src/viewer/scene/math/math.js
// Some temporary vars to help avoid garbage collection
let doublePrecision = true;
let FloatArrayType = doublePrecision ? Float64Array : Float32Array;
const tempVec3a = new FloatArrayType(3);
const tempMat1 = new FloatArrayType(16);
const tempMat2 = new FloatArrayType(16);
const tempVec4 = new FloatArrayType(4);
/**
* @private
*/
const math = {
setDoublePrecisionEnabled(enable) {
doublePrecision = enable;
FloatArrayType = doublePrecision ? Float64Array : Float32Array;
},
getDoublePrecisionEnabled() {
return doublePrecision;
},
MIN_DOUBLE: -Number.MAX_SAFE_INTEGER,
MAX_DOUBLE: Number.MAX_SAFE_INTEGER,
MAX_INT: 10000000,
/**
* 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,
unglobalizeObjectId(modelId, globalId) {
const idx = globalId.indexOf("#");
return (idx === modelId.length && globalId.startsWith(modelId)) ? globalId.substring(idx + 1) : globalId;
},
globalizeObjectId(modelId, objectId) {
return (modelId + "#" + objectId)
},
/**
* Returns:
* - x != 0 => 1/x,
* - x == 1 => 1
*
* @param {number} x
*/
safeInv(x) {
const retVal = 1 / x;
if (isNaN(retVal) || !isFinite(retVal)) {
return 1;
}
return retVal;
},
/**
* 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);
},
/**
* Converts a list of double-precision values to a list of high-part floats and a list of low-part floats.
* @param doubleVals
* @param floatValsHigh
* @param floatValsLow
*/
doublesToFloats(doubleVals, floatValsHigh, floatValsLow) {
const floatPair = new FloatArrayType(2);
for (let i = 0, len = doubleVals.length; i < len; i++) {
math.splitDouble(doubleVals[i], floatPair);
floatValsHigh[i] = floatPair[0];
floatValsLow[i] = floatPair[1];
}
},
/**
* Splits a double value into two floats.
* @param value
* @param floatPair
*/
splitDouble(value, floatPair) {
const hi = FloatArrayType.from([value])[0];
const low = value - hi;
floatPair[0] = hi;
floatPair[1] = low;
},
/**
* Returns a new UUID.
* @method createUUID
* @static
* @return string The new UUID
*/
createUUID: ((() => {
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;
},
/**
* Returns true if the two 3-element vectors are the same.
* @param v1
* @param v2
* @returns {Boolean}
*/
compareVec3(v1, v2) {
return (v1[0] === v2[0] && v1[1] === v2[1] && v1[2] === v2[2]);
},
/**
* Negates a three-element vector.
* @method negateVec3
* @static
* @param {Array(Number)} v Vector to negate
* @param {Array(Number)} [dest] Destination vector
* @return {Array(Number)} dest if specified, v otherwise
*/
negateVec3(v, dest) {
if (!dest) {
dest = v;
}
dest[0] = -v[0];
dest[1] = -v[1];
dest[2] = -v[2];
return dest;
},
/**
* 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;
},
/**
* Get the geometric mean of the vectors.
* @method geometricMeanVec2
* @static
* @param {...Array(Number)} vectors Vec2 to mean
* @return {Array(Number)} The geometric mean vec2
*/
geometricMeanVec2(...vectors) {
const geometricMean = new FloatArrayType(vectors[0]);
for (let i = 1; i < vectors.length; i++) {
geometricMean[0] += vectors[i][0];
geometricMean[1] += vectors[i][1];
}
geometricMean[0] /= vectors.length;
geometricMean[1] /= vectors.length;
return geometricMean;
},
/**
* 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 || math.vec3();
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
*/
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;
},
/**
* Creates a new matrix that replaces the translation in the rightmost column of the given
* affine matrix with the given translation.
* @param m
* @param translation
* @param dest
* @returns {*}
*/
setMat4Translation(m, translation, dest) {
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] = translation[0];
dest[13] = translation[1];
dest[14] = translation[2];
dest[15] = m[15];
return dest;
},
/**
* 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;
};
})(),
/** @private */
getColMat4(mat, c) {
const i = c * 4;
return [mat[i], mat[i + 1], mat[i + 2], mat[i + 3]];
},
/** @private */
setRowMat4(mat, r, v) {
mat[r] = v[0];
mat[r + 4] = v[1];
mat[r + 8] = v[2];
mat[r + 12] = v[3];
},
/**
* 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);
},
/**
* Returns true if the two 4x4 matrices are the same.
* @param m1
* @param m2
* @returns {Boolean}
*/
compareMat4(m1, m2) {
return m1[0] === m2[0] &&
m1[1] === m2[1] &&
m1[2] === m2[2] &&
m1[3] === m2[3] &&
m1[4] === m2[4] &&
m1[5] === m2[5] &&
m1[6] === m2[6] &&
m1[7] === m2[7] &&
m1[8] === m2[8] &&
m1[9] === m2[9] &&
m1[10] === m2[10] &&
m1[11] === m2[11] &&
m1[12] === m2[12] &&
m1[13] === m2[13] &&
m1[14] === m2[14] &&
m1[15] === m2[15];
},
/**
* 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;
}
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 2D vector around a center point.
*
* @param a
* @param center
* @param angle
* @returns {math}
*/
rotateVec2(a, center, angle, dest = a) {
const c = Math.cos(angle);
const s = Math.sin(angle);
const x = a[0] - center[0];
const y = a[1] - center[1];
dest[0] = x * c - y * s + center[0];
dest[1] = x * s + y * c + center[1];
return a;
},
/**
* 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] = p[0] * f;
q[1] = p[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;
},
/**
* Linearly interpolates between two 4x4 matrices.
