Surfaces in computer aided geometric design: a survey with new results

'Surfaces in Computer Aided Geometric Design' focuses on the representation and design of surfaces in a computer graphics environment. This new area has the dual attractions of interesting research problems and important applications. The subject can be approached from two points of view: The design of surfaces which includes the interactive modification of geometric information and the representation of surfaces for which the geometric information is relatively fixed. Design takes place in 3-space whereas representation can be higher dimensional. 'Surfaces in CAGD' can be traced from its inception in rectangular Coons patches and Bezier patches to triangular patches which are current research topics. Triangular patches can interpolate and approximate to arbitrarily located data and require the preprocessing steps of triangulation and derivative estimation. New contouring methods have been found using these triangular patches. Finally, multidimensional interpolation schemes have been based on tetrahedral interpolants and are illustrated by surfaces in 4-space by means of color computer graphics.

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