Press n or j to go to the next uncovered block, b, p or k for the previous block.
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21x 10x 11x 6x 6x 6x 6x 1x 1x 1x 1x 554761x 1x 1x 1x 55x 55x 55x 165x 165x 55x 110x 110x 110x 110x 275x 275x 715x 715x 715x 171x 171x 171x 110x 110x 55x 55x 165x 165x 55x | import seedrandom from 'seedrandom';
import macro from 'vtk.js/Sources/macros';
import {
IDENTITY,
IDENTITY_3X3,
EPSILON,
VTK_SMALL_NUMBER,
} from 'vtk.js/Sources/Common/Core/Math/Constants';
const { vtkErrorMacro, vtkWarningMacro } = macro;
// ----------------------------------------------------------------------------
/* eslint-disable camelcase */
/* eslint-disable no-cond-assign */
/* eslint-disable no-bitwise */
/* eslint-disable no-multi-assign */
// ----------------------------------------------------------------------------
let randomSeedValue = 0;
const VTK_MAX_ROTATIONS = 20;
function notImplemented(method) {
return () => vtkErrorMacro(`vtkMath::${method} - NOT IMPLEMENTED`);
}
// Swap rows for n by n matrix
function swapRowsMatrix_nxn(matrix, n, row1, row2) {
let tmp;
for (let i = 0; i < n; i++) {
tmp = matrix[row1 * n + i];
matrix[row1 * n + i] = matrix[row2 * n + i];
matrix[row2 * n + i] = tmp;
}
}
// Swap columns for n by n matrix
function swapColumnsMatrix_nxn(matrix, n, column1, column2) {
let tmp;
for (let i = 0; i < n; i++) {
tmp = matrix[i * n + column1];
matrix[i * n + column1] = matrix[i * n + column2];
matrix[i * n + column2] = tmp;
}
}
// ----------------------------------------------------------------------------
// Global methods
// ----------------------------------------------------------------------------
export function createArray(size = 3) {
// faster than Array.from and/or while loop
const res = Array(size);
for (let i = 0; i < size; ++i) {
res[i] = 0;
}
return res;
}
export const Pi = () => Math.PI;
export function radiansFromDegrees(deg) {
return (deg / 180) * Math.PI;
}
export function degreesFromRadians(rad) {
return (rad * 180) / Math.PI;
}
export const { round, floor, ceil, min, max } = Math;
export function arrayMin(arr, offset = 0, stride = 1) {
let minValue = Infinity;
for (let i = offset, len = arr.length; i < len; i += stride) {
if (arr[i] < minValue) {
minValue = arr[i];
}
}
return minValue;
}
export function arrayMax(arr, offset = 0, stride = 1) {
let maxValue = -Infinity;
for (let i = offset, len = arr.length; i < len; i += stride) {
if (maxValue < arr[i]) {
maxValue = arr[i];
}
}
return maxValue;
}
export function arrayRange(arr, offset = 0, stride = 1) {
let minValue = Infinity;
let maxValue = -Infinity;
for (let i = offset, len = arr.length; i < len; i += stride) {
if (arr[i] < minValue) {
minValue = arr[i];
}
if (maxValue < arr[i]) {
maxValue = arr[i];
}
}
return [minValue, maxValue];
}
export const ceilLog2 = notImplemented('ceilLog2');
export const factorial = notImplemented('factorial');
export function nearestPowerOfTwo(xi) {
let v = 1;
while (v < xi) {
v *= 2;
}
return v;
}
export function isPowerOfTwo(x) {
return x === nearestPowerOfTwo(x);
}
export function binomial(m, n) {
let r = 1;
for (let i = 1; i <= n; ++i) {
r *= (m - i + 1) / i;
}
return Math.floor(r);
}
export function beginCombination(m, n) {
if (m < n) {
return 0;
}
const r = createArray(n);
for (let i = 0; i < n; ++i) {
r[i] = i;
}
return r;
}
export function nextCombination(m, n, r) {
let status = 0;
for (let i = n - 1; i >= 0; --i) {
if (r[i] < m - n + i) {
let j = r[i] + 1;
while (i < n) {
r[i++] = j++;
}
status = 1;
break;
}
}
return status;
}
export function randomSeed(seed) {
seedrandom(`${seed}`, { global: true });
randomSeedValue = seed;
}
export function getSeed() {
return randomSeedValue;
}
export function random(minValue = 0, maxValue = 1) {
const delta = maxValue - minValue;
return minValue + delta * Math.random();
}
export const gaussian = notImplemented('gaussian');
// Vect3 operations
export function add(a, b, out) {
out[0] = a[0] + b[0];
out[1] = a[1] + b[1];
out[2] = a[2] + b[2];
return out;
}
export function subtract(a, b, out) {
out[0] = a[0] - b[0];
out[1] = a[1] - b[1];
out[2] = a[2] - b[2];
return out;
}
export function multiplyScalar(vec, scalar) {
vec[0] *= scalar;
vec[1] *= scalar;
vec[2] *= scalar;
return vec;
}
export function multiplyScalar2D(vec, scalar) {
vec[0] *= scalar;
vec[1] *= scalar;
return vec;
}
export function multiplyAccumulate(a, b, scalar, out) {
out[0] = a[0] + b[0] * scalar;
out[1] = a[1] + b[1] * scalar;
out[2] = a[2] + b[2] * scalar;
return out;
}
export function multiplyAccumulate2D(a, b, scalar, out) {
out[0] = a[0] + b[0] * scalar;
out[1] = a[1] + b[1] * scalar;
return out;
}
export function dot(x, y) {
return x[0] * y[0] + x[1] * y[1] + x[2] * y[2];
}
export function outer(x, y, out_3x3) {
out_3x3[0] = x[0] * y[0];
out_3x3[1] = x[0] * y[1];
out_3x3[2] = x[0] * y[2];
out_3x3[3] = x[1] * y[0];
out_3x3[4] = x[1] * y[1];
out_3x3[5] = x[1] * y[2];
out_3x3[6] = x[2] * y[0];
out_3x3[7] = x[2] * y[1];
out_3x3[8] = x[2] * y[2];
}
export function cross(x, y, out) {
const Zx = x[1] * y[2] - x[2] * y[1];
const Zy = x[2] * y[0] - x[0] * y[2];
const Zz = x[0] * y[1] - x[1] * y[0];
out[0] = Zx;
out[1] = Zy;
out[2] = Zz;
return out;
}
export function norm(x, n = 3) {
switch (n) {
case 1:
return Math.abs(x);
case 2:
return Math.sqrt(x[0] * x[0] + x[1] * x[1]);
case 3:
return Math.sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
default: {
let sum = 0;
for (let i = 0; i < n; i++) {
sum += x[i] * x[i];
}
return Math.sqrt(sum);
}
}
}
export function normalize(x) {
const den = norm(x);
if (den !== 0.0) {
x[0] /= den;
x[1] /= den;
x[2] /= den;
}
return den;
}
export function perpendiculars(x, y, z, theta) {
const x2 = x[0] * x[0];
const y2 = x[1] * x[1];
const z2 = x[2] * x[2];
const r = Math.sqrt(x2 + y2 + z2);
let dx;
let dy;
let dz;
// transpose the vector to avoid divide-by-zero error
if (x2 > y2 && x2 > z2) {
dx = 0;
dy = 1;
dz = 2;
} else if (y2 > z2) {
dx = 1;
dy = 2;
dz = 0;
} else E{
dx = 2;
dy = 0;
dz = 1;
}
const a = x[dx] / r;
const b = x[dy] / r;
const c = x[dz] / r;
const tmp = Math.sqrt(a * a + c * c);
Iif (theta !== 0) {
const sintheta = Math.sin(theta);
const costheta = Math.cos(theta);
if (y) {
y[dx] = (c * costheta - a * b * sintheta) / tmp;
y[dy] = sintheta * tmp;
y[dz] = (-(a * costheta) - b * c * sintheta) / tmp;
}
if (z) {
z[dx] = (-(c * sintheta) - a * b * costheta) / tmp;
z[dy] = costheta * tmp;
z[dz] = (a * sintheta - b * c * costheta) / tmp;
}
} else {
if (y) {
y[dx] = c / tmp;
y[dy] = 0;
y[dz] = -a / tmp;
}
if (z) {
z[dx] = (-a * b) / tmp;
z[dy] = tmp;
z[dz] = (-b * c) / tmp;
}
}
}
export function projectVector(a, b, projection) {
const bSquared = dot(b, b);
