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-"use strict";
-
-Object.defineProperty(exports, "__esModule", {
- value: true
-});
-exports.Bezier = void 0;
-// math-inlining.
-const {
- abs,
- cos,
- sin,
- acos,
- atan2,
- sqrt,
- pow
-} = Math; // cube root function yielding real roots
-
-function crt(v) {
- return v < 0 ? -pow(-v, 1 / 3) : pow(v, 1 / 3);
-} // trig constants
-
-
-const pi = Math.PI,
- tau = 2 * pi,
- quart = pi / 2,
- // float precision significant decimal
-epsilon = 0.000001,
- // extremas used in bbox calculation and similar algorithms
-nMax = Number.MAX_SAFE_INTEGER || 9007199254740991,
- nMin = Number.MIN_SAFE_INTEGER || -9007199254740991,
- // a zero coordinate, which is surprisingly useful
-ZERO = {
- x: 0,
- y: 0,
- z: 0
-}; // Bezier utility functions
-
-const utils = {
- // Legendre-Gauss abscissae with n=24 (x_i values, defined at i=n as the roots of the nth order Legendre polynomial Pn(x))
- Tvalues: [-0.0640568928626056260850430826247450385909, 0.0640568928626056260850430826247450385909, -0.1911188674736163091586398207570696318404, 0.1911188674736163091586398207570696318404, -0.3150426796961633743867932913198102407864, 0.3150426796961633743867932913198102407864, -0.4337935076260451384870842319133497124524, 0.4337935076260451384870842319133497124524, -0.5454214713888395356583756172183723700107, 0.5454214713888395356583756172183723700107, -0.6480936519369755692524957869107476266696, 0.6480936519369755692524957869107476266696, -0.7401241915785543642438281030999784255232, 0.7401241915785543642438281030999784255232, -0.8200019859739029219539498726697452080761, 0.8200019859739029219539498726697452080761, -0.8864155270044010342131543419821967550873, 0.8864155270044010342131543419821967550873, -0.9382745520027327585236490017087214496548, 0.9382745520027327585236490017087214496548, -0.9747285559713094981983919930081690617411, 0.9747285559713094981983919930081690617411, -0.9951872199970213601799974097007368118745, 0.9951872199970213601799974097007368118745],
- // Legendre-Gauss weights with n=24 (w_i values, defined by a function linked to in the Bezier primer article)
- Cvalues: [0.1279381953467521569740561652246953718517, 0.1279381953467521569740561652246953718517, 0.1258374563468282961213753825111836887264, 0.1258374563468282961213753825111836887264, 0.121670472927803391204463153476262425607, 0.121670472927803391204463153476262425607, 0.1155056680537256013533444839067835598622, 0.1155056680537256013533444839067835598622, 0.1074442701159656347825773424466062227946, 0.1074442701159656347825773424466062227946, 0.0976186521041138882698806644642471544279, 0.0976186521041138882698806644642471544279, 0.086190161531953275917185202983742667185, 0.086190161531953275917185202983742667185, 0.0733464814110803057340336152531165181193, 0.0733464814110803057340336152531165181193, 0.0592985849154367807463677585001085845412, 0.0592985849154367807463677585001085845412, 0.0442774388174198061686027482113382288593, 0.0442774388174198061686027482113382288593, 0.0285313886289336631813078159518782864491, 0.0285313886289336631813078159518782864491, 0.0123412297999871995468056670700372915759, 0.0123412297999871995468056670700372915759],
- arcfn: function (t, derivativeFn) {
- const d = derivativeFn(t);
- let l = d.x * d.x + d.y * d.y;
-
- if (typeof d.z !== "undefined") {
- l += d.z * d.z;
- }
-
- return sqrt(l);
- },
- compute: function (t, points, _3d) {
- // shortcuts
- if (t === 0) {
- points[0].t = 0;
- return points[0];
- }
-
- const order = points.length - 1;
-
- if (t === 1) {
- points[order].t = 1;
- return points[order];
- }
-
- const mt = 1 - t;
- let p = points; // constant?
-
- if (order === 0) {
- points[0].t = t;
- return points[0];
- } // linear?
-
-
- if (order === 1) {
- const ret = {
- x: mt * p[0].x + t * p[1].x,
- y: mt * p[0].y + t * p[1].y,
- t: t
- };
-
- if (_3d) {
- ret.z = mt * p[0].z + t * p[1].z;
- }
-
- return ret;
- } // quadratic/cubic curve?
-
-
- if (order < 4) {
- let mt2 = mt * mt,
- t2 = t * t,
- a,
- b,
- c,
- d = 0;
-
- if (order === 2) {
- p = [p[0], p[1], p[2], ZERO];
- a = mt2;
- b = mt * t * 2;
- c = t2;
- } else if (order === 3) {
- a = mt2 * mt;
- b = mt2 * t * 3;
- c = mt * t2 * 3;
- d = t * t2;
- }
-
- const ret = {
- x: a * p[0].x + b * p[1].x + c * p[2].x + d * p[3].x,
- y: a * p[0].y + b * p[1].y + c * p[2].y + d * p[3].y,
- t: t
- };
-
- if (_3d) {
- ret.z = a * p[0].z + b * p[1].z + c * p[2].z + d * p[3].z;
- }
-
- return ret;
- } // higher order curves: use de Casteljau's computation
-
-
- const dCpts = JSON.parse(JSON.stringify(points));
-
- while (dCpts.length > 1) {
- for (let i = 0; i < dCpts.length - 1; i++) {
- dCpts[i] = {
- x: dCpts[i].x + (dCpts[i + 1].x - dCpts[i].x) * t,
- y: dCpts[i].y + (dCpts[i + 1].y - dCpts[i].y) * t
- };
-
- if (typeof dCpts[i].z !== "undefined") {
- dCpts[i] = dCpts[i].z + (dCpts[i + 1].z - dCpts[i].z) * t;
- }
- }
-
- dCpts.splice(dCpts.length - 1, 1);
- }
-
- dCpts[0].t = t;
- return dCpts[0];
- },
- computeWithRatios: function (t, points, ratios, _3d) {
- const mt = 1 - t,
- r = ratios,
- p = points;
- let f1 = r[0],
- f2 = r[1],
- f3 = r[2],
- f4 = r[3],
- d; // spec for linear
-
- f1 *= mt;
- f2 *= t;
-
- if (p.length === 2) {
- d = f1 + f2;
- return {
- x: (f1 * p[0].x + f2 * p[1].x) / d,
- y: (f1 * p[0].y + f2 * p[1].y) / d,
- z: !_3d ? false : (f1 * p[0].z + f2 * p[1].z) / d,
- t: t
- };
- } // upgrade to quadratic
-
-
- f1 *= mt;
- f2 *= 2 * mt;
- f3 *= t * t;
-
