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bezier curve tangent constraint

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Val Erastov (xibyte) 2020-03-11 03:42:47 -07:00
parent b1aabfed5c
commit 8254f3dbbb
8 changed files with 160 additions and 47 deletions
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1
web/app/math/bezier-cubic.js
View file

@ -1,5 +1,4 @@
import Vector from 'math/vector';
import * as math from './math'
export function LUT(a, b, cp1, cp2, scale) {
scale = 1 / scale;

12
web/app/sketcher/actions/constraintActions.js
View file

@ -44,7 +44,7 @@ export default [
selector: 'matchSequence',
sequence: [
{
types: [Circle, Arc],
types: [Circle, Arc, BezierCurve],
quantity: 1
},
{
@ -57,9 +57,13 @@ export default [
invoke: (ctx, matchedObjects) => {
const {viewer} = ctx;
const [circle, line] = matchedObjects;
const constraint = new AlgNumConstraint(ConstraintDefinitions.TangentLC, [line, circle]);
const [curve, line] = matchedObjects;
let constraint;
if (isInstanceOf(curve, BezierCurve) ) {
constraint = new AlgNumConstraint(ConstraintDefinitions.TangentLineBezier, [line, curve]);
} else {
constraint = new AlgNumConstraint(ConstraintDefinitions.TangentLC, [line, curve]);
}
constraint.initConstants();
const pm = viewer.parametricManager;
pm.add(constraint);

