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skia2/tools/pathops_sorter.htm
caryclark 08bc8488fa fix multiple intersection logic 
When three or more curves intersect at the same point, ensure that
each curve records the intersections of the others. This fixes a
number of cubic tests.

TBR=reed@google.com
BUG=skia:3588

Review URL: https://codereview.chromium.org/1105943002
2015-04-24 09:08:57 -07:00

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<!DOCTYPE html>
<html lang="en" xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<title></title>
<div style="height:0">
<div id="sect1">
{{{2.0185184099245816, 2.3784720550756902}, {1.9467591438442469, 2.1736109238117933}, {1.8796295076608658, 1.9722220152616501}, {1.8148146867752075, 1.7777775526046753}}},
{{{2.0185184099245816, 2.3784720550756902}, {1.9467591438442469, 2.1736109238117933}, {1.8796295076608658, 1.9722220152616501}, {1.8148146867752075, 1.7777775526046753}}},
</div>
</div>
<script type="text/javascript">
var testDivs = [
sect1,
];
var decimal_places = 3;
var tests = [];
var testTitles = [];
var testIndex = 0;
var ctx;
var subscale = 1;
var xmin, xmax, ymin, ymax;
var scale;
var initScale;
var mouseX, mouseY;
var mouseDown = false;
var srcLeft, srcTop;
var screenWidth, screenHeight;
var drawnPts;
var curveT = 0;
var curveW = -1;
var lastX, lastY;
var activeCurve = [];
var activePt;
var ids = [];
var focus_on_selection = 0;
var draw_t = false;
var draw_w = false;
var draw_closest_t = false;
var draw_cubic_red = false;
var draw_derivative = false;
var draw_endpoints = 2;
var draw_id = 0;
var draw_midpoint = 0;
var draw_mouse_xy = false;
var draw_order = false;
var draw_point_xy = false;
var draw_ray_intersect = false;
var draw_quarterpoint = 0;
var draw_tangents = 1;
var draw_sortpoint = 0;
var retina_scale = !!window.devicePixelRatio;
function parse(test, title) {
var curveStrs = test.split("{{");
var pattern = /-?\d+\.*\d*e?-?\d*/g;
var curves = [];
for (var c in curveStrs) {
var curveStr = curveStrs[c];
var idPart = curveStr.split("id=");
var id = -1;
if (idPart.length == 2) {
id = parseInt(idPart[1]);
curveStr = idPart[0];
}
var points = curveStr.match(pattern);
var pts = [];
for (var wd in points) {
var num = parseFloat(points[wd]);
if (isNaN(num)) continue;
pts.push(num);
}
if (pts.length > 2) {
curves.push(pts);
}
if (id >= 0) {
ids.push(id);
ids.push(pts);
}
}
if (curves.length >= 1) {
tests.push(curves);
testTitles.push(title);
}
}
function init(test) {
var canvas = document.getElementById('canvas');
if (!canvas.getContext) return;
ctx = canvas.getContext('2d');
var resScale = retina_scale && window.devicePixelRatio ? window.devicePixelRatio : 1;
var unscaledWidth = window.innerWidth - 20;
var unscaledHeight = window.innerHeight - 20;
screenWidth = unscaledWidth;
screenHeight = unscaledHeight;
canvas.width = unscaledWidth * resScale;
canvas.height = unscaledHeight * resScale;
canvas.style.width = unscaledWidth + 'px';
canvas.style.height = unscaledHeight + 'px';
if (resScale != 1) {
ctx.scale(resScale, resScale);
}
xmin = Infinity;
xmax = -Infinity;
ymin = Infinity;
ymax = -Infinity;
for (var curves in test) {
var curve = test[curves];
var last = curve.length - (curve.length % 2 == 1 ? 1 : 0);
for (var idx = 0; idx < last; idx += 2) {
xmin = Math.min(xmin, curve[idx]);
xmax = Math.max(xmax, curve[idx]);
ymin = Math.min(ymin, curve[idx + 1]);
ymax = Math.max(ymax, curve[idx + 1]);
}
}
xmin -= Math.min(1, Math.max(xmax - xmin, ymax - ymin));
var testW = xmax - xmin;
var testH = ymax - ymin;
subscale = 1;
while (testW * subscale < 0.1 && testH * subscale < 0.1) {
subscale *= 10;
}
while (testW * subscale > 10 && testH * subscale > 10) {
subscale /= 10;
}
setScale(xmin, xmax, ymin, ymax);
mouseX = (screenWidth / 2) / scale + srcLeft;
mouseY = (screenHeight / 2) / scale + srcTop;
initScale = scale;
}
function setScale(x0, x1, y0, y1) {
var srcWidth = x1 - x0;
var srcHeight = y1 - y0;
var usableWidth = screenWidth;
var xDigits = Math.ceil(Math.log(Math.abs(xmax)) / Math.log(10));
var yDigits = Math.ceil(Math.log(Math.abs(ymax)) / Math.log(10));
usableWidth -= (xDigits + yDigits) * 10;