* @method lerpMat4
* @static
*/
lerpMat4(t, t1, t2, m1, m2, dest) {
const result = dest || math.mat4();
const f = (t - t1) / (t2 - t1);
result[0] = m1[0] + (f * (m2[0] - m1[0]));
result[1] = m1[1] + (f * (m2[1] - m1[1]));
result[2] = m1[2] + (f * (m2[2] - m1[2]));
result[3] = m1[3] + (f * (m2[3] - m1[3]));
result[4] = m1[4] + (f * (m2[4] - m1[4]));
result[5] = m1[5] + (f * (m2[5] - m1[5]));
result[6] = m1[6] + (f * (m2[6] - m1[6]));
result[7] = m1[7] + (f * (m2[7] - m1[7]));
result[8] = m1[8] + (f * (m2[8] - m1[8]));
result[9] = m1[9] + (f * (m2[9] - m1[9]));
result[10] = m1[10] + (f * (m2[10] - m1[10]));
result[11] = m1[11] + (f * (m2[11] - m1[11]));
result[12] = m1[12] + (f * (m2[12] - m1[12]));
result[13] = m1[13] + (f * (m2[13] - m1[13]));
result[14] = m1[14] + (f * (m2[14] - m1[14]));
result[15] = m1[15] + (f * (m2[15] - m1[15]));
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 area of an AABB.
*
* @private
*/
getAABB3Area(aabb) {
const width = (aabb[3] - aabb[0]);
const height = (aabb[4] - aabb[1]);
const depth = (aabb[5] - aabb[2]);
return (width * height * depth);
},
/**
* 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.MIN_DOUBLE;
aabb[4] = math.MIN_DOUBLE;
aabb[5] = math.MIN_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.MIN_DOUBLE;
let ymax = math.MIN_DOUBLE;
let zmax = math.MIN_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.MIN_DOUBLE;
let ymax = math.MIN_DOUBLE;
let zmax = math.MIN_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.MIN_DOUBLE;
let ymax = math.MIN_DOUBLE;
let zmax = math.MIN_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;
},
/**
* Gets the 3D center of the given flat array of 3D positions.
*
* @private
*/
getPositionsCenter(positions, center = math.vec3()) {
let xCenter = 0;
let yCenter = 0;
let zCenter = 0;
for (var i = 0, len = positions.length; i < len; i += 3) {
xCenter += positions[i + 0];
yCenter += positions[i + 1];
zCenter += positions[i + 2];
}
const numPositions = positions.length / 3;
center[0] = xCenter / numPositions;
center[1] = yCenter / numPositions;
center[2] = zCenter / numPositions;
return center;
},
/**
* 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;
},
/**
* Expands an axis-aligned 3D boundary to enclose the given points, if needed.
*
* @private
*/
expandAABB3Points3(aabb, positions) {
var x;
var y;
var z;
for (var i = 0, len = positions.length; i < len; i += 3) {
x = positions[i];
y = positions[i + 1];
z = positions[i + 2];
if (aabb[0] > x) {
aabb[0] = x;
}
if (aabb[1] > y) {
aabb[1] = y;
}
if (aabb[2] > z) {
aabb[2] = z;
}
if (aabb[3] < x) {
aabb[3] = x;
}
if (aabb[4] < y) {
aabb[4] = y;
}
if (aabb[5] < z) {
aabb[5] = z;
}
}
return aabb;
},
/**
* Collapses a 2D axis-aligned boundary, ready to expand to fit 2D points.
* Creates new AABB if none supplied.
*
* @private
*/
collapseAABB2(aabb = math.AABB2()) {
aabb[0] = math.MAX_DOUBLE;
aabb[1] = math.MAX_DOUBLE;
aabb[2] = math.MIN_DOUBLE;
aabb[3] = math.MIN_DOUBLE;
return aabb;
},
point3AABB3Intersect(aabb, p) {
return aabb[0] > p[0] || aabb[3] < p[0] || aabb[1] > p[1] || aabb[4] < p[1] || aabb[2] > p[2] || aabb[5] < p[2];
},
/**
*
* @param dir
* @param constant
* @param aabb
* @returns {number}
*/
planeAABB3Intersect(dir, constant, aabb) {
let min, max;
if (dir[0] > 0) {
min = dir[0] * aabb[0];
max = dir[0] * aabb[3];
} else {
min = dir[0] * aabb[3];
max = dir[0] * aabb[0];
}
if (dir[1] > 0) {
min += dir[1] * aabb[1];
max += dir[1] * aabb[4];
} else {
min += dir[1] * aabb[4];
max += dir[1] * aabb[1];
}
if (dir[2] > 0) {
min += dir[2] * aabb[2];
max += dir[2] * aabb[5];
} else {
min += dir[2] * aabb[5];
max += dir[2] * aabb[2];
}
const outside = (min <= -constant) && (max <= -constant);
if (outside) {
return -1;
}
const inside = (min >= -constant) && (max >= -constant);
if (inside) {
return 1;
}
return 0;
},
/**
* Finds the minimum 2D projected axis-aligned boundary enclosing the given 3D points.
*
* @private
*/
OBB3ToAABB2(points, aabb = math.AABB2()) {
let xmin = math.MAX_DOUBLE;
let ymin = math.MAX_DOUBLE;
let xmax = math.MIN_DOUBLE;
let ymax = math.MIN_DOUBLE;
let x;
let y;
let w;
let f;
for (let i = 0, len = points.length; i < len; i += 4) {
x = points[i + 0];
y = points[i + 1];
w = points[i + 3] || 1.0;
f = 1.0 / w;
x *= f;
y *= f;
if (x < xmin) {
xmin = x;
}
if (y < ymin) {
ymin = y;
}
if (x > xmax) {
xmax = x;
}
if (y > ymax) {
ymax = y;
}
}
aabb[0] = xmin;
aabb[1] = ymin;
aabb[2] = xmax;
aabb[3] = ymax;
return aabb;
},
/**
* Expands the first axis-aligned 2D boundary to enclose the second, if required.
*
* @private
*/
expandAABB2(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];
}
return aabb1;
},
/**
* Expands an axis-aligned 2D boundary to enclose the given point, if required.
