On devices without battery consuming and specialized hardware for rendering, it is  important to improve the speed and quality so that these methods are suitable for 
real-time rendering. Furthermore such algorithms are needed on the coming multicore architectures.  We show how the methods by Gouraud and Phong, the commonly most used methods for shading, can be improved and made faster for both software rendering as well as simple low energy consuming hardware implementations. Moreover, this paper summarizes the authors’ achievements in increasing shading speed and performance and a Bidirectional Reflectance Distribution Function is simplified for faster computing and hardware implementatio

Hast, Anders

Lyashenko, Y. L.

Romanyuk, O. N.

Ляшенко, Ю. Л.

Романюк, А. Н.

Романюк, О. Н.

Хаст, Андерс

Хаста, Андерс

Repository of Vinnytsia National Technical University

Advances in Electrical and Computer Engineering                                                                       Volume 8, Number 2, 2008           82Efficient Methods for Fast Shading Alexander ROMANYUK1, Anders HAST2, Yuri LYASHENKO3, 1Vinnitsa National Technical University, Ivana Bohuna street, 119, Vinnitsa-21100, Ukraine,  2 Creative Media Lab University of Gavle, Sweden 3 Vinnitsa National Technical University, Stelmaha street, 34, Vinnitsa-21100, Ukraine 1ran@svitonline.com   Abstract—On devices without battery consuming and specialized hardware for rendering, it is  important to improve the speed and quality so that these methods are suitable for real-time rendering. Furthermore such algorithms are needed on the coming multicore architectures.  We show how the methods by Gouraud and Phong, the commonly most used methods for shading, can be improved and made faster for both software rendering as well as simple low energy consuming hardware implementations. Moreover, this paper summarizes the authors’ achievements in increasing shading speed and performance and a Bidirectional Reflectance Distribution Function is simplified for faster computing and hardware implementation.  Index Terms—shading, fast shading, BRDF approximation I. INTRODUCTION The shading methods by Gouraud [11] and Phong [12  are the most widespread methods for scanline rendering today. This is caused by their relative easiness, satisfactory quality and hardware supply ability. The trend today is to use specialized hardware for rendering. However, on small hand held devices like cell phones, where battery consumption is crucial there is still a need for fast software shading algorithms, which also can be implemented in simple and energy efficient hardware.  Moreover they could be used on multicore architectures, like the CELL-BE processor by IBM [15] and the coming multicore processor from intel [16], which are processors that both can be used for shading purposes. ]This paper summarizes some efficient methods by the authors that can be used for shading and that allows a considerable increase in both speed and quality. II. THE METHODS OF THE SHADING PRODUCTIVITY INCREASING It has theoretically been proved [1] that during the shading process according to Gouraud, the growth of the color intensities  and  correspondingly, both along scanlines and over the edges are constant values and this eliminates the necessity for re-computing them for every rasterization line. Let us describe the interconnection between growth of color intensities along the edge and the scanlines. It has been that the growth of the intensities , and  in horizontal, vertical and diagonal directions correspondingly are constants and are equal where  are the color intensities at the triangle vertexes as shown in figure 1.  ГIΔ BIΔHIΔ VIΔ DIΔCBA III ,,ACBCBCACACCBBCCAГ YXYXYIIYIII Δ⋅Δ−Δ⋅ΔΔ⋅−−Δ⋅−=Δ )()( ,    ACBCBCACACCABCCBВ YXYXYIIYIII Δ⋅Δ−Δ⋅ΔΔ⋅−−Δ⋅−=Δ )()( , ВГД ІII Δ+Δ=Δ   (1) This special property makes it possible to parallelize Gouraud rendering [2] by using the first order Serpinsky triangulation. This is done by dividing the initial triangle into four parts using the centers of each edge as shown in figure 2. While considering the fact that the color intensity change is constant an approach was theoretically founded. In this way we get three identical triangles and one that is mirrored.   Figure 1. Color Intensities Scheme.  Considering the fact that the color intensity growth is a constant value over the entire triangle we can shade it by computing the shading of only one of the new triangles and then transform the rendering results etc to the others.  