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Transformation of Rendering Algorithms for Hardware Implementation

This Ph.D. thesis by Ali Mohamed Ali Abbas, supervised by Professor Dr. Szirmay-Kalos László, explores the transformation of high-quality rendering algorithms to make them suitable for hardware realization. The presentation covers current rendering scheme challenges, proposes a general framework, and discusses specific algorithms such as filtered line drawing and spherical interpolation for Phong shading. Key contributions include incremental rendering methods and hardware support for global illumination, aiming to improve both the quality and efficiency of rendering in real-time applications.

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Transformation of Rendering Algorithms for Hardware Implementation

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  1. Transformation of Rendering Algorithmsfor Hardware Implementation Ph.D. Thesis by: Ali Mohamed Ali Abbas Scientific Supervisor: Professor Dr. Szirmay-Kalos László Department of Control Engineering and Information Technology Faculty of Electrical Engineering and Informatics Budapest University of Technology and Economics Budapest, 2003.

  2. The outlines of this talk • General rendering schemes. • Problems of current rendering approaches:- low quality, simple, hardware supported. - high quality, complex, not hardware supported. The main aim of this thesis is to convert high quality complex algorithms to make them appropriate for hardware realization.

  3. The proposed solutions - general framework (Thesis 1)- filtered line drawing (Thesis 2)- spherical interpolation for Phong shading (Thesis 3)- quadratic interpolation for Phong shading and texturing (Thesis 4)- hardware support for global illumination (Thesis 5)

  4. Incremental rendering • Gouraud shading. • Phong shading. L V y N z x

  5. Specular Gouraud shading R(X,Y)= a X + bY + c R,G,B Y R(X,Y) + a R(X+1,Y)= R(X,Y) X Ambient Diffuse

  6. Gouraud shading Phong exponent = 20 System outline of Gouraud shader Tessellation level 374 triangles 168 triangles 690 triangles

  7. Phong shading • vector interpolation • vector normalization • rendering equation V N L R,G,B Y N(X,Y) N(X,Y) = a X + bY + c L(X,Y) = · · · · V(X,Y) =· · · · X

  8. System outline of Phong shader Phong Gouraud

  9. General framework (Thesis 1) • Surface tessellation, to triangles and line segments • Transformation, projection and shading • Incremental concept, I(X+1,Y) = I(X,Y) + ΔI(X,Y)- reducing algorithms complexity- recursive computation • The accuracy of the fixed-point representation was investigated, and the number of fractional bits was computed

  10.  I (X +1,Y)= I (X,Y) 2T5 . + Incremental concept for quadratic and linear functions I(X,Y)= T5 X 2+T4 X Y+T3 Y 2 +T2 X+T1Y+T0 . I(X+1,Y)= I(X,Y)(2T5 X +T4 Y+T5 +T2). + I (X,Y)

  11. Publications 1. A. M. Abbas. “Photorealistic Images in Real-Time”, No 20, 2003, in the Journal of “Industrial Researches’’. 2. A. M. Abbas, L. Szirmay-Kalos, and T. Horváth. “Hardware Implementation of Phong Shading using Spherical Interpolation”. “Periodica Polytechnica”, 44(3-4): 283-301, 2000. 3. A. M. Abbas, L. Szirmay-Kalos, T. Horváth, and T. Fóris. “Quadratic Shading and its Hardware Interpolation”, “Machine GRAPHICS & VISION “, 9(4):625-839, 2000. 4. A. M. Abbas, L. Szirmay-Kalos, T. Horváth, T. Fóris, and G. Szijártó, “Quadratic Interpolation in Hardware Rendering”, In “Spring Conference on Computer Graphics”, Budmerice, Slovakia, April 2001. (Best paper award).

  12. Filtered Line Drawing (Thesis 2) Incremental cone-filtering Box-filtering Bresenham’s (Stair-like jaggies)

  13. Cone filtering of lines ΔX d . D = d . cos Φ = (ΔX)2 + (ΔY) 2 = d . ΔD DH = (1 - d) . cos Φ = - D + ΔD DL = (1 + d) . cos Φ = D + ΔD ΔY D(X+1) = D(X) + (ΔX)2 + (ΔY) 2 = D(X) + ΔD- ΔX - ΔY D(X+1) = - D(X) + (ΔX)2 + (ΔY) 2 = - D(X) + ΔD+

  14. Block scheme of incremental cone-filtering Publications: 1. A. M. Abbas. “On 2D Line Scan Conversion”.In “Conference on The Latest Results in Information Technology”. IIT, Technical University of Budapest, Hungary, 1998. 2. A. M. Abbas. “Photorealistic Images in Real-Time”. No 20, 2003, in the Journal of “Industrial Researches’’.

  15. Spherical Interpolation for Phong shading (Thesis 3) • vector interpolation • vector normalization • rendering equation V N L R,G,B Y N(X,Y) N(X,Y) = a X + bY + c L(X,Y) = · · · · V(X,Y) =· · · · X

  16. Linear interpolation + Normalization  Spherical Interpolation sin t sin (1-t) u1 + ·u2 u(t) = · sin sin  u1 ·u2=cos  For uniform interpolation the following equations must be proven for u(t): |u(t)|2 = 1 u1 ·u(t) = cos t u2 ·u(t) = cos (1 - t)

  17. cos θ(t) = u(t) · v(t) Simultaneous spherical interpolation of a pair of vectors cos θ(t) = u'(t) · v1 u'2 expressed by quaternion multiplication. rotating u2 by composition its own transformation and inverse transformation of v1to v2