usableWidth -= decimal_places * 10;
var hscale = usableWidth / srcWidth;
var vscale = screenHeight / srcHeight;
scale = Math.min(hscale, vscale);
var invScale = 1 / scale;
var sxmin = x0 - invScale * 5;
var symin = y0 - invScale * 10;
var sxmax = x1 + invScale * (6 * decimal_places + 10);
var symax = y1 + invScale * 10;
srcWidth = sxmax - sxmin;
srcHeight = symax - symin;
hscale = usableWidth / srcWidth;
vscale = screenHeight / srcHeight;
scale = Math.min(hscale, vscale);
srcLeft = sxmin;
srcTop = symin;
}
function dxy_at_t(curve, t) {
var dxy = {};
if (curve.length == 6) {
var a = t - 1;
var b = 1 - 2 * t;
var c = t;
dxy.x = a * curve[0] + b * curve[2] + c * curve[4];
dxy.y = a * curve[1] + b * curve[3] + c * curve[5];
} else if (curve.length == 7) {
var p20x = curve[4] - curve[0];
var p20y = curve[5] - curve[1];
var p10xw = (curve[2] - curve[0]) * curve[6];
var p10yw = (curve[3] - curve[1]) * curve[6];
var coeff0x = curve[6] * p20x - p20x;
var coeff0y = curve[6] * p20y - p20y;
var coeff1x = p20x - 2 * p10xw;
var coeff1y = p20y - 2 * p10yw;
dxy.x = t * (t * coeff0x + coeff1x) + p10xw;
dxy.y = t * (t * coeff0y + coeff1y) + p10yw;
} else if (curve.length == 8) {
var one_t = 1 - t;
var a = curve[0];
var b = curve[2];
var c = curve[4];
var d = curve[6];
dxy.x = 3 * ((b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t);
a = curve[1];
b = curve[3];
c = curve[5];
d = curve[7];
dxy.y = 3 * ((b - a) * one_t * one_t + 2 * (c - b) * t * one_t + (d - c) * t * t);
}
return dxy;
}
var flt_epsilon = 1.19209290E-07;
function approximately_zero(A) {
return Math.abs(A) < flt_epsilon;
}
function approximately_zero_inverse(A) {
return Math.abs(A) > (1 / flt_epsilon);
}
function quad_real_roots(A, B, C) {
var s = [];
var p = B / (2 * A);
var q = C / A;
if (approximately_zero(A) && (approximately_zero_inverse(p)
|| approximately_zero_inverse(q))) {
if (approximately_zero(B)) {
if (C == 0) {
s[0] = 0;
}
return s;
}
s[0] = -C / B;
return s;
}
/* normal form: x^2 + px + q = 0 */
var p2 = p * p;
if (!approximately_zero(p2 - q) && p2 < q) {
return s;
}
var sqrt_D = 0;
if (p2 > q) {
sqrt_D = Math.sqrt(p2 - q);
}
s[0] = sqrt_D - p;
var flip = -sqrt_D - p;
if (!approximately_zero(s[0] - flip)) {
s[1] = flip;
}
return s;
}
function cubic_real_roots(A, B, C, D) {
if (approximately_zero(A)) { // we're just a quadratic
return quad_real_roots(B, C, D);
}
if (approximately_zero(D)) { // 0 is one root
var s = quad_real_roots(A, B, C);
for (var i = 0; i < s.length; ++i) {
if (approximately_zero(s[i])) {
return s;
}
}
s.push(0);
return s;
}
if (approximately_zero(A + B + C + D)) { // 1 is one root
var s = quad_real_roots(A, A + B, -D);
for (var i = 0; i < s.length; ++i) {
if (approximately_zero(s[i] - 1)) {
return s;
}
}
s.push(1);
return s;
}
var a, b, c;
var invA = 1 / A;
a = B * invA;
b = C * invA;
c = D * invA;
var a2 = a * a;
var Q = (a2 - b * 3) / 9;
var R = (2 * a2 * a - 9 * a * b + 27 * c) / 54;
var R2 = R * R;
var Q3 = Q * Q * Q;
var R2MinusQ3 = R2 - Q3;
var adiv3 = a / 3;
var r;
var roots = [];
if (R2MinusQ3 < 0) { // we have 3 real roots
var theta = Math.acos(R / Math.sqrt(Q3));
var neg2RootQ = -2 * Math.sqrt(Q);
r = neg2RootQ * Math.cos(theta / 3) - adiv3;
roots.push(r);
r = neg2RootQ * Math.cos((theta + 2 * Math.PI) / 3) - adiv3;
if (!approximately_zero(roots[0] - r)) {
roots.push(r);
}
r = neg2RootQ * Math.cos((theta - 2 * Math.PI) / 3) - adiv3;
if (!approximately_zero(roots[0] - r) && (roots.length == 1
|| !approximately_zero(roots[1] - r))) {
roots.push(r);
}
} else { // we have 1 real root
var sqrtR2MinusQ3 = Math.sqrt(R2MinusQ3);
var A = Math.abs(R) + sqrtR2MinusQ3;
A = Math.pow(A, 1/3);
if (R > 0) {
A = -A;
}
if (A != 0) {
A += Q / A;
}
r = A - adiv3;
roots.push(r);
if (approximately_zero(R2 - Q3)) {
r = -A / 2 - adiv3;
if (!approximately_zero(roots[0] - r)) {
roots.push(r);
}
}
}
return roots;
}
function approximately_zero_or_more(tValue) {
return tValue >= -flt_epsilon;
}
function approximately_one_or_less(tValue) {
return tValue <= 1 + flt_epsilon;
}
function approximately_less_than_zero(tValue) {
return tValue < flt_epsilon;
}
function approximately_greater_than_one(tValue) {
