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math.module.js
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math.module.js
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/* Math (c) Kraft, MIT License */
const EPSILON = 1e-6;
const R2D = 180 / Math.PI;
const D2R = Math.PI / 180;
const TWO_PI = Math.PI * 2;
const constants = /*#__PURE__*/Object.freeze({
__proto__: null,
D2R,
EPSILON,
R2D,
TWO_PI
});
const epsilonEqual = (a, b, epsilon = EPSILON) => Math.abs(a - b) < epsilon;
const epsilonCompare = (a, b, epsilon = EPSILON) => (
epsilonEqual(a, b, epsilon) ? 0 : Math.sign(a - b)
);
const epsilonEqualVectors = (a, b, epsilon = EPSILON) => {
for (let i = 0; i < Math.max(a.length, b.length); i += 1) {
if (!epsilonEqual(a[i] || 0, b[i] || 0, epsilon)) { return false; }
}
return true;
};
const include = (n, epsilon = EPSILON) => n > -epsilon;
const exclude = (n, epsilon = EPSILON) => n > epsilon;
const includeL = () => true;
const excludeL = () => true;
const includeR = include;
const excludeR = exclude;
const includeS = (n, e = EPSILON) => n > -e && n < 1 + e;
const excludeS = (n, e = EPSILON) => n > e && n < 1 - e;
const clampLine = dist => dist;
const clampRay = dist => (dist < -EPSILON ? 0 : dist);
const clampSegment = (dist) => {
if (dist < -EPSILON) { return 0; }
if (dist > 1 + EPSILON) { return 1; }
return dist;
};
const mathFunctions = /*#__PURE__*/Object.freeze({
__proto__: null,
clampLine,
clampRay,
clampSegment,
epsilonCompare,
epsilonEqual,
epsilonEqualVectors,
exclude,
excludeL,
excludeR,
excludeS,
include,
includeL,
includeR,
includeS
});
const safeAdd = (a, b) => a + (b || 0);
const magnitude = v => Math.sqrt(v
.map(n => n * n)
.reduce(safeAdd, 0));
const magnitude2 = v => Math.sqrt(v[0] * v[0] + v[1] * v[1]);
const magnitude3 = v => Math.sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
const magSquared = v => v
.map(n => n * n)
.reduce(safeAdd, 0);
const normalize = (v) => {
const m = magnitude(v);
return m === 0 ? v : v.map(c => c / m);
};
const normalize2 = (v) => {
const m = magnitude2(v);
return m === 0 ? v : [v[0] / m, v[1] / m];
};
const normalize3 = (v) => {
const m = magnitude3(v);
return m === 0 ? v : [v[0] / m, v[1] / m, v[2] / m];
};
const scale = (v, s) => v.map(n => n * s);
const scale2 = (v, s) => [v[0] * s, v[1] * s];
const scale3 = (v, s) => [v[0] * s, v[1] * s, v[2] * s];
const add = (v, u) => v.map((n, i) => n + (u[i] || 0));
const add2 = (v, u) => [v[0] + u[0], v[1] + u[1]];
const add3 = (v, u) => [v[0] + u[0], v[1] + u[1], v[2] + u[2]];
const subtract = (v, u) => v.map((n, i) => n - (u[i] || 0));
const subtract2 = (v, u) => [v[0] - u[0], v[1] - u[1]];
const subtract3 = (v, u) => [v[0] - u[0], v[1] - u[1], v[2] - u[2]];
const dot = (v, u) => v
.map((_, i) => v[i] * u[i])
.reduce(safeAdd, 0);
const dot2 = (v, u) => v[0] * u[0] + v[1] * u[1];
const dot3 = (v, u) => v[0] * u[0] + v[1] * u[1] + v[2] * u[2];
const midpoint = (v, u) => v.map((n, i) => (n + u[i]) / 2);
const midpoint2 = (v, u) => scale2(add2(v, u), 0.5);
const midpoint3 = (v, u) => scale3(add3(v, u), 0.5);
const average = function () {
if (arguments.length === 0) { return undefined; }
const dimension = (arguments[0].length > 0) ? arguments[0].length : 0;
const sum = Array(dimension).fill(0);
Array.from(arguments)
.forEach(vec => sum
.forEach((_, i) => { sum[i] += vec[i] || 0; }));
return sum.map(n => n / arguments.length);
};
const average2 = (...vectors) => {
if (!vectors || !vectors.length) { return undefined; }
const inverseLength = 1 / vectors.length;
return vectors
.reduce((a, b) => add2(a, b), [0, 0])
.map(c => c * inverseLength);
};
const lerp = (v, u, t = 0) => {
const inv = 1.0 - t;
return v.map((n, i) => n * inv + (u[i] || 0) * t);
};
const cross2 = (v, u) => v[0] * u[1] - v[1] * u[0];
const cross3 = (v, u) => [
v[1] * u[2] - v[2] * u[1],
v[2] * u[0] - v[0] * u[2],
v[0] * u[1] - v[1] * u[0],
];
const distance = (v, u) => Math.sqrt(v
.map((_, i) => (v[i] - u[i]) ** 2)