*
* @private
*/
expandAABB2Point2(aabb, p) {
if (aabb[0] > p[0]) {
aabb[0] = p[0];
}
if (aabb[1] > p[1]) {
aabb[1] = p[1];
}
if (aabb[2] < p[0]) {
aabb[2] = p[0];
}
if (aabb[3] < p[1]) {
aabb[3] = p[1];
}
return aabb;
},
AABB2ToCanvas(aabb, canvasWidth, canvasHeight, aabb2 = aabb) {
const xmin = (aabb[0] + 1.0) * 0.5;
const ymin = (aabb[1] + 1.0) * 0.5;
const xmax = (aabb[2] + 1.0) * 0.5;
const ymax = (aabb[3] + 1.0) * 0.5;
aabb2[0] = Math.floor(xmin * canvasWidth);
aabb2[1] = canvasHeight - Math.floor(ymax * canvasHeight);
aabb2[2] = Math.floor(xmax * canvasWidth);
aabb2[3] = canvasHeight - Math.floor(ymin * canvasHeight);
return aabb2;
},
//------------------------------------------------------------------------------------------------------------------
// Curves
//------------------------------------------------------------------------------------------------------------------
tangentQuadraticBezier(t, p0, p1, p2) {
return 2 * (1 - t) * (p1 - p0) + 2 * t * (p2 - p1);
},
tangentQuadraticBezier3(t, p0, p1, p2, p3) {
return -3 * p0 * (1 - t) * (1 - t) +
3 * p1 * (1 - t) * (1 - t) - 6 * t * p1 * (1 - t) +
6 * t * p2 * (1 - t) - 3 * t * t * p2 +
3 * t * t * p3;
},
tangentSpline(t) {
const h00 = 6 * t * t - 6 * t;
const h10 = 3 * t * t - 4 * t + 1;
const h01 = -6 * t * t + 6 * t;
const h11 = 3 * t * t - 2 * t;
return h00 + h10 + h01 + h11;
},
catmullRomInterpolate(p0, p1, p2, p3, t) {
const v0 = (p2 - p0) * 0.5;
const v1 = (p3 - p1) * 0.5;
const t2 = t * t;
const t3 = t * t2;
return (2 * p1 - 2 * p2 + v0 + v1) * t3 + (-3 * p1 + 3 * p2 - 2 * v0 - v1) * t2 + v0 * t + p1;
},
// Bezier Curve formulii from http://en.wikipedia.org/wiki/B%C3%A9zier_curve
// Quad Bezier Functions
b2p0(t, p) {
const k = 1 - t;
return k * k * p;
},
b2p1(t, p) {
return 2 * (1 - t) * t * p;
},
b2p2(t, p) {
return t * t * p;
},
b2(t, p0, p1, p2) {
return this.b2p0(t, p0) + this.b2p1(t, p1) + this.b2p2(t, p2);
},
// Cubic Bezier Functions
b3p0(t, p) {
const k = 1 - t;
return k * k * k * p;
},
b3p1(t, p) {
const k = 1 - t;
return 3 * k * k * t * p;
},
b3p2(t, p) {
const k = 1 - t;
return 3 * k * t * t * p;
},
b3p3(t, p) {
return t * t * t * p;
},
b3(t, p0, p1, p2, p3) {
return this.b3p0(t, p0) + this.b3p1(t, p1) + this.b3p2(t, p2) + this.b3p3(t, p3);
},
//------------------------------------------------------------------------------------------------------------------
// Geometry
//------------------------------------------------------------------------------------------------------------------
/**
* 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
},
/**
* Finds the intersection of a 3D ray with a 3D triangle.
*
* @private
*/
rayTriangleIntersect: ((() => {
const tempVec3 = new FloatArrayType(3);
const tempVec3b = new FloatArrayType(3);
const tempVec3c = new FloatArrayType(3);
const tempVec3d = new FloatArrayType(3);
const tempVec3e = new FloatArrayType(3);
return (origin, dir, a, b, c, isect) => {
isect = isect || math.vec3();
const EPSILON = 0.000001;
const edge1 = math.subVec3(b, a, tempVec3);
const edge2 = math.subVec3(c, a, tempVec3b);
const pvec = math.cross3Vec3(dir, edge2, tempVec3c);
const det = math.dotVec3(edge1, pvec);
if (det < EPSILON) {
return null;
}
const tvec = math.subVec3(origin, a, tempVec3d);
const u = math.dotVec3(tvec, pvec);
if (u < 0 || u > det) {
return null;
}
const qvec = math.cross3Vec3(tvec, edge1, tempVec3e);
const v = math.dotVec3(dir, qvec);
if (v < 0 || u + v > det) {
return null;
}
const t = math.dotVec3(edge2, qvec) / det;
isect[0] = origin[0] + t * dir[0];
isect[1] = origin[1] + t * dir[1];
isect[2] = origin[2] + t * dir[2];
return isect;
};
}))(),
/**
* Finds the intersection of a 3D ray with a plane defined by 3 points.
*
* @private
*/
rayPlaneIntersect: ((() => {
const tempVec3 = new FloatArrayType(3);
const tempVec3b = new FloatArrayType(3);
const tempVec3c = new FloatArrayType(3);
const tempVec3d = new FloatArrayType(3);
return (origin, dir, a, b, c, isect) => {
isect = isect || math.vec3();
dir = math.normalizeVec3(dir, tempVec3);
const edge1 = math.subVec3(b, a, tempVec3b);
const edge2 = math.subVec3(c, a, tempVec3c);
const n = math.cross3Vec3(edge1, edge2, tempVec3d);
math.normalizeVec3(n, n);
const d = -math.dotVec3(a, n);
const t = -(math.dotVec3(origin, n) + d) / math.dotVec3(dir, n);
isect[0] = origin[0] + t * dir[0];
isect[1] = origin[1] + t * dir[1];
isect[2] = origin[2] + t * dir[2];
return isect;
};
}))(),
/**
* Gets barycentric coordinates from cartesian coordinates within a triangle.
* Gets barycentric coordinates from cartesian coordinates within a triangle.
