Bidirectional reflection functions from surface bump maps

ABSTRACT

The Torrance-Sparrow model for calculating bidirectional reflection functions contains a geometrical attenuation factor to account for shadowing and occlusions in a hypothetical distribution of grooves on a rough surface. Using an efficient table-based method for determining the shadows and occlusions, we calculate the geometric attenuation factor for surfaces defined by a specific table of bump heights.Diffuse and glossy specular reflection of the environment can be handled in a unified manner by using an integral of the bidirectional reflection function times the environmental illumination, over the hemisphere of solid angle above a surface. We present a method of estimating the integral, by expanding the bidirectional reflection coefficient in spherical harmonics, and show how the coefficients in this expansion can be determined efficiently by reorganizing our geometric attenuation calculation.

REFERENCES

• 1: James F. Blinn, Models of light reflection for computer synthesized pictures, Proceedings of the 4th annual conference on Computer graphics and interactive techniques, p.192-198, July 20-22, 1977, San Jose, California
• 2: James F. Blinn, Simulation of wrinkled surfaces, Proceedings of the 5th annual conference on Computer graphics and interactive techniques, p.286-292, August 23-25, 1978
• 3: James F. Blinn , Martin E. Newell, Texture and reflection in computer generated images, Communications of the ACM, v.19 n.10, p.542-547, Oct. 1976 [doi>10.1145/360349.360353]
• 4: Born, Max, and Wolf, Emil. Principles of Optics. Pergamon Press. Oxford 1980
• 5: Bresenham, 3. E. Algorithm for computer control of a digital plotter. IBM Systems Journal. Vol 4. pp. 25-30. 1965.
• 6: Catmull, Edwin~ and Rom, Raphael. A Class of Interpolating Splines, in Computer Aided Geometric Design. Barnhill and Pdesenfeld, Eds. Academic Press, pp. 31%326. New York.1974.
• 7: Robert L. Cook , Thomas Porter , Loren Carpenter, Distributed ray tracing, Proceedings of the 11th annual conference on Computer graphics and interactive techniques, p.137-145, January 1984
• 8: Robert L. Cook , Kenneth E. Torrance, A reflectance model for computer graphics, Proceedings of the 8th annual conference on Computer graphics and interactive techniques, p.307-316, August 03-07, 1981, Dallas, Texas, United States
• 9: Courant, R., and Hilbert, D. Methods of Mathematical Physics. Interscieuce Publishers, Inc., p. 513. New York. 1953.
• 10: Franklin C. Crow, Summed-area tables for texture mapping, Proceedings of the 11th annual conference on Computer graphics and interactive techniques, p.207-212, January 1984
• 11: Tom Duff, Compositing 3-D rendered images, ACM SIGGRAPH Computer Graphics, v.19 n.3, p.41-44, Jul. 1985
• 12: Andrew Glassner, Adaptive precision in texture mapping, Proceedings of the 13th annual conference on Computer graphics and interactive techniques, p.297-306, August 1986
• 13: Ned Greene, Environment mapping and other applications of world projections, IEEE Computer Graphics and Applications, v.6 n.11, p.21-29, November 1986 [doi>10.1109/MCG.1986.276658]
• 14: Ned Greene , Paul S. Heckbert, Creating raster Omnimax images from multiple perspective views using the elliptical weighted average filter, IEEE Computer Graphics and Applications, v.6 n.6, p.21-27, June 1986 [doi>10.1109/MCG.1986.276738]
• 15: Hall, Roy, and Greenberg~ Donald. A Testbed for Realistic Image Synthesis IEEE Computer Graphics and Applications Volume 3, No. 8, pp. 10-20 1984
• 16: Paul S. Heckbert, Filtering by repeated integration, Proceedings of the 13th annual conference on Computer graphics and interactive techniques, p.315-321, August 1986
• 17: Helmholtz, H.v. Helmoltz's Treatise on Physiological Optics. Optical Society Of America. Washington, D.C. 1924.
• 18: David S. Immel , Michael F. Cohen , Donald P. Greenberg, A radiosity method for non-diffuse environments, Proceedings of the 13th annual conference on Computer graphics and interactive techniques, p.133-142, August 1986
• 19: James T. Kajiya, The rendering equation, Proceedings of the 13th annual conference on Computer graphics and interactive techniques, p.143-150, August 1986
• 20: James T. Kajiya , Brian P Von Herzen, Ray tracing volume densities, Proceedings of the 11th annual conference on Computer graphics and interactive techniques, p.165-174, January 1984
• 21: N L Max, Shadows for bump-mapped surfaces, Proceedings of Computer Graphics Tokyo '86 on Advanced Computer Graphics, p.145-156, June 1986, Tokyo, Japan
• 22: Miller, Gene, and Hoffman, Robert. Illumination and Reflection Maps: Simulated Objects in Simulated and Real Environments. Advanced Image Synthesis Course Notes. Siggraph Conference. 1984.
• 23: Ohira, Tomohiro. A Shading Model for Anisotropic Reflection. Technical Report of The Institute of Electronics and Communication Engineers of Japan, in Japanese. Vol. 82, No. 235, pp. 47-54. 1983.
• 24: Perlin~ Kenneth. Course Notes. Siggraph Conference. 1984.
• 25: Perlin, Kenneth. Course Notes. SIGGRAPH '85 State of the Art in Image Synthesis Seminar Notes. submitted to IEEE CG&A, and personal communication. 1986.
• 26: Bui Tuong Phong, Illumination for computer generated pictures, Communications of the ACM, v.18 n.6, p.311-317, June 1975 [doi>10.1145/360825.360839]
• 27: Reuse, W. A. Polarization Studies of Light Diffusely Reflected from Ground and Etched Glass Surfaces. J. Opt. Soc. Am. Vol 40, No. 1. pp. 55-59. 1950.
• 28: " Snell, Jay. Radiometery and Photometery. Handbook of Optics. Driseoll, W. G. and Vaughen. W., Eds. McGraw-Hill. 1978.
• 29: Spangenberg, D. B., Strung, A. G., and Chamberlin, J. L. Surface Tezture Measumnents of Metal Surfaces National Bureau Standards, Special Publication 300 Vol 7. Washington, D.C. 1971.
• 30: Takagi, 3., Yokoi, S., and Tsurwoka, S. Comment on the Anisotropie Reflection Model. Bulletin of SIG. Graphics and CAD, Information Processing Society of Japan, in Japanese. Vol. 11. No. 1 pp. 2-9. 1983.
• 31: Tinkham, M. Group Theory and Quantum Mechanics. McGraw Hill pp.101-115. New York. 1964.
• 32: Torrance, Kenneth, and Sparrow, Ephraim. Theory for Off- Specular Reflection .from Roughened Surface. Journal of the Optical Society of America. Volume 57 No. 9 1967.
• 33: USA Standard Nomenclature and Definitions for Illuminating Engineering. USAS Z7.1-1967. 1967.
• 34: Turner Whitted, An improved illumination model for shaded display, Communications of the ACM, v.23 n.6, p.343-349, June 1980 [doi>10.1145/358876.358882]
• 35: Whltted, Turner, and Cook, Robert. A Comprehensive Shading Model. Image Rendering Tricks Course Notes. Siggraph Conference. 1985.
• 36: Lance Williams, Pyramidal parametrics, Proceedings of the 10th annual conference on Computer graphics and interactive techniques, p.1-11, July 25-29, 1983, Detroit, Michigan, United States

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Color, shading, shadowing, and texture

General Terms:
Design, Theory