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Clean up intersection-fix code.

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Jürg Lehni 2013-10-29 10:16:20 +01:00
parent 8ae1105236
commit fb27f92ede
1 changed files with 44 additions and 40 deletions
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84
src/path/Curve.js
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@ -1429,54 +1429,58 @@ new function() { // Scope for methods that require numerical integration
vl = flip ? v1 : v2,
l1x = vl[0], l1y = vl[1],
l2x = vl[6], l2y = vl[7],
vc0 = vc[0], vc1 = vc[1], vc2 = vc[2], vc3 = vc[3],
vc0 = vc[0], vc1 = vc[1],
vc2 = vc[2], vc3 = vc[3],
vc4 = vc[4], vc5 = vc[5],
// Equation of the line Ax + By + C = 0
A = l2y-l1y, //A=y2-y1
B = l1x-l2x, //B=x1-x2
C = l1x*(l1y-l2y) + l1y*(l2x-l1x), //C=x1*(y1-y2)+y1*(x2-x1)
// A = y2 - y1
// B = x1 - x2
// C = x1 * (y1 - y2) + y1 * (x2 - x1)
A = l2y - l1y,
B = l1x - l2x,
C = l1x * (l1y - l2y) + l1y * (l2x - l1x),
// Bernstein coefficients for the curve
bx0 = -vc0 + 3*vc2 + -3*vc4 + vc[6],
bx1 = 3*vc0 - 6*vc2 + 3*vc4,
bx2 = -3*vc0 + 3*vc2,
bx0 = -vc0 + 3 * vc2 + -3 * vc4 + vc[6],
bx1 = 3 * vc0 - 6 * vc2 + 3 * vc4,
bx2 = -3 * vc0 + 3 * vc2,
bx3 = vc0,
by0 = -vc1 + 3*vc3 + -3*vc5 + vc[7],
by1 = 3*vc1 - 6*vc3 + 3*vc5,
by2 = -3*vc1 + 3*vc3,
by0 = -vc1 + 3 * vc3 + -3 * vc5 + vc[7],
by1 = 3 * vc1 - 6 * vc3 + 3 * vc5,
by2 = -3 * vc1 + 3 * vc3,
by3 = vc1,
// Form the cubic equation
// a*t^3 + b*t^2 + c*t + d = 0
a = A*bx0 + B*by0, /*t^3*/
b = A*bx1 + B*by1, /*t^2*/
c = A*bx2 + B*by2, /*t*/
d = A*bx3 + B*by3 + C, /*1*/
roots = [], count, x, y, t, tl;
// Solve the cubic equation
count = Numerical.solveCubic(a, b, c, d, roots);
// a * t^3 + b*t^2 + c*t + d = 0
a = A * bx0 + B * by0, // t^3
b = A * bx1 + B * by1, // t^2
c = A * bx2 + B * by2, // t
d = A * bx3 + B * by3 + C, // t1
roots = [],
// Solve the cubic equation, interested only in results in [0 .. 1]
count = Numerical.solveCubic(a, b, c, d, roots, 0, 1);
// NOTE: count could be -1 for inifnite solutions, but that should only
// happen with lines, in which case we should not be here.
for (var i=0;i<count;i++) {
t = roots[i];
if(t >= 0 && t <= 1.0){
x = bx0*t*t*t + bx1*t*t + bx2*t + bx3;
y = by0*t*t*t + by1*t*t + by2*t + by3;
// tl is the parameter of the intersection point in line segment.
// Special case to override the tight tolerence in
// Curve.solveQuadratic when line is horizontal
if (l2y-l1y === 0)
y = l1y;
tl = Curve.getParameterOf(vl, x, y);
// We do have a point on the infinite line. Check if it falls on
// the line *segment*.
if(tl >= 0 && tl <= 1.0){
// Interpolate the parameter for the intersection on line.
var t1 = flip ? tl : t,
t2 = flip ? t : tl;
addLocation(locations,
curve1, t1, Curve.evaluate(v1, t1, 0),
curve2, t2, Curve.evaluate(v2, t2, 0));
}
for (var i = 0; i < count; i++) {
var t = roots[i],
tt = t * t,
ttt = tt * t,
x = bx0 * ttt + bx1 * tt + bx2 * t + bx3,
y = by0 * ttt + by1 * tt + by2 * t + by3;
// tl is the parameter of the intersection point in line segment.
// Special case to override the tight tolerence in
// Curve.solveQuadratic when line is horizontal
if (l2y === l1y)
y = l1y;
var tl = Curve.getParameterOf(vl, x, y),
t2;
// We do have a point on the infinite line. Check if it falls on
// the line *segment*.
if (tl >= 0 && tl <= 1) {
// Interpolate the parameter for the intersection on line.
t1 = flip ? tl : t;
t2 = flip ? t : tl;
addLocation(locations,
curve1, t1, Curve.evaluate(v1, t1, 0),
curve2, t2, Curve.evaluate(v2, t2, 0));
}
}
}