Accurate Rendering of Liquid-Crystals and Inhomogeneous Optically Anisotropic Media

We present a novel method for devising a closed-form analytic expression to the light transport through the bulk of inhomogeneous optically anisotropic media. Those optically anisotropic materials, e.g., liquid-crystals and elastic fluids, arise in a plethora of established applications and exciting new research; however, current state-of-the-art methods of visually deducing their optical properties or rendering their appearance are either lacking or non-existent. We formulate our light transport problemunder the context of electromagnetism and derive, from first principles, a differential equation of the transmitted complex wave fields that fully account for the complicated interference phenomena that arise. At the core of our proposed rendering framework is a powerful mathematical representation, carefully crafted to enable us to produce highly accurate analytic approximative solutions for the light transport. This approach is previously unused in computer rendering, and our framework is capable of accurately rendering optically anisotropic materials with spatially varying optical properties at orders-of-magnitude better performance compared to existing methods. We demonstrate a few practical applications of our method, and we validate it against polarized photos of liquid-crystals as well as numerically against numerical solvers and qualitatively against brute-force renderings.