scratchfoundation/paper.js
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Completely rewrite Path#arcTo() using Point class and vector geometry methods.

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This commit is contained in:
Jürg Lehni 2011-06-14 12:19:14 +01:00
parent 0cda1aa9dd
commit 2be18b8013
1 changed files with 27 additions and 53 deletions
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80
src/path/Path.js
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@ -1759,70 +1759,44 @@ var Path = this.Path = PathItem.extend({
through = middle[clockwise ? 'subtract' : 'add'](-step.y, step.x);
}
var x1 = from._x, x2 = through.x, x3 = to.x,
y1 = from._y, y2 = through.y, y3 = to.y,
f = x3 * x3 - x3 * x2 - x1 * x3 + x1 * x2 + y3 * y3 - y3 * y2
- y1 * y3 + y1 * y2,
g = x3 * y1 - x3 * y2 + x1 * y2 - x1 * y3 + x2 * y3 - x2 * y1,
m = g == 0 ? f : f / g,
e = x1 * x2 + y1 * y2 - m * (x1 * y2 - y1 * x2),
cx = (x1 + x2 + m * (y1 - y2)) / 2,
cy = (y1 + y2 + m * (x2 - x1)) / 2,
radius = Math.sqrt(cx * cx + cy * cy - e),
angle = Math.atan2(y1 - cy, x1 - cx),
middle = Math.atan2(y2 - cy, x2 - cx),
extent = Math.atan2(y3 - cy, x3 - cx),
diff = middle - angle,
d180 = Math.PI, // = 180 degrees in radians
d360 = d180 * 2; // = 360 degrees in radians
if (diff < -d180)
diff += d360;
else if (diff > d180)
diff -= d360;
extent -= angle;
if (extent <= 0)
extent += d360;
if (diff < 0)
extent -= d360;
// Construct the two perpendicular middle lines to (from, through)
// and (through, to), and intersect them to get the center
var l1 = new Line(from.add(through).divide(2),
through.subtract(from).rotate(90)),
l2 = new Line(through.add(to).divide(2),
to.subtract(through).rotate(90)),
center = l1.intersect(l2),
vector = from.subtract(center),
radius = vector.getLength(),
extent = vector.getDirectedAngle(to.subtract(center)),
line = new Line(from, to, true);
// If the center is on the same side of the line (from, to) than
// the through point, we're extending bellow 180 degrees and need
// to adapt extent.
if (line.getSide(center) == line.getSide(through))
extent -= 360 * (extent < 0 ? -1 : 1);
var ext = Math.abs(extent),
arcSegs = ext >= d360
? 4 : Math.ceil(ext * 2 / Math.PI),
inc = Math.min(Math.max(extent, -d360), d360) / arcSegs,
z = 4 / 3 * Math.sin(inc / 2) / (1 + Math.cos(inc / 2)),
count = ext >= 360 ? 4 : Math.ceil(ext / 90),
inc = extent / count,
half = inc * Math.PI / 360,
z = 4 / 3 * Math.sin(half) / (1 + Math.cos(half)),
segments = [];
// TODO: Use Point#setAngle() and Point vector algebra instead?
for (var i = 0; i <= arcSegs; i++) {
var relx = Math.cos(angle),
rely = Math.sin(angle);
for (var i = 0; i <= count; i++) {
// Explicitely use to point for last segment, since depending
// on values the calculation adds imprecision:
var pt = i == arcSegs
? to
: new Point(
cx + relx * radius,
cy + rely * radius
);
var out = i == arcSegs
? null
: new Point(
cx + (relx - z * rely) * radius - pt.x,
cy + (rely + z * relx) * radius - pt.y
);
var pt = i < count ? center.add(vector) : to;
var out = i < count ? vector.rotate(90).multiply(z) : null;
if (i == 0) {
// Modify startSegment
current.setHandleOut(out);
} else {
// Add new Segment
segments.push(new Segment(pt, new Point(
cx + (relx + z * rely) * radius - pt.x,
cy + (rely - z * relx) * radius - pt.y
), out));
segments.push(
new Segment(pt, vector.rotate(-90).multiply(z), out));
}
angle += inc;
vector = vector.rotate(inc);
}
// Add all segments at once at the end for higher performance
this._add(segments);