- if (p.length === 3) {
- d = f1 + f2 + f3;
- return {
- x: (f1 * p[0].x + f2 * p[1].x + f3 * p[2].x) / d,
- y: (f1 * p[0].y + f2 * p[1].y + f3 * p[2].y) / d,
- z: !_3d ? false : (f1 * p[0].z + f2 * p[1].z + f3 * p[2].z) / d,
- t: t
- };
- } // upgrade to cubic
-
-
- f1 *= mt;
- f2 *= 1.5 * mt;
- f3 *= 3 * mt;
- f4 *= t * t * t;
-
- if (p.length === 4) {
- d = f1 + f2 + f3 + f4;
- return {
- x: (f1 * p[0].x + f2 * p[1].x + f3 * p[2].x + f4 * p[3].x) / d,
- y: (f1 * p[0].y + f2 * p[1].y + f3 * p[2].y + f4 * p[3].y) / d,
- z: !_3d ? false : (f1 * p[0].z + f2 * p[1].z + f3 * p[2].z + f4 * p[3].z) / d,
- t: t
- };
- }
- },
- derive: function (points, _3d) {
- const dpoints = [];
-
- for (let p = points, d = p.length, c = d - 1; d > 1; d--, c--) {
- const list = [];
-
- for (let j = 0, dpt; j < c; j++) {
- dpt = {
- x: c * (p[j + 1].x - p[j].x),
- y: c * (p[j + 1].y - p[j].y)
- };
-
- if (_3d) {
- dpt.z = c * (p[j + 1].z - p[j].z);
- }
-
- list.push(dpt);
- }
-
- dpoints.push(list);
- p = list;
- }
-
- return dpoints;
- },
- between: function (v, m, M) {
- return m <= v && v <= M || utils.approximately(v, m) || utils.approximately(v, M);
- },
- approximately: function (a, b, precision) {
- return abs(a - b) <= (precision || epsilon);
- },
- length: function (derivativeFn) {
- const z = 0.5,
- len = utils.Tvalues.length;
- let sum = 0;
-
- for (let i = 0, t; i < len; i++) {
- t = z * utils.Tvalues[i] + z;
- sum += utils.Cvalues[i] * utils.arcfn(t, derivativeFn);
- }
-
- return z * sum;
- },
- map: function (v, ds, de, ts, te) {
- const d1 = de - ds,
- d2 = te - ts,
- v2 = v - ds,
- r = v2 / d1;
- return ts + d2 * r;
- },
- lerp: function (r, v1, v2) {
- const ret = {
- x: v1.x + r * (v2.x - v1.x),
- y: v1.y + r * (v2.y - v1.y)
- };
-
- if (!!v1.z && !!v2.z) {
- ret.z = v1.z + r * (v2.z - v1.z);
- }
-
- return ret;
- },
- pointToString: function (p) {
- let s = p.x + "/" + p.y;
-
- if (typeof p.z !== "undefined") {
- s += "/" + p.z;
- }
-
- return s;
- },
- pointsToString: function (points) {
- return "[" + points.map(utils.pointToString).join(", ") + "]";
- },
- copy: function (obj) {
- return JSON.parse(JSON.stringify(obj));
- },
- angle: function (o, v1, v2) {
- const dx1 = v1.x - o.x,
- dy1 = v1.y - o.y,
- dx2 = v2.x - o.x,
- dy2 = v2.y - o.y,
- cross = dx1 * dy2 - dy1 * dx2,
- dot = dx1 * dx2 + dy1 * dy2;
- return atan2(cross, dot);
- },
- // round as string, to avoid rounding errors
- round: function (v, d) {
- const s = "" + v;
- const pos = s.indexOf(".");
- return parseFloat(s.substring(0, pos + 1 + d));
- },
- dist: function (p1, p2) {
- const dx = p1.x - p2.x,
- dy = p1.y - p2.y;
- return sqrt(dx * dx + dy * dy);
- },
- closest: function (LUT, point) {
- let mdist = pow(2, 63),
- mpos,
- d;
- LUT.forEach(function (p, idx) {
- d = utils.dist(point, p);
-
- if (d < mdist) {
- mdist = d;
- mpos = idx;
- }
- });
- return {
- mdist: mdist,
- mpos: mpos
- };
- },
- abcratio: function (t, n) {
- // see ratio(t) note on http://pomax.github.io/bezierinfo/#abc
- if (n !== 2 && n !== 3) {
- return false;
- }
-
- if (typeof t === "undefined") {
- t = 0.5;
- } else if (t === 0 || t === 1) {
- return t;
- }
-
- const bottom = pow(t, n) + pow(1 - t, n),
- top = bottom - 1;
- return abs(top / bottom);
- },
- projectionratio: function (t, n) {
- // see u(t) note on http://pomax.github.io/bezierinfo/#abc
- if (n !== 2 && n !== 3) {
- return false;
- }
-
- if (typeof t === "undefined") {
- t = 0.5;
- } else if (t === 0 || t === 1) {
- return t;
- }
-
- const top = pow(1 - t, n),
- bottom = pow(t, n) + top;
- return top / bottom;
- },
- lli8: function (x1, y1, x2, y2, x3, y3, x4, y4) {
- const nx = (x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4),
- ny = (x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4),
- d = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4);
-
- if (d == 0) {
- return false;
- }
-
- return {
- x: nx / d,
- y: ny / d
- };
- },
- lli4: function (p1, p2, p3, p4) {
- const x1 = p1.x,
- y1 = p1.y,
- x2 = p2.x,
- y2 = p2.y,
- x3 = p3.x,
- y3 = p3.y,
- x4 = p4.x,
- y4 = p4.y;
- return utils.lli8(x1, y1, x2, y2, x3, y3, x4, y4);
- },
- lli: function (v1, v2) {
- return utils.lli4(v1, v1.c, v2, v2.c);
- },
- makeline: function (p1, p2) {
- const x1 = p1.x,
- y1 = p1.y,
- x2 = p2.x,
- y2 = p2.y,
- dx = (x2 - x1) / 3,
- dy = (y2 - y1) / 3;
- return new Bezier(x1, y1, x1 + dx, y1 + dy, x1 + 2 * dx, y1 + 2 * dy, x2, y2);
- },
- findbbox: function (sections) {
- let mx = nMax,
- my = nMax,
- MX = nMin,
- MY = nMin;
- sections.forEach(function (s) {
- const bbox = s.bbox();
- if (mx > bbox.x.min) mx = bbox.x.min;
- if (my > bbox.y.min) my = bbox.y.min;
- if (MX < bbox.x.max) MX = bbox.x.max;
- if (MY < bbox.y.max) MY = bbox.y.max;
- });
- return {
- x: {
- min: mx,
- mid: (mx + MX) / 2,
- max: MX,
- size: MX - mx
- },
- y: {
- min: my,
- mid: (my + MY) / 2,
- max: MY,
- size: MY - my
- }
- };
- },
- shapeintersections: function (s1, bbox1, s2, bbox2, curveIntersectionThreshold) {
- if (!utils.bboxoverlap(bbox1, bbox2)) return [];
- const intersections = [];
- const a1 = [s1.startcap, s1.forward, s1.back, s1.endcap];
- const a2 = [s2.startcap, s2.forward, s2.back, s2.endcap];
- a1.forEach(function (l1) {
- if (l1.virtual) return;
- a2.forEach(function (l2) {
- if (l2.virtual) return;
- const iss = l1.intersects(l2, curveIntersectionThreshold);
-
- if (iss.length > 0) {
- iss.c1 = l1;
- iss.c2 = l2;
- iss.s1 = s1;
- iss.s2 = s2;
- intersections.push(iss);
- }
- });