157
web/app/sketcher/constr/ANConstraints.js
View file

@ -6,6 +6,8 @@ import {COS_FN, Polynomial, POW_1_FN, POW_2_FN, POW_3_FN, SIN_FN} from "./polyno
import {Types} from "../io";
import Vector from "math/vector";
import {cubicBezierDer2, cubicBezierPoint} from "../../brep/geom/curves/bezierCubic";
import {greaterThanConstraint, lessThanConstraint} from "./barriers";
export const ConstraintDefinitions = {
@ -131,51 +133,107 @@ export const ConstraintDefinitions = {
name: 'Point On Bezier Curve',
defineParamsScope: ([pt, curve], callback) => {
const t = new Param(0.5, 't');
t.constraints = [greaterThanConstraint(0), lessThanConstraint(1)];
curve.visitParams(callback);
callback(new Param(0.5, 't'));
callback(t);
pt.visitParams(callback);
},
collectPolynomials: (polynomials, [p0x,p0y, p3x,p3y, p1x,p1y, p2x,p2y, t, px, py]) => {
const bz3Poly = (p, t, p0, p1, p2, p3) => new Polynomial()
.monomial(-1)
.term(t, POW_3_FN)
.term(p0, POW_1_FN)
.monomial(3)
.term(t, POW_2_FN)
.term(p0, POW_1_FN)
.monomial(-3)
.term(t, POW_1_FN)
.term(p0, POW_1_FN)
.monomial(1)
.term(p0, POW_1_FN)
polynomials.push(bezier3Polynomial(px, t, p0x, p1x, p2x, p3x));
polynomials.push(bezier3Polynomial(py, t, p0y, p1y, p2y, p3y));
},
.monomial(3)
.term(t, POW_3_FN)
.term(p1, POW_1_FN)
},
TangentLineBezier: {
id: 'TangentLineBezier',
name: 'Line & Bezier Tangency',
defineParamsScope: ([segment, curve], callback) => {
const t0 = new Param(0.5, 't');
t0.constraints = [greaterThanConstraint(0), lessThanConstraint(1)];
const [p0, p1, p2, p3] = [curve.p0, curve.p1, curve.p2, curve.p3].map(p => p.toVectorArray());
const [x0, y0] = cubicBezierPoint(p0, p1, p2, p3, t0.get());
const [nx0, ny0] = cubicBezierDer2(p0, p1, p2, p3, t0.get());
curve.visitParams(callback);
callback(t0);
callback(new Param(x0, 'X'));
callback(new Param(y0, 'Y'));
callback(new Param(nx0, 'X'));
callback(new Param(ny0, 'Y'));
callback(segment.params.ang);
segment.a.visitParams(callback);
},
collectPolynomials: (polynomials, [p0x,p0y, p3x,p3y, p1x,p1y, p2x,p2y, t, px,py, nx,ny, ang, ax,ay]) => {
polynomials.push(bezier3Polynomial(px, t, p0x, p1x, p2x, p3x));
polynomials.push(bezier3Polynomial(py, t, p0y, p1y, p2y, p3y));
//expanded second derivative: -6 P0 t + 6 P0 + 18 P1 t - 12 P1 - 18 P2 t + 6 P2 + 6 P3 t
const bzCubeD2 = (p, t, p0, p1, p2, p3) => new Polynomial()
.monomial(-6)
.term(t, POW_2_FN)
.term(p1, POW_1_FN)
.monomial(3)
.term(p0, POW_1_FN)
.term(t, POW_1_FN)
.monomial(6)
.term(p0, POW_1_FN)
.monomial(18)
.term(p1, POW_1_FN)
.monomial(-3)
.term(t, POW_3_FN)
.term(t, POW_1_FN)
.monomial(-12)
.term(p1, POW_1_FN)
.monomial(-18)
.term(p2, POW_1_FN)
.monomial(3)
.term(t, POW_2_FN)
.term(t, POW_1_FN)
.monomial(6)
.term(p2, POW_1_FN)
.monomial(1)
.term(t, POW_3_FN)
.monomial(6)
.term(p3, POW_1_FN)
.monomial(-1)
.term(t, POW_1_FN)
.monomial(-1)
.term(p, POW_1_FN);
//expanded first derivative: -3 P0 t^2 + 6 P0 t - 3 P0 + 9 P1 t^2 - 12 P1 t + 3 P1 - 9 P2 t^2 + 6 P2 t + 3 P3 t^2
const bzCubeD1 = (p, t, p0, p1, p2, p3) => new Polynomial()
.monomial(-3)
.term(p0, POW_1_FN)
.term(t, POW_2_FN)
.monomial(6)
.term(p0, POW_1_FN)
.term(t, POW_1_FN)
.monomial(-3)
.term(p0, POW_1_FN)
.monomial(9)
.term(p1, POW_1_FN)
.term(t, POW_2_FN)
.monomial(-12)
.term(p1, POW_1_FN)
.term(t, POW_1_FN)
.monomial(3)
.term(p1, POW_1_FN)
.monomial(-9)
.term(p2, POW_1_FN)
.term(t, POW_2_FN)
.monomial(6)
.term(p2, POW_1_FN)
.term(t, POW_1_FN)
.monomial(3)
.term(p3, POW_1_FN)
.term(t, POW_2_FN)
.monomial(-1)
.term(p, POW_1_FN);
polynomials.push(bz3Poly(px, t, p0x, p1x, p2x, p3x));
polynomials.push(bz3Poly(py, t, p0y, p1y, p2y, p3y));
polynomials.push(bzCubeD1(nx, t, p0x, p1x, p2x, p3x));
polynomials.push(bzCubeD1(ny, t, p0y, p1y, p2y, p3y));
polynomials.push(new Polynomial()
.monomial(-1)
.term(ny, POW_1_FN)
.term(ang, COS_FN)
.monomial()
.term(nx, POW_1_FN)
.term(ang, SIN_FN)
);
ConstraintDefinitions.PointOnLine.collectPolynomials(polynomials, [px, py, ax, ay, ang]);
},
},
@ -743,6 +801,43 @@ function tangentLCPolynomial(ang, ax, ay, cx, cy, r, inverted) {
.term(r, POW_1_FN);
}
const bezier3Polynomial = (p, t, p0, p1, p2, p3) => new Polynomial()
.monomial(-1)
.term(t, POW_3_FN)
.term(p0, POW_1_FN)
.monomial(3)
.term(t, POW_2_FN)
.term(p0, POW_1_FN)
.monomial(-3)
.term(t, POW_1_FN)
.term(p0, POW_1_FN)
.monomial(1)
.term(p0, POW_1_FN)
.monomial(3)
.term(t, POW_3_FN)
.term(p1, POW_1_FN)
.monomial(-6)
.term(t, POW_2_FN)
.term(p1, POW_1_FN)
.monomial(3)
.term(t, POW_1_FN)
.term(p1, POW_1_FN)
.monomial(-3)
.term(t, POW_3_FN)
.term(p2, POW_1_FN)
.monomial(3)
.term(t, POW_2_FN)
.term(p2, POW_1_FN)
.monomial(1)
.term(t, POW_3_FN)
.term(p3, POW_1_FN)
.monomial(-1)
.term(p, POW_1_FN);
export class AlgNumConstraint {
static Counter = 0;

