Surface polygonization is the process by which a representative polygonal mesh of a surface is constructed for rendering or analysis purposes. This work presents a new surface polygonization algorithm specifically tailored to be applied to a large class of models which are created with parametric surfaces having triangular meshes. This method has particular application in the area of building virtual environments from computer-aided-design (CAD) models. The algorithm is based on an edge reduction scheme that collapses two vertices of a given triangular polygon edge onto one new vertex. A two step approach is implemented consisting of boundary edge reduction followed by interior edge reduction. A maximum optimization is used to determine the location of the new vertex. The criterion that is used to control how well the approximate surface represents the actual surface is based on examining the angle between surface normals. The advantage of this approach is that the surface discretization is a function of two, user-controlled variables, a boundary edge angle error and a surface edge angle error. The method presented here differs from existing methods in that it takes advantage of the fact that for many models, the exact surface representation of the model is known before the polygonization is attempted. Because the precise surface definition is known, a maximum optimization procedure, that uses the surface information, can be used to locate the new vertex. The algorithm attempts to overcome the deficiencies in existing techniques while minimizing the number of triangular polygons required to represent a surface and still maintaining surface integrity in the rendered model. This paper presents the algorithm and testing results.

1.
Aukstakalnis, S., and Blatner, D., 1992, Silicon Mirage: The Art and Science of Virtual Reality, Peachpit Press, Berkeley, CA.
2.
Bajaj
C. L.
,
1990
, “
Rational Hypersurface Display
,”
Comput.-Aided Design
, Vol.
24
, pp.
117
127
.
3.
Hoppe
H.
,
DeRose
T.
,
Duchamp
T.
,
McDonald
J.
, and
Stuetzle
W.
,
1993
, “
Mesh Optimization
,”
Computer Graphics
, Vol.
27
, pp.
19
26
.
4.
Khan, M., 1994, “A Mesh Reduction Approach to Parametric Surface Polygonization,” M. S. Thesis, Iowa State University.
5.
Kosters
M.
,
1991
, “
Curvature-dependent Parameterization of Curves and Surfaces
,”
Comput.-Aided Design
, Vol.
23
, pp.
569
578
.
6.
IDEAS, Solid Modeling, User’s Guide, 1991, Structural Dynamics Research Corporation.
7.
Lawrence, C., Zhou, J. L., and Tits, A. L., 1994, “User’s Guide for CF-SQP Version 2.0: A C Code for Solving Large Scale Constrained Nonlinear Minimax Optimization Problems, Generating Iterates Satisfying All Inequality Constraints,” Electrical Engineering Department Institute for Systems Research TR-94-16, University of Maryland, College Park.
8.
O’Rourke, J., 1987, Art Gallery Theorems and Algorithms, Oxford University Press, New York.
9.
Piegl
L.
,
1991
, “
On NURBS: A Survey
,”
IEEE Computer Graphics & Applications
, Vol.
11
, pp.
55
71
.
10.
Preparata, F., and Shamos, M., 1985, Computational Geometry, Springer-Verlag. New York.
11.
Pro/ENGINEER Modeling User’s Guide, 1993, Parametric Technology Corporation.
12.
Renze, K. J., 1994, “Unstructured Surface and Volume Decimation of Tessellated Domains,” Ph.D. Dissertation, Iowa State University.
13.
Schroeder
W. J.
,
Zarge
J. A.
, and
Lorensen
W. E.
,
1992
, “
Decimation of Triangle Meshes
,”
Computer Graphics
, Vol.
26
, pp.
65
70
.
14.
Snyder, J. M., 1992, Generative Modeling for Computer Graphics and CAD Academic Press, Inc.
15.
Turk
G.
,
1992
, “
Re-tiling Polygonal Surfaces
,”
Computer Graphics
, Vol.
26
, pp.
55
64
.
16.
Von Herzen
B.
, and
Barr
A. H.
,
1987
, “
Accurate Triangulations of Deformed, Intersecting Surfaces
,”
Computer Graphics
, Vol.
21
, pp.
103
110
.
This content is only available via PDF.
You do not currently have access to this content.