Direct manipulation of curve and surface properties using a piecewise polynomial basis function.

This dissertation presents new techniques for the direct manipulation of curve and surface properties in the context of computer aided geometric design. A new piecewise polynomial basis function (PPBF) is devised for a variety of shape design tasks, including the direct manipulation of reflection characteristics on surfaces. The new basis function permits the retention of the original polynomial format in the manipulated curves and surfaces. With this PPBF, the DCM technique is customized for practical use. An automatic discontinuity removal algorithm is developed which eliminates the third or higher order discontinuities contained in the curve. To provide a complete toolkit for free-form curve design, a direct curvature manipulation technique is presented to achieve the desired curvature distribution of the curve by using the optimization technique. The issue of surface shape control through reflection characteristic analysis is extensively explored in this dissertation. A scheme for finding new surface normals with respect to the desired reflection characteristics is introduced, and a new, direct solution to the inverse problem is developed. The direct solution is, in part, based on reasonable problem simplifications that are compatible with practical applications. With this new solution, a generalized reflection characteristic line manipulation algorithm is developed which can handle different types of reflection characteristic lines such as physical reflection line, isophotes and highlight lines on regular, composite and trimmed surfaces. The surface shape is automatically adjusted with the desired reflection characteristics by directly manipulating reflection characteristic lines. An extension to multiple connected trimmed surfaces is also investigated for future work. Therefore, this body of research provides new powerful tools for free-form shape design. The developed algorithms are automatic, robust and provide the user with real time response. The algorithms have been implemented and tested with the Interactive Curve Modifier (ICM) and the Interactive Surface Modifier (ISM) programs for use at Chrysler Corporation.PhDNaval Architecture and Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104512/1/9527691.pdfDescription of 9527691.pdf : Restricted to UM users only