*
* @private
*/
cartesianToBarycentric: ((() => {
const tempVec3 = new FloatArrayType(3);
const tempVec3b = new FloatArrayType(3);
const tempVec3c = new FloatArrayType(3);
return (cartesian, a, b, c, dest) => {
const v0 = math.subVec3(c, a, tempVec3);
const v1 = math.subVec3(b, a, tempVec3b);
const v2 = math.subVec3(cartesian, a, tempVec3c);
const dot00 = math.dotVec3(v0, v0);
const dot01 = math.dotVec3(v0, v1);
const dot02 = math.dotVec3(v0, v2);
const dot11 = math.dotVec3(v1, v1);
const dot12 = math.dotVec3(v1, v2);
const denom = (dot00 * dot11 - dot01 * dot01);
// Colinear or singular triangle
if (denom === 0) {
// Arbitrary location outside of triangle
return null;
}
const invDenom = 1 / denom;
const u = (dot11 * dot02 - dot01 * dot12) * invDenom;
const v = (dot00 * dot12 - dot01 * dot02) * invDenom;
dest[0] = 1 - u - v;
dest[1] = v;
dest[2] = u;
return dest;
};
}))(),
/**
* Returns true if the given barycentric coordinates are within their triangle.
*
* @private
*/
barycentricInsideTriangle(bary) {
const v = bary[1];
const u = bary[2];
return (u >= 0) && (v >= 0) && (u + v < 1);
},
/**
* Gets cartesian coordinates from barycentric coordinates within a triangle.
*
* @private
*/
barycentricToCartesian(bary, a, b, c, cartesian = math.vec3()) {
const u = bary[0];
const v = bary[1];
const w = bary[2];
cartesian[0] = a[0] * u + b[0] * v + c[0] * w;
cartesian[1] = a[1] * u + b[1] * v + c[1] * w;
cartesian[2] = a[2] * u + b[2] * v + c[2] * w;
return cartesian;
},
/**
* Given geometry defined as an array of positions, optional normals, option uv and an array of indices, returns
* modified arrays that have duplicate vertices removed.
*
* Note: does not work well when co-incident vertices have same positions but different normals and UVs.
*
* @param positions
* @param normals
* @param uv
* @param indices
* @returns {{positions: Array, indices: Array}}
* @private
*/
mergeVertices(positions, normals, uv, indices) {
const positionsMap = {}; // Hashmap for looking up vertices by position coordinates (and making sure they are unique)
const indicesLookup = [];
const uniquePositions = [];
const uniqueNormals = normals ? [] : null;
const uniqueUV = uv ? [] : null;
const indices2 = [];
let vx;
let vy;
let vz;
let key;
const precisionPoints = 4; // number of decimal points, e.g. 4 for epsilon of 0.0001
const precision = 10 ** precisionPoints;
let i;
let len;
let uvi = 0;
for (i = 0, len = positions.length; i < len; i += 3) {
vx = positions[i];
vy = positions[i + 1];
vz = positions[i + 2];
key = `${Math.round(vx * precision)}_${Math.round(vy * precision)}_${Math.round(vz * precision)}`;
if (positionsMap[key] === undefined) {
positionsMap[key] = uniquePositions.length / 3;
uniquePositions.push(vx);
uniquePositions.push(vy);
uniquePositions.push(vz);
if (normals) {
uniqueNormals.push(normals[i]);
uniqueNormals.push(normals[i + 1]);
uniqueNormals.push(normals[i + 2]);
}
if (uv) {
uniqueUV.push(uv[uvi]);
uniqueUV.push(uv[uvi + 1]);
}
}
indicesLookup[i / 3] = positionsMap[key];
uvi += 2;
}
for (i = 0, len = indices.length; i < len; i++) {
indices2[i] = indicesLookup[indices[i]];
}
const result = {
positions: uniquePositions,
indices: indices2
};
if (uniqueNormals) {
result.normals = uniqueNormals;
}
if (uniqueUV) {
result.uv = uniqueUV;
}
return result;
},
/**
* Builds normal vectors from positions and indices.
*
* @private
*/
buildNormals: ((() => {
const a = new FloatArrayType(3);
const b = new FloatArrayType(3);
const c = new FloatArrayType(3);
const ab = new FloatArrayType(3);
const ac = new FloatArrayType(3);
const crossVec = new FloatArrayType(3);
return (positions, indices, normals) => {
let i;
let len;
const nvecs = new Array(positions.length / 3);
let j0;
let j1;
let j2;
for (i = 0, len = indices.length; i < len; i += 3) {
j0 = indices[i];
j1 = indices[i + 1];
j2 = indices[i + 2];
a[0] = positions[j0 * 3];
a[1] = positions[j0 * 3 + 1];
a[2] = positions[j0 * 3 + 2];
b[0] = positions[j1 * 3];
b[1] = positions[j1 * 3 + 1];
b[2] = positions[j1 * 3 + 2];
c[0] = positions[j2 * 3];
c[1] = positions[j2 * 3 + 1];
c[2] = positions[j2 * 3 + 2];
math.subVec3(b, a, ab);
math.subVec3(c, a, ac);
const normVec = math.vec3();
math.normalizeVec3(math.cross3Vec3(ab, ac, crossVec), normVec);
if (!nvecs[j0]) {
nvecs[j0] = [];
}
if (!nvecs[j1]) {
nvecs[j1] = [];
}
if (!nvecs[j2]) {
nvecs[j2] = [];
}
nvecs[j0].push(normVec);
nvecs[j1].push(normVec);
nvecs[j2].push(normVec);
}
normals = (normals && normals.length === positions.length) ? normals : new Float32Array(positions.length);
let count;
let x;
let y;
let z;
for (i = 0, len = nvecs.length; i < len; i++) { // Now go through and average out everything
count = nvecs[i].length;
x = 0;
y = 0;
z = 0;
for (let j = 0; j < count; j++) {
x += nvecs[i][j][0];
y += nvecs[i][j][1];
z += nvecs[i][j][2];
}
normals[i * 3] = (x / count);
normals[i * 3 + 1] = (y / count);
normals[i * 3 + 2] = (z / count);
}
return normals;
};
}))(),
/**
* Builds vertex tangent vectors from positions, UVs and indices.
