Shapes in the system are specified using a language which builds multi-dimensional parametric functions. The language is based on a set of symbolic operators on continuous, piecewise differentiable parametric functions. We present several shape examples to show how conveniently shapes can be specified in the system We also discuss the kinds of operators useful in a geometric modeling system, including arithmetic operators, vector and matrix operators, integration, differentiation, constraint solution, and constrained minimization. Associated with each operator are several methods, which compute properties about the parametric functions represented with the operators. We show how many powerful rendering and analytical operations can be supported with only three methods: evaluation of the parametric function at a point, symbolic differentiation of the parametric function, and evaluation of an inclusion function for the parametric function.
Like CSG, and unlike most other geometric modeling approaches, this modeling approach is closed, meaning that further modeling operations can be applied to any results of modeling operations, yielding valid models. Because of this closure property, the symbolic operators can be composed very flexibly, allowing the construction of higher-level operators without changing the underlying implementation of the system. Because the modeling operations are described symbolically, specified models can capture the designer's intent without approximation error.