.reduce(safeAdd, 0));
const distance2 = (v, u) => {
const p = v[0] - u[0];
const q = v[1] - u[1];
return Math.sqrt((p * p) + (q * q));
};
const distance3 = (v, u) => {
const a = v[0] - u[0];
const b = v[1] - u[1];
const c = v[2] - u[2];
return Math.sqrt((a * a) + (b * b) + (c * c));
};
const flip = v => v.map(n => -n);
const rotate90 = v => [-v[1], v[0]];
const rotate270 = v => [v[1], -v[0]];
const degenerate = (v, epsilon = EPSILON) => v
.map(n => Math.abs(n))
.reduce(safeAdd, 0) < epsilon;
const parallelNormalized = (v, u, epsilon = EPSILON) => 1 - Math
.abs(dot(v, u)) < epsilon;
const parallel = (v, u, epsilon = EPSILON) => parallelNormalized(
normalize(v),
normalize(u),
epsilon,
);
const parallel2 = (v, u, epsilon = EPSILON) => Math
.abs(cross2(v, u)) < epsilon;
const resize = (dimension, vector) => (vector.length === dimension
? vector
: Array(dimension).fill(0).map((z, i) => (vector[i] ? vector[i] : z)));
const resizeUp = (a, b) => [a, b]
.map(v => resize(Math.max(a.length, b.length), v));
const basisVectors2 = (vector = [1, 0]) => {
const normalized = normalize2(vector);
return [normalized, rotate90(normalized)];
};
const basisVectors3 = (vector = [1, 0, 0]) => {
const normalized = normalize3(vector);
const crosses = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
.map(v => cross3(v, normalized));
const index = crosses
.map(magnitude3)
.map((n, i) => ({ n, i }))
.sort((a, b) => b.n - a.n)
.map(el => el.i)
.shift();
const perpendicular = normalize3(crosses[index]);
return [normalized, perpendicular, cross3(normalized, perpendicular)];
};
const basisVectors = (vector) => (vector.length === 2
? basisVectors2(vector)
: basisVectors3(vector)
);
const vector$1 = /*#__PURE__*/Object.freeze({
__proto__: null,
add,
add2,
add3,
average,
average2,
basisVectors,
basisVectors2,
basisVectors3,
cross2,
cross3,
degenerate,
distance,
distance2,
distance3,
dot,
dot2,
dot3,
flip,
lerp,
magSquared,
magnitude,
magnitude2,
magnitude3,
midpoint,
midpoint2,
midpoint3,
normalize,
normalize2,
normalize3,
parallel,
parallel2,
parallelNormalized,
resize,
resizeUp,
rotate270,
rotate90,
scale,
scale2,
scale3,
subtract,
subtract2,
subtract3
});
const identity2x2 = [1, 0, 0, 1];
const identity2x3 = identity2x2.concat(0, 0);
const multiplyMatrix2Vector2 = (matrix, vector) => [
matrix[0] * vector[0] + matrix[2] * vector[1] + matrix[4],
matrix[1] * vector[0] + matrix[3] * vector[1] + matrix[5],
];
const multiplyMatrix2Line2 = (matrix, vector, origin) => ({
vector: [
matrix[0] * vector[0] + matrix[2] * vector[1],
matrix[1] * vector[0] + matrix[3] * vector[1],
],
origin: [
matrix[0] * origin[0] + matrix[2] * origin[1] + matrix[4],
matrix[1] * origin[0] + matrix[3] * origin[1] + matrix[5],
],
});
const multiplyMatrices2 = (m1, m2) => [
m1[0] * m2[0] + m1[2] * m2[1],
m1[1] * m2[0] + m1[3] * m2[1],
m1[0] * m2[2] + m1[2] * m2[3],
m1[1] * m2[2] + m1[3] * m2[3],
m1[0] * m2[4] + m1[2] * m2[5] + m1[4],
m1[1] * m2[4] + m1[3] * m2[5] + m1[5],
];
const determinant2 = m => m[0] * m[3] - m[1] * m[2];
const invertMatrix2 = (m) => {
const det = determinant2(m);
if (Math.abs(det) < 1e-12
|| Number.isNaN(det)
|| !Number.isFinite(m[4])
|| !Number.isFinite(m[5])) {
return undefined;
}
return [
m[3] / det,
-m[1] / det,
-m[2] / det,
m[0] / det,
(m[2] * m[5] - m[3] * m[4]) / det,
(m[1] * m[4] - m[0] * m[5]) / det,
];
};
const makeMatrix2Translate = (x = 0, y = 0) => identity2x2.concat(x, y);
const makeMatrix2Scale = (scale = [1, 1], origin = [0, 0]) => [
scale[0],
0,
0,
scale[1],
scale[0] * -origin[0] + origin[0],
scale[1] * -origin[1] + origin[1],
];
const makeMatrix2UniformScale = (scale = 1, origin = [0, 0]) => (
makeMatrix2Scale([scale, scale], origin)
);
const makeMatrix2Rotate = (angle, origin = [0, 0]) => {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
return [
cos,
sin,
-sin,
cos,
origin[0],
origin[1],
];
};
const makeMatrix2Reflect = (vector, origin = [0, 0]) => {
const angle = Math.atan2(vector[1], vector[0]);
