Real-time rendering of Energy-Wave using general explicit function curves

Abstract

Cartoons, animations, and video games contain representations known as energy waves. Energy waves represent a moving mass of energy accompanied by strong luminescence. The authors have defined analytically integrable energy distributions for primitive shapes and have used numerical integration for energy distributions representing quadratic curves and circular shapes. In this study, we propose a method to represent distributional states such as trigonometric curves and parametric curves as a single function that can be quickly rendered by taking two correspondences between the mediating variable in line integrals and the mediating variable in explicit curves. We constructed an integral function for spiral curves and B-spline curves and integrated it using the composite Simpson method to maintain real-time rendering speed.