*
* @private
*/
buildTangents: ((() => {
const tempVec3 = new FloatArrayType(3);
const tempVec3b = new FloatArrayType(3);
const tempVec3c = new FloatArrayType(3);
const tempVec3d = new FloatArrayType(3);
const tempVec3e = new FloatArrayType(3);
const tempVec3f = new FloatArrayType(3);
const tempVec3g = new FloatArrayType(3);
return (positions, indices, uv) => {
const tangents = new Float32Array(positions.length);
// The vertex arrays needs to be calculated
// before the calculation of the tangents
for (let location = 0; location < indices.length; location += 3) {
// Recontructing each vertex and UV coordinate into the respective vectors
let index = indices[location];
const v0 = positions.subarray(index * 3, index * 3 + 3);
const uv0 = uv.subarray(index * 2, index * 2 + 2);
index = indices[location + 1];
const v1 = positions.subarray(index * 3, index * 3 + 3);
const uv1 = uv.subarray(index * 2, index * 2 + 2);
index = indices[location + 2];
const v2 = positions.subarray(index * 3, index * 3 + 3);
const uv2 = uv.subarray(index * 2, index * 2 + 2);
const deltaPos1 = math.subVec3(v1, v0, tempVec3);
const deltaPos2 = math.subVec3(v2, v0, tempVec3b);
const deltaUV1 = math.subVec2(uv1, uv0, tempVec3c);
const deltaUV2 = math.subVec2(uv2, uv0, tempVec3d);
const r = 1 / ((deltaUV1[0] * deltaUV2[1]) - (deltaUV1[1] * deltaUV2[0]));
const tangent = math.mulVec3Scalar(
math.subVec3(
math.mulVec3Scalar(deltaPos1, deltaUV2[1], tempVec3e),
math.mulVec3Scalar(deltaPos2, deltaUV1[1], tempVec3f),
tempVec3g
),
r,
tempVec3f
);
// Average the value of the vectors
let addTo;
for (let v = 0; v < 3; v++) {
addTo = indices[location + v] * 3;
tangents[addTo] += tangent[0];
tangents[addTo + 1] += tangent[1];
tangents[addTo + 2] += tangent[2];
}
}
return tangents;
};
}))(),
/**
* Builds vertex and index arrays needed by color-indexed triangle picking.
*
* @private
*/
buildPickTriangles(positions, indices, compressGeometry) {
const numIndices = indices.length;
const pickPositions = compressGeometry ? new Uint16Array(numIndices * 9) : new Float32Array(numIndices * 9);
const pickColors = new Uint8Array(numIndices * 12);
let primIndex = 0;
let vi;// Positions array index
let pvi = 0;// Picking positions array index
let pci = 0; // Picking color array index
// Triangle indices
let i;
let r;
let g;
let b;
let a;
for (let location = 0; location < numIndices; location += 3) {
// Primitive-indexed triangle pick color
a = (primIndex >> 24 & 0xFF);
b = (primIndex >> 16 & 0xFF);
g = (primIndex >> 8 & 0xFF);
r = (primIndex & 0xFF);
// A
i = indices[location];
vi = i * 3;
pickPositions[pvi++] = positions[vi];
pickPositions[pvi++] = positions[vi + 1];
pickPositions[pvi++] = positions[vi + 2];
pickColors[pci++] = r;
pickColors[pci++] = g;
pickColors[pci++] = b;
pickColors[pci++] = a;
// B
i = indices[location + 1];
vi = i * 3;
pickPositions[pvi++] = positions[vi];
pickPositions[pvi++] = positions[vi + 1];
pickPositions[pvi++] = positions[vi + 2];
pickColors[pci++] = r;
pickColors[pci++] = g;
pickColors[pci++] = b;
pickColors[pci++] = a;
// C
i = indices[location + 2];
vi = i * 3;
pickPositions[pvi++] = positions[vi];
pickPositions[pvi++] = positions[vi + 1];
pickPositions[pvi++] = positions[vi + 2];
pickColors[pci++] = r;
pickColors[pci++] = g;
pickColors[pci++] = b;
pickColors[pci++] = a;
primIndex++;
}
return {
positions: pickPositions,
colors: pickColors
};
},
/**
* Converts surface-perpendicular face normals to vertex normals. Assumes that the mesh contains disjoint triangles
* that don't share vertex array elements. Works by finding groups of vertices that have the same location and
* averaging their normal vectors.
*
* @returns {{positions: Array, normals: *}}
*/
faceToVertexNormals(positions, normals, options = {}) {
const smoothNormalsAngleThreshold = options.smoothNormalsAngleThreshold || 20;
const vertexMap = {};
const vertexNormals = [];
const vertexNormalAccum = {};
let acc;
let vx;
let vy;
let vz;
let key;
const precisionPoints = 4; // number of decimal points, e.g. 4 for epsilon of 0.0001
const precision = 10 ** precisionPoints;
let posi;
let i;
let j;
let len;
let a;
let b;
let c;
for (i = 0, len = positions.length; i < len; i += 3) {
posi = i / 3;
vx = positions[i];
vy = positions[i + 1];
vz = positions[i + 2];
key = `${Math.round(vx * precision)}_${Math.round(vy * precision)}_${Math.round(vz * precision)}`;
if (vertexMap[key] === undefined) {
vertexMap[key] = [posi];
} else {
vertexMap[key].push(posi);
}
const normal = math.normalizeVec3([normals[i], normals[i + 1], normals[i + 2]]);
vertexNormals[posi] = normal;
acc = math.vec4([normal[0], normal[1], normal[2], 1]);
vertexNormalAccum[posi] = acc;
}
for (key in vertexMap) {
if (vertexMap.hasOwnProperty(key)) {
const vertices = vertexMap[key];
const numVerts = vertices.length;
for (i = 0; i < numVerts; i++) {
const ii = vertices[i];
acc = vertexNormalAccum[ii];
for (j = 0; j < numVerts; j++) {
if (i === j) {
continue;
}
const jj = vertices[j];
a = vertexNormals[ii];
b = vertexNormals[jj];
const angle = Math.abs(math.angleVec3(a, b) / math.DEGTORAD);
if (angle < smoothNormalsAngleThreshold) {
acc[0] += b[0];
acc[1] += b[1];
acc[2] += b[2];
acc[3] += 1.0;
}
}
}
}
}
for (i = 0, len = normals.length; i < len; i += 3) {
acc = vertexNormalAccum[i / 3];
normals[i + 0] = acc[0] / acc[3];
normals[i + 1] = acc[1] / acc[3];
normals[i + 2] = acc[2] / acc[3];
}
},
//------------------------------------------------------------------------------------------------------------------
// Ray casting
//------------------------------------------------------------------------------------------------------------------
/**
Transforms a ray by a matrix.
