"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;