Surface Approximations in Geometric Modeling
PURDUE UNIV LAFAYETTE IN DEPT OF COMPUTER SCIENCES
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One of the major research efforts in the field of solid modeling focuses on extending the geometric coverage of modeling systems and on incorporating complex free-form surfaces. Some major obstacles to this goal include computing and rendering very complex surfaces, including offset, Voronoi, and blending surfaces. We present local and global approximation schemes that are expected to be of practical value in overcoming the above problems. For parametric curves and surfaces, we present a method for computing an implicit approximant of low degree that approximates the curves or surface locally and achieves an order of contact that can be prescribed in advance. In principle, the method is capable of exact implicitization.
- Numerical Mathematics
- Theoretical Mathematics