@method transformRay
@static
@param {Number[]} matrix 4x4 matrix
@param {Number[]} rayOrigin The ray origin
@param {Number[]} rayDir The ray direction
@param {Number[]} rayOriginDest The transformed ray origin
@param {Number[]} rayDirDest The transformed ray direction
*/
transformRay: ((() => {
const tempVec4a = new FloatArrayType(4);
const tempVec4b = new FloatArrayType(4);
return (matrix, rayOrigin, rayDir, rayOriginDest, rayDirDest) => {
tempVec4a[0] = rayOrigin[0];
tempVec4a[1] = rayOrigin[1];
tempVec4a[2] = rayOrigin[2];
tempVec4a[3] = 1;
math.transformVec4(matrix, tempVec4a, tempVec4b);
rayOriginDest[0] = tempVec4b[0];
rayOriginDest[1] = tempVec4b[1];
rayOriginDest[2] = tempVec4b[2];
tempVec4a[0] = rayDir[0];
tempVec4a[1] = rayDir[1];
tempVec4a[2] = rayDir[2];
math.transformVec3(matrix, tempVec4a, tempVec4b);
math.normalizeVec3(tempVec4b);
rayDirDest[0] = tempVec4b[0];
rayDirDest[1] = tempVec4b[1];
rayDirDest[2] = tempVec4b[2];
};
}))(),
/**
Transforms a Canvas-space position into a World-space ray, in the context of a Camera.
@method canvasPosToWorldRay
@static
@param {Number[]} viewMatrix View matrix
@param {Number[]} projMatrix Projection matrix
@param {Number[]} canvasPos The Canvas-space position.
@param {Number[]} worldRayOrigin The World-space ray origin.
@param {Number[]} worldRayDir The World-space ray direction.
*/
canvasPosToWorldRay: ((() => {
const tempMat4b = new FloatArrayType(16);
const tempMat4c = new FloatArrayType(16);
const tempVec4a = new FloatArrayType(4);
const tempVec4b = new FloatArrayType(4);
const tempVec4c = new FloatArrayType(4);
const tempVec4d = new FloatArrayType(4);
return (canvas, viewMatrix, projMatrix, canvasPos, worldRayOrigin, worldRayDir) => {
const pvMat = math.mulMat4(projMatrix, viewMatrix, tempMat4b);
const pvMatInverse = math.inverseMat4(pvMat, tempMat4c);
// Calculate clip space coordinates, which will be in range
// of x=[-1..1] and y=[-1..1], with y=(+1) at top
const canvasWidth = canvas.width;
const canvasHeight = canvas.height;
const clipX = (canvasPos[0] - canvasWidth / 2) / (canvasWidth / 2); // Calculate clip space coordinates
const clipY = -(canvasPos[1] - canvasHeight / 2) / (canvasHeight / 2);
tempVec4a[0] = clipX;
tempVec4a[1] = clipY;
tempVec4a[2] = -1;
tempVec4a[3] = 1;
math.transformVec4(pvMatInverse, tempVec4a, tempVec4b);
math.mulVec4Scalar(tempVec4b, 1 / tempVec4b[3]);
tempVec4c[0] = clipX;
tempVec4c[1] = clipY;
tempVec4c[2] = 1;
tempVec4c[3] = 1;
math.transformVec4(pvMatInverse, tempVec4c, tempVec4d);
math.mulVec4Scalar(tempVec4d, 1 / tempVec4d[3]);
worldRayOrigin[0] = tempVec4d[0];
worldRayOrigin[1] = tempVec4d[1];
worldRayOrigin[2] = tempVec4d[2];
math.subVec3(tempVec4d, tempVec4b, worldRayDir);
math.normalizeVec3(worldRayDir);
};
}))(),
/**
Transforms a Canvas-space position to a Mesh's Local-space coordinate system, in the context of a Camera.
@method canvasPosToLocalRay
@static
@param {Camera} camera The Camera.
@param {Mesh} mesh The Mesh.
@param {Number[]} viewMatrix View matrix
@param {Number[]} projMatrix Projection matrix
@param {Number[]} worldMatrix Modeling matrix
@param {Number[]} canvasPos The Canvas-space position.
@param {Number[]} localRayOrigin The Local-space ray origin.
@param {Number[]} localRayDir The Local-space ray direction.
*/
canvasPosToLocalRay: ((() => {
const worldRayOrigin = new FloatArrayType(3);
const worldRayDir = new FloatArrayType(3);
return (canvas, viewMatrix, projMatrix, worldMatrix, canvasPos, localRayOrigin, localRayDir) => {
math.canvasPosToWorldRay(canvas, viewMatrix, projMatrix, canvasPos, worldRayOrigin, worldRayDir);
math.worldRayToLocalRay(worldMatrix, worldRayOrigin, worldRayDir, localRayOrigin, localRayDir);
};
}))(),
/**
Transforms a ray from World-space to a Mesh's Local-space coordinate system.
@method worldRayToLocalRay
@static
@param {Number[]} worldMatrix The World transform matrix
@param {Number[]} worldRayOrigin The World-space ray origin.
@param {Number[]} worldRayDir The World-space ray direction.
@param {Number[]} localRayOrigin The Local-space ray origin.
@param {Number[]} localRayDir The Local-space ray direction.