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
const cos_Angle = Math.cos(-angle);
const sin_Angle = Math.sin(-angle);
const a = cosAngle * cos_Angle + sinAngle * sin_Angle;
const b = cosAngle * -sin_Angle + sinAngle * cos_Angle;
const c = sinAngle * cos_Angle + -cosAngle * sin_Angle;
const d = sinAngle * -sin_Angle + -cosAngle * cos_Angle;
const tx = origin[0] + a * -origin[0] + -origin[1] * c;
const ty = origin[1] + b * -origin[0] + -origin[1] * d;
return [a, b, c, d, tx, ty];
};
const matrix2 = /*#__PURE__*/Object.freeze({
__proto__: null,
determinant2,
identity2x2,
identity2x3,
invertMatrix2,
makeMatrix2Reflect,
makeMatrix2Rotate,
makeMatrix2Scale,
makeMatrix2Translate,
makeMatrix2UniformScale,
multiplyMatrices2,
multiplyMatrix2Line2,
multiplyMatrix2Vector2
});
const identity3x3 = Object.freeze([1, 0, 0, 0, 1, 0, 0, 0, 1]);
const identity3x4 = Object.freeze(identity3x3.concat(0, 0, 0));
const isIdentity3x4 = m => identity3x4
.map((n, i) => Math.abs(n - m[i]) < EPSILON)
.reduce((a, b) => a && b, true);
const multiplyMatrix3Vector3 = (m, vector) => [
m[0] * vector[0] + m[3] * vector[1] + m[6] * vector[2] + m[9],
m[1] * vector[0] + m[4] * vector[1] + m[7] * vector[2] + m[10],
m[2] * vector[0] + m[5] * vector[1] + m[8] * vector[2] + m[11],
];
const multiplyMatrix3Line3 = (m, vector, origin) => ({
vector: [
m[0] * vector[0] + m[3] * vector[1] + m[6] * vector[2],
m[1] * vector[0] + m[4] * vector[1] + m[7] * vector[2],
m[2] * vector[0] + m[5] * vector[1] + m[8] * vector[2],
],
origin: [
m[0] * origin[0] + m[3] * origin[1] + m[6] * origin[2] + m[9],
m[1] * origin[0] + m[4] * origin[1] + m[7] * origin[2] + m[10],
m[2] * origin[0] + m[5] * origin[1] + m[8] * origin[2] + m[11],
],
});
const multiplyMatrices3 = (m1, m2) => [
m1[0] * m2[0] + m1[3] * m2[1] + m1[6] * m2[2],
m1[1] * m2[0] + m1[4] * m2[1] + m1[7] * m2[2],
m1[2] * m2[0] + m1[5] * m2[1] + m1[8] * m2[2],
m1[0] * m2[3] + m1[3] * m2[4] + m1[6] * m2[5],
m1[1] * m2[3] + m1[4] * m2[4] + m1[7] * m2[5],
m1[2] * m2[3] + m1[5] * m2[4] + m1[8] * m2[5],
m1[0] * m2[6] + m1[3] * m2[7] + m1[6] * m2[8],
m1[1] * m2[6] + m1[4] * m2[7] + m1[7] * m2[8],
m1[2] * m2[6] + m1[5] * m2[7] + m1[8] * m2[8],
m1[0] * m2[9] + m1[3] * m2[10] + m1[6] * m2[11] + m1[9],
m1[1] * m2[9] + m1[4] * m2[10] + m1[7] * m2[11] + m1[10],
m1[2] * m2[9] + m1[5] * m2[10] + m1[8] * m2[11] + m1[11],
];
const determinant3 = m => (
m[0] * m[4] * m[8]
- m[0] * m[7] * m[5]
- m[3] * m[1] * m[8]
+ m[3] * m[7] * m[2]
+ m[6] * m[1] * m[5]
- m[6] * m[4] * m[2]
);
const invertMatrix3 = (m) => {
const det = determinant3(m);
if (Math.abs(det) < 1e-12 || Number.isNaN(det)
|| !Number.isFinite(m[9]) || !Number.isFinite(m[10]) || !Number.isFinite(m[11])) {
return undefined;
}
const inv = [
m[4] * m[8] - m[7] * m[5],
-m[1] * m[8] + m[7] * m[2],
m[1] * m[5] - m[4] * m[2],
-m[3] * m[8] + m[6] * m[5],
m[0] * m[8] - m[6] * m[2],
-m[0] * m[5] + m[3] * m[2],
m[3] * m[7] - m[6] * m[4],
-m[0] * m[7] + m[6] * m[1],
m[0] * m[4] - m[3] * m[1],
-m[3] * m[7] * m[11] + m[3] * m[8] * m[10] + m[6] * m[4] * m[11]
- m[6] * m[5] * m[10] - m[9] * m[4] * m[8] + m[9] * m[5] * m[7],
m[0] * m[7] * m[11] - m[0] * m[8] * m[10] - m[6] * m[1] * m[11]
+ m[6] * m[2] * m[10] + m[9] * m[1] * m[8] - m[9] * m[2] * m[7],
-m[0] * m[4] * m[11] + m[0] * m[5] * m[10] + m[3] * m[1] * m[11]
- m[3] * m[2] * m[10] - m[9] * m[1] * m[5] + m[9] * m[2] * m[4],
];
const invDet = 1.0 / det;
return inv.map(n => n * invDet);
};
const makeMatrix3Translate = (x = 0, y = 0, z = 0) => identity3x3.concat(x, y, z);
const singleAxisRotate = (angle, origin, i0, i1, sgn) => {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
const rotate = identity3x3.concat([0, 0, 0]);
rotate[i0 * 3 + i0] = cos;
rotate[i0 * 3 + i1] = (sgn ? +1 : -1) * sin;
rotate[i1 * 3 + i0] = (sgn ? -1 : +1) * sin;
rotate[i1 * 3 + i1] = cos;
const origin3 = [0, 1, 2].map(i => origin[i] || 0);
const trans = identity3x3.concat(flip(origin3));
const trans_inv = identity3x3.concat(origin3);
