针对薄层介质的多极漫射模型扩展

摘要

The Multipole diffusion model is a simple model that well describes light scattering in translucent materials. However,it is not well suited for very thin medium, particularly those close to or thinner than one Mean Free Path ( MFP) . This paper tries to extend the Multipole diffusion model for very thin medium with reasonable accuracy. It reviews the Multipole diffusion model and its assumptions,and to relax one of the assumptions by separating the direct transmitting component and the diffuse component of light. It adjusts the way the Multipole model places its point light sources to better match characteristics of light transport in thin medium. The diffuse part of the light is calculated using the modified source placement, and the direct transmitting part is approximated using a Dirac delta distribution. To evaluate the accuracy of the extended model,it is compared with the classical Multipole and Monte-Carlo simulations. The resulting profiles is predicted by the three models,as well as actual renderings. It is shown that the classical Multipole model is unable to compute profiles correctly for materials close to or less than one MFP thick. The extended model matches Monte-Carlo results better than the classical Multipole model. The extension of the current Multipole diffusion model proposed is suitable for medium close to or thinner than one MFP, and matches the Monte-Carlo method with reasonable accuracy. It can be easily integrated with existing Multipole implementations.%多极( Multipole)漫射模型能较准确地模拟半透明介质的次表面散射现象，但并不适用于厚度接近或小于一个平均自由程( MFP)的薄层介质。为此，在Multipole漫射模型的基础上扩展该模型使之适用于薄层介质。根据Multipole漫射模型所依赖的假设条件，针对薄层介质加以修改，将光线分解为直接透射和漫射部分，并调整Multipole放置点光源的方式，使之更符合薄层介质中光传输的特征。使用修改后的光源计算漫射部分，而直接透射部分则采用狄拉克δ分布来近似。对扩展方法和传统Multipole以及蒙特卡罗方法进行分布数值和实际渲染效果的对比，在处理厚度接近或小于一个MFP的薄层介质时，扩展方法的结果均较传统Multipole更吻合蒙特卡罗方法的结果，可直接和现有Multipole模型实现集成。