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28937843f4
skia2/tools/pathops_sorter.htm
caryclark 612f70d5fa handle large conic strokes better 
A stroked conic computes the outset quad's control point by
computing the intersection of the quad's endpoints. If the
the denominator used to compute the scale factor for the
control point is small, check to see if the numerator is also
small so that the division stays bounded.

Also clean up error returns and internal function calls to
simplify the code.

Additionally, remove comic max curvature (unimplemented) and call
extrema functions instead to handle cases where the conic is degenerate
or is a line.

R=reed@google.com, fmalita@chromium.org
BUG=skia:3843

Review URL: https://codereview.chromium.org/1144883003
2015-05-19 11:05:37 -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">
{{{fX=1.97000003 fY=2.00000000 }, {fX=1.97000003 fY=3.97000003 }, {fX=0.000000000 fY=3.97000003 }} fW: 0.707106769
{{{fX=1.99750006 fY=2.00000000 } {fX=1.99750006 fY=2.02749991 }
{{{fX=1.96415257 fY=2.36347127 } {fX=1.95914865 fY=2.39051223 }
</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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