A Preliminary Investigation on Surface-to-Surface Intersection Algorithms

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Although the shape representations offered by contemporary Computer Aided Design Systems are adequate to do routine calculations, they are deficient in having reliable sectioning and offsetting capabilities. The P.I. is seeking a way to mathematically represent the surface so that the computer realization can serve not only visualization but important manufacturing issues such as the computation of the offset surface. The principal investigator proposes to use an algebraic representation of the surface. However, the two problems with such an implicit representation are that it does not allow for representing finite segments and the coefficients do not have geometric meaning. The P.I. proposes a novel approach to overcoming these problems. The first is his use of a windowing method for bounding the algebraic surface. The second is his approach to determining the characteristic points of the solution through a guided subdivision algorithm. The research will test the feasibility and robustness of this novel approach. The principal investigator is a new investigator who shows excellent promise. Funding is recommended under the program for Expedited Awards for Novel Research.