3(u, u) * math.dotVec3(v, v));
let real_part = norm_u_norm_v + math.dotVec3(u, v);
if (real_part < 0.00000001 * norm_u_norm_v) {
// If u and v are exactly opposite, rotate 180 degrees
// around an arbitrary orthogonal axis. Axis normalisation
// can happen later, when we normalise the quaternion.
real_part = 0.0;
if (Math.abs(u[0]) > Math.abs(u[2])) {
dest[0] = -u[1];
dest[1] = u[0];
dest[2] = 0;
} else {
dest[0] = 0;
dest[1] = -u[2];
dest[2] = u[1]
}
} else {
// Otherwise, build quaternion the standard way.
math.cross3Vec3(u, v, dest);
}
dest[3] = real_part;
return math.normalizeQuaternion(dest);
},
angleAxisToQuaternion(angleAxis, dest = math.vec4()) {
const halfAngle = angleAxis[3] / 2.0;
const fsin = Math.sin(halfAngle);
dest[0] = fsin * angleAxis[0];
dest[1] = fsin * angleAxis[1];
dest[2] = fsin * angleAxis[2];
dest[3] = Math.cos(halfAngle);
return dest;
},
quaternionToEuler: ((() => {
const mat = new FloatArrayType(16);
return (q, order, dest) => {
dest = dest || math.vec3();
math.quaternionToRotationMat4(q, mat);
math.mat4ToEuler(mat, order, dest);
return dest;
};
}))(),
mulQuaternions(p, q, dest = math.vec4()) {
const p0 = p[0];
const p1 = p[1];
const p2 = p[2];
const p3 = p[3];
const q0 = q[0];
const q1 = q[1];
const q2 = q[2];
const q3 = q[3];
dest[0] = p3 * q0 + p0 * q3 + p1 * q2 - p2 * q1;
dest[1] = p3 * q1 + p1 * q3 + p2 * q0 - p0 * q2;
dest[2] = p3 * q2 + p2 * q3 + p0 * q1 - p1 * q0;
dest[3] = p3 * q3 - p0 * q0 - p1 * q1 - p2 * q2;
return dest;
},
vec3ApplyQuaternion(q, vec, dest = math.vec3()) {
const x = vec[0];
const y = vec[1];
const z = vec[2];
const qx = q[0];
const qy = q[1];
const qz = q[2];
const qw = q[3];
// calculate quat * vector
const ix = qw * x + qy * z - qz * y;
const iy = qw * y + qz * x - qx * z;
const iz = qw * z + qx * y - qy * x;
const iw = -qx * x - qy * y - qz * z;
// calculate result * inverse quat
dest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
dest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
dest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
return dest;
},
quaternionToMat4(q, dest) {
dest = math.identityMat4(dest);
const q0 = q[0]; //x
const q1 = q[1]; //y
const q2 = q[2]; //z
const q3 = q[3]; //w
const tx = 2.0 * q0;
const ty = 2.0 * q1;
const tz = 2.0 * q2;
const twx = tx * q3;
const twy = ty * q3;
const twz = tz * q3;
const txx = tx * q0;
const txy = ty * q0;
const txz = tz * q0;
const tyy = ty * q1;
const tyz = tz * q1;
const tzz = tz * q2;
dest[0] = 1.0 - (tyy + tzz);
dest[1] = txy + twz;
dest[2] = txz - twy;
dest[4] = txy - twz;
dest[5] = 1.0 - (txx + tzz);
dest[6] = tyz + twx;
dest[8] = txz + twy;
dest[9] = tyz - twx;
dest[10] = 1.0 - (txx + tyy);
return dest;
},
quaternionToRotationMat4(q, m) {
const x = q[0];
const y = q[1];
const z = q[2];
const 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;
m[0] = 1 - (yy + zz);
m[4] = xy - wz;
m[8] = xz + wy;
m[1] = xy + wz;
m[5] = 1 - (xx + zz);
m[9] = yz - wx;
m[2] = xz - wy;
m[6] = yz + wx;
m[10] = 1 - (xx + yy);
// last column
m[3] = 0;
m[7] = 0;
m[11] = 0;
// bottom row
m[12] = 0;
m[13] = 0;
m[14] = 0;
m[15] = 1;
return m;
},
normalizeQuaternion(q, dest = q) {
const len = math.lenVec4([q[0], q[1], q[2], q[3]]);
dest[0] = q[0] / len;
dest[1] = q[1] / len;
