Essay Sample on Modeling Light Interaction to Improve Quality of Appearance Modeling

Introduction

Modeling the appearance of materials is an essential task in the computer graphics for reproducing the appearance of real-world materials under varied lighting and viewing conditions. Since the past decade, the field has experienced rapid advances in learning techniques owing to the development of technology. As such, several learning-based approaches have been proposed for improving the quality of appearance modeling and efficiency. Precisely, the appearance means how the light interacts with the surface, geometry shape, and lighting conditions to determine the final geometry. The major challenge of appearance modeling is the high dimensionality of data, which in raw form occurs as an 8D light field, 6D Reflectance function, 4D light transport, and so on. This paper describes how Cook-Torrance aids in modeling the reflectance properties of different materials.

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The Cook-Torrance shading model is based on the microfacet theory that describes a surface as a collection of tiny mirrors oriented at random angles concerning the normal surface over a wide area. Therefore, light traveling along a path wi towards point x on the surface is likely to undergo any of the three possible events: Shadowing- this occurs when a micro-facet blocks light before it reaches the point x. The other possible event is Masking-this occurs when a micro-facet blocks light after being reflected from point x. The last possible event is when the light enters the environment after reflecting off the Fresnel mirror at x.

This model shows that the spectral distribution of light reflected into wo is proportional to the number of microfacets with an orientation which is parallel to wo+wi, the number of microfacets that were neither masked nor shadowed, and the reflectance of each appropriately oriented microfacet. The final Cook-Torrance BRDF is

frwi,wo=dkdp+sFpDG(n.wi)(n.wo)

Where d and s are scalar quantity parameters that control the amount of specular reflectance, kd is the surface albedo, F is the Fresnel tern describing light from each smooth micro-facet, D controls the micro-facet surface distribution and G is the geometry term accounting for masking or shading effect.

Therefore, the rougher a surface is, the more unsystematically aligned each microfacet will be along the surface. The incoming light rays are, therefore, likely to scatter along completely different directions on a rougher surface compared to a smooth surface. On the centrally, a smooth surface is likely to reflect rays smoothly in the same direction and give sharper reflections. However, no surface can be said to be smooth on a microscopic level. Still, the microfacets are small enough and thus not easily distinct between per-pixel bases, and thus the roughness is estimated as per the roughness parameter. The Fresnel term F describes the dependency of surface reflectance on an angle of incidence illumination. This reflectance is based on the Fresnel equation from classical optics, which relates surface reflectance to a material's index of refraction, extinction coefficient, and the angle of incoming light. Cook-Torrance proposes a simplification that depends only on the material's reflectance at a normal incident assuming that k=0. The simplified Fresnel equation is shown below:

F=12(g-c)2(g=c)2{1+cg+c-12cg-c+12}Where c=w0. h and g2=n2+c2-1 which can be used to induce reflectance at the normal incident of F0

Some surfaces have many scales of roughness, for example, a metallic sphere covered with a shiny glaze. In such a case, light is reflected from both the shiny glaze and the underlying metallic paint. The material thus appears as having two specular highlights of different widths. These surfaces are very appropriate in phenomena with a weighted combination of multiple distributions. This phenomenon is given by:

D=j=1NwjD(mJ)Where wj are the weights for each distribution, ( j=1Nwj=1 ) and D (mj) are the microfacet distribution functions, each with RMS slope of mj.

Conclusion

In conclusion, the Cook-Torrance model is based on the physics of light-matter interaction and, thus, can represent a broader class of materials than the other models like Phong and Lambertian. This model has been successfully incorporated in interactive rendering algorithms. The fact that the F0 for most materials has been measured, this model provides a useful approach to modeling the reflectance of many real-world materials.

References

Bagher, M.M., Soler, C., and Holzschuch, N., 2012, June. Accurate fitting of measured reflectances using a shifted gamma microfacet distribution. In Computer Graphics Forum (Vol. 31, No. 4, pp. 1509-1518). Oxford, UK: Blackwell Publishing Ltd.

Malti, A., and Bartoli, A., 2014. Combining Conformal Deformation and Cook-Torrance Shading for 3-D Reconstruction in Laparoscopy. IEEE Transactions on Biomedical Engineering, 61(6), pp.1684-1692.