Transformation Transformation of of Rendering AlgorithmsRendering Algorithms

for Hardware Implementationfor Hardware ImplementationPh.D. Thesis by:Ph.D. Thesis by:

Ali Mohamed Ali AbbasAli Mohamed Ali Abbas

Scientific Supervisor: Scientific Supervisor: Professor Dr. Szirmay-Kalos LászlóProfessor Dr. Szirmay-Kalos László

Department of Control Engineering and Information TechnologyDepartment of Control Engineering and Information TechnologyFaculty of Electrical Engineering and InformaticsFaculty of Electrical Engineering and Informatics

Budapest University of Technology and EconomicsBudapest University of Technology and Economics

Budapest, 200Budapest, 20033..

The outlines of this talkThe 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.

The proposed solutionsThe 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)

Incremental renderingIncremental rendering

x

y

z

• Gouraud shading.• Phong shading.

N

LV

Gouraud shadingGouraud shading

Diffuse

X

Y

R,G,BR(X,Y) = a X + bY + c

R(X,Y)

R(X+1,Y) = R(X,Y)

Specular

+a

Ambient

System outline of Gouraud shaderSystem outline of Gouraud shader

Gouraud Gouraud shadingshading

Phong exponent = 20

168 triangles 374 triangles 690 trianglesTessellation level

Phong shadingPhong shading

X

Y

R,G,B

N(X,Y) = a X + bY + c

L(X,Y) = · · · ·

V(X,Y) = · · · ·

N(X,Y)

N VL

• vector interpolation• vector normalization• rendering equation

System outline of Phong shaderSystem outline of Phong shader

PhongGouraud

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

General framework (Thesis 1)General framework (Thesis 1)

Incremental concept for Incremental concept for quadratic and linear functionsquadratic 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)

+

+

I (X +1,Y) = I (X,Y) 2T5 .

PublicationsPublications1. 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).

Filtered Line Drawing (Thesis 2)Filtered Line Drawing (Thesis 2)

Bresenham’s

Box-filtering

Incremental cone-filtering

(Stair-like jaggies)

Cone filtering of linesCone filtering of lines

(ΔX)2 + (ΔY) 2

ΔXD = d . cos Φ =

DH = (1 - d) . cos Φ = - D + ΔD

DL = (1 + d) . cos Φ = D + ΔD

D(X+1) = D(X) +

D(X+1) = - D(X) + (ΔX)2 + (ΔY) 2

= - D(X) + ΔD+

ΔX - ΔY = D(X) + ΔD-

= d . ΔD

d .

ΔY

(ΔX)2 + (ΔY) 2

Block scheme of incremental cone-filteringBlock 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’’.

Spherical Interpolation Spherical Interpolation for Phong shading (Thesis 3)for Phong shading (Thesis 3)

X

Y

R,G,B

N(X,Y) = a X + bY + c

L(X,Y) = · · · ·

V(X,Y) = · · · ·

N(X,Y)

N VL

• vector interpolation• vector normalization• rendering equation

Linear interpolation + Normalization Linear interpolation + Normalization Spherical Interpolation Spherical Interpolation

u(t) = sin (1-t)sin

u1 +sin tsin ·u2

u1 · u2 = cos

|u(t)|2 = 1

u1 ·u(t) = cos t

u2 ·u(t) = cos (1 - t)

·

For uniform interpolation the followingequations must be proven for u(t):

Simultaneous spherical Simultaneous spherical interpolation of a pair of vectorsinterpolation of a pair of vectors

cos θ(t) = u(t) · v(t)

cos θ(t) = u'(t) · v1

u'2 expressed by quaternion multiplication.

rotating u2 by composition its own transformation and inverse

transformation of v1 to v2

Iout = Ie + ka · Ia + Iin(L) · kd · cos θL + Iin(L) · ks · coscosn n δδ

Calculation of specular reflection for Calculation of specular reflection for Blinn BRDF and single light-sourceBlinn BRDF and single light-source

cos θ(t) = u'(t) · v1 =sin (1-t)

sin (u1 · v1 ) +

sin tsin · (u'2 · v1)·

cos θ(t) = A · cos (t - α)

Iin(L)·ks · (N ·H) =

Iin(L) · ks · An · cosn (t - α)

C

cosn (t - α): exponentiation with a non-constant n

Solution: cosn x cos2 ax

cosn x, for n = 5,10,50,100,500

cos2 ax, for a = 1.45,1.98,2.76

Elimination of the exponentiationElimination of the exponentiation

na

2 5 10 20 50 100 5001.0000 1.4502 1.9845 2.7582 4.3143 6.0791 13.5535

Table of correspondence between n and a:

n=5, a=1.4502 n=500, a=13.5535

0

0

cosn x ·sin x dx cos2 ax ·sin x dx2

2a

Correspondence of Correspondence of nn and and aa

cos2 ax for a = 1.4502, 1.9845, 2.7582

cosn x for n = 5,10,20

Evaluation of the visual accuracy of the functions cosn x cos2 ax

6 bits4 bits

Quantization errors of address/data bits by cos2 ax

6 bits4 bits

cos2 ax cos2 ax

cos2 axcos2 ax

cos2 x cos2 x

Block scheme of spherical interpolationBlock 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.

Quadratic Interpolation Quadratic Interpolation for Phong shading (Thesis 4)for Phong shading (Thesis 4)

X

Y

R,G,B

N(X,Y) = a X + bY + c

L(X,Y) = · · · ·

V(X,Y) = · · · ·

N(X,Y)

N VL

• vector interpolation• vector normalization• rendering equation

I1

I12

I23

I13

I3

I2

Quadratic interpolation 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 .

Error control

I33

Subdivision

Hardware implementationHardware implementationI(X,Y)

I (X,Y)

2T5

Register

Register

X Counter

X

Xstart

Clk

Y Counter

Y1 Istart (X,Y)

Register

2(T5 A2start + T4 Astart + T3 )

Istart (X,Y)

Register

I (Xstart ,Y)

Register

2T5 Astart + T4

Y

The corresponding between pixel and texel coordinates is obtained by a homogeneous linear transformation.

Linear

u

v

X

Y

x

yz

auX+buY+cu

avX+bvY+cv

dX+eY+f

dX+eY+f

u =

v =

,

.

Quadratic interpolation in texturing (Thesis 4.2)

Texture space Screen space

Real world

Linear and quadratic Linear and quadratic texturingtexturingLinearLinear QuadraticQuadratic

System outlineSystem outlineof quadraticof quadraticinterpolationinterpolation

Gouraud Phong QuadraticSimulation results of quadratic interpolationSimulation results of quadratic interpolation

PublicationsPublications1. 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 17 th.

Spring Conference on Computer Graphics”, Budmerice, Slovakia, April 2001.

Hardware support for Hardware support for global illumination (Thesis 5)global illumination (Thesis 5)

Local illumination Local illumination + ambient term

Global illumination

Radiance transfer by transillumination bufferRadiance transfer by transillumination buffer

Transillumination image buffer

Random, global direction

1

2

3

3

1 3

1 2 3

2

- 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

Block scheme of global illuminationBlock 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.

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.

SummarySummary

Simulation environments:– the proposed algorithms first simulated in software using C++,

then transformed 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

Simulation, applicationSimulation, application