scratchfoundation/paper.js
1
0
Fork 0
mirror of https://github.com/scratchfoundation/paper.js.git synced 2025-01-01 02:38:43 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

Improve tangent direction handling in isCrossing()

Browse source 
Find unambiguous vectors by taking inception points and “peaks” into account.

Relates to #1073, #1074
This commit is contained in:
Jürg Lehni 2017-01-24 07:50:40 -05:00
parent 4e215b0eab
commit 1806b5959e
2 changed files with 58 additions and 19 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

2
src/path/Curve.js
View file

@ -1468,8 +1468,6 @@ new function() { // Scope for methods that require private functions
// 1: tangent, 1st derivative
// 2: normal, 1st derivative
// 3: curvature, 1st derivative & 2nd derivative
// Simply use the derivation of the bezier function for both
// the x and y coordinates:
// Prevent tangents and normals of length 0:
// http://stackoverflow.com/questions/10506868/
if (t < tMin) {

75
src/path/CurveLocation.js
View file

@ -427,6 +427,55 @@ var CurveLocation = Base.extend(/** @lends CurveLocation# */{
if (!c1 || !c2 || !c3 || !c4)
return false;
// 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 the taking the shortest distance on all
// involved curves that is unambiguous. We do this by determining the
// largest offsets of unambiguous direction on each curve by finding
// their inflections points and "peaks", and then use half of that.
var offsets = [];
function addOffsets(curve, end) {
var v = curve.getValues(),
info = Curve.classify(v),
roots = info.roots || getPeaks(v),
count = roots.length,
t = end && count > 1 ? roots[count - 1]
: count > 0 ? roots[0]
: 0.5;
offsets.push(Curve.getLength(v, end ? t : 0, end ? 1 : t) / 2);
}
// Peaks are locations sharing some qualities of curvature extrema but
// are cheaper to compute. They fulfill their purpose here quite well.
// See: http://math.stackexchange.com/questions/1954845/bezier-curvature-extrema
function getPeaks(v) {
var x0 = v[0], y0 = v[1],
x1 = v[2], y1 = v[3],
x2 = v[4], y2 = v[5],
x3 = v[6], y3 = v[7],
ax = -x0 + 3 * x1 - 3 * x2 + x3,
bx = 3 * x0 - 6 * x1 + 3 * x2,
cx = -3 * x0 + 3 * x1,
ay = -y0 + 3 * y1 - 3 * y2 + y3,
by = 3 * y0 - 6 * y1 + 3 * y2,
cy = -3 * y0 + 3 * y1,
roots = [];
Numerical.solveCubic(
9 * (ax * ax + ay * ay),
9 * (ax * bx + by * ay),
2 * (bx * bx + by * by) + 3 * (cx * ax + cy * ay),
(cx * bx + by * cy),
// Exclude 0 and 1 as we don't want to use them as peaks.
roots, tMin, tMax);
return roots.sort();
}
function isInRange(angle, min, max) {
return min < max
? angle > min && angle < max
@ -434,23 +483,16 @@ var CurveLocation = Base.extend(/** @lends CurveLocation# */{
: angle > min || angle < max;
}
// 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?
var lenghts = [];
if (!t1Inside)
lenghts.push(c1.getLength(), c2.getLength());
if (!t2Inside)
lenghts.push(c3.getLength(), c4.getLength());
if (!t1Inside) {
addOffsets(c1, true);
addOffsets(c2, false);
}
if (!t2Inside) {
addOffsets(c3, true);
addOffsets(c4, false);
}
var pt = this.getPoint(),
offset = Math.min.apply(Math, lenghts) / 64,
offset = Math.min.apply(Math, offsets),
v2 = t1Inside ? c2.getTangentAtTime(t1)
: c2.getPointAt(offset).subtract(pt),
v1 = t1Inside ? v2.negate()
@ -459,7 +501,6 @@ var CurveLocation = Base.extend(/** @lends CurveLocation# */{
: 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(),
a3 = v3.getAngle(),