А       С B H E G 1  2 4 3       Figure 2. Shading directions of rectangular triangles. Digital Object Identifier 10.4316/AECE.2008.02015[Downloaded from www.aece.ro on Tuesday, December 25, 2012 at 16:00:06 (UTC) by 194.146.140.5. Redistribution subject to AECE license or copyright. Online distribution is expressly prohibited.]Advances in Electrical and Computer Engineering                                                                       Volume 8, Number 2, 2008           83It is necessary to compute the shading rasterization of only the top triangle 1 and then the elementary step change is repeated for all the other interior triangles, considering that triangles 1, 2 and 3 have identical shading directions and triangle 4 is shaded in the oncoming direction (figure 2). Before rasterization all coordinates of the triangle vertices must be defined. Analogously, the code for interpolation of color intensities of internal points belonging to the top left triangle can be duplicated for all the other triangles, however it is performed according to their vertexes. Inasmuch as initial triangle triangulation is performed by the bisection of its edges and change of initial triangle sides are not always even numbers so the task of dividing the triangle without non-rasterized points appears. Different divisions’ variants were examined and optimal ones were defined. The second method for increasing Gouraud shading performance is based on the independent forming of even and odd points in the scan line. In the preparation cycle color intensities ,  are to be found according to the first and next points in the scanline. The intensities  of the first points in the scanlines are to be defined by means of interpolation of color intensities along the basic edges, and  1I 2IРБI2I  - with help of expression: . ГPБ III Δ+=2PIII Δ+= 224 ,  , ..., PIII Δ+= 246P2w2w2 I2II Δ+= − , ...; P13 I2II Δ+= , P35 I2II Δ+= , ,..., PIII Δ+= 257P1w21w2 I2II Δ+= −+ ,... . (2) Another possible approach for improving the Gouraud rendering lies in the detection of highlights on triangle borders and their further forming [3]. Let us assume that normal vectors  are given in the triangle edges , , . In computer graphics it is often assumed that both the light source and observer are situated in the infinity [2], i.e vector 210 ,, NNNrrr),( 00 yx ),( 11 yx ),( 22 yxLr has identical direction for all the triangle points. It was proved [4, 8], that in this case the maximal values of color intensity are at the edge points that fits equations  )cos)(cos1(coscoscoscost1 γβϕβϕγ+−−= , ,)cos)(cos1(coscoscoscost2 γλφλφγ+−−=)cos)(cos1(coscoscoscost3 βλϑλϑβ+−−= . (3)  The conformity of angles between normal vectors is represented in the figure 3.      Figure 3. Normal vectors of triangle ABC.  Variables  are parametric ones and varies in the interval from 0 to 1. An initial triangle can be divided into several depending on the result of the threshold values comparing with color intensities in the points .The triangles received are furthermore shaded with the Gouraud method. Such approach increases the Gouraud rendering quality due to finding out whether if highlights intersects one or several triangle edges. In the classic Gouraud shading method this detection is absent and highlights are being eliminated, yielding essential artifacts.  32,1 , ttt32,1 , ttt In computer graphics the Blinn illumination model [13] is widespread and the specular intensity is computed with following formula:  γnss kII cos= ,  (4) where I  - intensity of external light source;  - coefficient of specular reflection; skγ  - angle between normal vector Nr  and surface normal vector Hr, that is received by the adding of light direction vector Lr and observing vector Vr;  - exponent is surface specularity.  nThe major computational part of specular color takes place for BRDF computing the ,γncos 10001−=n . A new BRDF was proposed that has considerably lower power in comparison with such BRDF like . It’s expressed with the formula γncos)/(cos γ⋅knk , where  –  is a coefficient, that is detected depending on the surface specularity coefficient   ( ). kn nk <<The usage of various powers k  for different values of  was proposed for guaranteeing the necessary approximation accuracy. For instance in approximation of  by function nγncos)/(cos γ⋅knk  with relative error 3% it’s enough to take only to values of k: 1, 3. An modification of well known Schlick BRDF [14, 9] was proposed. It lies in using different values of powers depending on the specular exponent. This is the following formula [5]  [Downloaded from www.aece.ro on Tuesday, December 25, 2012 at 16:00:06 (UTC) by 194.146.140.5. Redistribution subject to AECE license or copyright. Online distribution is expressly prohibited.]Advances in Electrical and Computer Engineering                                                                       Volume 8, Number 2, 2008           84)( γγγ coscos/cos 22log2 +−⎥⎦⎥⎢⎣⎢ − nnn  (5) A problem of BRDF approximation with functions of 2nd [6] and 3rd [7] degree and its hardware realization was examined.   