Constructive shell representations for freeform surfaces and solids

We usually model freeform surfaces (mathematically, 2D r-sets embedded in 3D Euclidean space E/sup 3/) as a finite union of patches represented in the traditional parametric or the recently developed algebraic forms. The article introduces a new representation scheme for freeform surfaces called constructive shell representation (CSR), that draws on recent research on algebraic patches. CSRs of surfaces that constitute boundaries of solids are very useful for solid modeling. They represent thick shells derived from freeform surfaces and provide a means to compute exact CSG representations of freeform solids.<>