return multiplyMatrices3(trans_inv, multiplyMatrices3(rotate, trans));
};
const makeMatrix3RotateX = (angle, origin = [0, 0, 0]) => (
singleAxisRotate(angle, origin, 1, 2, true));
const makeMatrix3RotateY = (angle, origin = [0, 0, 0]) => (
singleAxisRotate(angle, origin, 0, 2, false));
const makeMatrix3RotateZ = (angle, origin = [0, 0, 0]) => (
singleAxisRotate(angle, origin, 0, 1, true));
const makeMatrix3Rotate = (angle, vector = [0, 0, 1], origin = [0, 0, 0]) => {
const pos = [0, 1, 2].map(i => origin[i] || 0);
const [x, y, z] = resize(3, normalize(vector));
const c = Math.cos(angle);
const s = Math.sin(angle);
const t = 1 - c;
const trans = identity3x3.concat(-pos[0], -pos[1], -pos[2]);
const trans_inv = identity3x3.concat(pos[0], pos[1], pos[2]);
return multiplyMatrices3(trans_inv, multiplyMatrices3([
t * x * x + c, t * y * x + z * s, t * z * x - y * s,
t * x * y - z * s, t * y * y + c, t * z * y + x * s,
t * x * z + y * s, t * y * z - x * s, t * z * z + c,
0, 0, 0], trans));
};
const makeMatrix3Scale = (scale = [1, 1, 1], origin = [0, 0, 0]) => [
scale[0], 0, 0,
0, scale[1], 0,
0, 0, scale[2],
scale[0] * -origin[0] + origin[0],
scale[1] * -origin[1] + origin[1],
scale[2] * -origin[2] + origin[2],
];
const makeMatrix3UniformScale = (scale = 1, origin = [0, 0, 0]) => (
makeMatrix3Scale([scale, scale, scale], origin)
);
const makeMatrix3ReflectZ = (vector, origin = [0, 0]) => {
const m = makeMatrix2Reflect(vector, origin);
return [m[0], m[1], 0, m[2], m[3], 0, 0, 0, 1, m[4], m[5], 0];
};
const matrix3 = /*#__PURE__*/Object.freeze({
__proto__: null,
determinant3,
identity3x3,
identity3x4,
invertMatrix3,
isIdentity3x4,
makeMatrix3ReflectZ,
makeMatrix3Rotate,
makeMatrix3RotateX,
makeMatrix3RotateY,
makeMatrix3RotateZ,
makeMatrix3Scale,
makeMatrix3Translate,
makeMatrix3UniformScale,
multiplyMatrices3,
multiplyMatrix3Line3,
multiplyMatrix3Vector3
});
const isIterable = (obj) => obj != null
&& typeof obj[Symbol.iterator] === "function";
const semiFlattenArrays = function () {
switch (arguments.length) {
case 0: return Array.from(arguments);
case 1: return isIterable(arguments[0]) && typeof arguments[0] !== "string"
? semiFlattenArrays(...arguments[0])
: [arguments[0]];
default:
return Array.from(arguments).map(a => (isIterable(a)
? [...semiFlattenArrays(a)]
: a));
}
};
const flattenArrays = function () {
switch (arguments.length) {
case 0: return Array.from(arguments);
case 1: return isIterable(arguments[0]) && typeof arguments[0] !== "string"
? flattenArrays(...arguments[0])
: [arguments[0]];
default:
return Array.from(arguments).map(a => (isIterable(a)
? [...flattenArrays(a)]
: a)).flat();
}
};
const arrayMethods = /*#__PURE__*/Object.freeze({
__proto__: null,
flattenArrays,
semiFlattenArrays
});
const getVector = function () {
let list = flattenArrays(arguments);
const a = list[0];
if (typeof a === "object" && a !== null && !Number.isNaN(a.x)) {
list = ["x", "y", "z"].map(c => a[c]).filter(b => b !== undefined);
}
return list.filter(n => typeof n === "number");
};
const getArrayOfVectors = function () {
return semiFlattenArrays(arguments).map(el => getVector(el));
};
const getSegment = function () {
const args = semiFlattenArrays(arguments);
return args.length === 4
? [[0, 1], [2, 3]].map(s => s.map(i => args[i]))
: args.map(el => getVector(el));
};
const vectorOriginForm = (vector, origin = []) => ({ vector, origin });
const getLine = function () {
const args = semiFlattenArrays(arguments);
if (args.length === 0 || args[0] == null) { return vectorOriginForm([], []); }
if (args[0].constructor === Object && args[0].vector !== undefined) {
return vectorOriginForm(args[0].vector, args[0].origin || []);
}
return typeof args[0] === "number"
? vectorOriginForm(getVector(args))
: vectorOriginForm(...args.map(a => getVector(a)));
};
const getMatrix2 = function () {
const m = getVector(arguments);
if (m.length === 6) { return m; }
if (m.length > 6) { return [m[0], m[1], m[2], m[3], m[4], m[5]]; }