- });
- return intersections;
- },
- makeshape: function (forward, back, curveIntersectionThreshold) {
- const bpl = back.points.length;
- const fpl = forward.points.length;
- const start = utils.makeline(back.points[bpl - 1], forward.points[0]);
- const end = utils.makeline(forward.points[fpl - 1], back.points[0]);
- const shape = {
- startcap: start,
- forward: forward,
- back: back,
- endcap: end,
- bbox: utils.findbbox([start, forward, back, end])
- };
-
- shape.intersections = function (s2) {
- return utils.shapeintersections(shape, shape.bbox, s2, s2.bbox, curveIntersectionThreshold);
- };
-
- return shape;
- },
- getminmax: function (curve, d, list) {
- if (!list) return {
- min: 0,
- max: 0
- };
- let min = nMax,
- max = nMin,
- t,
- c;
-
- if (list.indexOf(0) === -1) {
- list = [0].concat(list);
- }
-
- if (list.indexOf(1) === -1) {
- list.push(1);
- }
-
- for (let i = 0, len = list.length; i < len; i++) {
- t = list[i];
- c = curve.get(t);
-
- if (c[d] < min) {
- min = c[d];
- }
-
- if (c[d] > max) {
- max = c[d];
- }
- }
-
- return {
- min: min,
- mid: (min + max) / 2,
- max: max,
- size: max - min
- };
- },
- align: function (points, line) {
- const tx = line.p1.x,
- ty = line.p1.y,
- a = -atan2(line.p2.y - ty, line.p2.x - tx),
- d = function (v) {
- return {
- x: (v.x - tx) * cos(a) - (v.y - ty) * sin(a),
- y: (v.x - tx) * sin(a) + (v.y - ty) * cos(a)
- };
- };
-
- return points.map(d);
- },
- roots: function (points, line) {
- line = line || {
- p1: {
- x: 0,
- y: 0
- },
- p2: {
- x: 1,
- y: 0
- }
- };
- const order = points.length - 1;
- const aligned = utils.align(points, line);
-
- const reduce = function (t) {
- return 0 <= t && t <= 1;
- };
-
- if (order === 2) {
- const a = aligned[0].y,
- b = aligned[1].y,
- c = aligned[2].y,
- d = a - 2 * b + c;
-
- if (d !== 0) {
- const m1 = -sqrt(b * b - a * c),
- m2 = -a + b,
- v1 = -(m1 + m2) / d,
- v2 = -(-m1 + m2) / d;
- return [v1, v2].filter(reduce);
- } else if (b !== c && d === 0) {
- return [(2 * b - c) / (2 * b - 2 * c)].filter(reduce);
- }
-
- return [];
- } // see http://www.trans4mind.com/personal_development/mathematics/polynomials/cubicAlgebra.htm
-
-
- const pa = aligned[0].y,
- pb = aligned[1].y,
- pc = aligned[2].y,
- pd = aligned[3].y;
- let d = -pa + 3 * pb - 3 * pc + pd,
- a = 3 * pa - 6 * pb + 3 * pc,
- b = -3 * pa + 3 * pb,
- c = pa;
-
- if (utils.approximately(d, 0)) {
- // this is not a cubic curve.
- if (utils.approximately(a, 0)) {
- // in fact, this is not a quadratic curve either.
- if (utils.approximately(b, 0)) {
- // in fact in fact, there are no solutions.
- return [];
- } // linear solution:
-
-
- return [-c / b].filter(reduce);
- } // quadratic solution:
-
-
- const q = sqrt(b * b - 4 * a * c),
- a2 = 2 * a;
- return [(q - b) / a2, (-b - q) / a2].filter(reduce);
- } // at this point, we know we need a cubic solution:
-
-
- a /= d;
- b /= d;
- c /= d;
- const p = (3 * b - a * a) / 3,
- p3 = p / 3,
- q = (2 * a * a * a - 9 * a * b + 27 * c) / 27,
- q2 = q / 2,
- discriminant = q2 * q2 + p3 * p3 * p3;
- let u1, v1, x1, x2, x3;
-
- if (discriminant < 0) {
- const mp3 = -p / 3,
- mp33 = mp3 * mp3 * mp3,
- r = sqrt(mp33),
- t = -q / (2 * r),
- cosphi = t < -1 ? -1 : t > 1 ? 1 : t,
- phi = acos(cosphi),
- crtr = crt(r),
- t1 = 2 * crtr;
- x1 = t1 * cos(phi / 3) - a / 3;
- x2 = t1 * cos((phi + tau) / 3) - a / 3;
- x3 = t1 * cos((phi + 2 * tau) / 3) - a / 3;
- return [x1, x2, x3].filter(reduce);
- } else if (discriminant === 0) {
- u1 = q2 < 0 ? crt(-q2) : -crt(q2);
- x1 = 2 * u1 - a / 3;
- x2 = -u1 - a / 3;
- return [x1, x2].filter(reduce);
- } else {
- const sd = sqrt(discriminant);
- u1 = crt(-q2 + sd);
- v1 = crt(q2 + sd);
- return [u1 - v1 - a / 3].filter(reduce);
- }
- },
- droots: function (p) {
- // quadratic roots are easy
- if (p.length === 3) {
- const a = p[0],
- b = p[1],
- c = p[2],
- d = a - 2 * b + c;
-
- if (d !== 0) {
- const m1 = -sqrt(b * b - a * c),
- m2 = -a + b,
- v1 = -(m1 + m2) / d,
- v2 = -(-m1 + m2) / d;
- return [v1, v2];
- } else if (b !== c && d === 0) {
- return [(2 * b - c) / (2 * (b - c))];
- }
-
- return [];
- } // linear roots are even easier
-
-
- if (p.length === 2) {
- const a = p[0],
- b = p[1];
-
- if (a !== b) {
- return [a / (a - b)];
- }
-
- return [];
- }
-
- return [];
- },
- curvature: function (t, d1, d2, _3d, kOnly) {
- let num,
- dnm,
- adk,
- dk,
- k = 0,
- r = 0; //
- // We're using the following formula for curvature:
- //
- // x'y" - y'x"
- // k(t) = ------------------
- // (x'² + y'²)^(3/2)
- //
- // from https://en.wikipedia.org/wiki/Radius_of_curvature#Definition
- //
- // With it corresponding 3D counterpart:
- //
- // sqrt( (y'z" - y"z')² + (z'x" - z"x')² + (x'y" - x"y')²)
- // k(t) = -------------------------------------------------------
- // (x'² + y'² + z'²)^(3/2)
- //
-
- const d = utils.compute(t, d1);
- const dd = utils.compute(t, d2);
- const qdsum = d.x * d.x + d.y * d.y;
-
- if (_3d) {
- num = sqrt(pow(d.y * dd.z - dd.y * d.z, 2) + pow(d.z * dd.x - dd.z * d.x, 2) + pow(d.x * dd.y - dd.x * d.y, 2));
- dnm = pow(qdsum + d.z * d.z, 3 / 2);
- } else {
- num = d.x * dd.y - d.y * dd.x;
- dnm = pow(qdsum, 3 / 2);
- }
-
- if (num === 0 || dnm === 0) {
- return {
- k: 0,
- r: 0
- };
- }
-
- k = num / dnm;
- r = dnm / num; // We're also computing the derivative of kappa, because
- // there is value in knowing the rate of change for the
- // curvature along the curve. And we're just going to
- // ballpark it based on an epsilon.
