> From the beginning of the implementation of Triangle, and well into the development of Pyramid, floating-point roundoff problems plagued me. Each program would sometimes crash, sometimes find itself stuck in an endless loop, and sometimes produce garbled output. At first I believed that I would be able to fix the problems by understanding how the algorithms went wrong when roundoff error produced incorrect answers, and writing special-case code to handle each potential problem. Some of the robustness problems yielded to this approach, but others did not. Fortunately, Steven Fortune of AT&T Bell Laboratories convinced me, in a few brief but well-worded email messages (and in several longer and equally well-worded technical papers), to choose the alternative path to robustness, which led to the research described in this chapter. For reasons that will become apparent, exact arithmetic is the better approach to solving many, if not all, of the robustness worries associated with triangulation.
Of course, what can be done with polygons is often not feasible for more general kids of shapes like parametric cubics.
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What is a “clever vector path algorithm”, and how do you avoid them?