  18. Calculation of specular reflection for Blinn BRDF and single light-source sin t sin (1-t) (u1 ·v1 ) + · (u'2 · v1) cos θ(t) = u'(t) · v1 = · sin sin  cos θ(t) = A · cos (t - α) Iout = Ie + ka · Ia + Iin(L) · kd · cos θL + Iin(L) ·ks·cosn δ Iin(L)·ks· (N ·H) = Iin(L) · ks·An · cosn (t - α) C

  19. Elimination of the exponentiation cosn (t - α):exponentiation with a non-constantn Solution:cosn x  cos2 ax cos2 ax, for a = 1.45,1.98,2.76 cosn x, for n = 5,10,50,100,500

  20. n 2 10 500 20 5 50 100 a 1.0000 1.4502 13.5535 6.0791 1.9845 2.7582 4.3143 Correspondence of n and a    2 cosn x ·sin x dx  cos2 ax ·sin x dx 2a 0 0 Table of correspondence betweennanda: n=500, a=13.5535 n=5, a=1.4502

  21. Evaluation of the visual accuracy of the functions cosn xcos2 ax cosn x for n = 5,10,20 cos2 ax for a = 1.4502, 1.9845, 2.7582 

  22. Quantization errors of address/data bits by cos2 ax cos2 x cos2 x 4 bits 6 bits cos2 ax cos2 ax 6 bits 4 bits cos2 ax cos2 ax

  23. Block scheme of spherical interpolation Publications: 1. A. M. Abbas, L. Szirmay-Kalos, and T. Horváth. “Hardware Implementation of Phong Shading using Spherical Interpolation”. “Periodica Polytechnica”, 44(3-4):283--301, 2000.

  24. Quadratic Interpolation for Phong shading (Thesis 4) V N • vector interpolation • vector normalization • rendering equation L R,G,B Y N(X,Y) N(X,Y) = a X + bY + c L(X,Y) = · · · · V(X,Y) =· · · · X

  25. I3 I23 I2 I33 I13 Error control I12 Subdivision I1 Quadratic interpolation • The interpolation is done in image space. • The interpolation is not linear, but rather quadratic. • Quadratic form has 6 degrees of freedom. I(X,Y)= T5 X 2+T4 X Y+T3 Y 2 +T2 X+T1Y+T0 .

  26. Istart (X,Y) Register Y S Y Counter Y1  I(Xstart ,Y)  Istart (X,Y) Register Register S S 2(T5 A2start + T4 Astart + T3 ) 2T5 Astart + T4 Hardware implementation X I(X,Y) Clk X Counter Register Xstart S  I (X,Y) Register S 2T5

  27. Linear Quadratic interpolation in texturing (Thesis 4.2) v Texture space Screen space Y y z Real world u x X The corresponding between pixel and texel coordinates is obtained by a homogeneous linear transformation. auX+buY+cu u = , dX+eY+f avX+bvY+cv . v = dX+eY+f

  28. Linear and quadratic texturing Quadratic Linear System outline of quadratic interpolation

  29. Gouraud Phong Quadratic Simulation results of quadratic interpolation

  30. Publications 1. A. M. Abbas, L. Szirmay-Kalos, T. Horváth, and T. Fóris. “Quadratic Shading and its Hardware Interpolation”. “Machine GRAPHICS & VISION “, 9(4):625--839, 2000. 2. A. M. Abbas, L. Szirmay-Kalos, T. Horváth, T. Fóris, and G. Szijártó. “Quadratic Interpolation in Hardware Rendering”. In “Spring Conference on Computer Graphics”, Budmerice, Slovakia, April 2001, (Best paper award). 3. A. M. Abbas, L. Szirmay-Kalos, T. Horváth, T. Fóris, and G. Szijártó. “Quadratic Interpolation in Hardware Phong Shading and Texture Mapping”. In “IEEE Computer Society Press in the Post-Proceedings of The 17th. Spring Conference on Computer Graphics”, Budmerice, Slovakia, April 2001.

  31. Hardware support for global illumination (Thesis 5) Local illumination Global illumination Local illumination + ambient term

  32. Radiance transfer by transillumination buffer Random, global direction 3 3 1 3 1 3 1 2 2 2 Transillumination image buffer - identifying the patches that are visible from a given patch - solution of global visibility problem, transillumination direction - store in visibility map, extended (or modified ) z-buffer

  33. Block scheme of global illumination Publications: 1. L. Kovács, L. Szirmay-Kalos, and A. M. Abbas. “Testing Global Illumination Methods with Analytically Computable Scenes”. In “Winter School of Computer Graphics”, II:419--426, Plzen, Cz., February 2001. 2.R. Martinez, L. Szirmay-Kalos, M. Sbert, and A. M. Abbas. “Parallel implementation of Stochastic Iteration Algorithms”. In “Winter School of Computer Graphics”, II:344--351, Plzen, Cz., February 2001.

  34. Summary • Thesis 1:- general methodology based on incremental concept. • Thesis 2:- anti-aliased line drawing algorithm with simple operations • Thesis 3:- single cosine function (reduced number of dot-products) - no normalization or scalar exponentiation are required • Thesis 4:- approximates non-linear functions (Phong shading or texturing). - simple for hardware implementation. - arbitrary BRDF models.- independent of the number of light sources. • Thesis 5:- speedup global illumination.

  35. Simulation, application • Simulation environments: • the proposed algorithms first simulated in software using C++,thentransformed to hardware design, specified in VHDL and simulated in Model-Technology environments assuming the delay times of a real FPGA device. • the results demonstrate that, these hardware schemes could provide appropriate pixel drawing time, enough for real-time rendering These hardware schemes have not been build yet • Possible applications of the results: • Development of new hardware, • Efficient CPU level and vertex/pixel shader level program development. Thank you very much for your attention

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