“Surface simplification using quadric error metrics” by Garland and Heckbert

Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models.

1. Jonathan Cohen, Amitabh Varshney, Dinesh Manocha, Greg Turk, Hans Weber, Pankaj Agarwal, Frederick Brooks, and William Wright. Simplification envelopes. In SIGGRAPH ’96 Proc., pages 119-128, Aug. 1996. http://www.cs.unc.edu/~geom/ envelope.html.
2. Andr6 Gudziec. Surface simplification with variable tolerance. In Second Annual Intl. Syrup. on Medical Robotics and ComputerAssisted Surgery (MRCAS ’95), pages 132-139, November 1995.
3. Hugues Hoppe. Progressive meshes. InSIGGRAPH’96 Proc., pages 99-108, Aug. 1996. http://www.research.microsoft.com/ research/graphics/hoppe/.
4. Hugues Hoppe, Tony DeRose, Tom Duchamp, John Mc- Donald, and Werner Stuetzle. Mesh optimization. In SIGGRAPH ’93 Proc., pages 19-26, Aug. 1993. http:// www.research.microsoft.com/research/graphics/hoppe/.
5. Alan D. Kalvin and Russell H. Taylor. Superfaces:polygonal mesh simplification with bounded error. IEEE Computer Graphics and Appl., 16(3), May 1996. http://www.computer.oro/ pubs/cg&a/articles/g30064.pdf.
6. David Luebke and Carl Erikson. View-dependent simplification of arbitrary polygonal environments. In SIGGRAPH 97 Proc., August 1997.
7. Rdmi Ronfard and Jarek Rossignac. Full-range approximation of triangulated polyhedra. Computer Graphics Forum, 15(3), Aug. 1996. Proc. Eurographics ’96.
8. Jarek Rossignac and Paul Borrel. Multi-resolution 3D approximations for rendering complex scenes. In B. Falcidieno and T. Kunii, editors, Modeling in Computer Graphics: Methods and Applications, pages 455-465, 1993.
9. William J. Schroeder, Jonathan A. Zarge, and William E. Lorensen. Decimation of triangle meshes. Computer Graphics (SIGGRAPH ’92 Proc.), 26(2):65-70, July 1992.
10. Marc Soucy and Denis Laurendeau. Multiresolution surface modeling based on hierarchical triangulation. Computer Vision and Image Understanding, 63(1):1-14, 1996.