“Decorating implicit surfaces” by Pedersen

This work presents a new general approach for applying textures onto implicit surfaces. Its main contributions are: * An improved set of interactive tools for subdividing implicit surfaces into convenient patches. * An efficient and reliable algorithm for deriving parameterizations for these patches. * A new set of useful texturing operations. These results provide a unified representation scheme for a variety of texturing techniques that were previously incompatible, allowing more efficient manipulation, storage, and rendering of textured objects and a fuller use of current texture mapping hardware.

1. E.A. Bier and K. R. Sloan, Jr. Two part texture mappings. IEEE Computer Graphics and Applications, 6(9):40-53, September 1986.
2. Nelson L. Max and Geoff Wyvill. Shapes and textures for rendering coral. In N. M. Patrikalakis, editor, Scientific Visualization of Physical Phenomena (P1vc eedin g s of CG International’ 91), pages 333-343. Springer-Verlag, 1991.
3. Geoff Wyvill, Brian Wyvill, and Craig McPheeters. Solid texturing of soft objects. In CG International’87. Tokyo, May 1987.
4. Darwyn R. Peachey. Solid texturing of complex surfaces. In B. A. Barsky, editor, Computer Graphics (SIGGRAPH’85 P1vceedings), volume 19, pages 279-286, July 1985.
5. Ken Perlin. An image synthesizer. In B. A. Barsky, editor, Computer Graphics (SIGGRAPH ’85 P1vceedings), volume 19, pages 287-296, July 1985.
6. Andrew R Witkin and Paul S. Heckbert. Using particles to sample and control implicit surfaces. In Andrew Glassner, editor, Proceedings of SIGGRAPH ’94 (Orlando, Florida, July 24-29, 1994), Computer Graphics Proceedings, Annual Conference Series, pages 269-278. ACM SIGGRAPH, ACM Press, July 1994. ISBN 0-89791-667-0.
7. Pat Hanrahan and Paul E. Haeberli. Direct WYSIWYG painting and texturing on 3D shapes. In Forest Baskett, editor, Computer Graphics (SIGGRAPH ’90 P1vceedings), volume 24, pages 215-223, August 1990.
8. Barbara Robertson. Fresh paint. Computer Graphics World, 17(12):28-37, December 1994.
9. Peter Litwinowicz and Gavin Miller. Efficient techniques for interactive texture placement. In Andrew Glassner, editor, Proceedings of SIGGRAPH ’94 (01- lando, Florida, July 24-29, i994), Computer Graphics Proceedings, Annual Conference Series, pages 119-122. ACM SIGGRAPH, ACM Press, July 1994.
10. Maneesh Agrawala, Andrew C. Beers, and Marc Levoy. 3 d painting on scanned surfaces. In P1vceedings 1995 Symposium on Interactive 3D Graphics (Monterey, California, April 9-12,1995), pages 145-152.
11. Chakib Bennis, Jean-Marc V6zien, G6rard Igl6sias, and Andr6 Gagalowicz. Piecewise surface flattening for non-distorted texture mapping. In Thomas W. Sederberg, editor, Computer Graphics (SIGGRAPH ’91 P1vceedings), volume 25, pages 237-246, July 1991.
12. J6r6me Maillot, Hussein Yahia, and Anne Verroust. Interactive texture mapping. In James T. Kajiya, editor, Computer Graphics (SIGGRAPH ’93 P1vceedings), volume 27, pages 27-34, August 1993.
13. M. Samek. Texture mapping and distortion in digital graphics. Visual Computer, 2(5):313-20,1986.
14. Richard Bartels, John Beatty, and Brian Barsky. An Intlvduction to Splines for Use in Computer Graphics and Geometric Modeling. Morgan Kaufmann Publishers, Palo Alto, CA, 1987.
15. S. Gabriel and James T. Kajiya. Spline interpolation in curved space. State of the Art Image Synthesis, Course notes for SIGGRAPH ’85, 1985.
16. William Welch and Andrew Witkin. Variational surface modeling. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ’92 P1vceedings), volume 26, pages 157-166, July 1992.
17. R. Dietz, J. Hoschek, and B. Jtittler. An algebraic approach to curves and surfaces on the sphere and on other quadrics. Computer Aided Geometric Design, 10(3):211-230, August 1993.
