情報処理学会研究報告 IPSJ SIG Technical Report Vol.2011-CG-145 No.10 Vol.2011-CVIM-179 No /11/17 1 Rendering Techniques for Realistic Material Property R

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1 1 Rendering Techniques for Realistic Material Property Representation Mikio Shinya 1 Simulating and representing material properties has been one of the most important area in the rendering research This paper reviews rendering techniques that can effectively synthesize realistic images of various materials ds n s i o (globel illumination) : ds s o i ray tracing, radiosity, path tracing, photon mapping ds (local illumination) : 1 BRDF BRDF(Bi-directional Reflectance Distribution Function) BSSRDF(Bi-directional Scattering Reflectance (intensity) Distribution Function) (imaging) : (depth of field) motion blur (radiance) 1 L (,flux) L(x, s) = dφ/((n s)ds dω) (1) n ds dφ dω 1 Toho University 1 1 c 2011 Information Processing Society of Japan

2 ( 1) CG R(s i, s o) = R(θ i, θ o, φ o) (5) 1 (isotropic) x x i x i E (anisotropic) E(x i ) = dφ i /ds = A cos 4 θ L(x, s) (2) BRDF A θ Helmholtz : R(s i, s o) = R(s o, s i) : 22 BRDF 1 n ds s i L i (s i ) R(s i, s o )(n s o )ds o 1 Ω ds s o L o (s o ) + CG Lambert L o (s o ) = R(s i, s o )L i (s i )(n s i ) (3) Phong Lambert R(s i, s o ) BRDF(Bi-directional Reflectance BRDF Distribution Function: ) Phong R s i,s o Lambert 23 L o(s i, s o) = R(s i, s o)l i(s i)(n s i)ds i (4) Snell Ω + Ω + incident light o Fresnel i Torrance-Sparrow o 1) V Fresnel Fresnel Beckmann 2 BRDF BRDF 4 2) 2 Cook-Torrance 3) Oren-Nayer 1 (irradiance) 4) dφ/ds CG irradiance 2 c 2011 Information Processing Society of Japan

3 BRDF Marschner 5) 8) BRDF 3-b Ward CCD BRDF 6) 3 24 BRDF BSSRDF BSSRDF BRDF BRDF plane-parallel 31 BSSRDF incident light (sub-surface scattering) i hair (a) Kajiya-Kay model o incident light + S(x i, s i ; x o, s o ) s i reflecting light x i x 0 1 st reflection incident 2 nd reflection virtual dipole - hair 4 BSSRDF transmission 4 x i s i (b) Marschner model x o s o S d 3 S d (x i, s i ; x o, s o ) BSSRDF (Bi-directional Scattering Surface Reflectance Distribution Function) I in (x, s) I out Kay-Kajiya 3-a θ i = θ o Phong I out (x, s) = L = k s cos n (θ i θ o ) (6) A S d (x i, s i ; x o, s o ) Ω + (7) I in (x, s )(n s o )dxds 3 c 2011 Information Processing Society of Japan

4 A n p(s, s ) s s Ω + BSSRDF I(x, s )p(s, s )σ sdl BRDF (4) s x BSSRDF e(x, s) e(x, s)dl BSSRDF di(x, s) = ( σ t I + σ s p(s, s )I(x, s )ds S +e(x, s))dl BRDF (Bidirectional (8) Reflectance Distribution Function) s d/dl s 1mm 50mm ( s)i(x, s) = σ t I + σ s p(s, s )I(x, s )ds Ω BRDF +e(x, s) BRDF BSSRDF (9) 12) Ω p(s, s ) 32 Henyey-Greenstein p(s, s ) = (1/4π)(1 g 2 )/(1 + 2g(s s ) + g 2 ) 2/3 321 g dl 1 α = σ s /σ t I(x,s) decrease by scattering/ (albedo) absorption I+dI (9) increase by scattering s path-tracing increase by emission 5 33 Plane-parallel BRDF 5 incident light x s I(x, s) s 0 x dl di(x, s) 0 l t (z) x s I(x,s) σ s σ a σ s + σ a = σ t z I(x, s)σ t dl 6 Plane-parallel s s 4 c 2011 Information Processing Society of Japan