return tValue > 1 - flt_epsilon;
}
function add_valid_ts(s) {
var t = [];
nextRoot:
for (var index = 0; index < s.length; ++index) {
var tValue = s[index];
if (approximately_zero_or_more(tValue) && approximately_one_or_less(tValue)) {
if (approximately_less_than_zero(tValue)) {
tValue = 0;
} else if (approximately_greater_than_one(tValue)) {
tValue = 1;
}
for (var idx2 = 0; idx2 < t.length; ++idx2) {
if (approximately_zero(t[idx2] - tValue)) {
continue nextRoot;
}
}
t.push(tValue);
}
}
return t;
}
function quad_roots(A, B, C) {
var s = quad_real_roots(A, B, C);
var foundRoots = add_valid_ts(s);
return foundRoots;
}
function cubic_roots(A, B, C, D) {
var s = cubic_real_roots(A, B, C, D);
var foundRoots = add_valid_ts(s);
return foundRoots;
}
function ray_curve_intersect(startPt, endPt, curve) {
var adj = endPt[0] - startPt[0];
var opp = endPt[1] - startPt[1];
var r = [];
var len = (curve.length == 7 ? 6 : curve.length) / 2;
for (var n = 0; n < len; ++n) {
r[n] = (curve[n * 2 + 1] - startPt[1]) * adj - (curve[n * 2] - startPt[0]) * opp;
}
if (curve.length == 6) {
var A = r[2];
var B = r[1];
var C = r[0];
A += C - 2 * B; // A = a - 2*b + c
B -= C; // B = -(b - c)
return quad_roots(A, 2 * B, C);
}
if (curve.length == 7) {
var A = r[2];
var B = r[1] * curve[6];
var C = r[0];
A += C - 2 * B; // A = a - 2*b + c
B -= C; // B = -(b - c)
return quad_roots(A, 2 * B, C);
}
var A = r[3]; // d
var B = r[2] * 3; // 3*c
var C = r[1] * 3; // 3*b
var D = r[0]; // a
A -= D - C + B; // A = -a + 3*b - 3*c + d
B += 3 * D - 2 * C; // B = 3*a - 6*b + 3*c
C -= 3 * D; // C = -3*a + 3*b
return cubic_roots(A, B, C, D);
}
function x_at_t(curve, t) {
var one_t = 1 - t;
if (curve.length == 4) {
return one_t * curve[0] + t * curve[2];
}
var one_t2 = one_t * one_t;
var t2 = t * t;
if (curve.length == 6) {
return one_t2 * curve[0] + 2 * one_t * t * curve[2] + t2 * curve[4];
}
if (curve.length == 7) {
var numer = one_t2 * curve[0] + 2 * one_t * t * curve[2] * curve[6]
+ t2 * curve[4];
var denom = one_t2 + 2 * one_t * t * curve[6]
+ t2;
return numer / denom;
}
var a = one_t2 * one_t;
var b = 3 * one_t2 * t;
var c = 3 * one_t * t2;
var d = t2 * t;
return a * curve[0] + b * curve[2] + c * curve[4] + d * curve[6];
}
function y_at_t(curve, t) {
var one_t = 1 - t;
if (curve.length == 4) {
return one_t * curve[1] + t * curve[3];
}
var one_t2 = one_t * one_t;
var t2 = t * t;
if (curve.length == 6) {
return one_t2 * curve[1] + 2 * one_t * t * curve[3] + t2 * curve[5];
}
if (curve.length == 7) {
var numer = one_t2 * curve[1] + 2 * one_t * t * curve[3] * curve[6]
+ t2 * curve[5];
var denom = one_t2 + 2 * one_t * t * curve[6]
+ t2;
return numer / denom;
}
var a = one_t2 * one_t;
var b = 3 * one_t2 * t;
var c = 3 * one_t * t2;
var d = t2 * t;
return a * curve[1] + b * curve[3] + c * curve[5] + d * curve[7];
}
function drawPointAtT(curve) {
var x = x_at_t(curve, curveT);
var y = y_at_t(curve, curveT);
drawPoint(x, y);
}
function drawLine(x1, y1, x2, y2) {
ctx.beginPath();
ctx.moveTo((x1 - srcLeft) * scale,
(y1 - srcTop) * scale);
ctx.lineTo((x2 - srcLeft) * scale,
(y2 - srcTop) * scale);
ctx.stroke();
}
function drawPoint(px, py) {
for (var pts = 0; pts < drawnPts.length; pts += 2) {
var x = drawnPts[pts];
var y = drawnPts[pts + 1];
if (px == x && py == y) {
return;
}
}
drawnPts.push(px);
drawnPts.push(py);
var _px = (px - srcLeft) * scale;
var _py = (py - srcTop) * scale;
ctx.beginPath();
ctx.arc(_px, _py, 3, 0, Math.PI * 2, true);
ctx.closePath();
ctx.stroke();
if (draw_point_xy) {
var label = px.toFixed(decimal_places) + ", " + py.toFixed(decimal_places);
ctx.font = "normal 10px Arial";
ctx.textAlign = "left";
ctx.fillStyle = "black";
ctx.fillText(label, _px + 5, _py);
}
}
function drawPointSolid(px, py) {
drawPoint(px, py);
ctx.fillStyle = "rgba(0,0,0, 0.4)";
ctx.fill();
}
function crossPt(origin, pt1, pt2) {
return ((pt1[0] - origin[0]) * (pt2[1] - origin[1])
- (pt1[1] - origin[1]) * (pt2[0] - origin[0])) > 0 ? 0 : 1;
}
// may not work well for cubics
function curveClosestT(curve, x, y) {
var closest = -1;
var closestDist = Infinity;
var l = Infinity, t = Infinity, r = -Infinity, b = -Infinity;
for (var i = 0; i < 16; ++i) {