if (bSquared === 0) {
projection[0] = 0;
projection[1] = 0;
projection[2] = 0;
return false;
}
const scale = dot(a, b) / bSquared;
for (let i = 0; i < 3; i++) {
projection[i] = b[i];
}
multiplyScalar(projection, scale);
return true;
}
export function dot2D(x, y) {
return x[0] * y[0] + x[1] * y[1];
}
export function projectVector2D(a, b, projection) {
const bSquared = dot2D(b, b);
if (bSquared === 0) {
projection[0] = 0;
projection[1] = 0;
return false;
}
const scale = dot2D(a, b) / bSquared;
for (let i = 0; i < 2; i++) {
projection[i] = b[i];
}
multiplyScalar2D(projection, scale);
return true;
}
export function distance2BetweenPoints(x, y) {
return (
(x[0] - y[0]) * (x[0] - y[0]) +
(x[1] - y[1]) * (x[1] - y[1]) +
(x[2] - y[2]) * (x[2] - y[2])
);
}
export function angleBetweenVectors(v1, v2) {
const crossVect = [0, 0, 0];
cross(v1, v2, crossVect);
return Math.atan2(norm(crossVect), dot(v1, v2));
}
export function signedAngleBetweenVectors(v1, v2, vN) {
const crossVect = [0, 0, 0];
cross(v1, v2, crossVect);
const angle = Math.atan2(norm(crossVect), dot(v1, v2));
return dot(crossVect, vN) >= 0 ? angle : -angle;
}
export function gaussianAmplitude(mean, variance, position) {
const distanceFromMean = Math.abs(mean - position);
return (
(1 / Math.sqrt(2 * Math.PI * variance)) *
Math.exp(-(distanceFromMean ** 2) / (2 * variance))
);
}
export function gaussianWeight(mean, variance, position) {
const distanceFromMean = Math.abs(mean - position);
return Math.exp(-(distanceFromMean ** 2) / (2 * variance));
}
export function outer2D(x, y, out_2x2) {
out_2x2[0] = x[0] * y[0];
out_2x2[1] = x[0] * y[1];
out_2x2[2] = x[1] * y[0];
out_2x2[3] = x[1] * y[1];
}
export function norm2D(x2D) {
return Math.sqrt(x2D[0] * x2D[0] + x2D[1] * x2D[1]);
}
export function normalize2D(x) {
const den = norm2D(x);
if (den !== 0.0) {
x[0] /= den;
x[1] /= den;
}
return den;
}
export function rowsToMat4(row0, row1, row2, row3, mat) {
for (let i = 0; i < 4; i++) {
mat[i] = row0[i];
mat[4 + i] = row1[i];
mat[8 + i] = row2[i];
mat[12 + i] = row3[i];
}
return mat;
}
export function columnsToMat4(column0, column1, column2, column3, mat) {
for (let i = 0; i < 4; i++) {
mat[4 * i] = column0[i];
mat[4 * i + 1] = column1[i];
mat[4 * i + 2] = column2[i];
mat[4 * i + 3] = column3[i];
}
return mat;
}
export function rowsToMat3(row0, row1, row2, mat) {
for (let i = 0; i < 3; i++) {
mat[i] = row0[i];
mat[3 + i] = row1[i];
mat[6 + i] = row2[i];
}
return mat;
}
export function columnsToMat3(column0, column1, column2, mat) {
for (let i = 0; i < 3; i++) {
mat[3 * i] = column0[i];
mat[3 * i + 1] = column1[i];
mat[3 * i + 2] = column2[i];
}
return mat;
}
export function determinant2x2(...args) {
if (args.length === 2) {
return args[0][0] * args[1][1] - args[1][0] * args[0][1];
}
if (args.length === 4) {
return args[0] * args[3] - args[1] * args[2];
}
return Number.NaN;
}
export function LUFactor3x3(mat_3x3, index_3) {
let maxI;
let tmp;
let largest;
const scale = [0, 0, 0];
// Loop over rows to get implicit scaling information
for (let i = 0; i < 3; i++) {
largest = Math.abs(mat_3x3[i * 3]);
Iif ((tmp = Math.abs(mat_3x3[i * 3 + 1])) > largest) {
largest = tmp;
}
Iif ((tmp = Math.abs(mat_3x3[i * 3 + 2])) > largest) {
largest = tmp;
}
scale[i] = 1 / largest;
}
// Loop over all columns using Crout's method
// first column
largest = scale[0] * Math.abs(mat_3x3[0]);
maxI = 0;
if ((tmp = scale[1] * Math.abs(mat_3x3[3])) >= largest) {
largest = tmp;
maxI = 1;
}
if ((tmp = scale[2] * Math.abs(mat_3x3[6])) >= largest) {
maxI = 2;
}
if (maxI !== 0) {
swapRowsMatrix_nxn(mat_3x3, 3, maxI, 0);
scale[maxI] = scale[0];
}
index_3[0] = maxI;
mat_3x3[3] /= mat_3x3[0];
mat_3x3[6] /= mat_3x3[0];
// second column
mat_3x3[4] -= mat_3x3[3] * mat_3x3[1];
mat_3x3[7] -= mat_3x3[6] * mat_3x3[1];
largest = scale[1] * Math.abs(mat_3x3[4]);
maxI = 1;
if ((tmp = scale[2] * Math.abs(mat_3x3[7])) >= largest) {
maxI = 2;
swapRowsMatrix_nxn(mat_3x3, 3, 1, 2);
scale[2] = scale[1];
}
index_3[1] = maxI;
mat_3x3[7] /= mat_3x3[4];
// third column
mat_3x3[5] -= mat_3x3[3] * mat_3x3[2];
mat_3x3[8] -= mat_3x3[6] * mat_3x3[2] + mat_3x3[7] * mat_3x3[5];
index_3[2] = 2;
}
export function LUSolve3x3(mat_3x3, index_3, x_3) {
// forward substitution
let sum = x_3[index_3[0]];
x_3[index_3[0]] = x_3[0];
x_3[0] = sum;
sum = x_3[index_3[1]];
x_3[index_3[1]] = x_3[1];
x_3[1] = sum - mat_3x3[3] * x_3[0];
sum = x_3[index_3[2]];
x_3[index_3[2]] = x_3[2];
x_3[2] = sum - mat_3x3[6] * x_3[0] - mat_3x3[7] * x_3[1];
// back substitution
x_3[2] /= mat_3x3[8];
x_3[1] = (x_3[1] - mat_3x3[5] * x_3[2]) / mat_3x3[4];
x_3[0] = (x_3[0] - mat_3x3[1] * x_3[1] - mat_3x3[2] * x_3[2]) / mat_3x3[0];
}
export function linearSolve3x3(mat_3x3, x_3, y_3) {
const a1 = mat_3x3[0];
const b1 = mat_3x3[1];
const c1 = mat_3x3[2];
const a2 = mat_3x3[3];
const b2 = mat_3x3[4];
const c2 = mat_3x3[5];
const a3 = mat_3x3[6];
const b3 = mat_3x3[7];
const c3 = mat_3x3[8];
// Compute the adjoint
const d1 = +determinant2x2(b2, b3, c2, c3);
const d2 = -determinant2x2(a2, a3, c2, c3);
const d3 = +determinant2x2(a2, a3, b2, b3);
const e1 = -determinant2x2(b1, b3, c1, c3);
const e2 = +determinant2x2(a1, a3, c1, c3);
const e3 = -determinant2x2(a1, a3, b1, b3);
const f1 = +determinant2x2(b1, b2, c1, c2);
const f2 = -determinant2x2(a1, a2, c1, c2);
const f3 = +determinant2x2(a1, a2, b1, b2);
// Compute the determinant
const det = a1 * d1 + b1 * d2 + c1 * d3;
// Multiply by the adjoint
const v1 = d1 * x_3[0] + e1 * x_3[1] + f1 * x_3[2];
const v2 = d2 * x_3[0] + e2 * x_3[1] + f2 * x_3[2];
const v3 = d3 * x_3[0] + e3 * x_3[1] + f3 * x_3[2];
// Divide by the determinant
y_3[0] = v1 / det;
y_3[1] = v2 / det;
y_3[2] = v3 / det;
}
export function multiply3x3_vect3(mat_3x3, in_3, out_3) {
const x = mat_3x3[0] * in_3[0] + mat_3x3[1] * in_3[1] + mat_3x3[2] * in_3[2];
const y = mat_3x3[3] * in_3[0] + mat_3x3[4] * in_3[1] + mat_3x3[5] * in_3[2];
const z = mat_3x3[6] * in_3[0] + mat_3x3[7] * in_3[1] + mat_3x3[8] * in_3[2];
out_3[0] = x;
out_3[1] = y;
out_3[2] = z;
}
export function multiply3x3_mat3(a_3x3, b_3x3, out_3x3) {
const copyA = [...a_3x3];
const copyB = [...b_3x3];
for (let i = 0; i < 3; i++) {
out_3x3[i] =
copyA[0] * copyB[i] + copyA[1] * copyB[i + 3] + copyA[2] * copyB[i + 6];
out_3x3[i + 3] =
copyA[3] * copyB[i] + copyA[4] * copyB[i + 3] + copyA[5] * copyB[i + 6];
out_3x3[i + 6] =
copyA[6] * copyB[i] + copyA[7] * copyB[i + 3] + copyA[8] * copyB[i + 6];
}
}
export function multiplyMatrix(a, b, rowA, colA, rowB, colB, outRowAColB) {
// we need colA == rowB
if (colA !== rowB) {
vtkErrorMacro('Number of columns of A must match number of rows of B.');
}
// If a or b is used to store the result, copying them is required
