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三維散亂點集的曲面三角剖分

注意:本論文已在《中國圖象圖形學報》 2003, 8(12):1379~1388上發表
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張永春 達飛鵬 宋文忠
(東南大學自動化研究所, 南京 210096)

摘要:根據三維散亂點集構造曲面剖分在CA GDˆCAD、反求工程等方面有著十分廣泛的應用. 本文回顧了三維散亂點集曲面三角剖分的兩種主要方法即平面投影法和直接剖分法, 對幾種常用的算法作了較為詳細的描述, 同時對剖分算法中經常出現的數據結構作了詳細的介紹. 由于剖分采用的優化準則決定了剖分結果, 因此本文討論了幾種常用的剖分優化準則, 并舉例對幾種優化準則進行了較詳細的分析比較. 最后簡要地討論了算法復雜度以及目前剖分的主要研究方向, 并指出在實際工程應用中對復雜曲面采樣得到的散亂點集, 要得到光順和保形的三角剖分, 需要新的剖分準則和算法.
關鍵詞:圖象處理,三維散亂點集,曲面三角剖分,數據結構,優化準則

 

Surface Triangulations Based on 3D Arbitrary Point-sets

Yong-chun Zhang(張永春), Fei-peng Da, Wen-zhong Song
(Research Institute of Automation, Southeast University, Nanjing, China, 210096)

Abstract: Surface triangulations based on 3D arbit rary point sets are widely applied in CA GD/CAD and reverse engineering, etc. In the first place, this paper reviews two main methods in surface triangulations, named as plane projection and direct triangulation. For the former, Delaunay triangulations are mainly enunciated. For the later, algorithm developed by B. K. Choi is particularized. Some typical algorithms are introduced in detail, as well as various data-structures built in these algorithms. Next, since the final result of triangulation is determined by the optimal criterion, some proverbial optimal criteria are specified and analyzed in this paper, and they are thoroughly compared with each other here through anatomizing an example. It is pointed that, in practical engineering, it is necessary to develop new algorithms with new criteria for triangulations of scattered points sampled from complicated surfaces so as to maintain the properties such as better smoothness and shape preserving. Finally the time and space complexities of various algorithms are briefly and concisely discussed, also the research trend of surface triangulations based on 3D arbit rary point-sets.
Keywords:
 3D arbitrary point-sets, Surface triangulations, Data structures, Optimal criteria

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