var testX = x_at_t(curve, i / 16);
l = Math.min(testX, l);
r = Math.max(testX, r);
var testY = y_at_t(curve, i / 16);
t = Math.min(testY, t);
b = Math.max(testY, b);
var dx = testX - x;
var dy = testY - y;
var dist = dx * dx + dy * dy;
if (closestDist > dist) {
closestDist = dist;
closest = i;
}
}
var boundsX = r - l;
var boundsY = b - t;
var boundsDist = boundsX * boundsX + boundsY * boundsY;
if (closestDist > boundsDist) {
return -1;
}
console.log("closestDist = " + closestDist + " boundsDist = " + boundsDist
+ " t = " + closest / 16);
return closest / 16;
}
var kMaxConicToQuadPOW2 = 5;
function computeQuadPOW2(curve, tol) {
var a = curve[6] - 1;
var k = a / (4 * (2 + a));
var x = k * (curve[0] - 2 * curve[2] + curve[4]);
var y = k * (curve[1] - 2 * curve[3] + curve[5]);
var error = Math.sqrt(x * x + y * y);
var pow2;
for (pow2 = 0; pow2 < kMaxConicToQuadPOW2; ++pow2) {
if (error <= tol) {
break;
}
error *= 0.25;
}
return pow2;
}
function subdivide_w_value(w) {
return Math.sqrt(0.5 + w * 0.5);
}
function chop(curve, part1, part2) {
var w = curve[6];
var scale = 1 / (1 + w);
part1[0] = curve[0];
part1[1] = curve[1];
part1[2] = (curve[0] + curve[2] * w) * scale;
part1[3] = (curve[1] + curve[3] * w) * scale;
part1[4] = part2[0] = (curve[0] + (curve[2] * w) * 2 + curve[4]) * scale * 0.5;
part1[5] = part2[1] = (curve[1] + (curve[3] * w) * 2 + curve[5]) * scale * 0.5;
part2[2] = (curve[2] * w + curve[4]) * scale;
part2[3] = (curve[3] * w + curve[5]) * scale;
part2[4] = curve[4];
part2[5] = curve[5];
part1[6] = part2[6] = subdivide_w_value(w);
}
function subdivide(curve, level, pts) {
if (0 == level) {
pts.push(curve[2]);
pts.push(curve[3]);
pts.push(curve[4]);
pts.push(curve[5]);
} else {
var part1 = [], part2 = [];
chop(curve, part1, part2);
--level;
subdivide(part1, level, pts);
subdivide(part2, level, pts);
}
}
function chopIntoQuadsPOW2(curve, pow2, pts) {
subdivide(curve, pow2, pts);
return 1 << pow2;
}
function drawConic(curve, srcLeft, srcTop, scale) {
var tol = 1 / scale;
var pow2 = computeQuadPOW2(curve, tol);
var pts = [];
chopIntoQuadsPOW2(curve, pow2, pts);
for (var i = 0; i < pts.length; i += 4) {
ctx.quadraticCurveTo(
(pts[i + 0] - srcLeft) * scale, (pts[i + 1] - srcTop) * scale,
(pts[i + 2] - srcLeft) * scale, (pts[i + 3] - srcTop) * scale);
}
}
function draw(test, title) {
ctx.font = "normal 50px Arial";
ctx.textAlign = "left";
ctx.fillStyle = "rgba(0,0,0, 0.1)";
ctx.fillText(title, 50, 50);
ctx.font = "normal 10px Arial";
// ctx.lineWidth = "1.001"; "0.999";
var hullStarts = [];
var hullEnds = [];
var midSpokes = [];
var midDist = [];
var origin = [];
var shortSpokes = [];
var shortDist = [];
var sweeps = [];
drawnPts = [];
for (var curves in test) {
var curve = test[curves];
origin.push(curve[0]);
origin.push(curve[1]);
var startPt = [];
startPt.push(curve[2]);
startPt.push(curve[3]);
hullStarts.push(startPt);
var endPt = [];
if (curve.length == 4) {
endPt.push(curve[2]);
endPt.push(curve[3]);
} else if (curve.length == 6 || curve.length == 7) {
endPt.push(curve[4]);
endPt.push(curve[5]);
} else if (curve.length == 8) {
endPt.push(curve[6]);
endPt.push(curve[7]);
}
hullEnds.push(endPt);
var sweep = crossPt(origin, startPt, endPt);
sweeps.push(sweep);
var midPt = [];
midPt.push(x_at_t(curve, 0.5));
midPt.push(y_at_t(curve, 0.5));
midSpokes.push(midPt);
var shortPt = [];
shortPt.push(x_at_t(curve, 0.25));
shortPt.push(y_at_t(curve, 0.25));
shortSpokes.push(shortPt);
var dx = midPt[0] - origin[0];
var dy = midPt[1] - origin[1];
var dist = Math.sqrt(dx * dx + dy * dy);
midDist.push(dist);
dx = shortPt[0] - origin[0];
dy = shortPt[1] - origin[1];
dist = Math.sqrt(dx * dx + dy * dy);
shortDist.push(dist);
}
var intersect = [];
var useIntersect = false;
var maxWidth = Math.max(xmax - xmin, ymax - ymin);
for (var curves in test) {
var curve = test[curves];
if (curve.length >= 6 && curve.length <= 8) {
var opp = curves == 0 || curves == 1 ? 0 : 1;
var sects = ray_curve_intersect(origin, hullEnds[opp], curve);
intersect.push(sects);
if (sects.length > 1) {
var intersection = sects[0];
if (intersection == 0) {
intersection = sects[1];
}
