@openhps/core
Version:
Open Hybrid Positioning System - Core component
251 lines (235 loc) • 7.61 kB
JavaScript
"use strict";
Object.defineProperty(exports, "__esModule", {
value: true
});
exports.CatmullRomCurve3 = void 0;
var _Vector = require("../../math/Vector3.js");
var _Curve = require("../core/Curve.js");
function CubicPoly() {
/**
* Centripetal CatmullRom Curve - which is useful for avoiding
* cusps and self-intersections in non-uniform catmull rom curves.
* http://www.cemyuksel.com/research/catmullrom_param/catmullrom.pdf
*
* curve.type accepts centripetal(default), chordal and catmullrom
* curve.tension is used for catmullrom which defaults to 0.5
*/
/*
Based on an optimized c++ solution in
- http://stackoverflow.com/questions/9489736/catmull-rom-curve-with-no-cusps-and-no-self-intersections/
- http://ideone.com/NoEbVM
This CubicPoly class could be used for reusing some variables and calculations,
but for three.js curve use, it could be possible inlined and flatten into a single function call
which can be placed in CurveUtils.
*/
let c0 = 0,
c1 = 0,
c2 = 0,
c3 = 0;
/*
* Compute coefficients for a cubic polynomial
* p(s) = c0 + c1*s + c2*s^2 + c3*s^3
* such that
* p(0) = x0, p(1) = x1
* and
* p'(0) = t0, p'(1) = t1.
*/
function init(x0, x1, t0, t1) {
c0 = x0;
c1 = t0;
c2 = -3 * x0 + 3 * x1 - 2 * t0 - t1;
c3 = 2 * x0 - 2 * x1 + t0 + t1;
}
return {
initCatmullRom: function (x0, x1, x2, x3, tension) {
init(x1, x2, tension * (x2 - x0), tension * (x3 - x1));
},
initNonuniformCatmullRom: function (x0, x1, x2, x3, dt0, dt1, dt2) {
// compute tangents when parameterized in [t1,t2]
let t1 = (x1 - x0) / dt0 - (x2 - x0) / (dt0 + dt1) + (x2 - x1) / dt1;
let t2 = (x2 - x1) / dt1 - (x3 - x1) / (dt1 + dt2) + (x3 - x2) / dt2;
// rescale tangents for parametrization in [0,1]
t1 *= dt1;
t2 *= dt1;
init(x1, x2, t1, t2);
},
calc: function (t) {
const t2 = t * t;
const t3 = t2 * t;
return c0 + c1 * t + c2 * t2 + c3 * t3;
}
};
}
//
const tmp = /*@__PURE__*/new _Vector.Vector3();
const px = /*@__PURE__*/new CubicPoly();
const py = /*@__PURE__*/new CubicPoly();
const pz = /*@__PURE__*/new CubicPoly();
/**
* A curve representing a Catmull-Rom spline.
*
* ```js
* //Create a closed wavey loop
* const curve = new THREE.CatmullRomCurve3( [
* new THREE.Vector3( -10, 0, 10 ),
* new THREE.Vector3( -5, 5, 5 ),
* new THREE.Vector3( 0, 0, 0 ),
* new THREE.Vector3( 5, -5, 5 ),
* new THREE.Vector3( 10, 0, 10 )
* ] );
*
* const points = curve.getPoints( 50 );
* const geometry = new THREE.BufferGeometry().setFromPoints( points );
*
* const material = new THREE.LineBasicMaterial( { color: 0xff0000 } );
*
* // Create the final object to add to the scene
* const curveObject = new THREE.Line( geometry, material );
* ```
*
* @augments Curve
*/
class CatmullRomCurve3 extends _Curve.Curve {
/**
* Constructs a new Catmull-Rom curve.
*
* @param {Array<Vector3>} [points] - An array of 3D points defining the curve.
* @param {boolean} [closed=false] - Whether the curve is closed or not.
* @param {('centripetal'|'chordal'|'catmullrom')} [curveType='centripetal'] - The curve type.
* @param {number} [tension=0.5] - Tension of the curve.
*/
constructor(points = [], closed = false, curveType = 'centripetal', tension = 0.5) {
super();
/**
* This flag can be used for type testing.
*
* @type {boolean}
* @readonly
* @default true
*/
this.isCatmullRomCurve3 = true;
this.type = 'CatmullRomCurve3';
/**
* An array of 3D points defining the curve.
