PDE-based models for advanced rendering in computer graphics

To accurately model global illumination, light transport, shadow formation and surface interaction in a complex geometry, mathematically accurate physical models are required for advanced rendering in computer graphics.In this paper, a partial differential equation based rendering framework is proposed which incorporates the radiative transfer, diffusion and geometric evolution models.The framework is solved by the Finite Element Method with an implicit Crank-Nicolson time integration to maintain the numerical stability and convergence.Peak Signal to Noise Ratio, Structural Similarity Index, Mean Squared Error, rendering time and convergence stability are used to evaluate the performance.The result showed that the proposed model can obtain PSNR of 39.8 dB, SSIM of 0.962, MSE of 0.0038, 16.9% reduction in rendering time and 98.4% numerical convergence, which indicates that the proposed model has high visual quality, fast running speed, and physically correct rendering.