var ix = x_at_t(curve, intersection) - origin[0];
var iy = y_at_t(curve, intersection) - origin[1];
var ex = hullEnds[opp][0] - origin[0];
var ey = hullEnds[opp][1] - origin[1];
if (ix * ex >= 0 && iy * ey >= 0) {
var iDist = Math.sqrt(ix * ix + iy * iy);
var eDist = Math.sqrt(ex * ex + ey * ey);
var delta = Math.abs(iDist - eDist) / maxWidth;
if (delta > (curve.length != 8 ? 1e-5 : 1e-4)) {
useIntersect ^= true;
}
}
}
}
}
var midLeft = curves != 0 ? crossPt(origin, midSpokes[0], midSpokes[1]) : 0;
var firstInside;
if (useIntersect) {
var sect1 = intersect[0].length > 1;
var sIndex = sect1 ? 0 : 1;
var sects = intersect[sIndex];
var intersection = sects[0];
if (intersection == 0) {
intersection = sects[1];
}
var curve = test[sIndex];
var ix = x_at_t(curve, intersection) - origin[0];
var iy = y_at_t(curve, intersection) - origin[1];
var opp = sect1 ? 1 : 0;
var ex = hullEnds[opp][0] - origin[0];
var ey = hullEnds[opp][1] - origin[1];
var iDist = ix * ix + iy * iy;
var eDist = ex * ex + ey * ey;
firstInside = (iDist > eDist) ^ (sIndex == 0) ^ sweeps[0];
// console.log("iDist=" + iDist + " eDist=" + eDist + " sIndex=" + sIndex
// + " sweeps[0]=" + sweeps[0]);
} else {
// console.log("midLeft=" + midLeft);
firstInside = midLeft != 0;
}
var shorter = midDist[1] < midDist[0];
var shortLeft = shorter ? crossPt(origin, shortSpokes[0], midSpokes[1])
: crossPt(origin, midSpokes[0], shortSpokes[1]);
var startCross = crossPt(origin, hullStarts[0], hullStarts[1]);
var disallowShort = midLeft == startCross && midLeft == sweeps[0]
&& midLeft == sweeps[1];
// console.log("midLeft=" + midLeft + " startCross=" + startCross);
var intersectIndex = 0;
for (var curves in test) {
var curve = test[draw_id != 2 ? curves : test.length - curves - 1];
if (curve.length != 4 && curve.length != 6 && curve.length != 7 && curve.length != 8) {
continue;
}
ctx.lineWidth = 1;
if (draw_tangents != 0) {
if (draw_cubic_red ? curve.length == 8 : firstInside == curves) {
ctx.strokeStyle = "rgba(255,0,0, 0.3)";
} else {
ctx.strokeStyle = "rgba(0,0,255, 0.3)";
}
drawLine(curve[0], curve[1], curve[2], curve[3]);
if (draw_tangents != 2) {
if (curve.length > 4) drawLine(curve[2], curve[3], curve[4], curve[5]);
if (curve.length == 8) drawLine(curve[4], curve[5], curve[6], curve[7]);
}
if (draw_tangents != 1) {
if (curve.length == 6 || curve.length == 7) {
drawLine(curve[0], curve[1], curve[4], curve[5]);
}
if (curve.length == 8) drawLine(curve[0], curve[1], curve[6], curve[7]);
}
}
ctx.beginPath();
ctx.moveTo((curve[0] - srcLeft) * scale, (curve[1] - srcTop) * scale);
if (curve.length == 4) {
ctx.lineTo((curve[2] - srcLeft) * scale, (curve[3] - srcTop) * scale);
} else if (curve.length == 6) {
ctx.quadraticCurveTo(
(curve[2] - srcLeft) * scale, (curve[3] - srcTop) * scale,
(curve[4] - srcLeft) * scale, (curve[5] - srcTop) * scale);
} else if (curve.length == 7) {
drawConic(curve, srcLeft, srcTop, scale);
} else {
ctx.bezierCurveTo(
(curve[2] - srcLeft) * scale, (curve[3] - srcTop) * scale,
(curve[4] - srcLeft) * scale, (curve[5] - srcTop) * scale,
(curve[6] - srcLeft) * scale, (curve[7] - srcTop) * scale);
}
if (draw_cubic_red ? curve.length == 8 : firstInside == curves) {
ctx.strokeStyle = "rgba(255,0,0, 1)";
} else {
ctx.strokeStyle = "rgba(0,0,255, 1)";
}
ctx.stroke();
if (draw_endpoints > 0) {
drawPoint(curve[0], curve[1]);
if (draw_endpoints > 1 || curve.length == 4) {
drawPoint(curve[2], curve[3]);
}
if (curve.length == 6 || curve.length == 7 ||
(draw_endpoints > 1 && curve.length == 8)) {
drawPoint(curve[4], curve[5]);
}
if (curve.length == 8) drawPoint(curve[6], curve[7]);
}
if (draw_midpoint != 0) {
if ((curves == 0) == (midLeft == 0)) {
ctx.strokeStyle = "rgba(0,180,127, 0.6)";
} else {
ctx.strokeStyle = "rgba(127,0,127, 0.6)";
}
var midX = x_at_t(curve, 0.5);
var midY = y_at_t(curve, 0.5);
drawPointSolid(midX, midY);
if (draw_midpoint > 1) {
drawLine(curve[0], curve[1], midX, midY);
}
}
if (draw_quarterpoint != 0) {
if ((curves == 0) == (shortLeft == 0)) {
ctx.strokeStyle = "rgba(0,191,63, 0.6)";
} else {
ctx.strokeStyle = "rgba(63,0,191, 0.6)";
}
var midT = (curves == 0) == shorter ? 0.25 : 0.5;
var midX = x_at_t(curve, midT);