if (m.length < 6) {
return identity2x3.map((n, i) => m[i] || n);
}
return [...identity2x3];
};
const maps3x4 = [
[0, 1, 3, 4, 9, 10],
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11],
[0, 1, 2, undefined, 3, 4, 5, undefined, 6, 7, 8, undefined, 9, 10, 11],
];
[11, 7, 3].forEach(i => delete maps3x4[2][i]);
const matrixMap3x4 = len => (len < 8
? maps3x4[0]
: (len < 13 ? maps3x4[1] : maps3x4[2]));
const getMatrix3x4 = function () {
const mat = flattenArrays(arguments);
const matrix = [...identity3x4];
matrixMap3x4(mat.length)
.forEach((n, i) => { if (mat[i] != null) { matrix[n] = mat[i]; } });
return matrix;
};
const get_rect_params = (x = 0, y = 0, width = 0, height = 0) => ({
x, y, width, height,
});
const getRect = function () {
const list = flattenArrays(arguments);
if (list.length > 0
&& typeof list[0] === "object"
&& list[0] !== null
&& !Number.isNaN(list[0].width)) {
return get_rect_params(...["x", "y", "width", "height"]
.map(c => list[0][c])
.filter(a => a !== undefined));
}
const numbers = list.filter(n => typeof n === "number");
const rect_params = numbers.length < 4
? [, , ...numbers]
: numbers;
return get_rect_params(...rect_params);
};
const get_circle_params = (radius = 1, ...args) => ({
radius,
origin: [...args],
});
const getCircle = function () {
const vectors = getArrayOfVectors(arguments);
const numbers = flattenArrays(arguments).filter(a => typeof a === "number");
if (arguments.length === 2) {
if (vectors[1].length === 1) {
return get_circle_params(vectors[1][0], ...vectors[0]);
}
if (vectors[0].length === 1) {
return get_circle_params(vectors[0][0], ...vectors[1]);
}
if (vectors[0].length > 1 && vectors[1].length > 1) {
return get_circle_params(distance2(...vectors), ...vectors[0]);
}
} else {
switch (numbers.length) {
case 0: return get_circle_params(1, 0, 0, 0);
case 1: return get_circle_params(numbers[0], 0, 0, 0);
default: return get_circle_params(numbers.pop(), ...numbers);
}
}
return get_circle_params(1, 0, 0, 0);
};
const getMethods = /*#__PURE__*/Object.freeze({
__proto__: null,
getArrayOfVectors,
getCircle,
getLine,
getMatrix2,
getMatrix3x4,
getRect,
getSegment,
getVector,
get_rect_params
});
const vectorToAngle = v => Math.atan2(v[1], v[0]);
const angleToVector = a => [Math.cos(a), Math.sin(a)];
const pointsToLine = (...args) => {
const points = getArrayOfVectors(...args);
return {
vector: subtract(points[1], points[0]),
origin: points[0],
};
};
const vecLineToUniqueLine = ({ vector, origin }) => {
const mag = magnitude(vector);
const normal = rotate90(vector);
const distance = dot(origin, normal) / mag;
return { normal: scale(normal, 1 / mag), distance };
};
const uniqueLineToVecLine = ({ normal, distance }) => ({
vector: rotate270(normal),
origin: scale(normal, distance),
});
const convertMethods = /*#__PURE__*/Object.freeze({
__proto__: null,
angleToVector,
pointsToLine,
uniqueLineToVecLine,
vecLineToUniqueLine,
vectorToAngle
});
const countPlaces = function (num) {
const m = (`${num}`).match(/(?:\.(\d+))?(?:[eE]([+-]?\d+))?$/);
return Math.max(0, (m[1] ? m[1].length : 0) - (m[2] ? +m[2] : 0));
};
const cleanNumber = function (number, places = 15) {
const num = typeof number === "number" ? number : parseFloat(number);
if (Number.isNaN(num)) { return number; }
const crop = parseFloat(num.toFixed(places));
if (countPlaces(crop) === Math.min(places, countPlaces(num))) {
return num;
}
return crop;
};
const numberMethods = /*#__PURE__*/Object.freeze({
__proto__: null,
cleanNumber
});
const smallestComparisonSearch = (array, obj, compare_func) => {
const objs = array.map((o, i) => ({ i, d: compare_func(obj, o) }));
let index;
let smallest_value = Infinity;
for (let i = 0; i < objs.length; i += 1) {
if (objs[i].d < smallest_value) {
index = i;
smallest_value = objs[i].d;
}
}
return index;
};
const smallestVectorSearch = (vectors, axis, compFn, epsilon) => {
let smallSet = [0];
for (let i = 1; i < vectors.length; i += 1) {
