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

来源：

JOURNAL OF MECHANICAL DESIGN | 1994年 / 116卷 / 02期

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

页码：357 / 363

页数：7

共 22 条

[1]

Anderson D.P., Efficient Algorithms for Automatic Viewer Orientation, Comp. & Grap, 9, 4, pp. 407-413, (1985)

[2]

Besl P.J., Surfaces in Range Image Understanding, (1988)

[3]

Bollobas B., Graph Theory, an Introductory Course, (1979)

[4]

Calladine C.R., Gaussian Curvature and Shell Structure, The Mathematics of Surfaces, (1986)

[5]

Chen Y.J., Ravani B., Offset Surface Generation and Contouring in Computer Aided Design, ASME Journal of Mechanisms, Transmissions, and Automation in Design, (1987)

[6]

Chen L.L., Woo T.C., Computational Geometry on the Sphere with Application to Automated Machining, ASME Journal of Mechanisms, Transmissions, and Automation in Design, 114, 2, pp. 288-295, (1992)

[7]

Do Carmo M.P., Differential Geometry of Curves and Surfaces, (1976)

[8]

Farouki R.T., The Approximation of Non-Degenerate Surfaces, Comp. Aided Geometric Design, 2, 1, pp. 257-279, (1985)

[9]

Faux I.D., Pratt M.J., Computational Geometry for Design and Manufacture, (1979)

[10]

Gan J., Spherical Algorithms for Setup Orientations of Workpieces with Sculptured Surfaces, (1989)

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