var Transform = require('./transform.js'); var ANGLES = 12; var VERYCROWD = 2; var SMALLANGLE = 0.05; var SMALLANGLE_CLEANMORE = 0.075; var CROWD = 4; var LOOSE = 6; var SMALL = 1e-4; var CLOSE = 1; function cross(z1, z2, z3) { return (z2.x - z1.x) * (z3.y - z1.y) - (z3.x - z1.x) * (z2.y - z1.y); } function dot(z1, z2, z3) { return (z2.x - z1.x) * (z3.x - z1.x) + (z3.y - z1.y) * (z2.y - z1.y); } function solveTS(a, b, c, out, flag) { var delta = b * b - 4 * a * c; if (delta > 0) { var t1 = (Math.sqrt(delta) - b) / (2 * a); var t2 = (-Math.sqrt(delta) - b) / (2 * a); if (flag) { if (t1 >= 0 && t1 <= 1) out.push(t1); if (t2 >= 0 && t2 <= 1) out.push(t2); } else { if (t1 > 0 && t1 < 1) out.push(t1); if (t2 > 0 && t2 < 1) out.push(t2); } } else if (delta === 0) { var t = -b / (2 * a); if (flag) { if (t >= 0 && t <= 1) out.push(t); } else { if (t > 0 && t < 1) out.push(t); } } } function findExtrema(z1, z2, z3, z4, out) { var a = 3 * (-z1.y + 3 * z2.y - 3 * z3.y + z4.y); var b = 6 * (z1.y - 2 * z2.y + z3.y); var c = 3 * (z2.y - z1.y); solveTS(a, b, c, out); } function findInflections(z1, z2, z3, z4, out) { var ax = z2.x - z1.x; var ay = z2.y - z1.y; var bx = z3.x - z2.x - ax; var by = z3.y - z2.y - ay; var cx = z4.x - z3.x - ax - 2 * bx; var cy = z4.y - z3.y - ay - 2 * by; solveTS(bx * cy - by * cx, ax * cy - ay * cx, ax * by - ay * bx, out, true); } function rotate(z, angle) { var c = Math.cos(angle), s = Math.sin(angle); return { x: c * z.x + s * z.y, y: -s * z.x + c * z.y }; } function ASCEND(a, b) { return a - b; } function fineAllExtrema(z1, z2, z3, z4, angles) { var exs = []; findInflections(z1, z2, z3, z4, exs); for (var a = 0; a < angles; a += 1) { findExtrema(z1, z2, z3, z4, exs); z1 = rotate(z1, Math.PI / angles); z2 = rotate(z2, Math.PI / angles); z3 = rotate(z3, Math.PI / angles); z4 = rotate(z4, Math.PI / angles); } return exs.sort(ASCEND); } function mix(z1, z2, t) { if (t <= 0) return z1; if (t >= 1) return z2; var x = (1 - t) * z1.x + t * z2.x, y = (1 - t) * z1.y + t * z2.y return { x: x, y: y }; } function bez2(z1, z2, z3, t) { if (t <= 0) return z1; if (t >= 1) return z3; var c1 = (1 - t) * (1 - t), c2 = 2 * (1 - t) * t, c3 = t * t; return { x: c1 * z1.x + c2 * z2.x + c3 * z3.x, y: c1 * z1.y + c2 * z2.y + c3 * z3.y }; } function bez3(z1, z2, z3, z4, t) { if (t <= 0) return z1; if (t >= 1) return z4; var c1 = (1 - t) * (1 - t) * (1 - t), c2 = 3 * t * (1 - t) * (1 - t), c3 = 3 * t * t * (1 - t), c4 = t * t * t; return { x: c1 * z1.x + c2 * z2.x + c3 * z3.x + c4 * z4.x, y: c1 * z1.y + c2 * z2.y + c3 * z3.y + c4 * z4.y }; } function splitBefore(z1, z2, z3, z4, t) { return [z1, mix(z1, z2, t), bez2(z1, z2, z3, t), bez3(z1, z2, z3, z4, t)]; } function splitAfter(z1, z2, z3, z4, t) { return [bez3(z1, z2, z3, z4, t), bez2(z2, z3, z4, t), mix(z3, z4, t), z4]; } function splitAtExtrema(z1, z2, z3, z4, angles, splitpoints) { var ts = fineAllExtrema(z1, z2, z3, z4, angles); if (ts[0] < SMALL) { ts[0] = 0; } else { ts.unshift(0); } if (ts[ts.length - 1] > 1 - SMALL) { ts[ts.length - 1] = 1; } else { ts.push(1); } for (var k = 0; k < ts.length; k++) { if (k > 0) { var t1 = ts[k - 1]; var t2 = ts[k]; var bef = splitBefore(z1, z2, z3, z4, t2); var seg = splitAfter(bef[0], bef[1], bef[2], bef[3], t1 / t2); seg[1].onCurve = seg[2].onCurve = false; seg[1].cubic = seg[2].cubic = true; seg[3].onCurve = true; splitpoints.push(seg[1], seg[2], seg[3]); } } } function splitSegment(z1, z2, z3, z4, angles, splitpoints) { var ts = []; var inflectAtEnd = false; findInflections(z1, z2, z3, z4, ts); ts = ts.sort(ASCEND); if (ts[0] < SMALL) { ts[0] = 0; splitpoints[splitpoints.length - 1].inflect = true; } else { ts.unshift(0); } if (ts[ts.length - 1] > 1 - SMALL) { inflectAtEnd = true; ts[ts.length - 1] = 1; } else { ts.push(1); } for (var k = 0; k < ts.length; k++) { if (k > 0) { var t1 = ts[k - 1]; var t2 = ts[k]; var bef = splitBefore(z1, z2, z3, z4, t2); var seg = splitAfter(bef[0], bef[1], bef[2], bef[3], t1 / t2); splitAtExtrema(seg[0], seg[1], seg[2], seg[3], angles, splitpoints); if (t2 < 1 || inflectAtEnd) splitpoints[splitpoints.length - 1].inflect = true; } } } function fitpts(p1, c1, c2, p2) { var d1 = { x: c1.x - p1.x, y: c1.y - p1.y }; var d2 = { x: c2.x - p2.x, y: c2.y - p2.y }; var det = d2.x * d1.y - d2.y * d1.x; if (Math.abs(det) < 1e-6) return null; var u = ((p2.y - p1.y) * d2.x - (p2.x - p1.x) * d2.y) / det; var v = ((p2.y - p1.y) * d1.x - (p2.x - p1.x) * d1.y) / det; if (u <= 0 || v <= 0) return null; var mid = { x: p1.x + d1.x * u, y: p1.y + d1.y * u }; return [mix(mid, p1, 1 / 3), mix(mid, p2, 1 / 3)]; } function distance(z1, z2) { return Math.sqrt((z1.x - z2.x) * (z1.x - z2.x) + (z1.y - z2.y) * (z1.y - z2.y)); } function veryclose(z1, z2) { return (z1.x - z2.x) * (z1.x - z2.x) + (z1.y - z2.y) * (z1.y - z2.y) <= SMALL; } function angleBetween(z1, z2, z3, z4) { return (Math.atan2(z2.y - z1.y, z2.x - z1.x) - Math.atan2(z4.y - z3.y, z4.x - z3.x)) % Math.PI; } function pldistance(z1, z2, z) { return Math.abs((z2.y - z1.y) * z.x - (z2.x - z1.x) * z.y + z2.x * z1.y - z2.y * z1.x) / Math.sqrt((z2.x - z1.x) * (z2.x - z1.x) + (z2.y - z1.y) * (z2.y - z1.y)); } function estimateSegments(z1, z2) { var hspan = Math.abs(z1.x - z2.x); var vspan = Math.abs(z1.y - z2.y); return hspan <= 5 * CROWD || vspan <= 5 * CROWD ? VERYCROWD : hspan <= 10 * LOOSE || vspan <= 10 * LOOSE ? CROWD : LOOSE; } function enoughRotate(bef, z0, z1, z2, aft, cleanMore, flagl, flagr) { var angleRotatedBefore = Math.abs(angleBetween(bef.next || z1, bef, z1, z0)); var angleRotatedAfter = Math.abs(angleBetween(aft.prev || z1, aft, z1, z2)); var smallanglel = (cleanMore ? SMALLANGLE_CLEANMORE : SMALLANGLE) * (flagl && cleanMore ? 1 : 2); var smallangler = (cleanMore ? SMALLANGLE_CLEANMORE : SMALLANGLE) * (flagr && cleanMore ? 1 : 2); return !((angleRotatedBefore < smallanglel || angleRotatedBefore > Math.PI - smallanglel) && pldistance(z1, z0, bef) <= CLOSE && distance(z1, bef) <= 5 * CROWD || (flagr ? false : (angleRotatedAfter < smallangler || angleRotatedAfter > Math.PI - smallangler) && pldistance(z1, z2, aft) <= CLOSE && distance(z1, aft) <= 5 * CROWD)); } function fairify(scurve, gizmo, denseQ, cleanMore) { for (var j = 0; j < scurve.length; j++) { scurve[j] = Transform.untransform(gizmo, scurve[j]); } var splitpoints = [scurve[0]]; var last = scurve[0]; for (var j = 1; j < scurve.length; j++) { if (scurve[j].onCurve) { splitpoints.push(last = scurve[j]); } else if (scurve[j].cubic) { var z1 = last, z2 = scurve[j], z3 = scurve[j + 1], z4 = scurve[j + 2]; if (!(veryclose(z1, z2) && veryclose(z2, z3) && veryclose(z3, z4))) { splitSegment(z1, z2, z3, z4, ANGLES, splitpoints); last = z4; } j += 2; } else { var z1 = last, zm = scurve[j], z4 = scurve[j + 1]; if (!