switch (compFn(vectors[smallSet[0]][axis], vectors[i][axis], epsilon)) {
case 0: smallSet.push(i); break;
case 1: smallSet = [i]; break;
}
}
return smallSet;
};
const minimum2DPointIndex = (points, epsilon = EPSILON) => {
if (!points || !points.length) { return undefined; }
const smallSet = smallestVectorSearch(points, 0, epsilonCompare, epsilon);
let sm = 0;
for (let i = 1; i < smallSet.length; i += 1) {
if (points[smallSet[i]][1] < points[smallSet[sm]][1]) { sm = i; }
}
return smallSet[sm];
};
const searchMethods = /*#__PURE__*/Object.freeze({
__proto__: null,
minimum2DPointIndex,
smallestComparisonSearch
});
const projectPointOnPlane = (point, vector = [1, 0, 0], origin = [0, 0, 0]) => {
const point3 = resize(3, point);
const originToPoint = subtract3(point3, resize(3, origin));
const normalized = normalize3(resize(3, vector));
const magnitude = dot3(normalized, originToPoint);
const planeToPoint = scale3(normalized, magnitude);
return subtract3(point3, planeToPoint);
};
const planeMethods = /*#__PURE__*/Object.freeze({
__proto__: null,
projectPointOnPlane
});
const sortAgainstItem = (array, item, compareFn) => array
.map((el, i) => ({ i, n: compareFn(el, item) }))
.sort((a, b) => a.n - b.n)
.map(a => a.i);
const sortPointsAlongVector = (points, vector) => (
sortAgainstItem(points, vector, dot)
);
const clusterIndicesOfSortedNumbers = (numbers, epsilon = EPSILON) => {
const clusters = [[0]];
let clusterIndex = 0;
for (let i = 1; i < numbers.length; i += 1) {
if (epsilonEqual(numbers[i], numbers[i - 1], epsilon)) {
clusters[clusterIndex].push(i);
} else {
clusterIndex = clusters.length;
clusters.push([i]);
}
}
return clusters;
};
const radialSortPointIndices2 = (points, epsilon = EPSILON) => {
const first = minimum2DPointIndex(points, epsilon);
if (first === undefined) { return []; }
const angles = points
.map(p => subtract2(p, points[first]))
.map(v => normalize2(v))
.map(vec => dot2([0, 1], vec));
const rawOrder = angles
.map((a, i) => ({ a, i }))
.sort((a, b) => a.a - b.a)
.map(el => el.i)
.filter(i => i !== first);
return [[first]]
.concat(clusterIndicesOfSortedNumbers(rawOrder.map(i => angles[i]), epsilon)
.map(arr => arr.map(i => rawOrder[i]))
.map(cluster => (cluster.length === 1 ? cluster : cluster
.map(i => ({ i, len: distance2(points[i], points[first]) }))
.sort((a, b) => a.len - b.len)
.map(el => el.i))));
};
const radialSortUnitVectors2 = (vectors) => {
const quadrantConditions = [
v => v[0] >= 0 && v[1] >= 0,
v => v[0] < 0 && v[1] >= 0,
v => v[0] < 0 && v[1] < 0,
v => v[0] >= 0 && v[1] < 0,
];
const quadrantSorts = [
(a, b) => vectors[b][0] - vectors[a][0],
(a, b) => vectors[b][0] - vectors[a][0],
(a, b) => vectors[a][0] - vectors[b][0],
(a, b) => vectors[a][0] - vectors[b][0],
];
const vectorsQuadrant = vectors
.map(vec => quadrantConditions
.map((fn, i) => (fn(vec) ? i : undefined))
.filter(a => a !== undefined)
.shift());
const quadrantsVectors = [[], [], [], []];
vectorsQuadrant.forEach((q, v) => { quadrantsVectors[q].push(v); });
return quadrantsVectors
.flatMap((indices, i) => indices.sort(quadrantSorts[i]));
};
const radialSortPointIndices3 = (
points,
vector = [1, 0, 0],
origin = [0, 0, 0],
) => {
const threeVectors = basisVectors3(vector);
const basis = [threeVectors[1], threeVectors[2], threeVectors[0]];
const projectedPoints = points
.map(point => projectPointOnPlane(point, vector, origin));
const projectedVectors = projectedPoints
.map(point => subtract(point, origin));
const pointsUV = projectedVectors
.map(vec => [dot(vec, basis[0]), dot(vec, basis[1])]);
const vectorsUV = pointsUV.map(normalize2);
return radialSortUnitVectors2(vectorsUV);
};
const sortMethods = /*#__PURE__*/Object.freeze({
__proto__: null,
clusterIndicesOfSortedNumbers,
radialSortPointIndices2,
radialSortPointIndices3,
radialSortUnitVectors2,
sortAgainstItem,
sortPointsAlongVector
});
const typeOf = (obj) => {
if (typeof obj !== "object") { return typeof obj; }
if (obj.radius !== undefined) { return "circle"; }
