molstar
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A comprehensive macromolecular library.
138 lines (137 loc) • 6.3 kB
JavaScript
"use strict";
/**
* Copyright (c) 2018-2022 mol* contributors, licensed under MIT, See LICENSE file for more info.
*
* @author Alexander Rose <alexander.rose@weirdbyte.de>
*/
Object.defineProperty(exports, "__esModule", { value: true });
exports.PrincipalAxes = void 0;
var matrix_1 = require("./matrix");
var vec3_1 = require("../3d/vec3");
var svd_1 = require("./svd");
var geometry_1 = require("../../geometry");
var common_1 = require("../3d/common");
var PrincipalAxes;
(function (PrincipalAxes) {
function ofPositions(positions) {
var momentsAxes = calculateMomentsAxes(positions);
var boxAxes = calculateBoxAxes(positions, momentsAxes);
return { momentsAxes: momentsAxes, boxAxes: boxAxes };
}
PrincipalAxes.ofPositions = ofPositions;
function calculateMomentsAxes(positions) {
if (positions.length === 3) {
return geometry_1.Axes3D.create(vec3_1.Vec3.fromArray((0, vec3_1.Vec3)(), positions, 0), vec3_1.Vec3.create(1, 0, 0), vec3_1.Vec3.create(0, 1, 0), vec3_1.Vec3.create(0, 1, 0));
}
var points = matrix_1.Matrix.fromArray(positions, 3, positions.length / 3);
var n = points.rows;
var n3 = n / 3;
var A = matrix_1.Matrix.create(3, 3);
var W = matrix_1.Matrix.create(1, 3);
var U = matrix_1.Matrix.create(3, 3);
var V = matrix_1.Matrix.create(3, 3);
// calculate
var mean = matrix_1.Matrix.meanRows(points);
var pointsM = matrix_1.Matrix.subRows(matrix_1.Matrix.clone(points), mean);
var pointsT = matrix_1.Matrix.transpose(matrix_1.Matrix.create(n, 3), pointsM);
matrix_1.Matrix.multiplyABt(A, pointsT, pointsT);
(0, svd_1.svd)(A, W, U, V);
// origin
var origin = vec3_1.Vec3.create(mean[0], mean[1], mean[2]);
// directions
var dirA = vec3_1.Vec3.create(U.data[0], U.data[3], U.data[6]);
var dirB = vec3_1.Vec3.create(U.data[1], U.data[4], U.data[7]);
var dirC = vec3_1.Vec3.create(U.data[2], U.data[5], U.data[8]);
vec3_1.Vec3.scale(dirA, dirA, Math.sqrt(W.data[0] / n3));
vec3_1.Vec3.scale(dirB, dirB, Math.sqrt(W.data[1] / n3));
vec3_1.Vec3.scale(dirC, dirC, Math.sqrt(W.data[2] / n3));
return geometry_1.Axes3D.create(origin, dirA, dirB, dirC);
}
PrincipalAxes.calculateMomentsAxes = calculateMomentsAxes;
function calculateNormalizedAxes(momentsAxes) {
var a = geometry_1.Axes3D.clone(momentsAxes);
if (vec3_1.Vec3.magnitude(a.dirC) < common_1.EPSILON) {
vec3_1.Vec3.cross(a.dirC, a.dirA, a.dirB);
}
return geometry_1.Axes3D.normalize(a, a);
}
PrincipalAxes.calculateNormalizedAxes = calculateNormalizedAxes;
var tmpBoxVec = (0, vec3_1.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 geometry_1.Axes3D.clone(momentsAxes);
}
var d1a = -Infinity;
var d1b = -Infinity;
var d2a = -Infinity;
var d2b = -Infinity;
var d3a = -Infinity;
var d3b = -Infinity;
var p = (0, vec3_1.Vec3)();
var t = (0, vec3_1.Vec3)();
var center = momentsAxes.origin;
var a = calculateNormalizedAxes(momentsAxes);
for (var i = 0, il = positions.length; i < il; i += 3) {
vec3_1.Vec3.projectPointOnVector(p, vec3_1.Vec3.fromArray(p, positions, i), a.dirA, center);
var dp1 = vec3_1.Vec3.dot(a.dirA, vec3_1.Vec3.normalize(t, vec3_1.Vec3.sub(t, p, center)));
var dt1 = vec3_1.Vec3.distance(p, center);
if (dp1 > 0) {
if (dt1 > d1a)
d1a = dt1;
}
else {
if (dt1 > d1b)
d1b = dt1;
}
vec3_1.Vec3.projectPointOnVector(p, vec3_1.Vec3.fromArray(p, positions, i), a.dirB, center);
var dp2 = vec3_1.Vec3.dot(a.dirB, vec3_1.Vec3.normalize(t, vec3_1.Vec3.sub(t, p, center)));
var dt2 = vec3_1.Vec3.distance(p, center);
if (dp2 > 0) {
if (dt2 > d2a)
d2a = dt2;
}
else {
if (dt2 > d2b)
d2b = dt2;
}
vec3_1.Vec3.projectPointOnVector(p, vec3_1.Vec3.fromArray(p, positions, i), a.dirC, center);
var dp3 = vec3_1.Vec3.dot(a.dirC, vec3_1.Vec3.normalize(t, vec3_1.Vec3.sub(t, p, center)));
var dt3 = vec3_1.Vec3.distance(p, center);
if (dp3 > 0) {
if (dt3 > d3a)
d3a = dt3;
}
else {
if (dt3 > d3b)
d3b = dt3;
}
}
var dirA = vec3_1.Vec3.setMagnitude((0, vec3_1.Vec3)(), a.dirA, (d1a + d1b) / 2);
var dirB = vec3_1.Vec3.setMagnitude((0, vec3_1.Vec3)(), a.dirB, (d2a + d2b) / 2);
var dirC = vec3_1.Vec3.setMagnitude((0, vec3_1.Vec3)(), a.dirC, (d3a + d3b) / 2);
var origin = (0, vec3_1.Vec3)();
var addCornerHelper = function (d1, d2, d3) {
vec3_1.Vec3.copy(tmpBoxVec, center);
vec3_1.Vec3.scaleAndAdd(tmpBoxVec, tmpBoxVec, a.dirA, d1);
vec3_1.Vec3.scaleAndAdd(tmpBoxVec, tmpBoxVec, a.dirB, d2);
vec3_1.Vec3.scaleAndAdd(tmpBoxVec, tmpBoxVec, a.dirC, d3);
vec3_1.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_1.Vec3.scale(origin, origin, 1 / 8);
return geometry_1.Axes3D.create(origin, dirA, dirB, dirC);
}
PrincipalAxes.calculateBoxAxes = calculateBoxAxes;
})(PrincipalAxes || (PrincipalAxes = {}));
exports.PrincipalAxes = PrincipalAxes;