const copyA = [...a];
const copyB = [...b];
// output matrix is rowA*colB
// output row
for (let i = 0; i < rowA; i++) {
// output col
for (let j = 0; j < colB; j++) {
outRowAColB[i * colB + j] = 0;
// sum for this point
for (let k = 0; k < colA; k++) {
outRowAColB[i * colB + j] += copyA[i * colA + k] * copyB[j + colB * k];
}
}
}
}
export function transpose3x3(in_3x3, outT_3x3) {
let tmp;
// off-diagonal elements
tmp = in_3x3[3];
outT_3x3[3] = in_3x3[1];
outT_3x3[1] = tmp;
tmp = in_3x3[6];
outT_3x3[6] = in_3x3[2];
outT_3x3[2] = tmp;
tmp = in_3x3[7];
outT_3x3[7] = in_3x3[5];
outT_3x3[5] = tmp;
// on-diagonal elements
outT_3x3[0] = in_3x3[0];
outT_3x3[4] = in_3x3[4];
outT_3x3[8] = in_3x3[8];
}
export function invert3x3(in_3x3, outI_3x3) {
const a1 = in_3x3[0];
const b1 = in_3x3[1];
const c1 = in_3x3[2];
const a2 = in_3x3[3];
const b2 = in_3x3[4];
const c2 = in_3x3[5];
const a3 = in_3x3[6];
const b3 = in_3x3[7];
const c3 = in_3x3[8];
// Compute the adjoint
const d1 = +determinant2x2(b2, b3, c2, c3);
const d2 = -determinant2x2(a2, a3, c2, c3);
const d3 = +determinant2x2(a2, a3, b2, b3);
const e1 = -determinant2x2(b1, b3, c1, c3);
const e2 = +determinant2x2(a1, a3, c1, c3);
const e3 = -determinant2x2(a1, a3, b1, b3);
const f1 = +determinant2x2(b1, b2, c1, c2);
const f2 = -determinant2x2(a1, a2, c1, c2);
const f3 = +determinant2x2(a1, a2, b1, b2);
// Divide by the determinant
const det = a1 * d1 + b1 * d2 + c1 * d3;
Iif (det === 0) {
vtkWarningMacro('Matrix has 0 determinant');
}
outI_3x3[0] = d1 / det;
outI_3x3[3] = d2 / det;
outI_3x3[6] = d3 / det;
outI_3x3[1] = e1 / det;
outI_3x3[4] = e2 / det;
outI_3x3[7] = e3 / det;
outI_3x3[2] = f1 / det;
outI_3x3[5] = f2 / det;
outI_3x3[8] = f3 / det;
}
export function determinant3x3(mat_3x3) {
return (
mat_3x3[0] * mat_3x3[4] * mat_3x3[8] +
mat_3x3[3] * mat_3x3[7] * mat_3x3[2] +
mat_3x3[6] * mat_3x3[1] * mat_3x3[5] -
mat_3x3[0] * mat_3x3[7] * mat_3x3[5] -
mat_3x3[3] * mat_3x3[1] * mat_3x3[8] -
mat_3x3[6] * mat_3x3[4] * mat_3x3[2]
);
}
/**
* Returns true if elements of both arrays are equals.
* @param {Array} a an array of numbers (vector, point, matrix...)
* @param {Array} b an array of numbers (vector, point, matrix...)
* @param {Number} eps tolerance
*/
export function areEquals(a, b, eps = EPSILON) {
if (a.length !== b.length) {
return false;
}
function isEqual(element, index) {
return Math.abs(element - b[index]) <= eps;
}
return a.every(isEqual);
}
export const areMatricesEqual = areEquals;
export function identity3x3(mat_3x3) {
for (let i = 0; i < 3; i++) {
/* eslint-disable-next-line no-multi-assign */
mat_3x3[i * 3] = mat_3x3[i * 3 + 1] = mat_3x3[i * 3 + 2] = 0;
mat_3x3[i * 3 + i] = 1;
}
}
export function identity(n, mat) {
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
mat[i * n + j] = 0;
}
mat[i * n + i] = 1;
}
return mat;
}
export function isIdentity(mat, eps = EPSILON) {
return areMatricesEqual(mat, IDENTITY, eps);
}
export function isIdentity3x3(mat, eps = EPSILON) {
return areMatricesEqual(mat, IDENTITY_3X3, eps);
}
export function quaternionToMatrix3x3(quat_4, mat_3x3) {
const ww = quat_4[0] * quat_4[0];
const wx = quat_4[0] * quat_4[1];
const wy = quat_4[0] * quat_4[2];
const wz = quat_4[0] * quat_4[3];
const xx = quat_4[1] * quat_4[1];
const yy = quat_4[2] * quat_4[2];
const zz = quat_4[3] * quat_4[3];
const xy = quat_4[1] * quat_4[2];
const xz = quat_4[1] * quat_4[3];
const yz = quat_4[2] * quat_4[3];
const rr = xx + yy + zz;
// normalization factor, just in case quaternion was not normalized
let f = 1 / (ww + rr);
const s = (ww - rr) * f;
f *= 2;
mat_3x3[0] = xx * f + s;
mat_3x3[3] = (xy + wz) * f;
mat_3x3[6] = (xz - wy) * f;
mat_3x3[1] = (xy - wz) * f;
mat_3x3[4] = yy * f + s;
mat_3x3[7] = (yz + wx) * f;
mat_3x3[2] = (xz + wy) * f;
mat_3x3[5] = (yz - wx) * f;
mat_3x3[8] = zz * f + s;
}
export function roundNumber(num, digits = 0) {
if (!`${num}`.includes('e')) {
return +`${Math.round(`${num}e+${digits}`)}e-${digits}`;
}
const arr = `${num}`.split('e');
let sig = '';
Iif (+arr[1] + digits > 0) {
sig = '+';
}
return +`${Math.round(`${+arr[0]}e${sig}${+arr[1] + digits}`)}e-${digits}`;
}
export function roundVector(vector, out = [0, 0, 0], digits = 0) {
out[0] = roundNumber(vector[0], digits);
out[1] = roundNumber(vector[1], digits);
out[2] = roundNumber(vector[2], digits);
return out;
}
export function jacobiN(a, n, w, v) {
let i;
let j;
let k;
let iq;
let ip;
let numPos;
let tresh;
let theta;
let t;
let tau;
let sm;
let s;
let h;
let g;
let c;
let tmp;
const b = createArray(n);
const z = createArray(n);
const vtkROTATE = (aa, ii, jj) => {
g = aa[ii];
h = aa[jj];
aa[ii] = g - s * (h + g * tau);
aa[jj] = h + s * (g - h * tau);
};
// initialize
identity(n, v);
for (ip = 0; ip < n; ip++) {
b[ip] = w[ip] = a[ip + ip * n];
z[ip] = 0.0;
}
// begin rotation sequence
for (i = 0; i < VTK_MAX_ROTATIONS; i++) {
sm = 0.0;
for (ip = 0; ip < n - 1; ip++) {
for (iq = ip + 1; iq < n; iq++) {
sm += Math.abs(a[ip * n + iq]);
}
}
if (sm === 0.0) {
break;
}
// first 3 sweeps
if (i < 3) {
tresh = (0.2 * sm) / (n * n);
} else {
tresh = 0.0;
}
for (ip = 0; ip < n - 1; ip++) {
for (iq = ip + 1; iq < n; iq++) {
g = 100.0 * Math.abs(a[ip * n + iq]);
// after 4 sweeps
if (
i > 3 &&
Math.abs(w[ip]) + g === Math.abs(w[ip]) &&
Math.abs(w[iq]) + g === Math.abs(w[iq])
) {
a[ip * n + iq] = 0.0;
} else if (Math.abs(a[ip * n + iq]) > tresh) {
h = w[iq] - w[ip];
if (Math.abs(h) + g === Math.abs(h)) {
t = a[ip * n + iq] / h;
} else {
theta = (0.5 * h) / a[ip * n + iq];
t = 1.0 / (Math.abs(theta) + Math.sqrt(1.0 + theta * theta));
if (theta < 0.0) {
t = -t;
}
}
c = 1.0 / Math.sqrt(1 + t * t);
s = t * c;
tau = s / (1.0 + c);
h = t * a[ip * n + iq];
z[ip] -= h;
z[iq] += h;
w[ip] -= h;
w[iq] += h;
a[ip * n + iq] = 0.0;
// ip already shifted left by 1 unit
for (j = 0; j <= ip - 1; j++) {
vtkROTATE(a, j * n + ip, j * n + iq);
}
// ip and iq already shifted left by 1 unit
for (j = ip + 1; j <= iq - 1; j++) {
vtkROTATE(a, ip * n + j, j * n + iq);
}
// iq already shifted left by 1 unit
for (j = iq + 1; j < n; j++) {
vtkROTATE(a, ip * n + j, iq * n + j);
}
for (j = 0; j < n; j++) {
vtkROTATE(v, j * n + ip, j * n + iq);
}
}
}
}
for (ip = 0; ip < n; ip++) {
b[ip] += z[ip];
w[ip] = b[ip];
z[ip] = 0.0;
}
}
// this is NEVER called
Iif (i >= VTK_MAX_ROTATIONS) {
vtkWarningMacro('vtkMath::Jacobi: Error extracting eigenfunctions');
return 0;
}
// sort eigenfunctions: these changes do not affect accuracy
for (j = 0; j < n - 1; j++) {
// boundary incorrect
k = j;
tmp = w[k];
for (i = j + 1; i < n; i++) {
// boundary incorrect, shifted already
if (w[i] >= tmp || Math.abs(w[i] - tmp) < VTK_SMALL_NUMBER) {
// why exchange if same?