*/
worldRayToLocalRay: ((() => {
const tempMat4 = new FloatArrayType(16);
const tempVec4a = new FloatArrayType(4);
const tempVec4b = new FloatArrayType(4);
return (worldMatrix, worldRayOrigin, worldRayDir, localRayOrigin, localRayDir) => {
const modelMatInverse = math.inverseMat4(worldMatrix, tempMat4);
tempVec4a[0] = worldRayOrigin[0];
tempVec4a[1] = worldRayOrigin[1];
tempVec4a[2] = worldRayOrigin[2];
tempVec4a[3] = 1;
math.transformVec4(modelMatInverse, tempVec4a, tempVec4b);
localRayOrigin[0] = tempVec4b[0];
localRayOrigin[1] = tempVec4b[1];
localRayOrigin[2] = tempVec4b[2];
math.transformVec3(modelMatInverse, worldRayDir, localRayDir);
};
}))(),
buildKDTree: ((() => {
const KD_TREE_MAX_DEPTH = 10;
const KD_TREE_MIN_TRIANGLES = 20;
const dimLength = new Float32Array();
function buildNode(triangles, indices, positions, depth) {
const aabb = new FloatArrayType(6);
const node = {
triangles: null,
left: null,
right: null,
leaf: false,
splitDim: 0,
aabb
};
aabb[0] = aabb[1] = aabb[2] = Number.POSITIVE_INFINITY;
aabb[3] = aabb[4] = aabb[5] = Number.NEGATIVE_INFINITY;
let t;
let i;
let len;
for (t = 0, len = triangles.length; t < len; ++t) {
var ii = triangles[t] * 3;
for (let j = 0; j < 3; ++j) {
const pi = indices[ii + j] * 3;
if (positions[pi] < aabb[0]) {
aabb[0] = positions[pi]
}
if (positions[pi] > aabb[3]) {
aabb[3] = positions[pi]
}
if (positions[pi + 1] < aabb[1]) {
aabb[1] = positions[pi + 1]
}
if (positions[pi + 1] > aabb[4]) {
aabb[4] = positions[pi + 1]
}
if (positions[pi + 2] < aabb[2]) {
aabb[2] = positions[pi + 2]
}
if (positions[pi + 2] > aabb[5]) {
aabb[5] = positions[pi + 2]
}
}
}
if (triangles.length < KD_TREE_MIN_TRIANGLES || depth > KD_TREE_MAX_DEPTH) {
node.triangles = triangles;
node.leaf = true;
return node;
}
dimLength[0] = aabb[3] - aabb[0];
dimLength[1] = aabb[4] - aabb[1];
dimLength[2] = aabb[5] - aabb[2];
let dim = 0;
if (dimLength[1] > dimLength[dim]) {
dim = 1;
}
if (dimLength[2] > dimLength[dim]) {
dim = 2;
}
node.splitDim = dim;
const mid = (aabb[dim] + aabb[dim + 3]) / 2;
const left = new Array(triangles.length);
let numLeft = 0;
const right = new Array(triangles.length);
let numRight = 0;
for (t = 0, len = triangles.length; t < len; ++t) {
var ii = triangles[t] * 3;
const i0 = indices[ii];
const i1 = indices[ii + 1];
const i2 = indices[ii + 2];
const pi0 = i0 * 3;
const pi1 = i1 * 3;
const pi2 = i2 * 3;
if (positions[pi0 + dim] <= mid || positions[pi1 + dim] <= mid || positions[pi2 + dim] <= mid) {
left[numLeft++] = triangles[t];
} else {
right[numRight++] = triangles[t];
}
}
left.length = numLeft;
right.length = numRight;
node.left = buildNode(left, indices, positions, depth + 1);
node.right = buildNode(right, indices, positions, depth + 1);
return node;
}
return (indices, positions) => {
const numTris = indices.length / 3;
const triangles = new Array(numTris);
for (let i = 0; i < numTris; ++i) {
triangles[i] = i;
}
return buildNode(triangles, indices, positions, 0);
};
}))(),
decompressPosition(position, decodeMatrix, dest) {
dest = dest || position;
dest[0] = position[0] * decodeMatrix[0] + decodeMatrix[12];
dest[1] = position[1] * decodeMatrix[5] + decodeMatrix[13];
dest[2] = position[2] * decodeMatrix[10] + decodeMatrix[14];
},
decompressPositions(positions, decodeMatrix, dest = new Float32Array(positions.length)) {
for (let i = 0, len = positions.length; i < len; i += 3) {
dest[i + 0] = positions[i + 0] * decodeMatrix[0] + decodeMatrix[12];
dest[i + 1] = positions[i + 1] * decodeMatrix[5] + decodeMatrix[13];
dest[i + 2] = positions[i + 2] * decodeMatrix[10] + decodeMatrix[14];
}
return dest;
},
decompressUV(uv, decodeMatrix, dest) {
dest[0] = uv[0] * decodeMatrix[0] + decodeMatrix[6];
dest[1] = uv[1] * decodeMatrix[4] + decodeMatrix[7];
},
decompressUVs(uvs, decodeMatrix, dest = new Float32Array(uvs.length)) {
for (let i = 0, len = uvs.length; i < len; i += 3) {
dest[i + 0] = uvs[i + 0] * decodeMatrix[0] + decodeMatrix[6];
dest[i + 1] = uvs[i + 1] * decodeMatrix[4] + decodeMatrix[7];
}
return dest;
},
octDecodeVec2(oct, result) {
let x = oct[0];
let y = oct[1];
x = (2 * x + 1) / 255;
y = (2 * y + 1) / 255;
const z = 1 - Math.abs(x) - Math.abs(y);
if (z < 0) {
x = (1 - Math.abs(y)) * (x >= 0 ? 1 : -1);
y = (1 - Math.abs(x)) * (y >= 0 ? 1 : -1);
}
const length = Math.sqrt(x * x + y * y + z * z);
result[0] = x / length;
result[1] = y / length;
result[2] = z / length;
return result;
},
octDecodeVec2s(octs, result) {
for (let i = 0, j = 0, len = octs.length; i < len; i += 2) {
let x = octs[i + 0];
let y = octs[i + 1];
x = (2 * x + 1) / 255;
y = (2 * y + 1) / 255;
const z = 1 - Math.abs(x) - Math.abs(y);
if (z < 0) {
x = (1 - Math.abs(y)) * (x >= 0 ? 1 : -1);
y = (1 - Math.abs(x)) * (y >= 0 ? 1 : -1);
}
const length = Math.sqrt(x * x + y * y + z * z);
result[j + 0] = x / length;
result[j + 1] = y / length;
result[j + 2] = z / length;
j += 3;
}
return result;
}
};
math.buildEdgeIndices = (function () {
const uniquePositions = [];
const indicesLookup = [];
const indicesReverseLookup = [];
const weldedIndices = [];