-
- if (!kOnly) {
- // compute k'(t) based on the interval before, and after it,
- // to at least try to not introduce forward/backward pass bias.
- const pk = utils.curvature(t - 0.001, d1, d2, _3d, true).k;
- const nk = utils.curvature(t + 0.001, d1, d2, _3d, true).k;
- dk = (nk - k + (k - pk)) / 2;
- adk = (abs(nk - k) + abs(k - pk)) / 2;
- }
-
- return {
- k: k,
- r: r,
- dk: dk,
- adk: adk
- };
- },
- inflections: function (points) {
- if (points.length < 4) return []; // FIXME: TODO: add in inflection abstraction for quartic+ curves?
-
- const p = utils.align(points, {
- p1: points[0],
- p2: points.slice(-1)[0]
- }),
- a = p[2].x * p[1].y,
- b = p[3].x * p[1].y,
- c = p[1].x * p[2].y,
- d = p[3].x * p[2].y,
- v1 = 18 * (-3 * a + 2 * b + 3 * c - d),
- v2 = 18 * (3 * a - b - 3 * c),
- v3 = 18 * (c - a);
-
- if (utils.approximately(v1, 0)) {
- if (!utils.approximately(v2, 0)) {
- let t = -v3 / v2;
- if (0 <= t && t <= 1) return [t];
- }
-
- return [];
- }
-
- const trm = v2 * v2 - 4 * v1 * v3,
- sq = Math.sqrt(trm),
- d2 = 2 * v1;
- if (utils.approximately(d2, 0)) return [];
- return [(sq - v2) / d2, -(v2 + sq) / d2].filter(function (r) {
- return 0 <= r && r <= 1;
- });
- },
- bboxoverlap: function (b1, b2) {
- const dims = ["x", "y"],
- len = dims.length;
-
- for (let i = 0, dim, l, t, d; i < len; i++) {
- dim = dims[i];
- l = b1[dim].mid;
- t = b2[dim].mid;
- d = (b1[dim].size + b2[dim].size) / 2;
- if (abs(l - t) >= d) return false;
- }
-
- return true;
- },
- expandbox: function (bbox, _bbox) {
- if (_bbox.x.min < bbox.x.min) {
- bbox.x.min = _bbox.x.min;
- }
-
- if (_bbox.y.min < bbox.y.min) {
- bbox.y.min = _bbox.y.min;
- }
-
- if (_bbox.z && _bbox.z.min < bbox.z.min) {
- bbox.z.min = _bbox.z.min;
- }
-
- if (_bbox.x.max > bbox.x.max) {
- bbox.x.max = _bbox.x.max;
- }
-
- if (_bbox.y.max > bbox.y.max) {
- bbox.y.max = _bbox.y.max;
- }
-
- if (_bbox.z && _bbox.z.max > bbox.z.max) {
- bbox.z.max = _bbox.z.max;
- }
-
- bbox.x.mid = (bbox.x.min + bbox.x.max) / 2;
- bbox.y.mid = (bbox.y.min + bbox.y.max) / 2;
-
- if (bbox.z) {
- bbox.z.mid = (bbox.z.min + bbox.z.max) / 2;
- }
-
- bbox.x.size = bbox.x.max - bbox.x.min;
- bbox.y.size = bbox.y.max - bbox.y.min;
-
- if (bbox.z) {
- bbox.z.size = bbox.z.max - bbox.z.min;
- }
- },
- pairiteration: function (c1, c2, curveIntersectionThreshold) {
- const c1b = c1.bbox(),
- c2b = c2.bbox(),
- r = 100000,
- threshold = curveIntersectionThreshold || 0.5;
-
- if (c1b.x.size + c1b.y.size < threshold && c2b.x.size + c2b.y.size < threshold) {
- return [(r * (c1._t1 + c1._t2) / 2 | 0) / r + "/" + (r * (c2._t1 + c2._t2) / 2 | 0) / r];
- }
-
- let cc1 = c1.split(0.5),
- cc2 = c2.split(0.5),
- pairs = [{
- left: cc1.left,
- right: cc2.left
- }, {
- left: cc1.left,
- right: cc2.right
- }, {
- left: cc1.right,
- right: cc2.right
- }, {
- left: cc1.right,
- right: cc2.left
- }];
- pairs = pairs.filter(function (pair) {
- return utils.bboxoverlap(pair.left.bbox(), pair.right.bbox());
- });
- let results = [];
- if (pairs.length === 0) return results;
- pairs.forEach(function (pair) {
- results = results.concat(utils.pairiteration(pair.left, pair.right, threshold));
- });
- results = results.filter(function (v, i) {
- return results.indexOf(v) === i;
- });
- return results;
- },
- getccenter: function (p1, p2, p3) {
- const dx1 = p2.x - p1.x,
- dy1 = p2.y - p1.y,
- dx2 = p3.x - p2.x,
- dy2 = p3.y - p2.y,
- dx1p = dx1 * cos(quart) - dy1 * sin(quart),
- dy1p = dx1 * sin(quart) + dy1 * cos(quart),
- dx2p = dx2 * cos(quart) - dy2 * sin(quart),
- dy2p = dx2 * sin(quart) + dy2 * cos(quart),
- // chord midpoints
- mx1 = (p1.x + p2.x) / 2,
- my1 = (p1.y + p2.y) / 2,
- mx2 = (p2.x + p3.x) / 2,
- my2 = (p2.y + p3.y) / 2,
- // midpoint offsets
- mx1n = mx1 + dx1p,
- my1n = my1 + dy1p,
- mx2n = mx2 + dx2p,
- my2n = my2 + dy2p,
- // intersection of these lines:
- arc = utils.lli8(mx1, my1, mx1n, my1n, mx2, my2, mx2n, my2n),
- r = utils.dist(arc, p1); // arc start/end values, over mid point:
-
- let s = atan2(p1.y - arc.y, p1.x - arc.x),
- m = atan2(p2.y - arc.y, p2.x - arc.x),
- e = atan2(p3.y - arc.y, p3.x - arc.x),
- _; // determine arc direction (cw/ccw correction)
-
-
- if (s < e) {
- // if s<m<e, arc(s, e)
- // if m<s<e, arc(e, s + tau)
- // if s<e<m, arc(e, s + tau)
- if (s > m || m > e) {
- s += tau;
- }
-
- if (s > e) {
- _ = e;
- e = s;
- s = _;
- }
- } else {
- // if e<m<s, arc(e, s)
- // if m<e<s, arc(s, e + tau)
- // if e<s<m, arc(s, e + tau)
- if (e < m && m < s) {
- _ = e;
- e = s;
- s = _;
- } else {
- e += tau;
- }
- } // assign and done.