(veryclose(z1, zm) && veryclose(zm, z4))) { var z2 = mix(zm, z1, 1 / 3); var z3 = mix(zm, z4, 1 / 3); splitSegment(z1, z2, z3, z4, ANGLES, splitpoints); last = z4; } j += 1; } } // Mark corners and extrema for (var j = 1; j < splitpoints.length - 1; j++) { if (splitpoints[j].onCurve && !splitpoints[j - 1].onCurve) { splitpoints[j].prev = splitpoints[j - 1]; } if (splitpoints[j].onCurve && !splitpoints[j + 1].onCurve) { splitpoints[j].next = splitpoints[j + 1]; } if (splitpoints[j].onCurve && !splitpoints[j - 1].onCurve && !splitpoints[j + 1].onCurve) { var z1 = splitpoints[j], z0 = splitpoints[j - 1], z2 = splitpoints[j + 1]; if (cross(z1, z0, z2) < 1e-6 && dot(z1, z0, z2) < 0) { var angle0 = Math.atan2(z2.y - z0.y, z2.x - z0.x); var angle = Math.abs(angle0 / Math.PI * 2 % 1); if (Math.abs(Math.abs(angle0) - Math.PI / 2) <= SMALL || angle <= SMALL || angle >= 1 - SMALL) { z1.mark = true; // extremum z1.inflect = false; } else { var isInflection = false; if (j > 2 && j < splitpoints.length - 2) { var za = bez3(z1, z0, splitpoints[j - 2], splitpoints[j - 3], SMALL); var zb = bez3(z1, z2, splitpoints[j + 2], splitpoints[j + 3], SMALL); var inflect = ((z0.y - z2.y) * (za.x - z0.x) + (z2.x - z0.x) * (za.y - z0.y)) * ((z0.y - z2.y) * (zb.x - z0.x) + (z2.x - z0.x) * (zb.y - z0.y)); if (inflect < 0) isInflection = true; } if (z1.inflect || isInflection) { z1.mark = true; z1.asinflect = true; } } } else { z1.mark = true; // also corner } } else if (splitpoints[j].onCurve) { splitpoints[j].mark = true; // corner } } splitpoints[0].mark = splitpoints[splitpoints.length - 1].mark = true; // Mark cleanup inflections for (var pass = 0; pass < 2; pass++) { for (var j = 1; j < splitpoints.length - 1; j++) { if (splitpoints[j].mark) { for (var k = j - 1; k >= 0 && !splitpoints[k].mark; k--); lastmark = splitpoints[k]; for (var k = j + 1; k < splitpoints.length && !splitpoints[k].mark; k++); nextmark = splitpoints[k]; } if (splitpoints[j].mark && splitpoints[j].asinflect) { var z1 = splitpoints[j], z0 = splitpoints[j - 1], z2 = splitpoints[j + 1]; if (!(denseQ || enoughRotate(lastmark, z0, z1, z2, nextmark, cleanMore, lastmark.asinflect, nextmark.asinflect))) { //z1.mark = false; z0.remove = z1.remove = z2.remove = true; } } } for (var j = 0; j < splitpoints.length; j++) if (splitpoints[j].remove) { splitpoints[j].mark = false; } } // Mark diagonals var lastmark = splitpoints[0]; for (var k = 1; k < splitpoints.length && !splitpoints[k].mark; k++); var nextmark = splitpoints[k]; var segments = estimateSegments(lastmark, nextmark); for (var j = 1; j < splitpoints.length - 1; j++) { if (splitpoints[j].mark) { lastmark = splitpoints[j]; for (var k = j + 1; k < splitpoints.length && !splitpoints[k].mark; k++); nextmark = splitpoints[k]; segments = estimateSegments(lastmark, nextmark); } if (splitpoints[j].onCurve && !splitpoints[j].mark) { var z1 = splitpoints[j], z0 = splitpoints[j - 1], z2 = splitpoints[j + 1]; var angle0 = Math.atan2(z2.y - z0.y, z2.x - z0.x); var angle = Math.abs(angle0 / Math.PI * segments % 1); var angleRotatedBefore = Math.abs(angleBetween(z1, lastmark, z1, z0)); var angleRotatedAfter = Math.abs(angleBetween(z1, nextmark, z1, z2)); if (!(Math.abs(Math.abs(angle0) - Math.PI / 2) <= SMALL || angle <= SMALL || angle >= 1 - SMALL) || !(denseQ || enoughRotate(lastmark, z0, z1, z2, nextmark))) { z1.remove = z0.remove = z2.remove = true; } } } // Rebuild curve for (var j = 0; j < splitpoints.length; j++) if (splitpoints[j].onCurve && !splitpoints[j].remove && splitpoints[j + 1] && !splitpoints[j + 1].onCurve) { for (var k = j + 2; k < splitpoints.length && splitpoints[k].remove; k++); if (k - j > 2) { var zs = fitpts(splitpoints[j], splitpoints[j + 1], splitpoints[k], splitpoints[k + 1]); if (zs) { zs[0].onCurve = zs[1].onCurve = false; zs[0].cubic = zs[1].cubic = true; splitpoints[j + 1] = zs[0]; splitpoints[k] = zs[1]; } } j = k; } var ans = []; for (var j = 0; j < splitpoints.length; j++)if (splitpoints[j] && !splitpoints[j].remove) { ans.push(Transform.transformPoint(gizmo, splitpoints[j])); } return ans; } module.exports = fairify;