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molstar

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A comprehensive macromolecular library.

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/** * Copyright (c) 2018-2023 mol* contributors, licensed under MIT, See LICENSE file for more info. * * @author Alexander Rose <alexander.rose@weirdbyte.de> * @author Gianluca Tomasello <giagitom@gmail.com> */ import { Matrix } from './matrix'; import { Vec3 } from '../3d/vec3'; import { svd } from './svd'; import { Axes3D } from '../../geometry'; import { EPSILON } from '../3d/common'; export { PrincipalAxes }; var PrincipalAxes; (function (PrincipalAxes) { function ofPositions(positions) { const momentsAxes = calculateMomentsAxes(positions); const boxAxes = calculateBoxAxes(positions, momentsAxes); return { momentsAxes, boxAxes }; } PrincipalAxes.ofPositions = ofPositions; function calculateMomentsAxes(positions) { if (positions.length === 3) { return Axes3D.create(Vec3.fromArray(Vec3(), positions, 0), Vec3.create(1, 0, 0), Vec3.create(0, 1, 0), Vec3.create(0, 0, 1)); } const points = Matrix.fromArray(positions, 3, positions.length / 3); const n = points.rows; const n3 = n / 3; const A = Matrix.create(3, 3); const W = Matrix.create(1, 3); const U = Matrix.create(3, 3); const V = Matrix.create(3, 3); // calculate const mean = Matrix.meanRows(points); const pointsM = Matrix.subRows(Matrix.clone(points), mean); const pointsT = Matrix.transpose(Matrix.create(n, 3), pointsM); Matrix.multiplyABt(A, pointsT, pointsT); svd(A, W, U, V); // origin const origin = Vec3.create(mean[0], mean[1], mean[2]); // directions const dirA = Vec3.create(U.data[0], U.data[3], U.data[6]); const dirB = Vec3.create(U.data[1], U.data[4], U.data[7]); const dirC = Vec3.create(U.data[2], U.data[5], U.data[8]); Vec3.scale(dirA, dirA, Math.sqrt(W.data[0] / n3)); Vec3.scale(dirB, dirB, Math.sqrt(W.data[1] / n3)); Vec3.scale(dirC, dirC, Math.sqrt(W.data[2] / n3)); return Axes3D.create(origin, dirA, dirB, dirC); } PrincipalAxes.calculateMomentsAxes = calculateMomentsAxes; function calculateNormalizedAxes(momentsAxes) { const a = Axes3D.clone(momentsAxes); if (Vec3.magnitude(a.dirC) < EPSILON) { Vec3.cross(a.dirC, a.dirA, a.dirB); } return Axes3D.normalize(a, a); } PrincipalAxes.calculateNormalizedAxes = calculateNormalizedAxes; const tmpBoxVec = Vec3(); /** * Get the scale/length for each dimension for a box around the axes * to enclose the given positions */ function calculateBoxAxes(positions, momentsAxes) { if (positions.length === 3) { return Axes3D.clone(momentsAxes); } let d1a = -Infinity; let d1b = -Infinity; let d2a = -Infinity; let d2b = -Infinity; let d3a = -Infinity; let d3b = -Infinity; const p = Vec3(); const t = Vec3(); const center = momentsAxes.origin; const a = calculateNormalizedAxes(momentsAxes); for (let i = 0, il = positions.length; i < il; i += 3) { Vec3.projectPointOnVector(p, Vec3.fromArray(p, positions, i), a.dirA, center); const dp1 = Vec3.dot(a.dirA, Vec3.normalize(t, Vec3.sub(t, p, center))); const dt1 = Vec3.distance(p, center); if (dp1 > 0) { if (dt1 > d1a) d1a = dt1; } else { if (dt1 > d1b) d1b = dt1; } Vec3.projectPointOnVector(p, Vec3.fromArray(p, positions, i), a.dirB, center); const dp2 = Vec3.dot(a.dirB, Vec3.normalize(t, Vec3.sub(t, p, center))); const dt2 = Vec3.distance(p, center); if (dp2 > 0) { if (dt2 > d2a) d2a = dt2; } else { if (dt2 > d2b) d2b = dt2; } Vec3.projectPointOnVector(p, Vec3.fromArray(p, positions, i), a.dirC, center); const dp3 = Vec3.dot(a.dirC, Vec3.normalize(t, Vec3.sub(t, p, center))); const dt3 = Vec3.distance(p, center); if (dp3 > 0) { if (dt3 > d3a) d3a = dt3; } else { if (dt3 > d3b) d3b = dt3; } } const dirA = Vec3.setMagnitude(Vec3(), a.dirA, (d1a + d1b) / 2); const dirB = Vec3.setMagnitude(Vec3(), a.dirB, (d2a + d2b) / 2); const dirC = Vec3.setMagnitude(Vec3(), a.dirC, (d3a + d3b) / 2); const okDirA = Vec3.isFinite(dirA); const okDirB = Vec3.isFinite(dirB); const okDirC = Vec3.isFinite(dirC); const origin = Vec3(); const addCornerHelper = function (d1, d2, d3) { Vec3.copy(tmpBoxVec, center); if (okDirA) Vec3.scaleAndAdd(tmpBoxVec, tmpBoxVec, a.dirA, d1); if (okDirB) Vec3.scaleAndAdd(tmpBoxVec, tmpBoxVec, a.dirB, d2); if (okDirC) Vec3.scaleAndAdd(tmpBoxVec, tmpBoxVec, a.dirC, d3); Vec3.add(origin, origin, tmpBoxVec); }; addCornerHelper(d1a, d2a, d3a); addCornerHelper(d1a, d2a, -d3b); addCornerHelper(d1a, -d2b, -d3b); addCornerHelper(d1a, -d2b, d3a); addCornerHelper(-d1b, -d2b, -d3b); addCornerHelper(-d1b, -d2b, d3a); addCornerHelper(-d1b, d2a, d3a); addCornerHelper(-d1b, d2a, -d3b); Vec3.scale(origin, origin, 1 / 8); return Axes3D.create(origin, dirA, dirB, dirC); } PrincipalAxes.calculateBoxAxes = calculateBoxAxes; })(PrincipalAxes || (PrincipalAxes = {}));