var midY = y_at_t(curve, midT);
drawPointSolid(midX, midY);
if (draw_quarterpoint > 1) {
drawLine(curve[0], curve[1], midX, midY);
}
}
if (draw_sortpoint != 0) {
if ((curves == 0) == ((disallowShort == -1 ? midLeft : shortLeft) == 0)) {
ctx.strokeStyle = "rgba(0,155,37, 0.6)";
} else {
ctx.strokeStyle = "rgba(37,0,155, 0.6)";
}
var midT = (curves == 0) == shorter && disallowShort != curves ? 0.25 : 0.5;
console.log("curves=" + curves + " disallowShort=" + disallowShort
+ " midLeft=" + midLeft + " shortLeft=" + shortLeft
+ " shorter=" + shorter + " midT=" + midT);
var midX = x_at_t(curve, midT);
var midY = y_at_t(curve, midT);
drawPointSolid(midX, midY);
if (draw_sortpoint > 1) {
drawLine(curve[0], curve[1], midX, midY);
}
}
if (draw_ray_intersect != 0) {
ctx.strokeStyle = "rgba(75,45,199, 0.6)";
if (curve.length >= 6 && curve.length <= 8) {
var intersections = intersect[intersectIndex];
for (var i in intersections) {
var intersection = intersections[i];
var x = x_at_t(curve, intersection);
var y = y_at_t(curve, intersection);
drawPointSolid(x, y);
if (draw_ray_intersect > 1) {
drawLine(curve[0], curve[1], x, y);
}
}
}
++intersectIndex;
}
if (draw_order) {
var px = x_at_t(curve, 0.75);
var py = y_at_t(curve, 0.75);
var _px = (px - srcLeft) * scale;
var _py = (py - srcTop) * scale;
ctx.beginPath();
ctx.arc(_px, _py, 15, 0, Math.PI * 2, true);
ctx.closePath();
ctx.fillStyle = "white";
ctx.fill();
if (draw_cubic_red ? curve.length == 8 : firstInside == curves) {
ctx.strokeStyle = "rgba(255,0,0, 1)";
ctx.fillStyle = "rgba(255,0,0, 1)";
} else {
ctx.strokeStyle = "rgba(0,0,255, 1)";
ctx.fillStyle = "rgba(0,0,255, 1)";
}
ctx.stroke();
ctx.font = "normal 16px Arial";
ctx.textAlign = "center";
ctx.fillText(parseInt(curves) + 1, _px, _py + 5);
}
if (draw_closest_t) {
var t = curveClosestT(curve, mouseX, mouseY);
if (t >= 0) {
var x = x_at_t(curve, t);
var y = y_at_t(curve, t);
drawPointSolid(x, y);
}
}
if (!approximately_zero(scale - initScale)) {
ctx.font = "normal 20px Arial";
ctx.fillStyle = "rgba(0,0,0, 0.3)";
ctx.textAlign = "right";
ctx.fillText(scale.toFixed(decimal_places) + 'x',
screenWidth - 10, screenHeight - 5);
}
if (draw_t) {
drawPointAtT(curve);
}
if (draw_id != 0) {
var id = -1;
for (var i = 0; i < ids.length; i += 2) {
if (ids[i + 1] == curve) {
id = ids[i];
break;
}
}
if (id >= 0) {
var px = x_at_t(curve, 0.5);
var py = y_at_t(curve, 0.5);
var _px = (px - srcLeft) * scale;
var _py = (py - srcTop) * scale;
ctx.beginPath();
ctx.arc(_px, _py, 15, 0, Math.PI * 2, true);
ctx.closePath();
ctx.fillStyle = "white";
ctx.fill();
ctx.strokeStyle = "rgba(255,0,0, 1)";
ctx.fillStyle = "rgba(255,0,0, 1)";
ctx.stroke();
ctx.font = "normal 16px Arial";
ctx.textAlign = "center";
ctx.fillText(id, _px, _py + 5);
}
}
}
if (draw_t) {
drawCurveTControl();
}
if (draw_w) {
drawCurveWControl();
}
}
function drawCurveTControl() {
ctx.lineWidth = 2;
ctx.strokeStyle = "rgba(0,0,0, 0.3)";
ctx.beginPath();
ctx.rect(screenWidth - 80, 40, 28, screenHeight - 80);
ctx.stroke();
var ty = 40 + curveT * (screenHeight - 80);
ctx.beginPath();
ctx.moveTo(screenWidth - 80, ty);
ctx.lineTo(screenWidth - 85, ty - 5);
ctx.lineTo(screenWidth - 85, ty + 5);
ctx.lineTo(screenWidth - 80, ty);
ctx.fillStyle = "rgba(0,0,0, 0.6)";
ctx.fill();
var num = curveT.toFixed(decimal_places);
ctx.font = "normal 10px Arial";
ctx.textAlign = "left";
ctx.fillText(num, screenWidth - 78, ty);
}
function drawCurveWControl() {
var w = -1;
var choice = 0;
for (var curves in tests[testIndex]) {
var curve = tests[testIndex][curves];
if (curve.length != 7) {
continue;
}
if (choice == curveW) {
w = curve[6];
break;
}
++choice;
}
if (w < 0) {
return;
}
ctx.lineWidth = 2;
ctx.strokeStyle = "rgba(0,0,0, 0.3)";
ctx.beginPath();
ctx.rect(screenWidth - 40, 40, 28, screenHeight - 80);
ctx.stroke();
var ty = 40 + w * (screenHeight - 80);
ctx.beginPath();
ctx.moveTo(screenWidth - 40, ty);
ctx.lineTo(screenWidth - 45, ty - 5);
ctx.lineTo(screenWidth - 45, ty + 5);
ctx.lineTo(screenWidth - 40, ty);
ctx.fillStyle = "rgba(0,0,0, 0.6)";
ctx.fill();
var num = w.toFixed(decimal_places);
ctx.font = "normal 10px Arial";
ctx.textAlign = "left";