dest[2] = q[2] / len;
dest[3] = q[3] / len;
return dest;
},
conjugateQuaternion(q, dest = q) {
dest[0] = -q[0];
dest[1] = -q[1];
dest[2] = -q[2];
dest[3] = q[3];
return dest;
},
inverseQuaternion(q, dest) {
return math.normalizeQuaternion(math.conjugateQuaternion(q, dest));
},
quaternionToAngleAxis(q, angleAxis = math.vec4()) {
q = math.normalizeQuaternion(q, tempVec4);
const q3 = q[3];
const angle = 2 * Math.acos(q3);
const s = Math.sqrt(1 - q3 * q3);
if (s < 0.001) { // test to avoid divide by zero, s is always positive due to sqrt
angleAxis[0] = q[0];
angleAxis[1] = q[1];
angleAxis[2] = q[2];
} else {
angleAxis[0] = q[0] / s;
angleAxis[1] = q[1] / s;
angleAxis[2] = q[2] / s;
}
angleAxis[3] = angle; // * 57.295779579;
return angleAxis;
},
//------------------------------------------------------------------------------------------------------------------
// Boundaries
//------------------------------------------------------------------------------------------------------------------
/**
* Returns a new, uninitialized 3D axis-aligned bounding box.
*
* @private
*/
AABB3(values) {
return new FloatArrayType(values || 6);
},
/**
* Returns a new, uninitialized 2D axis-aligned bounding box.
*
* @private
*/
AABB2(values) {
return new FloatArrayType(values || 4);
},
/**
* Returns a new, uninitialized 3D oriented bounding box (OBB).
*
* @private
*/
OBB3(values) {
return new FloatArrayType(values || 32);
},
/**
* Returns a new, uninitialized 2D oriented bounding box (OBB).
*
* @private
*/
OBB2(values) {
return new FloatArrayType(values || 16);
},
/** Returns a new 3D bounding sphere */
Sphere3(x, y, z, r) {
return new FloatArrayType([x, y, z, r]);
},
/**
* Transforms an OBB3 by a 4x4 matrix.
*
* @private
*/
transformOBB3(m, p, p2 = p) {
let i;
const len = p.length;
let x;
let y;
let z;
const m0 = m[0];
const m1 = m[1];
const m2 = m[2];
const m3 = m[3];
const m4 = m[4];
const m5 = m[5];
const m6 = m[6];
const m7 = m[7];
const m8 = m[8];
const m9 = m[9];
const m10 = m[10];
const m11 = m[11];
const m12 = m[12];
const m13 = m[13];
const m14 = m[14];
const m15 = m[15];
for (i = 0; i < len; i += 4) {
x = p[i + 0];
y = p[i + 1];
z = p[i + 2];
p2[i + 0] = (m0 * x) + (m4 * y) + (m8 * z) + m12;
p2[i + 1] = (m1 * x) + (m5 * y) + (m9 * z) + m13;
p2[i + 2] = (m2 * x) + (m6 * y) + (m10 * z) + m14;
p2[i + 3] = (m3 * x) + (m7 * y) + (m11 * z) + m15;
}
return p2;
},
/** Returns true if the first AABB contains the second AABB.
* @param aabb1
* @param aabb2
* @returns {boolean}
*/
containsAABB3: function (aabb1, aabb2) {
const result = (
aabb1[0] <= aabb2[0] && aabb2[3] <= aabb1[3] &&
aabb1[1] <= aabb2[1] && aabb2[4] <= aabb1[4] &&
aabb1[2] <= aabb2[2] && aabb2[5] <= aabb1[5]);
return result;
},
/**
* Gets the diagonal size of an AABB3 given as minima and maxima.
*
* @private
*/
getAABB3Diag: ((() => {
const min = new FloatArrayType(3);
const max = new FloatArrayType(3);
const tempVec3 = new FloatArrayType(3);
return aabb => {
min[0] = aabb[0];
min[1] = aabb[1];
min[2] = aabb[2];
max[0] = aabb[3];
max[1] = aabb[4];
max[2] = aabb[5];
math.subVec3(max, min, tempVec3);
return Math.abs(math.lenVec3(tempVec3));
};
}))(),
/**
* Get a diagonal boundary size that is symmetrical about the given point.