5 6 35 / z s (dipole) Jensen (9) z σ tr = σ aσ t exp( σ tr (x a ))/ x a cos θdi(z, s)/dz = σ t I + (S(x) = 0) σ s p(s, s )I(z, s)ds (10) Ω θ s z (4) BSSRDF S d (10) s N S d (x i, s i; x o, s o) = (1/π)F t(x i, s i) 1 R d ( x i x o )F t (x o, s o )(16) R d = A exp( σ tr (x p + ))/ x p + N B exp( σ tr (x p )/ x p (17) I(z) = V Ĩ(z) = A j exp(λ j d(z))v j (11) F t Fresnel j=0 1 V i,λ i R d A j p +, p z = 0 A, B N I(0) = A j v j (12) j=0 A i (multipole) BRDF BRDF Plane-parallel BRDF BTDF(Bi-directional Transmittance S(x) Distribution Function) d Eon BSSRDF 34 BSSRDF BSSRDF (7) 341 I 0 BRDF I d I d I d (x, s) (1/4π)(φ(x) + 3(s E(x)), φ(x) I d (x, s) s E(x) 4 (9) (κ(x) φ(x)) = σ a φ + S(x) (13) κ(x) = 1/(3(σ a + σ s)) (14) σ s = (1 g)σ s (15) g S(x) E E(x) = φ(x) 41 self-shadow opacity map 22), deep opacity map 23) 5 c 2011 Information Processing Society of Japan

5 まとめ質感表現の CG 技法を散乱物質の表現を中心に紹介した技術的に残されている課題としては不均質な散乱物体の高速表示技術があげられるまた人間の視覚系は散乱物体の表示の精度には寛大であり視覚特性に基づいた散乱レンダリング手法も重要な課題である a directional source 参考 an extent source 文献 1) K Torrance, E

273282, 1990 3) R Cook, K Torrance, A reflectance model for Computer Graphics, ACM Transactions on Graphics, vol 1, No 1, pp 7-24, 1982 4) M Oren, S Nayer, Generalization of Lambert s reflectance

anisotropic reflection, SIGGRAPH 92, pp 265272, 1992 7) J Kajiya and T Kay, Rendering fur with three dimensional textures, SIGGRAPH 89, pp 271-280, 1989 8) S R Marschner, H W Jensen, M Cammarano, S

6 5 まとめ質感表現の CG 技法を散乱物質の表現を中心に紹介した技術的に残されている課題としては不均質な散乱物体の高速表示技術があげられるまた人間の視覚系は散乱物体の表示の精度には寛大であり視覚特性に基づいた散乱レンダリング手法も重要な課題である a directional source 参考 an extent source 文献 1) K Torrance, E M Sparrow, Theory for offspecular reflectance from roughened surfaces, J Opt Soc Am, vol 56, No 7, pp , ) P Poulin, A Fournier, A model for anisotropic reflection, SIGGRAPH 90, pp , ) R Cook, K Torrance, A reflectance model for Computer Graphics, ACM Transactions on Graphics, vol 1, No 1, pp 7-24, ) M Oren, S Nayer, Generalization of Lambert s reflectance model, SIGGRAPH 94, pp , ) S H Westin, J Arvo, K Torrance, Predictiong reflectance functions from complex surfaces, SIGGRAPH 92, pp , ) G J Ward, Measuring and modeling anisotropic reflection, SIGGRAPH 92, pp , ) J Kajiya and T Kay, Rendering fur with three dimensional textures, SIGGRAPH 89, pp , ) S R Marschner, H W Jensen, M Cammarano, S Worley, and P Hanrahan, Light scattering from human hair fibers, SIGGRAPH 03, pp , ) Hanrahan, P and Krueger, W, Reflection from layered surfaces due to subsurface scattering, SIGGRAPH93, pp , ) A Ishimaru, Wave propergation and scattering in random media, volume 1, Academic Press, New York, ) Tong, X and Wang, J and Lin, S and Guo, B and Shum, H-Y, Modeling and rendering of quasi-homogeneous materials, ACM Transactions on Graphics, vol 24, No3, pp , ) C Donner, J Lawrence, R Ramamoorthi, T Hachisuka, H W Jensen, S Nayar, An Empirical BSSRDF Model, SIGGRAPH 2009 (2009) 13) J Stam, An illumination model for a skin layer bounded by rough surfaces, Proceedings of the 12th Eurographics Workshop on Render- 図 7 髪の生成画像例左は平行光線右は面光源で照明した場合しかしながら金髪などの明るい髪においては多重散乱が優位になり無視することができなくなる Zinke らは dual scattering 法24) と呼ばれる髪の高速な多重散乱表現手法を提案したこの手法では局所的には髪が平行であるとして多重反射を平行面間の繰り返し反射みなす経験主義的であり理論的基盤が弱い側面があるが視覚的には良い結果を与えているまた Plane-parallel 近似を用いることで多重散乱を高速に計算することもできる Dual-scattering と比較して物理的基盤が強いので面光源など多様な光源への適用が可能である25) 生成画像例を図 7 に示す 42 樹木の質感表現図 8 桜の生成画像例樹木の葉や花は透過性がありこんもりとした質感を表現するには多重散乱を考慮することが重要である Qin らは葉の多重反射を平行面の繰り返し反射で置き換え経験的な計算手法を提案した26) また Boulanger らは２次散乱まで考慮した画像生成法を提案した27) この手法は実時間表示可能であるが前処理は重く形状や光源変化には実時間対応できない Plane-parallel 近似は対象依存性が低い物理近似モデルであり髪や表面下散乱と同様に樹木にも適用可能である前計算等も重くなく高速な表示が可能である28) 生成画像例を図 8 に示す Information Processing Society of Japan