k = i;
tmp = w[k];
}
}
if (k !== j) {
w[k] = w[j];
w[j] = tmp;
swapColumnsMatrix_nxn(v, n, j, k);
}
}
// ensure eigenvector consistency (i.e., Jacobi can compute vectors that
// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
// reek havoc in hyperstreamline/other stuff. We will select the most
// positive eigenvector.
const ceil_half_n = (n >> 1) + (n & 1);
for (numPos = 0, i = 0; i < n * n; i++) {
if (v[i] >= 0.0) {
numPos++;
}
}
// if ( numPos < ceil(double(n)/double(2.0)) )
Iif (numPos < ceil_half_n) {
for (i = 0; i < n; i++) {
v[i * n + j] *= -1.0;
}
}
return 1;
}
export function matrix3x3ToQuaternion(mat_3x3, quat_4) {
const tmp = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
// on-diagonal elements
tmp[0] = mat_3x3[0] + mat_3x3[4] + mat_3x3[8];
tmp[5] = mat_3x3[0] - mat_3x3[4] - mat_3x3[8];
tmp[10] = -mat_3x3[0] + mat_3x3[4] - mat_3x3[8];
tmp[15] = -mat_3x3[0] - mat_3x3[4] + mat_3x3[8];
// off-diagonal elements
tmp[1] = tmp[4] = mat_3x3[7] - mat_3x3[5];
tmp[2] = tmp[8] = mat_3x3[2] - mat_3x3[6];
tmp[3] = tmp[12] = mat_3x3[3] - mat_3x3[1];
tmp[6] = tmp[9] = mat_3x3[3] + mat_3x3[1];
tmp[7] = tmp[13] = mat_3x3[2] + mat_3x3[6];
tmp[11] = tmp[14] = mat_3x3[7] + mat_3x3[5];
const eigenvectors = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
const eigenvalues = [0, 0, 0, 0];
// convert into format that JacobiN can use,
// then use Jacobi to find eigenvalues and eigenvectors
// tmp is copied because jacobiN may modify it
const NTemp = [...tmp];
jacobiN(NTemp, 4, eigenvalues, eigenvectors);
// the first eigenvector is the one we want
quat_4[0] = eigenvectors[0];
quat_4[1] = eigenvectors[4];
quat_4[2] = eigenvectors[8];
quat_4[3] = eigenvectors[12];
}
export function multiplyQuaternion(quat_1, quat_2, quat_out) {
const ww = quat_1[0] * quat_2[0];
const wx = quat_1[0] * quat_2[1];
const wy = quat_1[0] * quat_2[2];
const wz = quat_1[0] * quat_2[3];
const xw = quat_1[1] * quat_2[0];
const xx = quat_1[1] * quat_2[1];
const xy = quat_1[1] * quat_2[2];
const xz = quat_1[1] * quat_2[3];
const yw = quat_1[2] * quat_2[0];
const yx = quat_1[2] * quat_2[1];
const yy = quat_1[2] * quat_2[2];
const yz = quat_1[2] * quat_2[3];
const zw = quat_1[3] * quat_2[0];
const zx = quat_1[3] * quat_2[1];
const zy = quat_1[3] * quat_2[2];
const zz = quat_1[3] * quat_2[3];
quat_out[0] = ww - xx - yy - zz;
quat_out[1] = wx + xw + yz - zy;
quat_out[2] = wy - xz + yw + zx;
quat_out[3] = wz + xy - yx + zw;
}
export function orthogonalize3x3(a_3x3, out_3x3) {
// copy the matrix
for (let i = 0; i < 9; i++) {
out_3x3[i] = a_3x3[i];
}
// Pivot the matrix to improve accuracy
const scale = createArray(3);
const index = createArray(3);
let largest;
// Loop over rows to get implicit scaling information
for (let i = 0; i < 3; i++) {
const x1 = Math.abs(out_3x3[i * 3]);
const x2 = Math.abs(out_3x3[i * 3 + 1]);
const x3 = Math.abs(out_3x3[i * 3 + 2]);
largest = x2 > x1 ? x2 : x1;
largest = x3 > largest ? x3 : largest;
scale[i] = 1;
if (largest !== 0) {
scale[i] /= largest;
}
}
// first column
const x1 = Math.abs(out_3x3[0]) * scale[0];
const x2 = Math.abs(out_3x3[3]) * scale[1];
const x3 = Math.abs(out_3x3[6]) * scale[2];
index[0] = 0;
largest = x1;
if (x2 >= largest) {
largest = x2;
index[0] = 1;
}
if (x3 >= largest) {
index[0] = 2;
}
if (index[0] !== 0) {
// swap vectors
swapColumnsMatrix_nxn(out_3x3, 3, index[0], 0);
scale[index[0]] = scale[0];
}
// second column
const y2 = Math.abs(out_3x3[4]) * scale[1];
const y3 = Math.abs(out_3x3[7]) * scale[2];
index[1] = 1;
largest = y2;
if (y3 >= largest) {
index[1] = 2;
// swap vectors
swapColumnsMatrix_nxn(out_3x3, 3, 1, 2);
}
// third column
index[2] = 2;
// A quaternion can only describe a pure rotation, not
// a rotation with a flip, therefore the flip must be
// removed before the matrix is converted to a quaternion.
let flip = 0;
if (determinant3x3(out_3x3) < 0) {
flip = 1;
for (let i = 0; i < 9; i++) {
out_3x3[i] = -out_3x3[i];
}
}
// Do orthogonalization using a quaternion intermediate
// (this, essentially, does the orthogonalization via
// diagonalization of an appropriately constructed symmetric
// 4x4 matrix rather than by doing SVD of the 3x3 matrix)
const quat = createArray(4);
matrix3x3ToQuaternion(out_3x3, quat);
quaternionToMatrix3x3(quat, out_3x3);
// Put the flip back into the orthogonalized matrix.