*
* @private
*/
getAABB3DiagPoint: ((() => {
const min = new FloatArrayType(3);
const max = new FloatArrayType(3);
const tempVec3 = new FloatArrayType(3);
return (aabb, p) => {
min[0] = aabb[0];
min[1] = aabb[1];
min[2] = aabb[2];
max[0] = aabb[3];
max[1] = aabb[4];
max[2] = aabb[5];
const diagVec = math.subVec3(max, min, tempVec3);
const xneg = p[0] - aabb[0];
const xpos = aabb[3] - p[0];
const yneg = p[1] - aabb[1];
const ypos = aabb[4] - p[1];
const zneg = p[2] - aabb[2];
const zpos = aabb[5] - p[2];
diagVec[0] += (xneg > xpos) ? xneg : xpos;
diagVec[1] += (yneg > ypos) ? yneg : ypos;
diagVec[2] += (zneg > zpos) ? zneg : zpos;
return Math.abs(math.lenVec3(diagVec));
};
}))(),
/**
* Gets the center of an AABB.
*
* @private
*/
getAABB3Center(aabb, dest) {
const r = dest || math.vec3();
r[0] = (aabb[0] + aabb[3]) / 2;
r[1] = (aabb[1] + aabb[4]) / 2;
r[2] = (aabb[2] + aabb[5]) / 2;
return r;
},
/**
* Gets the center of a 2D AABB.
*
* @private
*/
getAABB2Center(aabb, dest) {
const r = dest || math.vec2();
r[0] = (aabb[2] + aabb[0]) / 2;
r[1] = (aabb[3] + aabb[1]) / 2;
return r;
},
/**
* Collapses a 3D axis-aligned boundary, ready to expand to fit 3D points.
* Creates new AABB if none supplied.
*
* @private
*/
collapseAABB3(aabb = math.AABB3()) {
aabb[0] = math.MAX_DOUBLE;
aabb[1] = math.MAX_DOUBLE;
aabb[2] = math.MAX_DOUBLE;
aabb[3] = -math.MAX_DOUBLE;
aabb[4] = -math.MAX_DOUBLE;
aabb[5] = -math.MAX_DOUBLE;
return aabb;
},
/**
* Converts an axis-aligned 3D boundary into an oriented boundary consisting of
* an array of eight 3D positions, one for each corner of the boundary.
*
* @private
*/
AABB3ToOBB3(aabb, obb = math.OBB3()) {
obb[0] = aabb[0];
obb[1] = aabb[1];
obb[2] = aabb[2];
obb[3] = 1;
obb[4] = aabb[3];
obb[5] = aabb[1];
obb[6] = aabb[2];
obb[7] = 1;
obb[8] = aabb[3];
obb[9] = aabb[4];
obb[10] = aabb[2];
obb[11] = 1;
obb[12] = aabb[0];
obb[13] = aabb[4];
obb[14] = aabb[2];
obb[15] = 1;
obb[16] = aabb[0];
obb[17] = aabb[1];
obb[18] = aabb[5];
obb[19] = 1;
obb[20] = aabb[3];
obb[21] = aabb[1];
obb[22] = aabb[5];
obb[23] = 1;
obb[24] = aabb[3];
obb[25] = aabb[4];
obb[26] = aabb[5];
obb[27] = 1;
obb[28] = aabb[0];
obb[29] = aabb[4];
obb[30] = aabb[5];
obb[31] = 1;
return obb;
},
/**
* Finds the minimum axis-aligned 3D boundary enclosing the homogeneous 3D points (x,y,z,w) given in a flattened array.