15
web/app/sketcher/constr/AlgNumSystem.js
View file

@ -3,7 +3,7 @@ import {eqEps} from "../../brep/geom/tolerance";
import {Polynomial, POW_1_FN} from "./polynomial";
import {compositeFn} from "gems/func";
const DEBUG = false;
const DEBUG = true;
export class AlgNumSubSystem {
@ -472,17 +472,20 @@ class Isolation {
}
this.dof = this.beingSolvedParams.size - polynomials.length;
let penaltyFunction = new PolynomialResidual();
this.beingSolvedParams.forEach(sp => {
const param = sp.objectParam;
if (param.constraints) {
param.constraints.forEach(pc => penaltyFunction.add(sp, pc))
param.constraints.forEach(pc => {
let penaltyFunction = new PolynomialResidual();
penaltyFunction.add(sp, pc);
residuals.push(penaltyFunction);
})
}
});
if (penaltyFunction.params.length) {
// residuals.push(penaltyFunction);
}
// if (penaltyFunction.params.length) {
// residuals.push(penaltyFunction);
// }
this.numericalSolver = prepare(residuals);
}

3
web/app/sketcher/shapes/arc.js
View file

@ -2,8 +2,6 @@ import * as math from '../../math/math';
import Vector from 'math/vector';
import {SketchObject} from './sketch-object';
import {Param} from "./param";
import {greaterThanConstraint} from "../constr/barriers";
import {MIN_RADIUS} from "./circle";
import {AlgNumConstraint, ConstraintDefinitions} from "../constr/ANConstraints";
import {makeAngle0_360} from "../../math/math";
@ -20,7 +18,6 @@ export class Arc extends SketchObject {
this.children.push(a, b, c);
this.r = new Param(0, 'R');
this.r.constraints = [greaterThanConstraint(MIN_RADIUS)];
this.r.enforceVisualLimit = true;
this.ang1 = new Param(0, 'A');

13
web/app/sketcher/shapes/bezier-curve.js
View file

@ -23,6 +23,19 @@ export class BezierCurve extends SketchObject {
}
}
get p0() {
return this.a;
}
get p1() {
return this.cp1;
}
get p2() {
return this.cp2;
}
get p3() {
return this.b;
}
stabilize(viewer) {
this.children.forEach(c => c.stabilize(viewer));
}

2
web/app/sketcher/shapes/circle.js
View file

@ -1,7 +1,6 @@
import * as math from '../../math/math';
import {SketchObject} from './sketch-object'
import {Param} from "./param";
import {greaterThanConstraint} from "../constr/barriers";
export const MIN_RADIUS = 100;
@ -13,7 +12,6 @@ export class Circle extends SketchObject {
c.parent = this;
this.children.push(c);
this.r = new Param(0, 'R');
this.r.constraints = [greaterThanConstraint(MIN_RADIUS)];
this.r.enforceVisualLimit = true;
}

4
web/app/sketcher/shapes/point.js
View file

@ -76,6 +76,10 @@ export class EndPoint extends SketchObject {
this.setXY(arr[0], arr[1]);
}
toVectorArray() {
return [this.x, this.y];
}
toVector() {
return new Vector(this.x, this.y);
}