if (flip) {
for (let i = 0; i < 9; i++) {
out_3x3[i] = -out_3x3[i];
}
}
// Undo the pivoting
if (index[1] !== 1) {
swapColumnsMatrix_nxn(out_3x3, 3, index[1], 1);
}
if (index[0] !== 0) {
swapColumnsMatrix_nxn(out_3x3, 3, index[0], 0);
}
}
export function diagonalize3x3(a_3x3, w_3, v_3x3) {
let i;
let j;
let k;
let maxI;
let tmp;
let maxVal;
// a is copied because jacobiN may modify it
const copyA = [...a_3x3];
// diagonalize using Jacobi
jacobiN(copyA, 3, w_3, v_3x3);
// if all the eigenvalues are the same, return identity matrix
if (w_3[0] === w_3[1] && w_3[0] === w_3[2]) {
identity3x3(v_3x3);
return;
}
// transpose temporarily, it makes it easier to sort the eigenvectors
transpose3x3(v_3x3, v_3x3);
// if two eigenvalues are the same, re-orthogonalize to optimally line
// up the eigenvectors with the x, y, and z axes
for (i = 0; i < 3; i++) {
// two eigenvalues are the same
if (w_3[(i + 1) % 3] === w_3[(i + 2) % 3]) {
// find maximum element of the independent eigenvector
maxVal = Math.abs(v_3x3[i * 3]);
maxI = 0;
for (j = 1; j < 3; j++) {
if (maxVal < (tmp = Math.abs(v_3x3[i * 3 + j]))) {
maxVal = tmp;
maxI = j;
}
}
// swap the eigenvector into its proper position
Iif (maxI !== i) {
tmp = w_3[maxI];
w_3[maxI] = w_3[i];
w_3[i] = tmp;
swapRowsMatrix_nxn(v_3x3, 3, i, maxI);
}
// maximum element of eigenvector should be positive
Iif (v_3x3[maxI * 3 + maxI] < 0) {
v_3x3[maxI * 3] = -v_3x3[maxI * 3];
v_3x3[maxI * 3 + 1] = -v_3x3[maxI * 3 + 1];
v_3x3[maxI * 3 + 2] = -v_3x3[maxI * 3 + 2];
}
// re-orthogonalize the other two eigenvectors
j = (maxI + 1) % 3;
k = (maxI + 2) % 3;
v_3x3[j * 3] = 0.0;
v_3x3[j * 3 + 1] = 0.0;
v_3x3[j * 3 + 2] = 0.0;
v_3x3[j * 3 + j] = 1.0;
const vectTmp1 = cross(
[v_3x3[maxI * 3], v_3x3[maxI * 3 + 1], v_3x3[maxI * 3 + 2]],
[v_3x3[j * 3], v_3x3[j * 3 + 1], v_3x3[j * 3 + 2]],
[]
);
normalize(vectTmp1);
const vectTmp2 = cross(
vectTmp1,
[v_3x3[maxI * 3], v_3x3[maxI * 3 + 1], v_3x3[maxI * 3 + 2]],
[]
);
for (let t = 0; t < 3; t++) {
v_3x3[k * 3 + t] = vectTmp1[t];
v_3x3[j * 3 + t] = vectTmp2[t];
}
// transpose vectors back to columns
transpose3x3(v_3x3, v_3x3);
return;
}
}
// the three eigenvalues are different, just sort the eigenvectors
// to align them with the x, y, and z axes
// find the vector with the largest x element, make that vector
// the first vector
maxVal = Math.abs(v_3x3[0]);
maxI = 0;
for (i = 1; i < 3; i++) {
if (maxVal < (tmp = Math.abs(v_3x3[i * 3]))) {
maxVal = tmp;
maxI = i;
}
}
// swap eigenvalue and eigenvector
if (maxI !== 0) {
const eigenValTmp = w_3[maxI];
w_3[maxI] = w_3[0];
w_3[0] = eigenValTmp;
swapRowsMatrix_nxn(v_3x3, 3, maxI, 0);
}
// do the same for the y element
if (Math.abs(v_3x3[4]) < Math.abs(v_3x3[7])) {
const eigenValTmp = w_3[2];
w_3[2] = w_3[1];
w_3[1] = eigenValTmp;
swapRowsMatrix_nxn(v_3x3, 3, 1, 2);
}
// ensure that the sign of the eigenvectors is correct
for (i = 0; i < 2; i++) {
if (v_3x3[i * 3 + i] < 0) {
v_3x3[i * 3] = -v_3x3[i * 3];
v_3x3[i * 3 + 1] = -v_3x3[i * 3 + 1];
v_3x3[i * 3 + 2] = -v_3x3[i * 3 + 2];
}
}
// set sign of final eigenvector to ensure that determinant is positive
if (determinant3x3(v_3x3) < 0) {
v_3x3[6] = -v_3x3[6];
v_3x3[7] = -v_3x3[7];
v_3x3[8] = -v_3x3[8];
}
// transpose the eigenvectors back again
transpose3x3(v_3x3, v_3x3);
}
export function singularValueDecomposition3x3(a_3x3, u_3x3, w_3, vT_3x3) {
let i;
// copy so that A can be used for U or VT without risk
const B = [...a_3x3];
// temporarily flip if determinant is negative
const d = determinant3x3(B);
if (d < 0) {
for (i = 0; i < 9; i++) {
B[i] = -B[i];
}
}
// orthogonalize, diagonalize, etc.
orthogonalize3x3(B, u_3x3);
transpose3x3(B, B);
multiply3x3_mat3(B, u_3x3, vT_3x3);
diagonalize3x3(vT_3x3, w_3, vT_3x3);
multiply3x3_mat3(u_3x3, vT_3x3, u_3x3);
transpose3x3(vT_3x3, vT_3x3);
// re-create the flip
if (d < 0) {
w_3[0] = -w_3[0];
w_3[1] = -w_3[1];
w_3[2] = -w_3[2];
}
}
/**
* Factor linear equations Ax = b using LU decomposition A = LU. Output factorization LU is in matrix A.
* @param {Matrix} A square matrix
* @param {Number} index integer array of pivot indices index[0->n-1]
* @param {Number} size matrix size
*/
export function luFactorLinearSystem(A, index, size) {
let i;
let j;
let k;
let largest;
let maxI = 0;
let sum;
let temp1;
let temp2;
const scale = createArray(size);
//
// Loop over rows to get implicit scaling information
//
for (i = 0; i < size; i++) {
for (largest = 0.0, j = 0; j < size; j++) {
if ((temp2 = Math.abs(A[i * size + j])) > largest) {
largest = temp2;
}
}
Iif (largest === 0.0) {
vtkWarningMacro('Unable to factor linear system');
return 0;
}
scale[i] = 1.0 / largest;
}
//
// Loop over all columns using Crout's method
//
for (j = 0; j < size; j++) {
for (i = 0; i < j; i++) {
sum = A[i * size + j];
for (k = 0; k < i; k++) {
sum -= A[i * size + k] * A[k * size + j];
}
A[i * size + j] = sum;
}
//
// Begin search for largest pivot element
//
for (largest = 0.0, i = j; i < size; i++) {
sum = A[i * size + j];
for (k = 0; k < j; k++) {
sum -= A[i * size + k] * A[k * size + j];
}
A[i * size + j] = sum;
if ((temp1 = scale[i] * Math.abs(sum)) >= largest) {
largest = temp1;
maxI = i;
}
}
//
// Check for row interchange
//
if (j !== maxI) {
for (k = 0; k < size; k++) {
temp1 = A[maxI * size + k];
A[maxI * size + k] = A[j * size + k];
A[j * size + k] = temp1;
}
scale[maxI] = scale[j];
}
//
// Divide by pivot element and perform elimination
//
index[j] = maxI;
Iif (Math.abs(A[j * size + j]) <= VTK_SMALL_NUMBER) {
vtkWarningMacro('Unable to factor linear system');
return 0;
}
if (j !== size - 1) {
temp1 = 1.0 / A[j * size + j];
for (i = j + 1; i < size; i++) {
A[i * size + j] *= temp1;
}
}
}
return 1;
}
export function luSolveLinearSystem(A, index, x, size) {
let i;
let j;
let ii;
let idx;
let sum;
//
// Proceed with forward and backsubstitution for L and U
// matrices. First, forward substitution.
//
for (ii = -1, i = 0; i < size; i++) {
idx = index[i];
sum = x[idx];
x[idx] = x[i];
if (ii >= 0) {
for (j = ii; j <= i - 1; j++) {
sum -= A[i * size + j] * x[j];
}
} else if (sum !== 0.0) {
ii = i;
}
x[i] = sum;
}
//
// Now, back substitution
//
for (i = size - 1; i >= 0; i--) {
sum = x[i];
for (j = i + 1; j < size; j++) {
sum -= A[i * size + j] * x[j];
}
x[i] = sum / A[i * size + i];
}
}
export function solveLinearSystem(A, x, size) {
// if we solving something simple, just solve it
if (size === 2) {
const y = createArray(2);
const det = determinant2x2(A[0], A[1], A[2], A[3]);
if (det === 0.0) {
// Unable to solve linear system
return 0;
}
y[0] = (A[3] * x[0] - A[1] * x[1]) / det;
y[1] = (-(A[2] * x[0]) + A[0] * x[1]) / det;
x[0] = y[0];
x[1] = y[1];
return 1;
}
if (size === 1) {
if (A[0] === 0.0) {
// Unable to solve linear system
return 0;
}
x[0] /= A[0];
return 1;
}
//
// System of equations is not trivial, use Crout's method
//
// Check on allocation of working vectors
const index = createArray(size);
// Factor and solve matrix
Iif (luFactorLinearSystem(A, index, size) === 0) {
return 0;
}
luSolveLinearSystem(A, index, x, size);
return 1;
}
// Note that A is modified during the inversion !
export function invertMatrix(A, AI, size, index = null, column = null) {
const tmp1Size = index || createArray(size);
const tmp2Size = column || createArray(size);
// Factor matrix; then begin solving for inverse one column at a time.