ctx.fillText(num, screenWidth - 38, ty);
}
function ptInTControl() {
var e = window.event;
var tgt = e.target || e.srcElement;
var left = tgt.offsetLeft;
var top = tgt.offsetTop;
var x = (e.clientX - left);
var y = (e.clientY - top);
if (x < screenWidth - 80 || x > screenWidth - 50) {
return false;
}
if (y < 40 || y > screenHeight - 80) {
return false;
}
curveT = (y - 40) / (screenHeight - 120);
if (curveT < 0 || curveT > 1) {
throw "stop execution";
}
return true;
}
function ptInWControl() {
var e = window.event;
var tgt = e.target || e.srcElement;
var left = tgt.offsetLeft;
var top = tgt.offsetTop;
var x = (e.clientX - left);
var y = (e.clientY - top);
if (x < screenWidth - 40 || x > screenWidth - 10) {
return false;
}
if (y < 40 || y > screenHeight - 80) {
return false;
}
var w = (y - 40) / (screenHeight - 120);
if (w < 0 || w > 1) {
throw "stop execution";
}
var choice = 0;
for (var curves in tests[testIndex]) {
var curve = tests[testIndex][curves];
if (curve.length != 7) {
continue;
}
if (choice == curveW) {
curve[6] = w;
break;
}
++choice;
}
return true;
}
function drawTop() {
init(tests[testIndex]);
redraw();
}
function redraw() {
if (focus_on_selection > 0) {
var focusXmin = focusYmin = Infinity;
var focusXmax = focusYmax = -Infinity;
var choice = 0;
for (var curves in tests[testIndex]) {
if (++choice != focus_on_selection) {
continue;
}
var curve = tests[testIndex][curves];
var last = curve.length - (curve.length % 2 == 1 ? 1 : 0);
for (var idx = 0; idx < last; idx += 2) {
focusXmin = Math.min(focusXmin, curve[idx]);
focusXmax = Math.max(focusXmax, curve[idx]);
focusYmin = Math.min(focusYmin, curve[idx + 1]);
focusYmax = Math.max(focusYmax, curve[idx + 1]);
}
}
focusXmin -= Math.min(1, Math.max(focusXmax - focusXmin, focusYmax - focusYmin));
if (focusXmin < focusXmax && focusYmin < focusYmax) {
setScale(focusXmin, focusXmax, focusYmin, focusYmax);
}
}
ctx.beginPath();
ctx.rect(0, 0, ctx.canvas.width, ctx.canvas.height);
ctx.fillStyle = "white";
ctx.fill();
draw(tests[testIndex], testTitles[testIndex]);
}
function doKeyPress(evt) {
var char = String.fromCharCode(evt.charCode);
var focusWasOn = false;
switch (char) {
case '0':
case '1':
case '2':
case '3':
case '4':
case '5':
case '6':
case '7':
case '8':
case '9':
decimal_places = char - '0';
redraw();
break;
case '-':
focusWasOn = focus_on_selection;
if (focusWasOn) {
focus_on_selection = false;
scale /= 1.2;
} else {
scale /= 2;
}
calcLeftTop();
redraw();
focus_on_selection = focusWasOn;
break;
case '=':
case '+':
focusWasOn = focus_on_selection;
if (focusWasOn) {
focus_on_selection = false;
scale *= 1.2;
} else {
scale *= 2;
}
calcLeftTop();
redraw();
focus_on_selection = focusWasOn;
break;
case 'b':
draw_cubic_red ^= true;
redraw();
break;
case 'c':
drawTop();
break;
case 'd':
var test = tests[testIndex];
var testClone = [];
for (var curves in test) {
var c = test[curves];
var cClone = [];
for (var index = 0; index < c.length; ++index) {
cClone.push(c[index]);
}
testClone.push(cClone);
}
tests.push(testClone);
testTitles.push(testTitles[testIndex] + " copy");
testIndex = tests.length - 1;
redraw();
break;
case 'e':
draw_endpoints = (draw_endpoints + 1) % 3;
redraw();
break;
case 'f':
draw_derivative ^= true;
redraw();
break;
case 'i':
draw_ray_intersect = (draw_ray_intersect + 1) % 3;
redraw();
break;
case 'l':
var test = tests[testIndex];
console.log("<div id=\"" + testTitles[testIndex] + "\" >");
for (var curves in test) {
var c = test[curves];
var s = "{{";
for (var i = 0; i < c.length; i += 2) {
s += "{";
s += c[i] + "," + c[i + 1];
s += "}";
if (i + 2 < c.length) {
s += ", ";
}
}
console.log(s + "}},");
}
console.log("</div>");
break;
case 'm':
draw_midpoint = (draw_midpoint + 1) % 3;
redraw();
break;
case 'N':
testIndex += 9;
case 'n':
testIndex = (testIndex + 1) % tests.length;
drawTop();
break;
case 'o':
draw_order ^= true;
redraw();
break;
case 'P':
testIndex -= 9;
case 'p':
if (--testIndex < 0)
testIndex = tests.length - 1;
drawTop();
break;
case 'q':
draw_quarterpoint = (draw_quarterpoint + 1) % 3;
redraw();
break;
case 'r':
for (var i = 0; i < testDivs.length; ++i) {
var title = testDivs[i].id.toString();
