To whom it may concern,
Cubic Bezier curve has been invented over fifty years, people are all expecting its great functionality and productivity to be used in CAD/CAM for free form curve design or photo-realistic solid modeling. However I believeits usage was limited as there is no effective way to solve the intersection points problem either in between curve-to-curve or within a curve itself.
Anyway, the problem is a history now. Enclosed are a picture of cubic Bezier curves intersection points and certain data related with the two curves that auto-generated by a program. Anyone, who feels interested are all welcome to verify them for the truth.
I wonder if Intel is interested to license this solution and add it into your library? If yes then please contact me.
Blue Curve control points: P0 (404.000000, 355.000000), P1 (169.000000, 264.000000), P2 (858.000000, 329.000000), P3 (438.000000, 239.000000);
Red Curve control points: P0 (556.000000, 334.000000), P1 (253.000000, 331.000000), P2 (765.000000, 48.000000), P3 (414.000000, 489.000000);
Self Intersection point at (521.381253777, 332.148294653); t = 0.844680894, t = 0.042885836;
The Intersection point(s) of those two curves:
x0(455.734152990, 299.109787062), x1(490.237592592, 250.732158097), x2(542.630905524, 264.568535791), x3(538.123536369, 292.686435169);
Blue Curve's t value(s):
t = 0.437206056, t = 0.952837683, t = 0.883884689, t = 0.596112430;
Red Curve's t value(s):
t = 0.232537221, t = 0.453969337, t = 0.713303391, t = 0.780607425;
Ps, my solution is fast, precise and by theory. It is not an approximation approach like bi-section or Bez-clipping or ...