18. Ron Kimmel, A. Amir, and A. M. Bruckstein. Finding shortest paths on surfaces. In Pierre-Jean Laurent, editor, Curves and Sulfaces in Geometric Design, pages 259-268. A. K. Peters, Wellesley, Massachusetts, August 1994.
19. Nicholas M. Patrikalakis and George A. Kriezis. Representation of piecewise continuous algebraic surfaces in terms of B-splines. The Visual Computer, 5 (6) :360-374, December 1989.
20. L. L. Schumaker and C. Traas. Fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines. Numerische Matematik, 60(1):129-139,1991.
21. J.S.B. Mitchell, D. M. Mount, and C. H. Papadimitriou. The discrete geodesic problem. SlAM J. Comput., 16(4):647-668,1987.
22. Karsten Opitz and Helmut Pottmann. Computing shortest paths on polyhedra: Applications in geometric modeling and scientific visualization. Intl. Journal of Computational Geometry and Applications, 4(2):165-178, June 1994.
23. Alan H. Barr, Bena Currin, Steven Gabriel, and John F. Hughes. Smooth interpolation of orientations with angular velocity constraints using quaternions. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ‘ 92 P1vceedings), volume 26, pages 313-320, July 1992.
24. J. Bloomenthal. Polygonization of implicit surfaces. Computer Aided Geometric Design, 5(4):341-356,1988.
25. Brian Wyvill, Craig McPheeters, and Geoff Wyvill. Data structure for soft objects. The Visual Computer, 2(4):227-234,1986.
26. Manfredo R do Carmo. Differential Geometry of Culwes and Sulfaces. Prentice-Hall Inc., 1976. ISBN 0-13-212589-7.
27. Thomas H. Cohen, Charles E. Leiserson, and Ronald L. Rivest. Intlvduction to Algorithms. MIT Press, Cambridge, Massachusetts, 1990.
28. Hugues Hoppe, Tony DeRose, Tom Duchamp, John McDonald, and Werner Stuetzle. Surface reconstruction from unorganized points. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ’92 P1vceedings), volume 26, pages 71-78, July 1992.
29. Greg Turk. Generating textures for arbitrary surfaces using reaction-diffusion. In Thomas W. Sederberg, editor, Computer Graphics (SIGGRAPH ’91 P1vceedings), volume 25, pages 289-298, July 1991.
30. Ron Kimmel and Nahum Kiryati. Finding shortest paths on surfaces by fast global approximation and precise local refinement. In SPIE Vision and Geometry III, pages 198-209, November 1994.
31. Richard E. Williamson, Richard H. Crowell, and Hale F. Trotter. Calculus of Vector Functions. Prentice-Hall Inc., 1962 (first edition). ISBN 0-13-112367.
32. Charles Loop. A G} triangular spline surface of arbitrary topological type. Computer Aided Geometric Design, (11):303-330,1994.
33. J/3rg Peters. C } surface splines. SIAM Journal on NumericalAnalysis, October 1993.
34. Paul Chew. Guaranteed quality mesh generation for curved surfaces. In ACM Symposium on Computational Geometry, 1993.
35. Greg Turk. Re-tiling polygonal surfaces. In Edwin E. Catmull, editor, Computer Graphics (SIGGRAPH ’92 P1vceedings), volume 26, pages 55-64, July 1992.
36. William Welch and Andrew Witkin. Free-Form shape design using triangulated surfaces. In Andrew Glassner, editor, P1vceedings of SIGGRAPH ’94 (Orlando, Florida, July 24-29, 1994), Computer Graphics Proceedings, Annual Conference Series, pages 247-256. ACM SIGGRAPH, ACM Press, July 1994. ISBN 0-89791-667-0.
37. Andrew J. Hanson. Geometry for N-dimensional graphics. In Paul Heckbert, editor, Graphics Gems IV, pages 149-170. Academic Press, Boston, 1994.
38. James D. Foley, Andries van Dam, Steven K. Feiner, and John F. Hughes. Computer Graphics, Principles and Practice, Second Edition. Addison-Wesley, Reading, Massachusetts, 1990. Overview of research to date.
39. James F. Blinn. A generalization of algebraic surface drawing. ACM Transactions on Graphics, 1 (3):235-256, July 1982.
40. F. Sebastian Grassia. Using particles to texture implicit surfaces. Assignment for Paul Heckbert’s Rendering course at CMU, unpublished, December 1993.