Abstract
This chapter describes the computer as a powerful tool in the design and analysis of 3D shape. Renderability measures the quality of visual feedback given to the designer. Visual feedback is extremely important in the design process. A deformation of a parametric surface yields another parametric surface that can be treated in the same way, and deformations of implicit surfaces can also be treated as implicit surfaces if the deformation is invertible. Shapes can be parameterized by scalar parameters or higher-dimensional parameters. Geometric queries such as point classification are simple for implicitly described shapes, whereas the sampling of points over an implicit shape is difficult. A user interface for less sophisticated users could be designed by assembling an appropriate set of meta-shapes for which users could supply the necessary curves and other parameters.
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