The Rendering of Geometrically Constrained Surfaces in Geometric Modeling
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 pro...
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ndltd-TW-081NCTU03920432016-07-20T04:11:36Z http://ndltd.ncl.edu.tw/handle/35097225125703467036 The Rendering of Geometrically Constrained Surfaces in Geometric Modeling 幾何模型中幾何限制曲面的圖形顯示 Ko Kun Ming 柯坤明 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. Prof. Chuang Jung Hong 莊榮宏 1993 學位論文 ; thesis 71 en_US |
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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.
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author2 |
Prof. Chuang Jung Hong |
author_facet |
Prof. Chuang Jung Hong Ko Kun Ming 柯坤明 |
author |
Ko Kun Ming 柯坤明 |
spellingShingle |
Ko Kun Ming 柯坤明 The Rendering of Geometrically Constrained Surfaces in Geometric Modeling |
author_sort |
Ko Kun Ming |
title |
The Rendering of Geometrically Constrained Surfaces in Geometric Modeling |
title_short |
The Rendering of Geometrically Constrained Surfaces in Geometric Modeling |
title_full |
The Rendering of Geometrically Constrained Surfaces in Geometric Modeling |
title_fullStr |
The Rendering of Geometrically Constrained Surfaces in Geometric Modeling |
title_full_unstemmed |
The Rendering of Geometrically Constrained Surfaces in Geometric Modeling |
title_sort |
rendering of geometrically constrained surfaces in geometric modeling |
publishDate |
1993 |
url |
http://ndltd.ncl.edu.tw/handle/35097225125703467036 |
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