# A Graph-Theoretic Approach to the Hidden Line Elimination Problem

• W. H. Chu
• D. T. Lee

## Abstract

We consider the hidden line elimination problem for displaying 3D solid objects represented as polyhedra on 2D display devices. The objects are assumed to be composed of polygonal faces. The algorithm presented is based on a graph-theoretic approach in that a certain graph representing the projections of the edges of the polyhedron is constructed and visible edges are found using depth-first search technique in the graph. The way in which visible edges are found is different from the previous ones in that it first assumes all the edges of the polygonal faces are invisible from the viewer and based on some criteria seeks out visible ones, whence the efficiency of the algorithm is, to some extent, independent of the number of hidden edges. In this sense it is more appropriate to refer to the algorithm as visible line determination algorithm.

The worst case time complexity of the algorithm is shown to be 0(nbnlog n) + F, where n is the total number of edges, nb the number of boundary edges and F the number of visible edges displayed. However, if the number nb of boundary edges is much smaller than n, which is true in most cases, the algorithm is more efficient than previous approaches whose worst case complexity may be 0(n2).

## Keywords

View Plane Front Face Intersection Graph Boundary Edge Back Face
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Plenum Press, New York 1985

## Authors and Affiliations

• W. H. Chu
• 1
• 2
• D. T. Lee
• 1
• 2
1. 1.Solo SystemsSan JoseUSA
2. 2.Department of Electrical Engineering and Computer ScienceNorthwestern UniversityEvanstonUSA