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Faster Shading by Equal Angle Interpolation of Vectors
March/April 2004 (vol. 10 no. 2)
pp. 217-223

Abstract—In this paper, we show how spherical linear interpolation can be used to produce shading with a quality at least similar to Phong shading at a computational effort in the inner loop that is close to that of the Gouraud method. We show how to use the Chebyshev's recurrence relation in order to compute the shading very efficiently. Furthermore, it can also be used to interpolate vectors in such a way that normalization is not necessary, which will make the interpolation very fast. The somewhat larger setup effort required by this approach can be handled through table look up techniques.

[1] A.M. Abbas, L. Szirmay-Kalos, and T. Horvath, Hardware Implementation of Phong Shading Using Spherical Interpolation Periodica Polytechnica, vol. 44, nos. 3-4, 2000.
[2] G. Bishop and D.M. Weimer, Fast Phong Shading Computer Graphics, vol. 20, no. 4, pp. 103-106, 1986.
[3] J.F. Blinn, Models of Light Reflection for Computer Synthesized Pictures Proc. SIGGRAPH, pp. 192-198, 1977.
[4] R.L. Burden and J.D. Faires, Numerical Analysis, pp. 507-516. Brooks/Cole, Thomson Learning, 2001.
[5] T. Duff, Smoothly Shaded Renderings of Polyhedral Objects on Raster Displays Computer Graphics, vol. 13, pp. 270-275, 1979.
[6] J.D. Foley, A. van Dam, S.K. Feiner, and J.F. Hughes, Computer Graphics Principles and Practice, pp. 735-736, 1063, Addison-Wesley, 1997.
[7] A. Glassner, Situation Normal Andrew Glassner's Notebook- Recreational Computer Graphics, pp. 87-97, Morgan Kaufmann, 1999.
[8] H. Gouraud, Continuous Shading of Curved Surfaces IEEE Trans. Computers, vol. 20, no. 6, June 1971.
[9] A. Hast, T. Barrera, and E. Bengtsson, Improved Shading Performance by Avoiding Vector Normalization Proc. Ninth Int'l Conf. Central Europe on Computer Graphics, Visualization, and Computer Vision (WSCG '01), pp. 1-8, 2001.
[10] A. Hast, T. Barrera, and E. Bengtsson, Improved Bump Mapping by Using Quadratic Vector Interpolation Proc. Eurographics, 2002.
[11] A. Hast, T. Barrera, and E. Bengtsson, Shading by Spherical Linear Interpolation Using De Moivre's Formula Proc. 11th Int'l Conf. Central Europe on Computer Graphics, Visualization, and Computer Vision (WSCG '03), 2003.
[12] C. Hecker, Perspective Texture Mapping Part I: Foundations Game Developers Magazine, pp. 16-25, Apr./May 1995.
[13] D. Kirk and D. Voorhies, The Rendering Architecture of the DN10000VS Computer Graphics, vol. 24, pp. 299-307, Aug. 1990.
[14] A.A.M. Kuijk and E.H. Blake, Faster Phong Shading via Angular Interpolation Computer Graphics Forum, vol. 8, no. 4, pp. 315-324, 1989.
[15] J.E. Marsden and M.J. Hoffman, Basic Complex Analysis, p. 17. W.H. Freeman and Company, 1996.
[16] W.K. Nicholson, Linear Algebra with Applications, pp. 275-276. PWS Publishing Company, 1995.
[17] S. Ouyang and D.E. Maynard, Phong Shading by Binary Interpolation Computers&Graphics, vol. 20, no. 6, pp. 839-848, 1996.
[18] B.T. Phong, Illumination for Computer Generated Pictures Comm. ACM, vol. 18, no. 6, June 1975.
[19] K. Shoemake, Animating Rotation with Quaternion Curves ACM SIGGRAPH Computer Graphics, Proc. 12th Ann. Conf. Computer Graphics and Interactive Techniques, vol. 19, no. 3, July 1985.

Index Terms:
Spherical linear interpolation, Chebyshev's recurrence relation, normalization.
Tony Barrera, Anders Hast, Ewert Bengtsson, "Faster Shading by Equal Angle Interpolation of Vectors," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 2, pp. 217-223, March-April 2004, doi:10.1109/TVCG.2004.1260773
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