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Implement improved strategy to handle tangents in CurveLocation#isCrossing()

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Relates to #1074
This commit is contained in:
Jürg Lehni 2016-06-13 08:56:45 +02:00
parent 4966f6250f
commit fc600595a4
1 changed files with 18 additions and 14 deletions
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32
src/path/CurveLocation.js
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@ -448,27 +448,31 @@ var CurveLocation = Base.extend(/** @lends CurveLocation# */{
: angle > min || angle < max;
}
// Calculate angles for all four tangents at the intersection point.
// If the intersection is on an actual segment, step away from it at
// equal offsets on each curve, to calculate tangential angles that are
// unambiguous. The offset is determined by taking 1/64th of the length
// of the shortest of all involved curves. This appears to work well.
// Calculate unambiguous angles for all 4 tangents at the intersection:
// - If the intersection is inside a curve (t1 / t2Inside), the tangent
// at t1 / t2 is unambiguous, because the curve is continuous.
// - If the intersection is on a segment, step away at equal offsets on
// each curve, to calculate unambiguous angles. The vector from the
// intersection to this new location is used to determine the angle.
// The offset is determined by taking 1/64th of the length of the
// shortest of all involved curves.
// NOTE: VectorBoolean has code that slowly shifts these offsets inwards
// until the resulting tangents are not ambiguous. Do we need this too?
// NOTE: We handle t1 / t2Inside here by getting the tangent at t1 / t2
// instead of at this calculated offset.
// The incomings tangents v1 & v3 are inverted, so that all angles
// are pointing outwards in the right direction from the intersection.
var lenghts = [];
if (!t1Inside)
lenghts.push(c1.getLength(), c2.getLength());
if (!t2Inside)
lenghts.push(c3.getLength(), c4.getLength());
var offset = Math.min.apply(null, lenghts) / 64;
var v2 = t1Inside ? c2.getTangentAtTime(t1) : c2.getTangentAt(offset),
v1 = (t1Inside ? v2 : c1.getTangentAt(-offset)).negate(),
v4 = t2Inside ? c4.getTangentAtTime(t2) : c4.getTangentAt(offset),
v3 = (t2Inside ? v4 : c3.getTangentAt(-offset)).negate(),
var pt = this.getPoint(),
offset = Math.min.apply(null, lenghts) / 64,
v2 = t1Inside ? c2.getTangentAtTime(t1)
: c2.getPointAt(offset).subtract(pt),
v1 = t1Inside ? v2.negate()
: c1.getPointAt(-offset).subtract(pt),
v4 = t2Inside ? c4.getTangentAtTime(t2)
: c4.getPointAt(offset).subtract(pt),
v3 = t2Inside ? v4.negate()
: c3.getPointAt(-offset).subtract(pt),
// NOTE: For shorter API calls we work with angles in degrees here:
a1 = v1.getAngle(),
a2 = v2.getAngle(),