The Rendering of Geometrically Constrained Surfaces in Geometric Modeling

• Main Authors: Ko Kun Ming, 柯坤明
• Other Authors: Prof. Chuang Jung Hong
• Format: Others
• Language: en_US
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/35097225125703467036

碩士 === 國立交通大學 === 資訊工程研究所 === 81 === Many surfaces in CAGD, including offsets and blends, are defined from given surfaces subject to certain geometric constraints. These geometrically constrained surfaces can be uniformly defined as the projection of two-dimensional manifolds (2-surfaces) in n-dimensional space, where n>3. Let F be a 2-surface in n-space, and let .pi.(F) be its projection into the subspace spanned by the first three coordinates. The closed-form representation of .pi.(F) is derivable in principle using resultant or Grobner bases. However, this is usually not practical becaues of the symbolic computation entailed has a very high complexity. In consequence, we should work with the n- space representation directly. To polygonize a constrained surface .pi.(F), we propose an algorithm that computes its pisecewise linear approximation (PLA) using the surface definition in n-space, but with major computations performed in 3-space. We also give some methods to retile and refine the PLA. With the polygonal approximation, the fast rendering of geometrically constrained surfaces can be achieved by taking advantage of hardware capabilities.