scratchfoundation/paper.js
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Simplify Path#arcTo() a lot (get rid of necessity to reverse coordinate system in y-direction, etc).

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This commit is contained in:
Jürg Lehni 2011-05-06 01:26:23 +01:00
parent 18ef19649c
commit 0b082289a6
1 changed files with 28 additions and 42 deletions
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70
src/path/Path.js
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@ -791,63 +791,49 @@ var Path = this.Path = PathItem.extend({
- y1 * y3 + y1 * y2,
g = x3 * y1 - x3 * y2 + x1 * y2 - x1 * y3 + x2 * y3 - x2 * y1,
m = g == 0 ? 0 : f / g,
c = (m * y2) - x2 - x1 - (m * y1),
d = (m * x1) - y1 - y2 - (x2 * m),
e = (x1 * x2) + (y1 * y2) - (m * x1 * y2) + (m * x2 * y1),
centerX = -c / 2,
centerY = -d / 2,
radius = Math.sqrt(centerX * centerX + centerY * centerY - e),
e = x1 * x2 + y1 * y2 - m * (x1 * y2 - y1 * x2),
cx = (x1 + x2 - m * (y2 - y1)) / 2,
cy = (y1 + y2 - m * (x1 - x2)) / 2,
radius = Math.sqrt(cx * cx + cy * cy - e),
// Note: reversing the Y equations negates the angle to adjust
// for the upside down coordinate system.
angle = Math.atan2(centerY - y1, x1 - centerX),
middle = Math.atan2(centerY - y2, x2 - centerX),
extent = Math.atan2(centerY - y3, x3 - centerX),
angle = Math.atan2(y1 - cy, x1 - cx),
middle = Math.atan2(y2 - cy, x2 - cx),
extent = Math.atan2(y3 - cy, x3 - cx),
diff = middle - angle,
d90 = Math.PI, // = 90 degrees in radians
d180 = d90 * 2; // = 180 degrees in radians
diff = middle - angle;
if (diff < -Math.PI)
diff += Math.PI * 2;
else if (diff > Math.PI)
diff -= Math.PI * 2;
if (diff < -d90)
diff += d180;
else if (diff > d90)
diff -= d180;
extent -= angle;
if (extent <= 0)
extent += Math.PI * 2;
if (diff < 0) extent = Math.PI * 2 - extent;
else extent = -extent;
angle = -angle;
extent += d180;
if (diff < 0)
extent -= d180;
var ext = Math.abs(extent),
arcSegs;
if (ext >= 2 * Math.PI) arcSegs = 4;
else arcSegs = Math.ceil(ext * 2 / Math.PI);
var inc = extent;
if (inc > 2 * Math.PI) inc = 2 * Math.PI;
else if (inc < -2 * Math.PI) inc = -2 * Math.PI;
inc /= arcSegs;
var halfInc = inc / 2,
z = 4 / 3 * Math.sin(halfInc) / (1 + Math.cos(halfInc));
var segments = [];
arcSegs = ext >= d180
? 4 : Math.ceil(ext * 2 / Math.PI),
inc = Math.min(Math.max(extent, -d180), d180) / arcSegs,
z = 4 / 3 * Math.sin(inc / 2) / (1 + Math.cos(inc / 2)),
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),
pt = new Point(
centerX + relx * radius,
centerY + rely * radius
cx + relx * radius,
cy + rely * radius
),
out = i == arcSegs
? null
: new Point(
centerX + (relx - z * rely) * radius - pt.x,
centerY + (rely + z * relx) * radius - pt.y
cx + (relx - z * rely) * radius - pt.x,
cy + (rely + z * relx) * radius - pt.y
);
if (i == 0) {
// Modify startSegment
@ -855,8 +841,8 @@ var Path = this.Path = PathItem.extend({
} else {
// Add new Segment
segments.push(new Segment(pt, new Point(
centerX + (relx + z * rely) * radius - pt.x,
centerY + (rely - z * relx) * radius - pt.y
cx + (relx + z * rely) * radius - pt.x,
cy + (rely - z * relx) * radius - pt.y
), out));
}
angle += inc;