-
-
- arc.s = s;
- arc.e = e;
- arc.r = r;
- return arc;
- },
- numberSort: function (a, b) {
- return a - b;
- }
-};
-/**
- * Poly Bezier
- * @param {[type]} curves [description]
- */
-
-class PolyBezier {
- constructor(curves) {
- this.curves = [];
- this._3d = false;
-
- if (!!curves) {
- this.curves = curves;
- this._3d = this.curves[0]._3d;
- }
- }
-
- valueOf() {
- return this.toString();
- }
-
- toString() {
- return "[" + this.curves.map(function (curve) {
- return utils.pointsToString(curve.points);
- }).join(", ") + "]";
- }
-
- addCurve(curve) {
- this.curves.push(curve);
- this._3d = this._3d || curve._3d;
- }
-
- length() {
- return this.curves.map(function (v) {
- return v.length();
- }).reduce(function (a, b) {
- return a + b;
- });
- }
-
- curve(idx) {
- return this.curves[idx];
- }
-
- bbox() {
- const c = this.curves;
- var bbox = c[0].bbox();
-
- for (var i = 1; i < c.length; i++) {
- utils.expandbox(bbox, c[i].bbox());
- }
-
- return bbox;
- }
-
- offset(d) {
- const offset = [];
- this.curves.forEach(function (v) {
- offset.push(...v.offset(d));
- });
- return new PolyBezier(offset);
- }
-
-}
-/**
- A javascript Bezier curve library by Pomax.
-
- Based on http://pomax.github.io/bezierinfo
-
- This code is MIT licensed.
-**/
-// math-inlining.
-
-
-const {
- abs: abs$1,
- min,
- max,
- cos: cos$1,
- sin: sin$1,
- acos: acos$1,
- sqrt: sqrt$1
-} = Math;
-const pi$1 = Math.PI;
-/**
- * Bezier curve constructor.
- *
- * ...docs pending...
- */
-
-class Bezier {
- constructor(coords) {
- let args = coords && coords.forEach ? coords : Array.from(arguments).slice();
- let coordlen = false;
-
- if (typeof args[0] === "object") {
- coordlen = args.length;
- const newargs = [];
- args.forEach(function (point) {
- ["x", "y", "z"].forEach(function (d) {
- if (typeof point[d] !== "undefined") {
- newargs.push(point[d]);
- }
- });
- });
- args = newargs;
- }
-
- let higher = false;
- const len = args.length;
-
- if (coordlen) {
- if (coordlen > 4) {
- if (arguments.length !== 1) {
- throw new Error("Only new Bezier(point[]) is accepted for 4th and higher order curves");
- }
-
- higher = true;
- }
- } else {
- if (len !== 6 && len !== 8 && len !== 9 && len !== 12) {
- if (arguments.length !== 1) {
- throw new Error("Only new Bezier(point[]) is accepted for 4th and higher order curves");
- }
- }
- }
-
- const _3d = this._3d = !higher && (len === 9 || len === 12) || coords && coords[0] && typeof coords[0].z !== "undefined";
-
- const points = this.points = [];
-
- for (let idx = 0, step = _3d ? 3 : 2; idx < len; idx += step) {
- var point = {
- x: args[idx],
- y: args[idx + 1]
- };
-
- if (_3d) {
- point.z = args[idx + 2];
- }
-
- points.push(point);
- }
-
- const order = this.order = points.length - 1;
- const dims = this.dims = ["x", "y"];
- if (_3d) dims.push("z");
- this.dimlen = dims.length;
- const aligned = utils.align(points, {
- p1: points[0],
- p2: points[order]
- });
- this._linear = !aligned.some(p => abs$1(p.y) > 0.0001);
- this._lut = [];
- this._t1 = 0;
- this._t2 = 1;
- this.update();
- }
-
- static quadraticFromPoints(p1, p2, p3, t) {
- if (typeof t === "undefined") {
- t = 0.5;
- } // shortcuts, although they're really dumb
-
-
- if (t === 0) {
- return new Bezier(p2, p2, p3);
- }
-
- if (t === 1) {
- return new Bezier(p1, p2, p2);
- } // real fitting.
-
-
- const abc = Bezier.getABC(2, p1, p2, p3, t);
- return new Bezier(p1, abc.A, p3);
- }
-
- static cubicFromPoints(S, B, E, t, d1) {
- if (typeof t === "undefined") {
- t = 0.5;
- }
-
- const abc = Bezier.getABC(3, S, B, E, t);
-
- if (typeof d1 === "undefined") {
- d1 = utils.dist(B, abc.C);
- }
-
- const d2 = d1 * (1 - t) / t;
- const selen = utils.dist(S, E),
- lx = (E.x - S.x) / selen,
- ly = (E.y - S.y) / selen,
- bx1 = d1 * lx,
- by1 = d1 * ly,
- bx2 = d2 * lx,
- by2 = d2 * ly; // derivation of new hull coordinates
-
- const e1 = {
- x: B.x - bx1,
- y: B.y - by1
- },
- e2 = {
- x: B.x + bx2,
- y: B.y + by2
- },
- A = abc.A,
- v1 = {
- x: A.x + (e1.x - A.x) / (1 - t),
- y: A.y + (e1.y - A.y) / (1 - t)
- },
- v2 = {
- x: A.x + (e2.x - A.x) / t,
- y: A.y + (e2.y - A.y) / t
- },
- nc1 = {
- x: S.x + (v1.x - S.x) / t,
- y: S.y + (v1.y - S.y) / t
- },
- nc2 = {
- x: E.x + (v2.x - E.x) / (1 - t),
- y: E.y + (v2.y - E.y) / (1 - t)
- }; // ...done
-
- return new Bezier(S, nc1, nc2, E);
- }
-
- static getUtils() {
- return utils;
- }
-
- getUtils() {
- return Bezier.getUtils();
- }
-
- static get PolyBezier() {
- return PolyBezier;
- }
-
- valueOf() {
- return this.toString();
- }
-
- toString() {
- return utils.pointsToString(this.points);
- }
-
- toSVG() {
- if (this._3d) return false;
- const p = this.points,
- x = p[0].x,
- y = p[0].y,
- s = ["M", x, y, this.order === 2 ? "Q" : "C"];
-
- for (let i = 1, last = p.length; i < last; i++) {
- s.push(p[i].x);
- s.push(p[i].y);
- }
-
- return s.join(" ");
- }
-
- setRatios(ratios) {
- if (ratios.length !== this.points.length) {
- throw new Error("incorrect number of ratio values");
- }
-
- this.ratios = ratios;
- this._lut = []; // invalidate any precomputed LUT
- }
-
- verify() {
- const print = this.coordDigest();
-
- if (print !== this._print) {
- this._print = print;
- this.update();
- }
- }
-
- coordDigest() {
- return this.points.map(function (c, pos) {