if (obj.min && obj.max && obj.span) { return "box"; }
if (typeof obj[0] === "number") { return "vector"; }
if (obj.vector !== undefined && obj.origin !== undefined) { return "line"; }
if (obj[0] !== undefined && obj[0].length && typeof obj[0][0] === "number") {
return obj.length === 2 ? "segment" : "polygon";
}
return "object";
};
const general = {
...constants,
...mathFunctions,
...getMethods,
...convertMethods,
...arrayMethods,
...numberMethods,
...searchMethods,
...sortMethods,
typeof: typeOf,
};
const identity4x4 = Object.freeze([1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]);
const isIdentity4x4 = m => identity4x4
.map((n, i) => Math.abs(n - m[i]) < EPSILON)
.reduce((a, b) => a && b, true);
const multiplyMatrix4Vector3 = (m, vector) => [
m[0] * vector[0] + m[4] * vector[1] + m[8] * vector[2] + m[12],
m[1] * vector[0] + m[5] * vector[1] + m[9] * vector[2] + m[13],
m[2] * vector[0] + m[6] * vector[1] + m[10] * vector[2] + m[14],
];
const multiplyMatrix4Line3 = (m, vector, origin) => ({
vector: [
m[0] * vector[0] + m[4] * vector[1] + m[8] * vector[2],
m[1] * vector[0] + m[5] * vector[1] + m[9] * vector[2],
m[2] * vector[0] + m[6] * vector[1] + m[10] * vector[2],
],
origin: [
m[0] * origin[0] + m[4] * origin[1] + m[8] * origin[2] + m[12],
m[1] * origin[0] + m[5] * origin[1] + m[9] * origin[2] + m[13],
m[2] * origin[0] + m[6] * origin[1] + m[10] * origin[2] + m[14],
],
});
const multiplyMatrices4 = (m1, m2) => [
m1[0] * m2[0] + m1[4] * m2[1] + m1[8] * m2[2] + m1[12] * m2[3],
m1[1] * m2[0] + m1[5] * m2[1] + m1[9] * m2[2] + m1[13] * m2[3],
m1[2] * m2[0] + m1[6] * m2[1] + m1[10] * m2[2] + m1[14] * m2[3],
m1[3] * m2[0] + m1[7] * m2[1] + m1[11] * m2[2] + m1[15] * m2[3],
m1[0] * m2[4] + m1[4] * m2[5] + m1[8] * m2[6] + m1[12] * m2[7],
m1[1] * m2[4] + m1[5] * m2[5] + m1[9] * m2[6] + m1[13] * m2[7],
m1[2] * m2[4] + m1[6] * m2[5] + m1[10] * m2[6] + m1[14] * m2[7],
m1[3] * m2[4] + m1[7] * m2[5] + m1[11] * m2[6] + m1[15] * m2[7],
m1[0] * m2[8] + m1[4] * m2[9] + m1[8] * m2[10] + m1[12] * m2[11],
m1[1] * m2[8] + m1[5] * m2[9] + m1[9] * m2[10] + m1[13] * m2[11],
m1[2] * m2[8] + m1[6] * m2[9] + m1[10] * m2[10] + m1[14] * m2[11],
m1[3] * m2[8] + m1[7] * m2[9] + m1[11] * m2[10] + m1[15] * m2[11],
m1[0] * m2[12] + m1[4] * m2[13] + m1[8] * m2[14] + m1[12] * m2[15],
m1[1] * m2[12] + m1[5] * m2[13] + m1[9] * m2[14] + m1[13] * m2[15],
m1[2] * m2[12] + m1[6] * m2[13] + m1[10] * m2[14] + m1[14] * m2[15],
m1[3] * m2[12] + m1[7] * m2[13] + m1[11] * m2[14] + m1[15] * m2[15],
];
const determinant4 = (m) => {
const A2323 = m[10] * m[15] - m[11] * m[14];
const A1323 = m[9] * m[15] - m[11] * m[13];
const A1223 = m[9] * m[14] - m[10] * m[13];
const A0323 = m[8] * m[15] - m[11] * m[12];
const A0223 = m[8] * m[14] - m[10] * m[12];
const A0123 = m[8] * m[13] - m[9] * m[12];
return (
m[0] * (m[5] * A2323 - m[6] * A1323 + m[7] * A1223)
- m[1] * (m[4] * A2323 - m[6] * A0323 + m[7] * A0223)
+ m[2] * (m[4] * A1323 - m[5] * A0323 + m[7] * A0123)
- m[3] * (m[4] * A1223 - m[5] * A0223 + m[6] * A0123)
);
};
const invertMatrix4 = (m) => {
const det = determinant4(m);
if (Math.abs(det) < 1e-12 || Number.isNaN(det)
|| !Number.isFinite(m[12]) || !Number.isFinite(m[13]) || !Number.isFinite(m[14])) {
return undefined;
}
const A2323 = m[10] * m[15] - m[11] * m[14];
const A1323 = m[9] * m[15] - m[11] * m[13];
const A1223 = m[9] * m[14] - m[10] * m[13];
const A0323 = m[8] * m[15] - m[11] * m[12];
const A0223 = m[8] * m[14] - m[10] * m[12];
const A0123 = m[8] * m[13] - m[9] * m[12];
const A2313 = m[6] * m[15] - m[7] * m[14];
const A1313 = m[5] * m[15] - m[7] * m[13];
const A1213 = m[5] * m[14] - m[6] * m[13];
const A2312 = m[6] * m[11] - m[7] * m[10];
const A1312 = m[5] * m[11] - m[7] * m[9];
const A1212 = m[5] * m[10] - m[6] * m[9];
const A0313 = m[4] * m[15] - m[7] * m[12];
const A0213 = m[4] * m[14] - m[6] * m[12];
const A0312 = m[4] * m[11] - m[7] * m[8];
const A0212 = m[4] * m[10] - m[6] * m[8];
const A0113 = m[4] * m[13] - m[5] * m[12];