*
* @private
*/
positions3ToAABB3: ((() => {
const p = new FloatArrayType(3);
return (positions, aabb, positionsDecodeMatrix) => {
aabb = aabb || math.AABB3();
let xmin = math.MAX_DOUBLE;
let ymin = math.MAX_DOUBLE;
let zmin = math.MAX_DOUBLE;
let xmax = -math.MAX_DOUBLE;
let ymax = -math.MAX_DOUBLE;
let zmax = -math.MAX_DOUBLE;
let x;
let y;
let z;
for (let i = 0, len = positions.length; i < len; i += 3) {
if (positionsDecodeMatrix) {
p[0] = positions[i + 0];
p[1] = positions[i + 1];
p[2] = positions[i + 2];
math.decompressPosition(p, positionsDecodeMatrix, p);
x = p[0];
y = p[1];
z = p[2];
} else {
x = positions[i + 0];
y = positions[i + 1];
z = positions[i + 2];
}
if (x < xmin) {
xmin = x;
}
if (y < ymin) {
ymin = y;
}
if (z < zmin) {
zmin = z;
}
if (x > xmax) {
xmax = x;
}
if (y > ymax) {
ymax = y;
}
if (z > zmax) {
zmax = z;
}
}
aabb[0] = xmin;
aabb[1] = ymin;
aabb[2] = zmin;
aabb[3] = xmax;
aabb[4] = ymax;
aabb[5] = zmax;
return aabb;
};
}))(),
/**
* Finds the minimum axis-aligned 3D boundary enclosing the homogeneous 3D points (x,y,z,w) given in a flattened array.
*
* @private
*/
OBB3ToAABB3(obb, aabb = math.AABB3()) {
let xmin = math.MAX_DOUBLE;
let ymin = math.MAX_DOUBLE;
let zmin = math.MAX_DOUBLE;
let xmax = -math.MAX_DOUBLE;
let ymax = -math.MAX_DOUBLE;
let zmax = -math.MAX_DOUBLE;
let x;
let y;
let z;
for (let i = 0, len = obb.length; i < len; i += 4) {
x = obb[i + 0];
y = obb[i + 1];
z = obb[i + 2];
if (x < xmin) {
xmin = x;
}
if (y < ymin) {
ymin = y;
}
if (z < zmin) {
zmin = z;
}
if (x > xmax) {
xmax = x;
}
if (y > ymax) {
ymax = y;
}
if (z > zmax) {
zmax = z;
}
}
aabb[0] = xmin;
aabb[1] = ymin;
aabb[2] = zmin;
aabb[3] = xmax;
aabb[4] = ymax;
aabb[5] = zmax;
return aabb;
},
/**
* Finds the minimum axis-aligned 3D boundary enclosing the given 3D points.
*
* @private
*/
points3ToAABB3(points, aabb = math.AABB3()) {
let xmin = math.MAX_DOUBLE;
let ymin = math.MAX_DOUBLE;
let zmin = math.MAX_DOUBLE;
let xmax = -math.MAX_DOUBLE;
let ymax = -math.MAX_DOUBLE;
let zmax = -math.MAX_DOUBLE;
let x;
let y;
let z;
for (let i = 0, len = points.length; i < len; i++) {
x = points[i][0];
y = points[i][1];
z = points[i][2];
if (x < xmin) {
xmin = x;
}
if (y < ymin) {
ymin = y;
}
if (z < zmin) {
zmin = z;
}
if (x > xmax) {
xmax = x;
}
if (y > ymax) {
ymax = y;
}
if (z > zmax) {
zmax = z;
}
}
aabb[0] = xmin;
aabb[1] = ymin;
aabb[2] = zmin;
aabb[3] = xmax;
aabb[4] = ymax;
aabb[5] = zmax;
return aabb;
},
/**
* Finds the minimum boundary sphere enclosing the given 3D points.
*
* @private
*/
points3ToSphere3: ((() => {
const tempVec3 = new FloatArrayType(3);
return (points, sphere) => {
sphere = sphere || math.vec4();
let x = 0;
let y = 0;
let z = 0;
let i;
const numPoints = points.length;
for (i = 0; i < numPoints; i++) {
x += points[i][0];
y += points[i][1];
z += points[i][2];
}
sphere[0] = x / numPoints;
sphere[1] = y / numPoints;
sphere[2] = z / numPoints;
let radius = 0;
let dist;
for (i = 0; i < numPoints; i++) {
dist = Math.abs(math.lenVec3(math.subVec3(points[i], sphere, tempVec3)));
if (dist > radius) {
radius = dist;
}
}
sphere[3] = radius;
return sphere;
};
}))(),
/**
* Finds the minimum boundary sphere enclosing the given 3D positions.
