Decimation of Triangle Meshes

The polygon remains a popular graphics primitive for computer graphics application. Besides having a simple representation, computer rendering of polygons is widely supported by commercial graphics hardware and software. However, because the polygon is linear, often thousands or millions of primitives are required to capture the details of complex geometry. Models of this size are generally not practical since rendering speeds and memory requirements are proportional to the number of polygons. Consequently applications that generate large polygonal meshes often use domain-specific knowledge to reduce model size. There remain algorithms, however, where domainspecific reduction techniques are not generally available or appropriate. One algorithm that generates many polygons is marching cubes. Marching cubes is a brute force surface construction algorithm that extracts isodensity surfaces from volume data, producing from one to five triangles within voxels that contain the surface. Although originally developed for medical applications, marching cubes has found more frequent use in scientific visualization where the size of the volume data sets are much smaller than those found in medical applications. A large computational fluid dynamics volume could have a finite difference grid size of order 100 by 100 by 100, while a typical medical computed tomography or magnetic resonance scanner produces over 100 slices at a resolution of 256 by 256 or 512 by 512 pixels each. Industrial computed tomography, used for inspection and analysis, has even greater resolution, varying from 512 by 512 to 1024 by 1024 pixels. For these sampled data sets, isosurface extraction using marching cubes can produce from 500k to 2,000k triangles. Even today’s graphics workstations have trouble storing and rendering models of this size. Other sampling devices can produce large polygonal models: range cameras, digital elevation data, and satellite data. The sampling resolution of these devices is also improving, resulting in model sizes that rival those obtained from medical scanners. This paper describes an application independent algorithm that uses local operations on geometry and topology to reduce the number of triangles in a triangle mesh. Although our implementation is for the triangle mesh, it can be directly applied to the more general polygon mesh. After describing other work related to model creation from sampled data, we describe the triangle decimation process and its implementation. Results from two different geometric modeling applications illustrate the strengths of the algorithm.