With the purpose of increasing the shading performance it is possible to use a combination of methods both Gouraud and Phong [5]. Therefore, for example, it is possible to divide the scanline into segments with length divisible by a power of  two [10]. The values of color intensities according to the Phong method are determined in end points of each segment, and intermediate pixels – according to the Gouraud method. The length of the segments can be adaptively changed and is determined by the curvature of a surface and the direction of the vector H. During the computation both specular and diffuse color intensity for points on a 3D surface, it is required that normalization of normal vectors is performed. This is explained by the fact that cosines of angles that are used in the shading function can easily be found by the inner product of unit length vectors. Taking into consideration that normalization is performed for the observer’s vector, light source’s vector and the normal vector, the challenging problem of decreasing the computational effort for this resource-intensive procedure is urgent. Therefore a method for adaptive normal vector normalization is proposed [5]. The normalization is performed only in cases of considerable change in colour intensity.  In figure 4 is provided an example of determination of intermediate normal vectors between vectors aNr and bNr, that are situated at the scanline endpoints. It is shown that 4)2/1()2/1(1≈+iidd. The following correlation is received for error detection : )2/1( id221 )2/1()2/1( 1iizd+−=+ .   Figure 4. Determination of intermediate vectors of normal.  It is proposed that when the error value is lower than a certain threshold value, then it is possible to use linear interpolation between normal vectors. )2/1( idThe normal vectors are received by the bisection of the angle between given vectors. Hence, for example,  ,)cos1(2 )21()21( zNNNNN babarrrrr +=++= ψ  where )cos1(2)21(ψ+=z .   (6) For the further division the following formulas are proposed ,2 )2/1()21()21( 1 nnn zNNNa++=+rrr    )2/1()2/1( 21 nn zz +=+ . The problem of spherical angular interpolation [17] for Phong rendering is examined. Recursive correlations are found, according to which the normal vector for the current pixel could be computed with help of normal vectors for two previous pixels, i.e.  )1(cos)(2)1( −−=+ tNtNtN rrr ϕ , where φ is the angle between the start and final vectors on the scanline. Analogous expression takes place for the determination of the diffuse color  ( ) ( )ddd tItItI 1cos2)1( −−=+ ϕ  (7) When using this recursive relation it is possible to compute diffuse color and thus the inner product using two multiplication operations: two subtraction operations and two swap operations that allows an increase in performance up to 40%. III. ALTERNATIVE BRDF MODEL Let us examine BRDF approximation with ( ) 211cos),( ⎟⎠⎞⎜⎝⎛ +−= γγBАnW  in conditions that .20πγ ≤≤   This function is chosen, because of the following: a) cosine – is a basic function for both functions;   b) at 0=γ   ( ) ,111coscos 2 =⎟⎠⎞⎜⎝⎛ +−= γγBАn  that fits boundary conditions;  c) both functions  in the interval 20π≤γ≤  are positive; d) the ( ) 211cos ⎟⎠⎞⎜⎝⎛ +−γBАfunction reaches zero value – this ensures  smooth fading; e) the А and В coefficients give a possibility to change highlight. [Downloaded from www.aece.ro on Tuesday, December 25, 2012 at 16:00:06 (UTC) by 194.146.140.5. Redistribution subject to AECE license or copyright. Online distribution is expressly prohibited.]Advances in Electrical and Computer Engineering                                                                       Volume 8, Number 2, 2008           85 Figure 5. BRDF Models.  In figure 5 the following functions are represented in the graph: Schlick function, ( ) 211cos2,cos ⎟⎠⎞⎜⎝⎛ +−γγ nn . The graph shows an extremely accurate approximation of the center part of the highlight  – and smooth fading after. IV. CONCLUSIONS The new approach for accelerated diffuse color computation according to the Phong method is proposed for shading 3D objects. The peculiarity of this approach lies in the synchronous hardware determination of two points at the scanline. For this approach the new approximation formula is used for normalization of normal vectors. The adaptive method for shading is efficient, in which two different illumination models are used depending on availability of highlight within the triangle. The increase of performance is possible when determining whether there are highlights within the triangle and then using the illumination model that considers specular color, and in all the other cases using the simple model, which is considerably faster. The method for detecting an actual intersection of the edge by the highlight or its detection within a triangle is proposed.  