- return "" + pos + c.x + c.y + (c.z ? c.z : 0);
- }).join("");
- }
-
- update() {
- // invalidate any precomputed LUT
- this._lut = [];
- this.dpoints = utils.derive(this.points, this._3d);
- this.computedirection();
- }
-
- computedirection() {
- const points = this.points;
- const angle = utils.angle(points[0], points[this.order], points[1]);
- this.clockwise = angle > 0;
- }
-
- length() {
- return utils.length(this.derivative.bind(this));
- }
-
- static getABC(order = 2, S, B, E, t = 0.5) {
- const u = utils.projectionratio(t, order),
- um = 1 - u,
- C = {
- x: u * S.x + um * E.x,
- y: u * S.y + um * E.y
- },
- s = utils.abcratio(t, order),
- A = {
- x: B.x + (B.x - C.x) / s,
- y: B.y + (B.y - C.y) / s
- };
- return {
- A,
- B,
- C,
- S,
- E
- };
- }
-
- getABC(t, B) {
- B = B || this.get(t);
- let S = this.points[0];
- let E = this.points[this.order];
- return Bezier.getABC(this.order, S, B, E, t);
- }
-
- getLUT(steps) {
- this.verify();
- steps = steps || 100;
-
- if (this._lut.length === steps) {
- return this._lut;
- }
-
- this._lut = []; // We want a range from 0 to 1 inclusive, so
- // we decrement and then use <= rather than <:
-
- steps--;
-
- for (let i = 0, p, t; i < steps; i++) {
- t = i / (steps - 1);
- p = this.compute(t);
- p.t = t;
-
- this._lut.push(p);
- }
-
- return this._lut;
- }
-
- on(point, error) {
- error = error || 5;
- const lut = this.getLUT(),
- hits = [];
-
- for (let i = 0, c, t = 0; i < lut.length; i++) {
- c = lut[i];
-
- if (utils.dist(c, point) < error) {
- hits.push(c);
- t += i / lut.length;
- }
- }
-
- if (!hits.length) return false;
- return t /= hits.length;
- }
-
- project(point) {
- // step 1: coarse check
- const LUT = this.getLUT(),
- l = LUT.length - 1,
- closest = utils.closest(LUT, point),
- mpos = closest.mpos,
- t1 = (mpos - 1) / l,
- t2 = (mpos + 1) / l,
- step = 0.1 / l; // step 2: fine check
-
- let mdist = closest.mdist,
- t = t1,
- ft = t,
- p;
- mdist += 1;
-
- for (let d; t < t2 + step; t += step) {
- p = this.compute(t);
- d = utils.dist(point, p);
-
- if (d < mdist) {
- mdist = d;
- ft = t;
- }
- }
-
- ft = ft < 0 ? 0 : ft > 1 ? 1 : ft;
- p = this.compute(ft);
- p.t = ft;
- p.d = mdist;
- return p;
- }
-
- get(t) {
- return this.compute(t);
- }
-
- point(idx) {
- return this.points[idx];
- }
-
- compute(t) {
- if (this.ratios) {
- return utils.computeWithRatios(t, this.points, this.ratios, this._3d);
- }
-
- return utils.compute(t, this.points, this._3d, this.ratios);
- }
-
- raise() {
- const p = this.points,
- np = [p[0]],
- k = p.length;
-
- for (let i = 1, pi, pim; i < k; i++) {
- pi = p[i];
- pim = p[i - 1];
- np[i] = {
- x: (k - i) / k * pi.x + i / k * pim.x,
- y: (k - i) / k * pi.y + i / k * pim.y
- };
- }
-
- np[k] = p[k - 1];
- return new Bezier(np);
- }
-
- derivative(t) {
- return utils.compute(t, this.dpoints[0]);
- }
-
- dderivative(t) {
- return utils.compute(t, this.dpoints[1]);
- }
-
- align() {
- let p = this.points;
- return new Bezier(utils.align(p, {
- p1: p[0],
- p2: p[p.length - 1]
- }));
- }
-
- curvature(t) {
- return utils.curvature(t, this.dpoints[0], this.dpoints[1], this._3d);
- }
-
- inflections() {
- return utils.inflections(this.points);
- }
-
- normal(t) {
- return this._3d ? this.__normal3(t) : this.__normal2(t);
- }
-
- __normal2(t) {
- const d = this.derivative(t);
- const q = sqrt$1(d.x * d.x + d.y * d.y);
- return {
- x: -d.y / q,
- y: d.x / q
- };
- }
-
- __normal3(t) {
- // see http://stackoverflow.com/questions/25453159
- const r1 = this.derivative(t),
- r2 = this.derivative(t + 0.01),
- q1 = sqrt$1(r1.x * r1.x + r1.y * r1.y + r1.z * r1.z),
- q2 = sqrt$1(r2.x * r2.x + r2.y * r2.y + r2.z * r2.z);
- r1.x /= q1;
- r1.y /= q1;
- r1.z /= q1;
- r2.x /= q2;
- r2.y /= q2;
- r2.z /= q2; // cross product
-
- const c = {
- x: r2.y * r1.z - r2.z * r1.y,
- y: r2.z * r1.x - r2.x * r1.z,
- z: r2.x * r1.y - r2.y * r1.x
- };
- const m = sqrt$1(c.x * c.x + c.y * c.y + c.z * c.z);
- c.x /= m;
- c.y /= m;
- c.z /= m; // rotation matrix
-
- const R = [c.x * c.x, c.x * c.y - c.z, c.x * c.z + c.y, c.x * c.y + c.z, c.y * c.y, c.y * c.z - c.x, c.x * c.z - c.y, c.y * c.z + c.x, c.z * c.z]; // normal vector:
-
- const n = {
- x: R[0] * r1.x + R[1] * r1.y + R[2] * r1.z,
- y: R[3] * r1.x + R[4] * r1.y + R[5] * r1.z,
- z: R[6] * r1.x + R[7] * r1.y + R[8] * r1.z
- };
- return n;
- }
-
- hull(t) {
- let p = this.points,
- _p = [],
- q = [],
- idx = 0;
- q[idx++] = p[0];
- q[idx++] = p[1];
- q[idx++] = p[2];
-
- if (this.order === 3) {
- q[idx++] = p[3];
- } // we lerp between all points at each iteration, until we have 1 point left.
-
-
- while (p.length > 1) {
- _p = [];
-
- for (let i = 0, pt, l = p.length - 1; i < l; i++) {
- pt = utils.lerp(t, p[i], p[i + 1]);
- q[idx++] = pt;
-
- _p.push(pt);
- }
-
- p = _p;
- }
-
- return q;
- }
-
- split(t1, t2) {
- // shortcuts
- if (t1 === 0 && !!t2) {
- return this.split(t2).left;
- }
-
- if (t2 === 1) {
- return this.split(t1).right;
- } // no shortcut: use "de Casteljau" iteration.
-
-
- const q = this.hull(t1);
- const result = {
- left: this.order === 2 ? new Bezier([q[0], q[3], q[5]]) : new Bezier([q[0], q[4], q[7], q[9]]),
- right: this.order === 2 ? new Bezier([q[5], q[4], q[2]]) : new Bezier([q[9], q[8], q[6], q[3]]),
- span: q
- }; // make sure we bind _t1/_t2 information!