// Note: tmp1Size returned value is used later, tmp2Size is just working
// memory whose values are not used in LUSolveLinearSystem
Iif (luFactorLinearSystem(A, tmp1Size, size, tmp2Size) === 0) {
return null;
}
for (let j = 0; j < size; j++) {
for (let i = 0; i < size; i++) {
tmp2Size[i] = 0.0;
}
tmp2Size[j] = 1.0;
luSolveLinearSystem(A, tmp1Size, tmp2Size, size);
for (let i = 0; i < size; i++) {
AI[i * size + j] = tmp2Size[i];
}
}
return AI;
}
export function estimateMatrixCondition(A, size) {
let minValue = +Number.MAX_VALUE;
let maxValue = -Number.MAX_VALUE;
// find the maximum value
for (let i = 0; i < size; i++) {
for (let j = i; j < size; j++) {
if (Math.abs(A[i * size + j]) > maxValue) {
maxValue = Math.abs(A[i * size + j]);
}
}
}
// find the minimum diagonal value
for (let i = 0; i < size; i++) {
if (Math.abs(A[i * size + i]) < minValue) {
minValue = Math.abs(A[i * size + i]);
}
}
if (minValue === 0.0) {
return Number.MAX_VALUE;
}
return maxValue / minValue;
}
export function jacobi(a_3x3, w, v) {
return jacobiN(a_3x3, 3, w, v);
}
export function solveHomogeneousLeastSquares(numberOfSamples, xt, xOrder, mt) {
// check dimensional consistency
if (numberOfSamples < xOrder) {
vtkWarningMacro('Insufficient number of samples. Underdetermined.');
return 0;
}
let i;
let j;
let k;
// set up intermediate variables
// Allocate matrix to hold X times transpose of X
const XXt = createArray(xOrder * xOrder); // size x by x
// Allocate the array of eigenvalues and eigenvectors
const eigenvals = createArray(xOrder);
const eigenvecs = createArray(xOrder * xOrder);
// Calculate XXt upper half only, due to symmetry
for (k = 0; k < numberOfSamples; k++) {
for (i = 0; i < xOrder; i++) {
for (j = i; j < xOrder; j++) {
XXt[i * xOrder + j] += xt[k * xOrder + i] * xt[k * xOrder + j];
}
}
}
// now fill in the lower half of the XXt matrix
for (i = 0; i < xOrder; i++) {
for (j = 0; j < i; j++) {
XXt[i * xOrder + j] = XXt[j * xOrder + i];
}
}
// Compute the eigenvectors and eigenvalues
jacobiN(XXt, xOrder, eigenvals, eigenvecs);
// Smallest eigenval is at the end of the list (xOrder-1), and solution is
// corresponding eigenvec.
for (i = 0; i < xOrder; i++) {
mt[i] = eigenvecs[i * xOrder + xOrder - 1];
}
return 1;
}
export function solveLeastSquares(
numberOfSamples,
xt,
xOrder,
yt,
yOrder,
mt,
checkHomogeneous = true
) {
// check dimensional consistency
if (numberOfSamples < xOrder || numberOfSamples < yOrder) {
vtkWarningMacro('Insufficient number of samples. Underdetermined.');
return 0;
}
const homogenFlags = createArray(yOrder);
let allHomogeneous = 1;
let hmt;
let homogRC = 0;
let i;
let j;
let k;
let someHomogeneous = 0;
// Ok, first init some flags check and see if all the systems are homogeneous
if (checkHomogeneous) {
// If Y' is zero, it's a homogeneous system and can't be solved via
// the pseudoinverse method. Detect this case, warn the user, and
// invoke SolveHomogeneousLeastSquares instead. Note that it doesn't
// really make much sense for yOrder to be greater than one in this case,
// since that's just yOrder occurrences of a 0 vector on the RHS, but
// we allow it anyway. N
// Initialize homogeneous flags on a per-right-hand-side basis
for (j = 0; j < yOrder; j++) {
homogenFlags[j] = 1;
}
for (i = 0; i < numberOfSamples; i++) {
for (j = 0; j < yOrder; j++) {
if (Math.abs(yt[i * yOrder + j]) > VTK_SMALL_NUMBER) {
allHomogeneous = 0;
homogenFlags[j] = 0;
}
}
}
// If we've got one system, and it's homogeneous, do it and bail out quickly.
if (allHomogeneous && yOrder === 1) {
vtkWarningMacro(
'Detected homogeneous system (Y=0), calling SolveHomogeneousLeastSquares()'
);
return solveHomogeneousLeastSquares(numberOfSamples, xt, xOrder, mt);
}
// Ok, we've got more than one system of equations.
// Figure out if we need to calculate the homogeneous equation solution for
// any of them.
Iif (allHomogeneous) {
someHomogeneous = 1;
} else {
for (j = 0; j < yOrder; j++) {
Iif (homogenFlags[j]) {
someHomogeneous = 1;
}
}
}
}
// If necessary, solve the homogeneous problem
Iif (someHomogeneous) {
// hmt is the homogeneous equation version of mt, the general solution.
// hmt should be xOrder x yOrder, but since we are solving only the homogeneous part, here it is xOrder x 1
hmt = createArray(xOrder);
// Ok, solve the homogeneous problem
homogRC = solveHomogeneousLeastSquares(numberOfSamples, xt, xOrder, hmt);
}
// set up intermediate variables
const XXt = createArray(xOrder * xOrder); // size x by x
const XXtI = createArray(xOrder * xOrder); // size x by x
const XYt = createArray(xOrder * yOrder); // size x by y
// first find the pseudoinverse matrix
for (k = 0; k < numberOfSamples; k++) {
for (i = 0; i < xOrder; i++) {
// first calculate the XXt matrix, only do the upper half (symmetrical)
for (j = i; j < xOrder; j++) {
XXt[i * xOrder + j] += xt[k * xOrder + i] * xt[k * xOrder + j];
}
// now calculate the XYt matrix
for (j = 0; j < yOrder; j++) {
XYt[i * yOrder + j] += xt[k * xOrder + i] * yt[k * yOrder + j];
}
}
}
// now fill in the lower half of the XXt matrix
for (i = 0; i < xOrder; i++) {
for (j = 0; j < i; j++) {
XXt[i * xOrder + j] = XXt[j * xOrder + i];
}
}
const successFlag = invertMatrix(XXt, XXtI, xOrder);
// next get the inverse of XXt
if (successFlag) {
for (i = 0; i < xOrder; i++) {
for (j = 0; j < yOrder; j++) {
mt[i * yOrder + j] = 0.0;
for (k = 0; k < xOrder; k++) {
mt[i * yOrder + j] += XXtI[i * xOrder + k] * XYt[k * yOrder + j];
}
}
}
}
// Fix up any of the solutions that correspond to the homogeneous equation
// problem.
Iif (someHomogeneous) {
for (j = 0; j < yOrder; j++) {
if (homogenFlags[j]) {
// Fix this one
for (i = 0; i < xOrder; i++) {
mt[i * yOrder + j] = hmt[i * yOrder];
}
}
}
}
Iif (someHomogeneous) {
return homogRC && successFlag;
}
return successFlag;
}
export function hex2float(hexStr, outFloatArray = [0, 0.5, 1]) {
switch (hexStr.length) {
case 3: // abc => #aabbcc
outFloatArray[0] = (parseInt(hexStr[0], 16) * 17) / 255;
outFloatArray[1] = (parseInt(hexStr[1], 16) * 17) / 255;
outFloatArray[2] = (parseInt(hexStr[2], 16) * 17) / 255;
return outFloatArray;
case 4: // #abc => #aabbcc
outFloatArray[0] = (parseInt(hexStr[1], 16) * 17) / 255;
outFloatArray[1] = (parseInt(hexStr[2], 16) * 17) / 255;
outFloatArray[2] = (parseInt(hexStr[3], 16) * 17) / 255;
return outFloatArray;
case 6: // ab01df => #ab01df
outFloatArray[0] = parseInt(hexStr.substr(0, 2), 16) / 255;
outFloatArray[1] = parseInt(hexStr.substr(2, 2), 16) / 255;
outFloatArray[2] = parseInt(hexStr.substr(4, 2), 16) / 255;
return outFloatArray;
case 7: // #ab01df
outFloatArray[0] = parseInt(hexStr.substr(1, 2), 16) / 255;
outFloatArray[1] = parseInt(hexStr.substr(3, 2), 16) / 255;
outFloatArray[2] = parseInt(hexStr.substr(5, 2), 16) / 255;
return outFloatArray;
case 9: // #ab01df00
outFloatArray[0] = parseInt(hexStr.substr(1, 2), 16) / 255;
outFloatArray[1] = parseInt(hexStr.substr(3, 2), 16) / 255;
outFloatArray[2] = parseInt(hexStr.substr(5, 2), 16) / 255;
outFloatArray[3] = parseInt(hexStr.substr(7, 2), 16) / 255;
return outFloatArray;
default:
return outFloatArray;
}
}
export function rgb2hsv(rgb, hsv) {
let h;
let s;
const [r, g, b] = rgb;
const onethird = 1.0 / 3.0;
const onesixth = 1.0 / 6.0;
const twothird = 2.0 / 3.0;
let cmax = r;
let cmin = r;
if (g > cmax) {
cmax = g;
} else if (g < cmin) {
cmin = g;
}
if (b > cmax) {
cmax = b;
} else if (b < cmin) {
cmin = b;
}
const v = cmax;
if (v > 0.0) {
s = (cmax - cmin) / cmax;
} else E{
s = 0.0;
}
if (s > 0) {
if (r === cmax) {
h = (onesixth * (g - b)) / (cmax - cmin);
} else if (g === cmax) {
h = onethird + (onesixth * (b - r)) / (cmax - cmin);
} else {
h = twothird + (onesixth * (r - g)) / (cmax - cmin);
}
if (h < 0.0) {
h += 1.0;
}
} else E{
h = 0.0;
}
// Set the values back to the array
hsv[0] = h;
hsv[1] = s;
hsv[2] = v;
}
export function hsv2rgb(hsv, rgb) {
const [h, s, v] = hsv;
const onethird = 1.0 / 3.0;
const onesixth = 1.0 / 6.0;
const twothird = 2.0 / 3.0;
const fivesixth = 5.0 / 6.0;
let r;
let g;
let b;
// compute RGB from HSV
if (h > onesixth && h <= onethird) {
// green/red
g = 1.0;
r = (onethird - h) / onesixth;
b = 0.0;
} else if (h > onethird && h <= 0.5) {
// green/blue
g = 1.0;
b = (h - onethird) / onesixth;
r = 0.0;
} else if (h > 0.5 && h <= twothird) {
// blue/green
b = 1.0;
g = (twothird - h) / onesixth;
r = 0.0;
} else if (h > twothird && h <= fivesixth) {
// blue/red
b = 1.0;
r = (h - twothird) / onesixth;
g = 0.0;
} else if (h > fivesixth && h <= 1.0) {
// red/blue
r = 1.0;
b = (1.0 - h) / onesixth;
g = 0.0;
} else {
// red/green
r = 1.0;
g = h / onesixth;
b = 0.0;
}
// add Saturation to the equation.
