Mathematical techniques in solid modeling

Basic computational problems in mathematics for solid modeling are discussed. It is shown how merging results from algebras, geometry, and approximation theory into effect tools can lead to a higher level of performance in solid modeling. Effective mathematical techniques are shown, such as singularity analysis and resolution, parameterization and implicitization, residue computation and Chinese remaindering, evaluation and interpolation, power-series computations and localization, and membership within ideal (i.e. special sets of polynomials). Set techniques have had and shall have a significant impact on solid modelling.<>