// TODO: Optimize with caching, but need to cater to both compressed and uncompressed positions
const faces = [];
let numFaces = 0;
const compa = new Uint16Array(3);
const compb = new Uint16Array(3);
const compc = new Uint16Array(3);
const a = math.vec3();
const b = math.vec3();
const c = math.vec3();
const cb = math.vec3();
const ab = math.vec3();
const cross = math.vec3();
const normal = math.vec3();
function weldVertices(positions, indices) {
const positionsMap = {}; // Hashmap for looking up vertices by position coordinates (and making sure they are unique)
let vx;
let vy;
let vz;
let key;
const precisionPoints = 4; // number of decimal points, e.g. 4 for epsilon of 0.0001
const precision = Math.pow(10, precisionPoints);
let i;
let len;
let lenUniquePositions = 0;
for (i = 0, len = positions.length; i < len; i += 3) {
vx = positions[i];
vy = positions[i + 1];
vz = positions[i + 2];
key = Math.round(vx * precision) + '_' + Math.round(vy * precision) + '_' + Math.round(vz * precision);
if (positionsMap[key] === undefined) {
positionsMap[key] = lenUniquePositions / 3;
uniquePositions[lenUniquePositions++] = vx;
uniquePositions[lenUniquePositions++] = vy;
uniquePositions[lenUniquePositions++] = vz;
}
indicesLookup[i / 3] = positionsMap[key];
}
for (i = 0, len = indices.length; i < len; i++) {
weldedIndices[i] = indicesLookup[indices[i]];
indicesReverseLookup[weldedIndices[i]] = indices[i];
}
}
function buildFaces(numIndices, positionsDecodeMatrix) {
numFaces = 0;
for (let i = 0, len = numIndices; i < len; i += 3) {
const ia = ((weldedIndices[i]) * 3);
const ib = ((weldedIndices[i + 1]) * 3);
const ic = ((weldedIndices[i + 2]) * 3);
if (positionsDecodeMatrix) {
compa[0] = uniquePositions[ia];
compa[1] = uniquePositions[ia + 1];
compa[2] = uniquePositions[ia + 2];
compb[0] = uniquePositions[ib];
compb[1] = uniquePositions[ib + 1];
compb[2] = uniquePositions[ib + 2];
compc[0] = uniquePositions[ic];
compc[1] = uniquePositions[ic + 1];
compc[2] = uniquePositions[ic + 2];
// Decode
math.decompressPosition(compa, positionsDecodeMatrix, a);
math.decompressPosition(compb, positionsDecodeMatrix, b);
math.decompressPosition(compc, positionsDecodeMatrix, c);
} else {
a[0] = uniquePositions[ia];
a[1] = uniquePositions[ia + 1];
a[2] = uniquePositions[ia + 2];
b[0] = uniquePositions[ib];
b[1] = uniquePositions[ib + 1];
b[2] = uniquePositions[ib + 2];
c[0] = uniquePositions[ic];
c[1] = uniquePositions[ic + 1];
c[2] = uniquePositions[ic + 2];
}
math.subVec3(c, b, cb);
math.subVec3(a, b, ab);
math.cross3Vec3(cb, ab, cross);
math.normalizeVec3(cross, normal);
const face = faces[numFaces] || (faces[numFaces] = {normal: math.vec3()});
face.normal[0] = normal[0];
face.normal[1] = normal[1];
face.normal[2] = normal[2];
numFaces++;
}
}
return function (positions, indices, positionsDecodeMatrix, edgeThreshold) {
weldVertices(positions, indices);
buildFaces(indices.length, positionsDecodeMatrix);
const edgeIndices = [];
const thresholdDot = Math.cos(math.DEGTORAD * edgeThreshold);
const edges = {};
let edge1;
let edge2;
let index1;
let index2;
let key;
let largeIndex = false;
let edge;
let normal1;
let normal2;
let dot;
let ia;
let ib;
for (let i = 0, len = indices.length; i < len; i += 3) {
const faceIndex = i / 3;
for (let j = 0; j < 3; j++) {
edge1 = weldedIndices[i + j];
edge2 = weldedIndices[i + ((j + 1) % 3)];
index1 = Math.min(edge1, edge2);
index2 = Math.max(edge1, edge2);
key = index1 + "," + index2;
if (edges[key] === undefined) {
edges[key] = {
index1: index1,
index2: index2,
face1: faceIndex,
face2: undefined
};
} else {
edges[key].face2 = faceIndex;
}
}
}
for (key in edges) {
edge = edges[key];
// an edge is only rendered if the angle (in degrees) between the face normals of the adjoining faces exceeds this value. default = 1 degree.
if (edge.face2 !== undefined) {
normal1 = faces[edge.face1].normal;
normal2 = faces[edge.face2].normal;
dot = math.dotVec3(normal1, normal2);
if (dot > thresholdDot) {
continue;
}
}
ia = indicesReverseLookup[edge.index1];
ib = indicesReverseLookup[edge.index2];
if (!largeIndex && ia > 65535 || ib > 65535) {
largeIndex = true;
}
edgeIndices.push(ia);
edgeIndices.push(ib);
}
return (largeIndex) ? new Uint32Array(edgeIndices) : new Uint16Array(edgeIndices);
};
})();
/**
* Returns `true` if a plane clips the given 3D positions.
* @param {Number[]} pos Position in plane
* @param {Number[]} dir Direction of plane
* @param {number} positions Flat array of 3D positions.
* @param {number} numElementsPerPosition Number of elements perposition - usually either 3 or 4.
* @returns {boolean}
*/
math.planeClipsPositions3 = function (pos, dir, positions, numElementsPerPosition = 3) {
for (let i = 0, len = positions.length; i < len; i += numElementsPerPosition) {
tempVec3a[0] = positions[i + 0] - pos[0];
tempVec3a[1] = positions[i + 1] - pos[1];
tempVec3a[2] = positions[i + 2] - pos[2];
let dotProduct = tempVec3a[0] * dir[0] + tempVec3a[1] * dir[1] + tempVec3a[2] * dir[2];
if (dotProduct < 0) {
return true;
}
}
return false;
}
export {math};
