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[Polynomial curves and surfaces have a long mathematical history. In CAD and modeling packages, Bézier and B-spline curves and surfaces have been the standard modeling techniques for several decades. Although there are now other competing methods (subdivision surfaces, triangle meshes), the...
[You should be familiar with the monomial form of a scalar-valued, degree n polynomial,
[Suppose we want to draw a complicated curve. We could use a high-degree Bézier curve, but there are several problems with this approach:
We cannot represent cusps (well, not easily, anyway).It is expensive to evaluate high-degree Bézier curves.A large number of control points may be required to...
[In addition to modeling curves, we would like to model surfaces. While we can model spline surfaces, the results are not as satisfying as they were for curves. Part of the problem is that we have more issues to deal with when modeling surfaces: what shape surfaces patches do we need and can we...
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