-
- result.left._t1 = utils.map(0, 0, 1, this._t1, this._t2);
- result.left._t2 = utils.map(t1, 0, 1, this._t1, this._t2);
- result.right._t1 = utils.map(t1, 0, 1, this._t1, this._t2);
- result.right._t2 = utils.map(1, 0, 1, this._t1, this._t2); // if we have no t2, we're done
-
- if (!t2) {
- return result;
- } // if we have a t2, split again:
-
-
- t2 = utils.map(t2, t1, 1, 0, 1);
- return result.right.split(t2).left;
- }
-
- extrema() {
- const result = {};
- let roots = [];
- this.dims.forEach(function (dim) {
- let mfn = function (v) {
- return v[dim];
- };
-
- let p = this.dpoints[0].map(mfn);
- result[dim] = utils.droots(p);
-
- if (this.order === 3) {
- p = this.dpoints[1].map(mfn);
- result[dim] = result[dim].concat(utils.droots(p));
- }
-
- result[dim] = result[dim].filter(function (t) {
- return t >= 0 && t <= 1;
- });
- roots = roots.concat(result[dim].sort(utils.numberSort));
- }.bind(this));
- result.values = roots.sort(utils.numberSort).filter(function (v, idx) {
- return roots.indexOf(v) === idx;
- });
- return result;
- }
-
- bbox() {
- const extrema = this.extrema(),
- result = {};
- this.dims.forEach(function (d) {
- result[d] = utils.getminmax(this, d, extrema[d]);
- }.bind(this));
- return result;
- }
-
- overlaps(curve) {
- const lbbox = this.bbox(),
- tbbox = curve.bbox();
- return utils.bboxoverlap(lbbox, tbbox);
- }
-
- offset(t, d) {
- if (typeof d !== "undefined") {
- const c = this.get(t),
- n = this.normal(t);
- const ret = {
- c: c,
- n: n,
- x: c.x + n.x * d,
- y: c.y + n.y * d
- };
-
- if (this._3d) {
- ret.z = c.z + n.z * d;
- }
-
- return ret;
- }
-
- if (this._linear) {
- const nv = this.normal(0),
- coords = this.points.map(function (p) {
- const ret = {
- x: p.x + t * nv.x,
- y: p.y + t * nv.y
- };
-
- if (p.z && nv.z) {
- ret.z = p.z + t * nv.z;
- }
-
- return ret;
- });
- return [new Bezier(coords)];
- }
-
- return this.reduce().map(function (s) {
- if (s._linear) {
- return s.offset(t)[0];
- }
-
- return s.scale(t);
- });
- }
-
- simple() {
- if (this.order === 3) {
- const a1 = utils.angle(this.points[0], this.points[3], this.points[1]);
- const a2 = utils.angle(this.points[0], this.points[3], this.points[2]);
- if (a1 > 0 && a2 < 0 || a1 < 0 && a2 > 0) return false;
- }
-
- const n1 = this.normal(0);
- const n2 = this.normal(1);
- let s = n1.x * n2.x + n1.y * n2.y;
-
- if (this._3d) {
- s += n1.z * n2.z;
- }
-
- return abs$1(acos$1(s)) < pi$1 / 3;
- }
-
- reduce() {
- // TODO: examine these var types in more detail...
- let i,
- t1 = 0,
- t2 = 0,
- step = 0.01,
- segment,
- pass1 = [],
- pass2 = []; // first pass: split on extrema
-
- let extrema = this.extrema().values;
-
- if (extrema.indexOf(0) === -1) {
- extrema = [0].concat(extrema);
- }
-
- if (extrema.indexOf(1) === -1) {
- extrema.push(1);
- }
-
- for (t1 = extrema[0], i = 1; i < extrema.length; i++) {
- t2 = extrema[i];
- segment = this.split(t1, t2);
- segment._t1 = t1;
- segment._t2 = t2;
- pass1.push(segment);
- t1 = t2;
- } // second pass: further reduce these segments to simple segments
-
-
- pass1.forEach(function (p1) {
- t1 = 0;
- t2 = 0;
-
- while (t2 <= 1) {
- for (t2 = t1 + step; t2 <= 1 + step; t2 += step) {
- segment = p1.split(t1, t2);
-
- if (!segment.simple()) {
- t2 -= step;
-
- if (abs$1(t1 - t2) < step) {
- // we can never form a reduction
- return [];
- }
-
- segment = p1.split(t1, t2);
- segment._t1 = utils.map(t1, 0, 1, p1._t1, p1._t2);
- segment._t2 = utils.map(t2, 0, 1, p1._t1, p1._t2);
- pass2.push(segment);
- t1 = t2;
- break;
- }
- }
- }
-
- if (t1 < 1) {
- segment = p1.split(t1, 1);
- segment._t1 = utils.map(t1, 0, 1, p1._t1, p1._t2);
- segment._t2 = p1._t2;
- pass2.push(segment);
- }
- });
- return pass2;
- }
-
- scale(d) {
- const order = this.order;
- let distanceFn = false;
-
- if (typeof d === "function") {
- distanceFn = d;
- }
-
- if (distanceFn && order === 2) {
- return this.raise().scale(distanceFn);
- } // TODO: add special handling for degenerate (=linear) curves.
-
-
- const clockwise = this.clockwise;
- const r1 = distanceFn ? distanceFn(0) : d;
- const r2 = distanceFn ? distanceFn(1) : d;
- const v = [this.offset(0, 10), this.offset(1, 10)];
- const points = this.points;
- const np = [];
- const o = utils.lli4(v[0], v[0].c, v[1], v[1].c);
-
- if (!o) {
- throw new Error("cannot scale this curve. Try reducing it first.");
- } // move all points by distance 'd' wrt the origin 'o'
- // move end points by fixed distance along normal.
-
-
- [0, 1].forEach(function (t) {
- const p = np[t * order] = utils.copy(points[t * order]);
- p.x += (t ? r2 : r1) * v[t].n.x;
- p.y += (t ? r2 : r1) * v[t].n.y;
- });
-
- if (!distanceFn) {
- // move control points to lie on the intersection of the offset
- // derivative vector, and the origin-through-control vector
- [0, 1].forEach(t => {
- if (order === 2 && !!t) return;
- const p = np[t * order];
- const d = this.derivative(t);
- const p2 = {
- x: p.x + d.x,
- y: p.y + d.y
- };
- np[t + 1] = utils.lli4(p, p2, o, points[t + 1]);
- });
- return new Bezier(np);
- } // move control points by "however much necessary to
- // ensure the correct tangent to endpoint".