Considering, that highlight on the surface of graphic objects occupies a tiny area the adaptive approach allows an essential increase of performance for shading. Not only problems dealt with adaptive usage of illumination models are highlighted but also the methods for shading. At the same time surface curvature is considered and level of specular and diffuse light.  The methods being proposed allows a considerable increase in shading performance, and can be used for designing software and hardware for computer graphics. V. REFERENCES [1] Romanyuk A.N. One of the ways of computation process simplification during the shading of 3D objects according to the Gouraud method. //Вимірювальна та обчислювальна техніка в технологічних процесах, №2, 2004, стр. 72-75. [2] Romanyuk O.N., Chornij A.V. Effective algorithms of rendering procedure parallelization for realistic image forming // Proceedings of the 6th international conference on Development and Application System. - Suceava. – 2002, - pp. 357 - 362. [3] Romanyuk A.N. The new approach of increasing the quality of 3D objects shading according to the Gouraud method // Інформаційні технології та комп'ютерна інженерія, 2005, №3, c. 106-110. [4] Romanyuk A.N., Chornij A.V. The new approach of specular colour constituent determination // Оптико – електронні інформаційно – енергетичні технології. - 2004.– №2. - С. 85-92. [5] Romanyuk A.N.., Lyashenko Y.L., Melnikov A.M., Savitska L.A. The new formula for computation BRDF //Вестник Херсонського национального технического университета, №25, 2006. –С.412-416. [6] Romanyuk O.N., Lyashenko Y.L. Acceleration of painting with guadratic BRDF interpolation // XIII Міжнародна конференція з автоматичного управління (Автоматика -2006). Тези доповідей тринадцятої міжнародної науково-технічної конференції.-Вінниця, УНІВЕРСУМ-Вінниця, 2006. –С. 364. [7] Romanyuk O.N., Lyashenko Y.L. BRDF approximation with 3rd degree polynomial // Збірник матеріалів п’ятої міжнародної конференції конференції «Інтернет-Освіта-Наука-2006. Том 2.- Вінниця: УНІВЕСУМ-Вінниця, 2006.-С.506-509. [8] Romanyuk O.N. The combined usage of binary and code linear interpolation for normalization of normal vectors during the 3D objects shading // Вестник Херсонського национального технического университета, №25, 2006. . –С.408-411. [9] Romanyuk O.N., Melnikov A.M Adaptive normalization of normal vectors during determination of diffusive and specular colour constituent // Реєстрація, зберігання і обробка даних, 2006, Т. 8, № 3, -С.11-19. [10] Romanyuk O.N., Chornij A.V. “Methods for Specular Color Component Accelerate Calculation”. IEEE Workshop on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications. September 2005, Sofia, Bulgaria, pp. 615-619. [11] J. F. Blinn, Models of Light Reflection for Computer Synthesized Pictures In Proceedings SIGGRAPH, pp. 192-198. 1977. [12] H. Gouraud, Continuous Shading of Curved Surfaces, IEEE transactions on computers, vol. c-20, No 6, June 1971. [13] B. T. Phong, Illumination for Computer Generated Pictures Communications of the ACM, Vol. 18, No 6, June 1975. [14] Schlick, C. A fast alternative to phong’s specular model. Graphics Gems 4,1994, pp 385–387. [15] A. Heirich, L. Bavoil, Deferred shading on the Playstation3, [16] Sony Computer Entertainment US Research and Development, http://research.scea.com/ps3_deferred_shading.pdf [17] Larrabee: A Many-Core x86 Architecture for Visual Computing [18] L. Seiler, D. Carmean, E. Sprangle, T. Forsyth, M. Abrash, [19] P. Dubey, S. Junkins, A. Lake, J. Sugerman, R. Cavin, R. Espasa, E. Grochowski, T. Juan and P. Hanrahan. ACM Transactions on Graphics(TOG), Volume 27 ,  Issue 3  (August 2008) [20]  T. Barrera, A. Hast, E. Bengtsson 2004. Faster shading by equal angle interpolation of vectors IEEE Transactions on Visualization and Computer Graphics, pp. 217-223.   [Downloaded from www.aece.ro on Tuesday, December 25, 2012 at 16:00:06 (UTC) by 194.146.140.5. Redistribution subject to AECE license or copyright. Online distribution is expressly prohibited.]

Efficient Methods for Fast Shading

Efficient Methods for Fast Shading

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