Fast Near Phong-Quality Software Shading

Quadratic shading has been proposed as a technique giving better results than Gouraud shading, but whi ch is substantially faster than Phong shading. Several te chniques for fitting a second order surface to six points have been proposed. We show in this paper how an approximation of the mid-edge samples can be done in a ver y efficient way. An approximation of the mid edge vec tors are derived. Several advantages are apparent w hen these vectors are put into the original formulation. Firs t of all it will only depend on the vertex vectors. Moreover, it will simplify the setup and no extra square roots a re necessary for normalizing the mid-edge vectors. The setup will be about three times faster than previous appr oaches. This makes quadratic shading very fast for interpolation of both diffuse and specular light, w hich will make it suitable for near Phong quality s oftware renderings .

[1]  Tom Duff.  Smoothly shaded renderings of polyhedral objects on raster displays , 1979, SIGGRAPH '79.

[2]  László Szirmay-Kalos,et al.  Quadratic interpolation in hardware Phong shading and texture mapping , 2001, Proceedings Spring Conference on Computer Graphics.

[3]  László Szirmay-Kalos,et al.  Quadratic shading and its hardware implementation , 2000 .

[4]  Michael R. Kappel.  Shading: fitting a smooth intensity surface , 1995, Comput. Aided Des..

[5]  Larry Seller.  Quadratic interpolation for near-Phong quality shading , 1998, SIGGRAPH '98.

[6]  Anders Hast,et al.  Faster Computer Graphics - by Reformulation and Simplification of Mathematical Formulas and Algorithms , 2001 .

[7]  Zoltan J. Cendes,et al.  C1 Quadratic Interpolation over Arbitrary Point Sets , 1987, IEEE Computer Graphics and Applications.

[8]  Anders Hast,et al.  Improved Bump Mapping by using Quadratic Vector Interpolation , 2002, Eurographics.

[9]  Anders Hast,et al.  Fast specular highlights by modifying the Phong-Blinn model , 2003, SIGGRAPH '03.

[10]  H. Gouraud.  Continuous Shading of Curved Surfaces , 1971, IEEE Transactions on Computers.

[11]  David Kirk,et al.  The rendering architecture of the DN10000VS , 1990, SIGGRAPH.

[12]  Henry Fuchs,et al.  Pixel-planes 5: a heterogeneous multiprocessor graphics system using processor-enhanced memories , 1989, SIGGRAPH.

[13]  Anders Hast.  Improved Fundamental Algorithms for Fast Computer Graphics , 2002 .

[14]  Hiroyuki Kawai,et al.  3D graphics LSI core for mobile phone "Z3D" , 2003, HWWS '03.

[15]  Bui Tuong Phong.  Illumination for computer generated pictures , 1975, Commun. ACM.

[16]  James F. Blinn,et al.  Models of light reflection for computer synthesized pictures , 1998 .

[17]  Malcolm A. Sabin,et al.  Piecewise Quadratic Approximations on Triangles , 1977, TOMS.

[18]  Anders Hast,et al.  Fast setup for bilinear and biquadratic interpolation over triangles , 2003 .