A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
A new class of algorithms for the processing of parametric curves
Computer-Aided Design
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing curve intersection by homotopy methods
Journal of Computational and Applied Mathematics
Tracking point-curve critical distances
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
SMI 2012: Full Curve intersection using hybrid clipping
Computers and Graphics
A geometric strategy for computing intersections of two spatial parametric curves
The Visual Computer: International Journal of Computer Graphics
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This paper treats the problem of how one can best compute the points of intersection of two planar rational curves. Three different algorithms are compared: the well known Bezier subdivision algorithm, a subdivision algorithm based on interval arithmetic, and the implicitization approach. Implementation considerations are discussed, with particular focus on how to make the implicitization method robust and fast. Report is made on a test in which the algorithms solved hundreds of randomly generated problems to eight digits of accuracy. The implicitization algorithm was faster than the others by a factor of five for degree two curves; by a factor of four for cubic curves; by a factor of three for quartic curves; and the interval method was faster for quintic curves by a factor of two.