Approximation of Glossy Reflection with Prefiltered Environment Maps

Abstract
a method is presented that can render glossy reflections with arbitrary isotropic bidirectional reflectance distribution functions (BRDFs) at interactive rates using texture mapping. this method is based on the well-known environment map technique for specular refletions.

our approach uses a single-or-multiple representation of bidirectional reflectance distribution functions, where the shape of each radially symmetric lobe 径向对称叶 is also a function of view elevation. this approximate representation can be computed efficiently using local greedy fitting techniques. each lobe is used to filter specular environment maps during a preprocessing step, resulting in a three-dimensional environment map. for many BRDFs, simplifications using lower-dimensional approximations, 关于视图高度的粗略采样 coarse sampling with respect to view elevation, and small numbers of lobes can still result in a convincing approximation to the true surface reflectance.

Key words: Environment map, glossy reflection, texture mapping, bidirectional reflectance distribution function.

1 introduction
the environment map technique [2] is widely used to approximate reflections in real-time rendering. environment maps are an approximation technique because they make an assumption that is often not true. namely that the environment is far from the reflectance surface. despite this, they are effective and efficient, and can be used to build more sophisticated techniques.

Heidrich and Seidel [12] preblurred environment maps with the Phong model [18] to approximate glossy reflectance in real time. however, the technique was limited to Phong lobes. 然而，这项技术是有限的冯氏叶。variation of lobe shape with incident angle was not supported, although self-shadowing and Fresnel scale factors that varied with the incident and view direction have been demonstrated.

we have extended and refined this idea to support the generation of glossy reflections with a relatively general class of isotropic bidirectional reflectance distribution functions (BRDFs).——s是函数的functions的复数的简写。 for a number of elevation angles we approximate the given BRDF with a sum of radially symmetic lobes. 通过辐射对称性叶进行求和模拟BRDF. in our representation each lobe must be symmetric around some axis, but need not be a Phong lobe: the radial shape function is arbitrary, and is derived from the data. furthermore, the axis of each lobe 波瓣 may be offset from the reflection direction.

for “glossy” BRDFs with large peaks, lobe-fitting can be performed using a greedy technique that is more efficient than the global optimization techniques previously used for multilobe BRDF representations[15]. while not optimal 尽管不是最佳的, the greedy fitting technique is easy to implement and produces usable results quickly.