7 ing, pp39-52, 2001 Computing CAD 14) W Wang, J Dorsey, X Yang, B Guo, and H- 2009, (2009) Y Shum, Real-time rendering of plant leaves, ACM Transactions on Graphics vol 24, No 3, pp , ), vol 38, No4, pp , ) Jensen, H W and Marschner, S R and Levoy, M and Hanrahan, P, A practical model for subsurface light transport, SIGGRAPH 2001,pp , ) Donner, C and Jensen, H W, Light diffusion in multi-layered translucent materials, ACM Transactions on Graphics, vol 24, No 3, pp , ) E d Eon, G Irving, A quantized-diffusion model for rendering translucent materials, ACM Transactions on Graphics, vol 30, No 4, 56, ) T Mertens, J Kautz, J and Bekaert, H Seidelz, F Van Reeth, Interactive rendering of translucent deformable objects, EGSR 2003, pp , ) K Xu, Y Gao, Y Li, T Ju, S Hu, Realtime homogeneous translucent material editing, Computer Graphics Forum, vol 26, No 3, pp , ) E d Eon, D Luebke, E Enderton, Efficient rendering of human skin, EGSR 2007, ) T Kim, U Neumann, Opacity shadow map, EGSR 2001, pp , ) C Yuksel,and J Keyser, Deep opacity map, Computer Graphics Forum, vol 27 No2, pp , ) A Zinke, C Yuksel, A Weber, and J Keyser, Dual scattering approximation for fast multiple scattering in hair, ACM Transactions on Graphics vol 26, No 3, pp 1-10 (2008) 25) M Shinya, M Shiraishi, Y Dobashi, K Iwasaki, T Nishita, A simplified plane-parallel scattering model and its application to hair rendering, Pacific Graphics 2010, pp85-92, ) X Qin, E Nakamae, K Tadamura, Y Nagai, Fast photo-realistic rendering of trees in daylight, Computer Graphics Forum, vol 22, No 3, pp , ) K Boulanger, K Bouatouch, S Pattanaik, Rendering trees with indirect lighting in real time, Computer Graphics Forum, vol 27, No4, pp , ),, Visual 7 c 2011 Information Processing Society of Japan

Ω + θr θi H α N β = + φ φ r x φ i 2 diffuse component specular component (a) 1 (b) BRDF (R) (G) (B) BRDF f BRDF (x, θ i, φ i, θ r, φ r ). (1) 1(b) N φ

Ω + θr θi H α N β = + φ φ r x φ i 2 diffuse component specular component (a) 1 (b) BRDF (R) (G) (B) BRDF f BRDF (x, θ i, φ i, θ r, φ r ). (1) 1(b) N φ 1 Measurement and Modeling of Reflection and Scattering Yasuhiro Mukaigawa 1 When an object is illuminated, part of the light reflects on the surface and some scatter underneath the surface. The appearance