-
-
- [0, 1].forEach(function (t) {
- if (order === 2 && !!t) return;
- var p = points[t + 1];
- var ov = {
- x: p.x - o.x,
- y: p.y - o.y
- };
- var rc = distanceFn ? distanceFn((t + 1) / order) : d;
- if (distanceFn && !clockwise) rc = -rc;
- var m = sqrt$1(ov.x * ov.x + ov.y * ov.y);
- ov.x /= m;
- ov.y /= m;
- np[t + 1] = {
- x: p.x + rc * ov.x,
- y: p.y + rc * ov.y
- };
- });
- return new Bezier(np);
- }
-
- outline(d1, d2, d3, d4) {
- d2 = typeof d2 === "undefined" ? d1 : d2;
- const reduced = this.reduce(),
- len = reduced.length,
- fcurves = [];
- let bcurves = [],
- p,
- alen = 0,
- tlen = this.length();
- const graduated = typeof d3 !== "undefined" && typeof d4 !== "undefined";
-
- function linearDistanceFunction(s, e, tlen, alen, slen) {
- return function (v) {
- const f1 = alen / tlen,
- f2 = (alen + slen) / tlen,
- d = e - s;
- return utils.map(v, 0, 1, s + f1 * d, s + f2 * d);
- };
- } // form curve oulines
-
-
- reduced.forEach(function (segment) {
- const slen = segment.length();
-
- if (graduated) {
- fcurves.push(segment.scale(linearDistanceFunction(d1, d3, tlen, alen, slen)));
- bcurves.push(segment.scale(linearDistanceFunction(-d2, -d4, tlen, alen, slen)));
- } else {
- fcurves.push(segment.scale(d1));
- bcurves.push(segment.scale(-d2));
- }
-
- alen += slen;
- }); // reverse the "return" outline
-
- bcurves = bcurves.map(function (s) {
- p = s.points;
-
- if (p[3]) {
- s.points = [p[3], p[2], p[1], p[0]];
- } else {
- s.points = [p[2], p[1], p[0]];
- }
-
- return s;
- }).reverse(); // form the endcaps as lines
-
- const fs = fcurves[0].points[0],
- fe = fcurves[len - 1].points[fcurves[len - 1].points.length - 1],
- bs = bcurves[len - 1].points[bcurves[len - 1].points.length - 1],
- be = bcurves[0].points[0],
- ls = utils.makeline(bs, fs),
- le = utils.makeline(fe, be),
- segments = [ls].concat(fcurves).concat([le]).concat(bcurves);
- return new PolyBezier(segments);
- }
-
- outlineshapes(d1, d2, curveIntersectionThreshold) {
- d2 = d2 || d1;
- const outline = this.outline(d1, d2).curves;
- const shapes = [];
-
- for (let i = 1, len = outline.length; i < len / 2; i++) {
- const shape = utils.makeshape(outline[i], outline[len - i], curveIntersectionThreshold);
- shape.startcap.virtual = i > 1;
- shape.endcap.virtual = i < len / 2 - 1;
- shapes.push(shape);
- }
-
- return shapes;
- }
-
- intersects(curve, curveIntersectionThreshold) {
- if (!curve) return this.selfintersects(curveIntersectionThreshold);
-
- if (curve.p1 && curve.p2) {
- return this.lineIntersects(curve);
- }
-
- if (curve instanceof Bezier) {
- curve = curve.reduce();
- }
-
- return this.curveintersects(this.reduce(), curve, curveIntersectionThreshold);
- }
-
- lineIntersects(line) {
- const mx = min(line.p1.x, line.p2.x),
- my = min(line.p1.y, line.p2.y),
- MX = max(line.p1.x, line.p2.x),
- MY = max(line.p1.y, line.p2.y);
- return utils.roots(this.points, line).filter(t => {
- var p = this.get(t);
- return utils.between(p.x, mx, MX) && utils.between(p.y, my, MY);
- });
- }
-
- selfintersects(curveIntersectionThreshold) {
- // "simple" curves cannot intersect with their direct
- // neighbour, so for each segment X we check whether
- // it intersects [0:x-2][x+2:last].
- const reduced = this.reduce(),
- len = reduced.length - 2,
- results = [];
-
- for (let i = 0, result, left, right; i < len; i++) {
- left = reduced.slice(i, i + 1);
- right = reduced.slice(i + 2);
- result = this.curveintersects(left, right, curveIntersectionThreshold);
- results.push(...result);
- }
-
- return results;
- }
-
- curveintersects(c1, c2, curveIntersectionThreshold) {
- const pairs = []; // step 1: pair off any overlapping segments
-
- c1.forEach(function (l) {
- c2.forEach(function (r) {
- if (l.overlaps(r)) {
- pairs.push({
- left: l,
- right: r
- });
- }
- });
- }); // step 2: for each pairing, run through the convergence algorithm.
-
- let intersections = [];
- pairs.forEach(function (pair) {
- const result = utils.pairiteration(pair.left, pair.right, curveIntersectionThreshold);
-
- if (result.length > 0) {
- intersections = intersections.concat(result);
- }
- });
- return intersections;
- }
-
- arcs(errorThreshold) {
- errorThreshold = errorThreshold || 0.5;
- return this._iterate(errorThreshold, []);
- }
-
- _error(pc, np1, s, e) {
- const q = (e - s) / 4,
- c1 = this.get(s + q),
- c2 = this.get(e - q),
- ref = utils.dist(pc, np1),
- d1 = utils.dist(pc, c1),
- d2 = utils.dist(pc, c2);
- return abs$1(d1 - ref) + abs$1(d2 - ref);
- }
-
- _iterate(errorThreshold, circles) {
- let t_s = 0,
- t_e = 1,
- safety; // we do a binary search to find the "good `t` closest to no-longer-good"
-
- do {
- safety = 0; // step 1: start with the maximum possible arc
-
- t_e = 1; // points:
-
- let np1 = this.get(t_s),
- np2,
- np3,
- arc,
- prev_arc; // booleans:
-
- let curr_good = false,
- prev_good = false,
- done; // numbers:
-
- let t_m = t_e,
- prev_e = 1; // step 2: find the best possible arc
-
- do {
- prev_good = curr_good;
- prev_arc = arc;
- t_m = (t_s + t_e) / 2;
- np2 = this.get(t_m);
- np3 = this.get(t_e);
- arc = utils.getccenter(np1, np2, np3); //also save the t values
-
- arc.interval = {
- start: t_s,
- end: t_e
- };
-
- let error = this._error(arc, np1, t_s, t_e);
-
- curr_good = error <= errorThreshold;
- done = prev_good && !curr_good;
- if (!done) prev_e = t_e; // this arc is fine: we can move 'e' up to see if we can find a wider arc
-
- if (curr_good) {
- // if e is already at max, then we're done for this arc.
- if (t_e >= 1) {
- // make sure we cap at t=1
- arc.interval.end = prev_e = 1;
- prev_arc = arc; // if we capped the arc segment to t=1 we also need to make sure that
- // the arc's end angle is correct with respect to the bezier end point.
-
- if (t_e > 1) {
- let d = {
- x: arc.x + arc.r * cos$1(arc.e),
- y: arc.y + arc.r * sin$1(arc.e)
- };
- arc.e += utils.angle({
- x: arc.x,
- y: arc.y
- }, d, this.get(1));
- }
-
- break;
- } // if not, move it up by half the iteration distance
-
-
- t_e = t_e + (t_e - t_s) / 2;
- } else {
- // this is a bad arc: we need to move 'e' down to find a good arc
- t_e = t_m;
- }
- } while (!done && safety++ < 100);
-
- if (safety >= 100) {
- break;
- } // console.log("L835: [F] arc found", t_s, prev_e, prev_arc.x, prev_arc.y, prev_arc.s, prev_arc.e);
-
-
- prev_arc = prev_arc ? prev_arc : arc;
- circles.push(prev_arc);
- t_s = prev_e;
- } while (t_e < 1);
-
- return circles;
- }
-
-}
-
-exports.Bezier = Bezier;
generated by cgit v1.2.3 (git 2.46.2) at 2024-12-23 18:12:30 +0000