r = s * r + (1.0 - s);
g = s * g + (1.0 - s);
b = s * b + (1.0 - s);
r *= v;
g *= v;
b *= v;
// Assign back to the array
rgb[0] = r;
rgb[1] = g;
rgb[2] = b;
}
export function lab2xyz(lab, xyz) {
// LAB to XYZ
const [L, a, b] = lab;
let var_Y = (L + 16) / 116;
let var_X = a / 500 + var_Y;
let var_Z = var_Y - b / 200;
if (var_Y ** 3 > 0.008856) {
var_Y **= 3;
} else {
var_Y = (var_Y - 16.0 / 116.0) / 7.787;
}
if (var_X ** 3 > 0.008856) {
var_X **= 3;
} else {
var_X = (var_X - 16.0 / 116.0) / 7.787;
}
if (var_Z ** 3 > 0.008856) {
var_Z **= 3;
} else {
var_Z = (var_Z - 16.0 / 116.0) / 7.787;
}
const ref_X = 0.9505;
const ref_Y = 1.0;
const ref_Z = 1.089;
xyz[0] = ref_X * var_X; // ref_X = 0.9505 Observer= 2 deg Illuminant= D65
xyz[1] = ref_Y * var_Y; // ref_Y = 1.000
xyz[2] = ref_Z * var_Z; // ref_Z = 1.089
}
export function xyz2lab(xyz, lab) {
const [x, y, z] = xyz;
const ref_X = 0.9505;
const ref_Y = 1.0;
const ref_Z = 1.089;
let var_X = x / ref_X; // ref_X = 0.9505 Observer= 2 deg, Illuminant= D65
let var_Y = y / ref_Y; // ref_Y = 1.000
let var_Z = z / ref_Z; // ref_Z = 1.089
if (var_X > 0.008856) var_X **= 1.0 / 3.0;
else var_X = 7.787 * var_X + 16.0 / 116.0;
if (var_Y > 0.008856) var_Y **= 1.0 / 3.0;
else var_Y = 7.787 * var_Y + 16.0 / 116.0;
if (var_Z > 0.008856) var_Z **= 1.0 / 3.0;
else var_Z = 7.787 * var_Z + 16.0 / 116.0;
lab[0] = 116 * var_Y - 16;
lab[1] = 500 * (var_X - var_Y);
lab[2] = 200 * (var_Y - var_Z);
}
export function xyz2rgb(xyz, rgb) {
const [x, y, z] = xyz;
let r = x * 3.2406 + y * -1.5372 + z * -0.4986;
let g = x * -0.9689 + y * 1.8758 + z * 0.0415;
let b = x * 0.0557 + y * -0.204 + z * 1.057;
// The following performs a "gamma correction" specified by the sRGB color
// space. sRGB is defined by a canonical definition of a display monitor and
// has been standardized by the International Electrotechnical Commission (IEC
// 61966-2-1). The nonlinearity of the correction is designed to make the
// colors more perceptually uniform. This color space has been adopted by
// several applications including Adobe Photoshop and Microsoft Windows color
// management. OpenGL is agnostic on its RGB color space, but it is reasonable
// to assume it is close to this one.
if (r > 0.0031308) r = 1.055 * r ** (1 / 2.4) - 0.055;
else r *= 12.92;
if (g > 0.0031308) g = 1.055 * g ** (1 / 2.4) - 0.055;
else g *= 12.92;
if (b > 0.0031308) b = 1.055 * b ** (1 / 2.4) - 0.055;
else b *= 12.92;
// Clip colors. ideally we would do something that is perceptually closest
// (since we can see colors outside of the display gamut), but this seems to
// work well enough.
let maxVal = r;
if (maxVal < g) maxVal = g;
if (maxVal < b) maxVal = b;
if (maxVal > 1.0) {
r /= maxVal;
g /= maxVal;
b /= maxVal;
}
if (r < 0) r = 0;
if (g < 0) g = 0;
if (b < 0) b = 0;
// Push values back to array
rgb[0] = r;
rgb[1] = g;
rgb[2] = b;
}
export function rgb2xyz(rgb, xyz) {
let [r, g, b] = rgb;
// The following performs a "gamma correction" specified by the sRGB color
// space. sRGB is defined by a canonical definition of a display monitor and
// has been standardized by the International Electrotechnical Commission (IEC
// 61966-2-1). The nonlinearity of the correction is designed to make the
// colors more perceptually uniform. This color space has been adopted by
// several applications including Adobe Photoshop and Microsoft Windows color
// management. OpenGL is agnostic on its RGB color space, but it is reasonable
// to assume it is close to this one.