*
* @type {Array<Vector3>}
*/
this.points = points;
/**
* Whether the curve is closed or not.
*
* @type {boolean}
* @default false
*/
this.closed = closed;
/**
* The curve type.
*
* @type {('centripetal'|'chordal'|'catmullrom')}
* @default 'centripetal'
*/
this.curveType = curveType;
/**
* Tension of the curve.
*
* @type {number}
* @default 0.5
*/
this.tension = tension;
}
/**
* Returns a point on the curve.
*
* @param {number} t - A interpolation factor representing a position on the curve. Must be in the range `[0,1]`.
* @param {Vector3} [optionalTarget] - The optional target vector the result is written to.
* @return {Vector3} The position on the curve.
*/
getPoint(t, optionalTarget = new _Vector.Vector3()) {
const point = optionalTarget;
const points = this.points;
const l = points.length;
const p = (l - (this.closed ? 0 : 1)) * t;
let intPoint = Math.floor(p);
let weight = p - intPoint;
if (this.closed) {
intPoint += intPoint > 0 ? 0 : (Math.floor(Math.abs(intPoint) / l) + 1) * l;
} else if (weight === 0 && intPoint === l - 1) {
intPoint = l - 2;
weight = 1;
}
let p0, p3; // 4 points (p1 & p2 defined below)
if (this.closed || intPoint > 0) {
p0 = points[(intPoint - 1) % l];
} else {
// extrapolate first point
tmp.subVectors(points[0], points[1]).add(points[0]);
p0 = tmp;
}
const p1 = points[intPoint % l];
const p2 = points[(intPoint + 1) % l];
if (this.closed || intPoint + 2 < l) {
p3 = points[(intPoint + 2) % l];
} else {
// extrapolate last point
tmp.subVectors(points[l - 1], points[l - 2]).add(points[l - 1]);
p3 = tmp;
}
if (this.curveType === 'centripetal' || this.curveType === 'chordal') {
// init Centripetal / Chordal Catmull-Rom
const pow = this.curveType === 'chordal' ? 0.5 : 0.25;
let dt0 = Math.pow(p0.distanceToSquared(p1), pow);
let dt1 = Math.pow(p1.distanceToSquared(p2), pow);
let dt2 = Math.pow(p2.distanceToSquared(p3), pow);
// safety check for repeated points
if (dt1 < 1e-4) dt1 = 1.0;
if (dt0 < 1e-4) dt0 = dt1;
if (dt2 < 1e-4) dt2 = dt1;
px.initNonuniformCatmullRom(p0.x, p1.x, p2.x, p3.x, dt0, dt1, dt2);
py.initNonuniformCatmullRom(p0.y, p1.y, p2.y, p3.y, dt0, dt1, dt2);
pz.initNonuniformCatmullRom(p0.z, p1.z, p2.z, p3.z, dt0, dt1, dt2);
} else if (this.curveType === 'catmullrom') {
px.initCatmullRom(p0.x, p1.x, p2.x, p3.x, this.tension);
py.initCatmullRom(p0.y, p1.y, p2.y, p3.y, this.tension);
pz.initCatmullRom(p0.z, p1.z, p2.z, p3.z, this.tension);
}
point.set(px.calc(weight), py.calc(weight), pz.calc(weight));
return point;
}
copy(source) {
super.copy(source);
this.points = [];
for (let i = 0, l = source.points.length; i < l; i++) {
const point = source.points[i];
this.points.push(point.clone());
}
this.closed = source.closed;
this.curveType = source.curveType;
this.tension = source.tension;
return this;
}
toJSON() {
const data = super.toJSON();
data.points = [];
for (let i = 0, l = this.points.length; i < l; i++) {
const point = this.points[i];
data.points.push(point.toArray());
}
data.closed = this.closed;
data.curveType = this.curveType;
data.tension = this.tension;
return data;
}
fromJSON(json) {
super.fromJSON(json);
this.points = [];
for (let i = 0, l = json.points.length; i < l; i++) {
const point = json.points[i];
this.points.push(new _Vector.Vector3().fromArray(point));
}
this.closed = json.closed;
this.curveType = json.curveType;
this.tension = json.tension;
return this;
}
}
exports.CatmullRomCurve3 = CatmullRomCurve3;