基于随机表面微面元理论的二向反射分布函数几何衰减因子修正

现有几何光学方法的二向反射分布函数BRDF (bidirectional reflection distribution function)模型在计算阴影遮蔽效应时普遍应用Blinn几何衰减效应假设, 其等倾角V形槽近似得出的分段折线形式的几何衰减因子导致BRDF曲线存在较大的误差. 基于倾斜角随机高斯分布的微面元理论提出了一种新的几何衰减模型, 得出了积分形式的几何衰减因子表达式, 数值模拟比较了Blinn几何衰减因子与修正后的积分型衰减因子以及对应的BRDF模型曲线. 结果表明: 提出的几何衰减因子在物理合理性以及模拟精度方面都有明显提升, 使BRDF模型曲线与已有BRDF 数据之间的标准误差由0.0636减小到0.0084.

Modification of geometrical attenuation factor of bidirectional reflection distribution function based on random surface microfacet theory

The reflection attenuation factor given by Blinn has been widely used as an important factor in the bidirectional reflectance distribution function (BRDF) model based on geometrical optics theory for nearly half a century. However, Blinn's attenuation factor is based on microfacet theory and geometry of equicrural V-grooves caused sharp turning points and obvious error in its function curves. In this paper, a modified geometry attenuation factor based on random surface microfacet theory is presented. We assume that the surface is composed of a large number of microfacets, and the slope of each microfacet is independent of each other and follows Gaussian distribution. The attenuation effect is caused by the masking and shadowing factors in adjacent microfacets. Depending on the slope angles of microfacets, reflection falls in three submodels, i.e., passing model, semi-passing model, and masking/shadowing model when discussing masking/shadowing factor. The modified attenuation factor is given in an integral expression. The modified geometry attenuation factor is simulated and compared with Blinn's geometry attenuation factor. The sharp turning point in Blinn's attenuation factor curve is eliminated and the error of the BRDF curve is reduced. The result shows that the modified geometry attenuation factor reaches better physical rationality and significantly improves the accuracy of BRDF model. Compared with Blinn's geometry attenuation factor, the modification reduces the standard error between BRDF model and existing data from 0.0636 to 0.0084. The cause of the error in Blinn's geometry attenuation factor is analyzed, the equicrural V-grooves assumption of Blinn's geometry attenuation model considers too much reflection attenuation in the condition of small incident angle and large reflect angle. The modification in this paper is based on random surface microfacet theory, in which the angular dependence of adjacent microfacet is eliminated, for this reason the accuracies of geometry attenuation model and BRDF model are improved.