法線ベクトル曲面を用いた曲面間交線算出法

一种利用法向量曲面计算曲面间交线的方法

• 批准号: 10780257
• 负责人: 山口 泰
• 金额: $ 1.28万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Encouragement of Young Scientists (A)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-10780257/
• 关键词: 形状モデリング; 自由曲面; 交線計算; 臨界点

3次元形状処理はCAD/CAMなど様々な応用を持つ基礎技術である.研究代表者は従来より,自由曲線・曲面の処理法などを始めとして,3次元形状処理に関して様々な研究を試みてきた.これまでに多くの研究がなされてきたものの,曲面の評価法,2曲面の接続法,2曲面間交線の算出法など多くの問題が残されている,研究代表者は,自由曲面の法線に着目することで,多くの問題を解決できると考えて研究を進めてきた.本研究は,特に曲面間交線算出問題の解決を目指すものである.曲面間交線の算出法としては,数値計算法,再帰的分割法,交線追跡法などの手法がある.一般に数値計算法は計算が不安定になりやすく,再帰的分割法は計算速度やデータ量の問題がある.交線追跡法は,これらの点で優れているが.追跡のための初期点算出や交線が分岐する特異点近傍での追跡などに問題がある.最近になって2曲面の法線が一致する点(臨界点)が重要な役割を果すことが示された.本研究ではm×n次ベジエ曲面の法線ベクトル曲面が(2m-1)×(2n-1)次のベジエ曲面であることを示すとともに,その制御点の算出式を導いた.この算出式をもとに,ベジエ法線ベクトル曲面を臨界点算出アルゴリズムを考案した.さらに,このアルゴリズムをプログラム化して,交線算出に有効であることを示した.

The 3-dimensional shape is based on the basic technology of CAD/CAM system. The representative of the research is in the field of free-curve surface theory, free-form surface theory and three-dimensional shape analysis. In order to improve the performance of multi-dimensional problems, the research representative, the free-form surface method, the free-form surface method, the multi-dimensional problem solving method, the multi-dimensional problem solving method, the free-form surface method, the surface method, the free-form surface method, the free-form surface method. In this study, the surface intersection is used to solve the problem. The method of calculating the intersection between surfaces is accurate, the algorithm of counting, the segmentation method of re-division, the method of intersection tracking, and the method of tracking. The general numerical calculation algorithm is used to calculate the instability, and then the segmentation method is used to calculate the speed, speed and quantity problems. The intersection tracking method is used to determine the accuracy of the method. At the initial stage of tracking, we can calculate the intersection, bifurcation, special point, near, and track down the problem. Recently, the normal line of two surfaces, the consistent point (boundary point), the important service cut, the result shows that. In this study, the normal line of the surface (2m-1) × (2n-1), the surface, the surface. The formula is calculated, the normal is calculated, the surface is calculated, and the boundary point is calculated. Please tell me that you need to know how to change the situation, so that you can figure out that there is a problem.

项目成果

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M. Shiraishi，Y. Yamaguchi：“光能传递方法的参数化表面细分”Proc。

Y. Yamaguchi et al.: "Surface-Surface Intersection with Critical Point Detection Based on Bezier Normal Vector Surfaces" Proc. of 6th IFIP WG 5.2 Workshop on Geometric Modeling: Fundamen-tals and Applications. 214-233 (1998)

Y. Yamaguchi 等人：“基于 Bezier 法向矢量曲面的具有临界点检测的表面-表面相交”Proc。