Controllable local monotonic cubic interpolation in fluid animations

While linear interpolation has been used frequently in computer graphics, higher-order interpolation is often desirable in applications requiring higher-order accuracy. In this paper, we study how interpolation filters, employed to resample such data as velocity, density, and temperature in simulating the equations of fluid dynamics, affect the animation of fluids. For this purpose, we have designed a controllable local cubic interpolation scheme that offers G1 (or C1) continuity globally. It is based on monotonic splines so does not suffer from undue overshooting. Furthermore, it is possible to control the general behavior of the interpolation through a global tension parameter, providing a continuous spectrum of linear to cubic interpolation. We analyze how this controllable interpolation filter may be effectively used to enhance the visual reality for physically based fluid animation.