if (title == testTitles[testIndex]) {
var str = testDivs[i].firstChild.data;
parse(str, title);
var original = tests.pop();
testTitles.pop();
tests[testIndex] = original;
break;
}
}
redraw();
break;
case 's':
draw_sortpoint = (draw_sortpoint + 1) % 3;
redraw();
break;
case 't':
draw_t ^= true;
redraw();
break;
case 'u':
draw_closest_t ^= true;
redraw();
break;
case 'v':
draw_tangents = (draw_tangents + 1) % 4;
redraw();
break;
case 'w':
++curveW;
var choice = 0;
draw_w = false;
for (var curves in tests[testIndex]) {
var curve = tests[testIndex][curves];
if (curve.length != 7) {
continue;
}
if (choice == curveW) {
draw_w = true;
break;
}
++choice;
}
if (!draw_w) {
curveW = -1;
}
redraw();
break;
case 'x':
draw_point_xy ^= true;
redraw();
break;
case 'y':
draw_mouse_xy ^= true;
redraw();
break;
case '\\':
retina_scale ^= true;
drawTop();
break;
case '`':
++focus_on_selection;
if (focus_on_selection >= tests[testIndex].length) {
focus_on_selection = 0;
}
setScale(xmin, xmax, ymin, ymax);
redraw();
break;
case '.':
draw_id = (draw_id + 1) % 3;
redraw();
break;
}
}
function doKeyDown(evt) {
var char = evt.keyCode;
var preventDefault = false;
switch (char) {
case 37: // left arrow
if (evt.shiftKey) {
testIndex -= 9;
}
if (--testIndex < 0)
testIndex = tests.length - 1;
if (evt.ctrlKey) {
redraw();
} else {
drawTop();
}
preventDefault = true;
break;
case 39: // right arrow
if (evt.shiftKey) {
testIndex += 9;
}
if (++testIndex >= tests.length)
testIndex = 0;
if (evt.ctrlKey) {
redraw();
} else {
drawTop();
}
preventDefault = true;
break;
}
if (preventDefault) {
evt.preventDefault();
return false;
}
return true;
}
function calcXY() {
var e = window.event;
var tgt = e.target || e.srcElement;
var left = tgt.offsetLeft;
var top = tgt.offsetTop;
mouseX = (e.clientX - left) / scale + srcLeft;
mouseY = (e.clientY - top) / scale + srcTop;
}
function calcLeftTop() {
srcLeft = mouseX - screenWidth / 2 / scale;
srcTop = mouseY - screenHeight / 2 / scale;
}
function handleMouseClick() {
if ((!draw_t || !ptInTControl()) && (!draw_w || !ptInWControl())) {
calcXY();
} else {
redraw();
}
}
function initDown() {
var test = tests[testIndex];
var bestDistance = 1000000;
activePt = -1;
for (var curves in test) {
var testCurve = test[curves];
if (testCurve.length != 4 && (testCurve.length < 6 || testCurve.length > 8)) {
continue;
}
var testMax = testCurve.length == 7 ? 6 : testCurve.length;
for (var i = 0; i < testMax; i += 2) {
var testX = testCurve[i];
var testY = testCurve[i + 1];
var dx = testX - mouseX;
var dy = testY - mouseY;
var dist = dx * dx + dy * dy;
if (dist > bestDistance) {
continue;
}
activeCurve = testCurve;
activePt = i;
bestDistance = dist;
}
}
if (activePt >= 0) {
lastX = mouseX;
lastY = mouseY;
}
}
function handleMouseOver() {
calcXY();
if (draw_mouse_xy) {
var num = mouseX.toFixed(decimal_places) + ", " + mouseY.toFixed(decimal_places);
ctx.beginPath();
ctx.rect(300, 100, num.length * 6, 10);
ctx.fillStyle = "white";
ctx.fill();
ctx.font = "normal 10px Arial";
ctx.fillStyle = "black";
ctx.textAlign = "left";
ctx.fillText(num, 300, 108);
}
if (!mouseDown) {
activePt = -1;
return;
}
if (activePt < 0) {
initDown();
return;
}
var deltaX = mouseX - lastX;
var deltaY = mouseY - lastY;
lastX = mouseX;
lastY = mouseY;
if (activePt == 0) {
var test = tests[testIndex];
for (var curves in test) {
var testCurve = test[curves];
testCurve[0] += deltaX;
testCurve[1] += deltaY;
}
} else {
activeCurve[activePt] += deltaX;
activeCurve[activePt + 1] += deltaY;
}
redraw();
}
function start() {
for (var i = 0; i < testDivs.length; ++i) {
var title = testDivs[i].id.toString();
var str = testDivs[i].firstChild.data;
parse(str, title);
}
drawTop();
window.addEventListener('keypress', doKeyPress, true);
window.addEventListener('keydown', doKeyDown, true);
window.onresize = function () {
drawTop();
}
}
</script>
</head>
<body onLoad="start();">
<canvas id="canvas" width="750" height="500"
onmousedown="mouseDown = true"
onmouseup="mouseDown = false"
onmousemove="handleMouseOver()"
onclick="handleMouseClick()"
></canvas >
</body>
</html>
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