SPHERICAL MAPS - THEIR CONSTRUCTION, PROPERTIES, AND APPROXIMATION

被引:50
作者
GAN, JG
WOO, TC
TANG, K
机构
[1] University of Michigan, Ann Arbor, MI, 48109-2117
关键词
D O I
10.1115/1.2919386
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
The Gaussian map and its allied visibility map on a unit sphere find wide applications for orientating the workpiece for machining by numerical control machines and for probing by coordinate measurement machines. They also provide useful aids in computerized scene analysis, computation of surface-surface intersection, component design for manufacturing and fabrication procedures. Spherical convex hulls and spherical circles are two geometric constructs used to approximate the Gaussian maps and the visibility maps. The duality and the complementarity of these spherical maps are examined so as to derive efficient algorithms.
引用
收藏
页码:357 / 363
页数:7
相关论文
共 22 条
[11]  
Hilbert D., Cohn-Vossen S., Geometry and the Imagination, (1983)
[12]  
Hohmeyer M., A Surface Intersection Algorithm Based on Loop Detection, Proc. Symp. On Solid Modeling Foundations and CAD/CAM Applications, J., Acmsiggraph, pp. 197-208, (1991)
[13]  
Kim D.S., Cones on Bezier Curves and Surfaces, (1990)
[14]  
Kriezis G.A., Patrikalakis N.M., Rational Polynomial Surface Intersections, Proc. 17Th ASME Design Automation Conf, Miami FL, Advances in Design Automation: CAD, 2, pp. 43-53, (1991)
[15]  
Laugwitz D., Differential and Riemannian Geometry, (1965)
[16]  
Preparata F.P., Shamos M.I., Computational Geometry-An Introduction, (1985)
[17]  
Sederberg T.W., Myers R.J., Loop Detection in Surface Patch Intersections, Comp. Aided Geometric Design, 5, pp. 161-171, (1988)
[18]  
Sedgewick R., Algorithms, Addison Wesley, (1983)
[19]  
Shamos M.I., Hoey D., Closest-point Problems, 16Th Annual Symposium on Foundations of Computer Science, pp. 155-162, (1975)
[20]  
Sinha P., Klassen E.E.E., Wang K.K., Exploiting Topological and Geometric Properties for Selective Subdivision, Proc. ACM Symp. On Computational Geometry, pp. 39-45, (1985)