if (r > 0.04045) r = ((r + 0.055) / 1.055) ** 2.4;
else r /= 12.92;
if (g > 0.04045) g = ((g + 0.055) / 1.055) ** 2.4;
else g /= 12.92;
if (b > 0.04045) b = ((b + 0.055) / 1.055) ** 2.4;
else b /= 12.92;
// Observer. = 2 deg, Illuminant = D65
xyz[0] = r * 0.4124 + g * 0.3576 + b * 0.1805;
xyz[1] = r * 0.2126 + g * 0.7152 + b * 0.0722;
xyz[2] = r * 0.0193 + g * 0.1192 + b * 0.9505;
}
export function rgb2lab(rgb, lab) {
const xyz = [0, 0, 0];
rgb2xyz(rgb, xyz);
xyz2lab(xyz, lab);
}
export function lab2rgb(lab, rgb) {
const xyz = [0, 0, 0];
lab2xyz(lab, xyz);
xyz2rgb(xyz, rgb);
}
export function uninitializeBounds(bounds) {
bounds[0] = 1.0;
bounds[1] = -1.0;
bounds[2] = 1.0;
bounds[3] = -1.0;
bounds[4] = 1.0;
bounds[5] = -1.0;
return bounds;
}
export function areBoundsInitialized(bounds) {
return !(bounds[1] - bounds[0] < 0.0);
}
/**
* @deprecated please use vtkBoundingBox.addPoints(vtkBoundingBox.reset([]), points)
*/
export function computeBoundsFromPoints(point1, point2, bounds) {
bounds[0] = Math.min(point1[0], point2[0]);
bounds[1] = Math.max(point1[0], point2[0]);
bounds[2] = Math.min(point1[1], point2[1]);
bounds[3] = Math.max(point1[1], point2[1]);
bounds[4] = Math.min(point1[2], point2[2]);
bounds[5] = Math.max(point1[2], point2[2]);
return bounds;
}
export function clampValue(value, minValue, maxValue) {
if (value < minValue) {
return minValue;
}
if (value > maxValue) {
return maxValue;
}
return value;
}
export function clampVector(vector, minVector, maxVector, out = [0, 0, 0]) {
out[0] = clampValue(vector[0], minVector[0], maxVector[0]);
out[1] = clampValue(vector[1], minVector[1], maxVector[1]);
out[2] = clampValue(vector[2], minVector[2], maxVector[2]);
return out;
}
export function clampAndNormalizeValue(value, range) {
let result = 0;
if (range[0] !== range[1]) {
// clamp
if (value < range[0]) {
result = range[0];
} else if (value > range[1]) {
result = range[1];
} else {
result = value;
}
// normalize
result = (result - range[0]) / (range[1] - range[0]);
}
return result;
}
export const getScalarTypeFittingRange = notImplemented(
'GetScalarTypeFittingRange'
);
export const getAdjustedScalarRange = notImplemented('GetAdjustedScalarRange');
export function extentIsWithinOtherExtent(extent1, extent2) {
if (!extent1 || !extent2) {
return 0;
}
for (let i = 0; i < 6; i += 2) {
if (
extent1[i] < extent2[i] ||
extent1[i] > extent2[i + 1] ||
extent1[i + 1] < extent2[i] ||
extent1[i + 1] > extent2[i + 1]
) {
return 0;
}
}
return 1;
}
export function boundsIsWithinOtherBounds(bounds1_6, bounds2_6, delta_3) {
if (!bounds1_6 || !bounds2_6) {
return 0;
}
for (let i = 0; i < 6; i += 2) {
if (
bounds1_6[i] + delta_3[i / 2] < bounds2_6[i] ||
bounds1_6[i] - delta_3[i / 2] > bounds2_6[i + 1] ||
bounds1_6[i + 1] + delta_3[i / 2] < bounds2_6[i] ||
bounds1_6[i + 1] - delta_3[i / 2] > bounds2_6[i + 1]
) {
return 0;
}
}
return 1;
}
export function pointIsWithinBounds(point_3, bounds_6, delta_3) {
if (!point_3 || !bounds_6 || !delta_3) {
return 0;
}
for (let i = 0; i < 3; i++) {
if (
point_3[i] + delta_3[i] < bounds_6[2 * i] ||
point_3[i] - delta_3[i] > bounds_6[2 * i + 1]
) {
return 0;
}
}
return 1;
}
export function solve3PointCircle(p1, p2, p3, center) {
const v21 = createArray(3);
const v32 = createArray(3);
const v13 = createArray(3);
const v12 = createArray(3);
const v23 = createArray(3);
const v31 = createArray(3);
for (let i = 0; i < 3; ++i) {
v21[i] = p1[i] - p2[i];
v32[i] = p2[i] - p3[i];
v13[i] = p3[i] - p1[i];
v12[i] = -v21[i];
v23[i] = -v32[i];
v31[i] = -v13[i];
}
const norm12 = norm(v12);
const norm23 = norm(v23);
const norm13 = norm(v13);
const crossv21v32 = createArray(3);
cross(v21, v32, crossv21v32);
const normCross = norm(crossv21v32);
const radius = (norm12 * norm23 * norm13) / (2 * normCross);
const normCross22 = 2 * normCross * normCross;
const alpha = (norm23 * norm23 * dot(v21, v31)) / normCross22;
const beta = (norm13 * norm13 * dot(v12, v32)) / normCross22;
const gamma = (norm12 * norm12 * dot(v13, v23)) / normCross22;
for (let i = 0; i < 3; ++i) {
center[i] = alpha * p1[i] + beta * p2[i] + gamma * p3[i];
}
return radius;
}
export const inf = Infinity;
export const negInf = -Infinity;
export const isInf = (value) => !Number.isFinite(value);
export const { isFinite, isNaN } = Number;
export const isNan = isNaN;
// JavaScript - add-on ----------------------
export function createUninitializedBounds() {
return [].concat([
Number.MAX_VALUE,
-Number.MAX_VALUE, // X
Number.MAX_VALUE,
-Number.MAX_VALUE, // Y
Number.MAX_VALUE,
-Number.MAX_VALUE, // Z
]);
}
export function getMajorAxisIndex(vector) {
let maxValue = -1;
let axisIndex = -1;
for (let i = 0; i < vector.length; i++) {
const value = Math.abs(vector[i]);
if (value > maxValue) {
axisIndex = i;
maxValue = value;
}
}
return axisIndex;
}
// Return the closest orthogonal matrix of 1, -1 and 0
// It works for both column major and row major matrices
// This function iteratively associate a column with a row by choosing
// the greatest absolute value from the remaining row and columns
// For each association, a -1 or a 1 is set in the output, depending on
// the sign of the value in the original matrix
export function getSparseOrthogonalMatrix(matrix, n = 3) {
// Initialize rows and columns to available indices
const rows = new Array(n);
const cols = new Array(n);
for (let i = 0; i < n; ++i) {
rows[i] = i;
cols[i] = i;
}
// No need for the last iteration: i = 0
for (let i = n - 1; i > 0; i--) {
// Loop invariant:
// rows[0:i] and cols[0:i] contain the remaining rows and columns
// rows]i:n[ and cols]i:n[ contain the associations found (rows[k] is associated with cols[k])
let bestValue = -Infinity;
let bestRowI = 0;
let bestColI = 0;
for (let rowI = 0; rowI <= i; ++rowI) {
const row = rows[rowI];
for (let colI = 0; colI <= i; ++colI) {
const col = cols[colI];
const absVal = Math.abs(matrix[row + n * col]);
if (absVal > bestValue) {
bestValue = absVal;
bestRowI = rowI;
bestColI = colI;
}
}
}
// Found an association between rows[bestRowI] and cols[bestColI]
// Put both at the end of their array by swapping with i
[rows[i], rows[bestRowI]] = [rows[bestRowI], rows[i]];
[cols[i], cols[bestColI]] = [cols[bestColI], cols[i]];
}
// Convert row/column association to a matrix
const output = new Array(n * n).fill(0);
for (let i = 0; i < n; ++i) {
const matIdx = rows[i] + n * cols[i];
output[matIdx] = matrix[matIdx] < 0 ? -1 : 1;
}
return output;
}
export function floatToHex2(value) {
const integer = Math.floor(value * 255);
if (integer > 15) {
return integer.toString(16);
}
return `0${integer.toString(16)}`;
}
export function floatRGB2HexCode(rgbArray, prefix = '#') {
return `${prefix}${rgbArray.map(floatToHex2).join('')}`;
}
function floatToChar(f) {
return Math.round(f * 255);
}
export function float2CssRGBA(rgbArray) {
if (rgbArray.length === 3) {
return `rgb(${rgbArray.map(floatToChar).join(', ')})`;
}
return `rgba(${floatToChar(rgbArray[0] || 0)}, ${floatToChar(
rgbArray[1] || 0
)}, ${floatToChar(rgbArray[2] || 0)}, ${rgbArray[3] || 0})`;
}
// ----------------------------------------------------------------------------
// Only Static API
// ----------------------------------------------------------------------------
export default {
Pi,
radiansFromDegrees,
degreesFromRadians,
round,
floor,
ceil,
ceilLog2,
min,
max,
arrayMin,
arrayMax,
arrayRange,
isPowerOfTwo,
nearestPowerOfTwo,
factorial,
binomial,
beginCombination,
nextCombination,
randomSeed,
getSeed,
random,
gaussian,
add,
subtract,
multiplyScalar,
multiplyScalar2D,
multiplyAccumulate,
multiplyAccumulate2D,
dot,
outer,
cross,
norm,
normalize,
perpendiculars,
projectVector,
projectVector2D,
distance2BetweenPoints,
angleBetweenVectors,
gaussianAmplitude,
gaussianWeight,
dot2D,
outer2D,
norm2D,
normalize2D,
determinant2x2,
LUFactor3x3,
LUSolve3x3,
linearSolve3x3,
multiply3x3_vect3,
multiply3x3_mat3,
multiplyMatrix,
transpose3x3,
invert3x3,
identity3x3,
identity,
isIdentity,
isIdentity3x3,
determinant3x3,
quaternionToMatrix3x3,
areEquals,
areMatricesEqual,
roundNumber,
roundVector,
matrix3x3ToQuaternion,
multiplyQuaternion,
orthogonalize3x3,
diagonalize3x3,
singularValueDecomposition3x3,
solveLinearSystem,
invertMatrix,
luFactorLinearSystem,
luSolveLinearSystem,
estimateMatrixCondition,
jacobi,
jacobiN,
solveHomogeneousLeastSquares,
solveLeastSquares,
hex2float,
rgb2hsv,
hsv2rgb,
lab2xyz,
xyz2lab,
xyz2rgb,
rgb2xyz,
rgb2lab,
lab2rgb,
uninitializeBounds,
areBoundsInitialized,
computeBoundsFromPoints,
clampValue,
clampVector,
clampAndNormalizeValue,
getScalarTypeFittingRange,
getAdjustedScalarRange,
extentIsWithinOtherExtent,
boundsIsWithinOtherBounds,
pointIsWithinBounds,
solve3PointCircle,
inf,
negInf,
isInf,
isNan: isNaN,
isNaN,
isFinite,
// JS add-on
createUninitializedBounds,
getMajorAxisIndex,
getSparseOrthogonalMatrix,
floatToHex2,
floatRGB2HexCode,
float2CssRGBA,
};
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