*
* @private
*/
positions3ToSphere3: ((() => {
const tempVec3a = new FloatArrayType(3);
const tempVec3b = new FloatArrayType(3);
return (positions, sphere) => {
sphere = sphere || math.vec4();
let x = 0;
let y = 0;
let z = 0;
let i;
const lenPositions = positions.length;
let radius = 0;
for (i = 0; i < lenPositions; i += 3) {
x += positions[i];
y += positions[i + 1];
z += positions[i + 2];
}
const numPositions = lenPositions / 3;
sphere[0] = x / numPositions;
sphere[1] = y / numPositions;
sphere[2] = z / numPositions;
let dist;
for (i = 0; i < lenPositions; i += 3) {
tempVec3a[0] = positions[i];
tempVec3a[1] = positions[i + 1];
tempVec3a[2] = positions[i + 2];
dist = Math.abs(math.lenVec3(math.subVec3(tempVec3a, sphere, tempVec3b)));
if (dist > radius) {
radius = dist;
}
}
sphere[3] = radius;
return sphere;
};
}))(),
/**
* Finds the minimum boundary sphere enclosing the given 3D points.
*
* @private
*/
OBB3ToSphere3: ((() => {
const point = new FloatArrayType(3);
const tempVec3 = new FloatArrayType(3);
return (points, sphere) => {
sphere = sphere || math.vec4();
let x = 0;
let y = 0;
let z = 0;
let i;
const lenPoints = points.length;
const numPoints = lenPoints / 4;
for (i = 0; i < lenPoints; i += 4) {
x += points[i + 0];
y += points[i + 1];
z += points[i + 2];
}
sphere[0] = x / numPoints;
sphere[1] = y / numPoints;
sphere[2] = z / numPoints;
let radius = 0;
let dist;
for (i = 0; i < lenPoints; i += 4) {
point[0] = points[i + 0];
point[1] = points[i + 1];
point[2] = points[i + 2];
dist = Math.abs(math.lenVec3(math.subVec3(point, sphere, tempVec3)));
if (dist > radius) {
radius = dist;
}
}
sphere[3] = radius;
return sphere;
};
}))(),
/**
* Gets the center of a bounding sphere.
*
* @private
*/
getSphere3Center(sphere, dest = math.vec3()) {
dest[0] = sphere[0];
dest[1] = sphere[1];
dest[2] = sphere[2];
return dest;
},
/**
* Expands the first axis-aligned 3D boundary to enclose the second, if required.
*
* @private
*/
expandAABB3(aabb1, aabb2) {
if (aabb1[0] > aabb2[0]) {
aabb1[0] = aabb2[0];
}
if (aabb1[1] > aabb2[1]) {
aabb1[1] = aabb2[1];
}
if (aabb1[2] > aabb2[2]) {
aabb1[2] = aabb2[2];
}
if (aabb1[3] < aabb2[3]) {
aabb1[3] = aabb2[3];
}
if (aabb1[4] < aabb2[4]) {
aabb1[4] = aabb2[4];
}
if (aabb1[5] < aabb2[5]) {
aabb1[5] = aabb2[5];
}
return aabb1;
},
/**
* Expands an axis-aligned 3D boundary to enclose the given point, if needed.
*
* @private
*/
expandAABB3Point3(aabb, p) {
if (aabb[0] > p[0]) {
aabb[0] = p[0];
}
if (aabb[1] > p[1]) {
aabb[1] = p[1];
}
if (aabb[2] > p[2]) {
aabb[2] = p[2];
}
if (aabb[3] < p[0]) {
aabb[3] = p[0];
}
if (aabb[4] < p[1]) {
aabb[4] = p[1];
}
if (aabb[5] < p[2]) {
aabb[5] = p[2];
}
return aabb;
},
/**
* Calculates the normal vector of a triangle.
*
* @private
*/
triangleNormal(a, b, c, normal = math.vec3()) {
const p1x = b[0] - a[0];
const p1y = b[1] - a[1];
const p1z = b[2] - a[2];
const p2x = c[0] - a[0];
const p2y = c[1] - a[1];
const p2z = c[2] - a[2];
const p3x = p1y * p2z - p1z * p2y;
const p3y = p1z * p2x - p1x * p2z;
const p3z = p1x * p2y - p1y * p2x;
const mag = Math.sqrt(p3x * p3x + p3y * p3y + p3z * p3z);
if (mag === 0) {
normal[0] = 0;
normal[1] = 0;
normal[2] = 0;
} else {
normal[0] = p3x / mag;
normal[1] = p3y / mag;
normal[2] = p3z / mag;
}
return normal
}
};
export {math};