const A0112 = m[4] * m[9] - m[5] * m[8];
const inv = [
+(m[5] * A2323 - m[6] * A1323 + m[7] * A1223),
-(m[1] * A2323 - m[2] * A1323 + m[3] * A1223),
+(m[1] * A2313 - m[2] * A1313 + m[3] * A1213),
-(m[1] * A2312 - m[2] * A1312 + m[3] * A1212),
-(m[4] * A2323 - m[6] * A0323 + m[7] * A0223),
+(m[0] * A2323 - m[2] * A0323 + m[3] * A0223),
-(m[0] * A2313 - m[2] * A0313 + m[3] * A0213),
+(m[0] * A2312 - m[2] * A0312 + m[3] * A0212),
+(m[4] * A1323 - m[5] * A0323 + m[7] * A0123),
-(m[0] * A1323 - m[1] * A0323 + m[3] * A0123),
+(m[0] * A1313 - m[1] * A0313 + m[3] * A0113),
-(m[0] * A1312 - m[1] * A0312 + m[3] * A0112),
-(m[4] * A1223 - m[5] * A0223 + m[6] * A0123),
+(m[0] * A1223 - m[1] * A0223 + m[2] * A0123),
-(m[0] * A1213 - m[1] * A0213 + m[2] * A0113),
+(m[0] * A1212 - m[1] * A0212 + m[2] * A0112),
];
const invDet = 1.0 / det;
return inv.map(n => n * invDet);
};
const identity4x3 = Object.freeze([1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0]);
const makeMatrix4Translate = (x = 0, y = 0, z = 0) => [...identity4x3, x, y, z, 1];
const singleAxisRotate4 = (angle, origin, i0, i1, sgn) => {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
const rotate = [...identity4x4];
rotate[i0 * 4 + i0] = cos;
rotate[i0 * 4 + i1] = (sgn ? +1 : -1) * sin;
rotate[i1 * 4 + i0] = (sgn ? -1 : +1) * sin;
rotate[i1 * 4 + i1] = cos;
const origin3 = [0, 1, 2].map(i => origin[i] || 0);
const trans = [...identity4x4];
const trans_inv = [...identity4x4];
[12, 13, 14].forEach((i, j) => {
trans[i] = -origin3[j];
trans_inv[i] = origin3[j];
});
return multiplyMatrices4(trans_inv, multiplyMatrices4(rotate, trans));
};
const makeMatrix4RotateX = (angle, origin = [0, 0, 0]) => (
singleAxisRotate4(angle, origin, 1, 2, true));
const makeMatrix4RotateY = (angle, origin = [0, 0, 0]) => (
singleAxisRotate4(angle, origin, 0, 2, false));
const makeMatrix4RotateZ = (angle, origin = [0, 0, 0]) => (
singleAxisRotate4(angle, origin, 0, 1, true));
const makeMatrix4Rotate = (angle, vector = [0, 0, 1], origin = [0, 0, 0]) => {
const pos = [0, 1, 2].map(i => origin[i] || 0);
const [x, y, z] = resize(3, normalize(vector));
const c = Math.cos(angle);
const s = Math.sin(angle);
const t = 1 - c;
const trans = makeMatrix4Translate(-pos[0], -pos[1], -pos[2]);
const trans_inv = makeMatrix4Translate(pos[0], pos[1], pos[2]);
return multiplyMatrices4(trans_inv, multiplyMatrices4([
t * x * x + c, t * y * x + z * s, t * z * x - y * s, 0,
t * x * y - z * s, t * y * y + c, t * z * y + x * s, 0,
t * x * z + y * s, t * y * z - x * s, t * z * z + c, 0,
0, 0, 0, 1], trans));
};
const makeMatrix4Scale = (scale = [1, 1, 1], origin = [0, 0, 0]) => [
scale[0], 0, 0, 0,
0, scale[1], 0, 0,
0, 0, scale[2], 0,
scale[0] * -origin[0] + origin[0],
scale[1] * -origin[1] + origin[1],
scale[2] * -origin[2] + origin[2],
1,
];
const makeMatrix4UniformScale = (scale = 1, origin = [0, 0, 0]) => (
makeMatrix4Scale([scale, scale, scale], origin)
);
const makeMatrix4ReflectZ = (vector, origin = [0, 0]) => {
const m = makeMatrix2Reflect(vector, origin);
return [m[0], m[1], 0, 0, m[2], m[3], 0, 0, 0, 0, 1, 0, m[4], m[5], 0, 1];
};
const makePerspectiveMatrix4 = (FOV, aspect, near, far) => {
const f = Math.tan(Math.PI * 0.5 - 0.5 * FOV);
const rangeInv = 1.0 / (near - far);
return [
f / aspect, 0, 0, 0,
0, f, 0, 0,
0, 0, (near + far) * rangeInv, -1,
0, 0, near * far * rangeInv * 2, 0,
];
};
const makeOrthographicMatrix4 = (top, right, bottom, left, near, far) => [
2 / (right - left), 0, 0, 0,
0, 2 / (top - bottom), 0, 0,
0, 0, 2 / (near - far), 0,
(left + right) / (left - right),
(bottom + top) / (bottom - top),
(near + far) / (near - far),
1,
];
const makeLookAtMatrix4 = (position, target, up) => {
const zAxis = normalize3(subtract3(position, target));
const xAxis = normalize3(cross3(up, zAxis));
const yAxis = normalize3(cross3(zAxis, xAxis));
return [
xAxis[0], xAxis[1], xAxis[2], 0,
yAxis[0], yAxis[1], yAxis[2], 0,
zAxis[0], zAxis[1], zAxis[2], 0,