Free-form deformation in a constructive solid geometry modeling system

Research in computer aided geometric design of free-form surfaces has provided elegant modeling techniques. However, there has been limited development of free-form design methods for solid geometric modeling. Most approaches have attempted to impose current free-form surface technology on solid modeling. This dissertation examines a new approach. This new technique proceeds by deforming solid geometric models in a free-form manner. This approach can be used with any existing solid modeling scheme such as constructive solid geometry or boundary representation. It can deform surface primitives of any type or degree such as planes, quadrics, parametric surface patches or implicitly defined surfaces. The deformation can be applied either globally or locally and can impose any desired degree of derivative continuity. The scheme is based on trivariate Bernstein polynomials. The deformation technique functions well in a constructive solid geometry modeling system. Implementation of such a system with specific design approaches are presented: primarily the polygonalization of deformed surfaces using adaptive subdivision and display by the use of a scan line hidden surface removal algorithm.