Line sampling in participating media

Participating media, such as fog, fire, dust, and smoke, surrounds us in our daily life. Rendering participating media efficiently has always been a challenging task in physically based rendering. Line sampling has been derived to be an alternative method in direct lighting recently. Since line sampling takes visibility into account, it could reduce variance in the same render time compared to point sampling. We leverage the benefits of line sampling in the context of evaluating direct lighting in participating media. We express the direct lighting as a three-dimensional integral and perform line sampling in any one of them. We show how to apply multiple importance sampling (MIS) with common point samples, improving the robustness of estimators. We also show the drawbacks of MIS between different directions of lines. We demonstrate the efficiency of line sampling in participating media and discuss the results with different setups, such as different phase functions and occluder size

Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type

99學年度楊定揮教師升等代表著作 100學年度研究獎補助論文[[abstract]]In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c *, and show the existence of traveling plane wave solutions connecting two different equilibria when the wave speeds are large than c *.[[incitationindex]]SCI[[booktype]]紙