“Using particles to sample and control implicit surfaces” by Witkin and Heckbert

We present a new particle-based approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement control points for direct manipulation by specifying particle motions, then solving for surface motion that maintains the constraint. For sampling and rendering, we run the constraint in the order direction, creating floater particles that roam freely over the surface. Local repulsion is used to make floaters spread evenly across the surface. By varying the radius of repulsion adaptively, and fissioning or killing particles based on the local density, we can achieve good sampling distributions very rapidly, and maintain them even in the face of rapid and extreme deformations and changes in surface topology.

1. Chandrajit Bajaj, Insung Ihm, and Joe Warren. Higher-order interpolation and least-squares approximation using implicit algebraic surfaces. ACM Trans. on Graphics, 12(4):327-347, Oct. 1993.
2. David Baraff. Analytical methods for dynamic simulation of non-penetrating rigid bodies. Computer Graphics, 23(3):223- 232, July 1989.
3. David Baraff. Curved surfaces and coherence for non-penetrating rigid body simulation. Computer Graphics, 24(4):19-28, August 1990.
4. David Baraff and AndrewWitkin. Dynamic simulation of non-penetrating flexible bodies. Computer Graphics, 26(2):303- 308, 1992. Proc. Siggraph ’92.
5. Ronen Barzel and Alan H. Barr. A modeling system based on dynamic constaints. Computer Graphics, 22:179-188, 1988.
6. J. Baumgarte. Stabilization of constraints and integrals of motion in dynamical systems. Computer Methods in Applied Mechanics, 1972.
7. Thaddeus Beier. Practical uses for implicit surfaces in an-imation. In Modeling, Visualizing, and Animating Implicit Surfaces (SIGGRAPH ’93 Course Notes), pages 20.1-20.10. 1993.
8. James F. Blinn. A generalization of algebraic surface drawing. ACM Trans. on Graphics, 1(3):235-256, July 1982.
9. Jules Bloomenthal. Polygonization of implicit surfaces. Com-puter Aided Geometric Design, 5:341-355, 1988.
10. Jules Bloomenthal. An implicit surface polygonizer. In Paul Heckbert, editor, Graphics Gems IV, pages 324-350. Aca-demic Press, Boston, 1994.
11. Jules Bloomenthal and Brian Wyvill. Interactive techniques for implicit modeling. Computer Graphics (1990 Symp. on Interactive 3D Graphics), 24(2):109-116, 1990.
12. Luiz Henrique de Figueiredo, Jonas de Miranda Gomes, Demetri Terzopoulos, and Luiz Velho. Physically-based meth-ods for polygonization of implicit surfaces. In Graphics Inter-face ’92, pages 250-257, May 1992.
13. Phillip Gill, Walter Murray, and Margret Wright. Practical Optimization. Academic Press, New York, NY, 1981.
14. Michael Gleicher and Andrew Witkin. Through-the-lens cam-era control. Computer Graphics, 26(2):331-340, 1992. Proc. Siggraph ’92.
15. Herbert Goldstein. Classical Mechanics. Addision Wesley, Reading, MA, 1950.
16. Huges Hoppe, Tony DeRose, TomDuchamp, John McDonald, and Werner Stuetzle. Mesh optimization. In SIGGRAPH 93 Proceedings, pages 19-26, July 1993.
17. David J. Jevans, Brian Wyvill, and Geoff Wyvill. Speeding up 3-D animation for simulation. In Proc. MAPCON IV (Multi and Array Processors), pages 94-100, Jan. 1988.
18. William E. Lorensen and Harvey E. Cline. Marching cubes: A high resolution 3D surface reconstruction algorithm. Com-puter Graphics (SIGGRAPH ’87 Proceedings), 21(4):163- 170, July 1987.
19. Henry Moreton and Carlo S~ equin. Functional minimization for fair surface design. Computer Graphics, 26(2):167-176, 1992. Proc. Siggraph ’92.
20. Shigeru Muraki. Volumetric shape description of range data using “blobby model”. Computer Graphics (SIGGRAPH ’91 Proceedings), 25(4):227-235, July 1991.
21. Paul Ning and Jules Bloomenthal. An evaluation of implicit surface tilers. Computer Graphics and Applications, pages 33-41, Nov. 1993.
22. Vaughan Pratt. Direct least-squares fitting of algebraic sur-faces. Computer Graphics (SIGGRAPH ’87 Proceedings), 21(4):145-152, July 1987.
23. W.H. Press, B.P. Flannery, S. A. Teukolsky, and W. T. Vetter-ling. Numerical Recipes in C. Cambridge University Press, Cambridge, England, 1988.
24. A. Ricci. A constructive geometry for computer graphics. Computer Journal, 16(2):157-160, May 1973.
25. T. Sederberg. Piecewise algebraic surface patches. Computer Aided Geometric Design, 2(1-3):53-60, 1985.
26. John M. Snyder. Generative Modeling for Computer Graphics and CAD. Academic Press, Boston, 1992.
27. Richard Szeliski and David Tonnesen. Surface modeling with oriented particle systems. Computer Graphics (SIGGRAPH ’92 Proceedings), 26(2):185-194, July 1992.
28. Greg Turk. Generating textures on arbitrary surfaces using reaction-diffusion. Computer Graphics (SIGGRAPH ’91 Pro-ceedings), 25(4):289-298, July 1991.
29. Greg Turk. Re-tiling polygonal surfaces. Computer Graphics (SIGGRAPH ’92 Proceedings), 26(2):55-64, July 1992.
30. William Welch and Andrew Witkin. Variational surface mod-eling. Computer Graphics, 26(2):157-166, 1992. Proc. Sig-graph ’92.
31. Andrew Witkin, Michael Gleicher, and William Welch. In-teractive dynamics. Computer Graphics, 24(2):11-21, March 1990. Proc. 1990 Symposium on 3-D Interactive Graphics.
32. AndrewWitkin and William Welch. Fast animation and control of non-rigid structures. Computer Graphics, 24(4):243-252, July 1990. Proc. Siggraph ’90.
33. Brian Wyvill, Craig McPheeters, and Geoff Wyvill. Data struc-ture for soft objects. The Visual Computer, 2(4):227-234, 1986.