Heat Simulation on Meshless Crafted-Made Shapes

Interactive shape crafting is an increasingly popular feature in video games, offering players a sense of freedom and personalization. In this work, we propose to combine a stochastic simulation approach to solve the heat equation on Implicit Surface, enabling crafting-ready shapes. Our simulation relies on the "Walk on Sphere"(WoS) approach allowing to solve the asymptotic solution of the heat PDE at any point in space without the need for an explicit mesh structure. To enable interactivity when the shape is moved near a heat source, we propose the integration of time-evolving modifiers. Firstly, using the separation of variables over the PDE enables the approximation of the heating evolution using an additional exponential time variation. Then, we procedurally attach local secondary heat sources to the surface for smooth cool-down. We demonstrate the effectiveness our approach on blended-material shapes generated using CSG operations, combining spatially-varying thermal diffusivity. Overall, our method offers a promising avenue for incorporating often-neglected physical interactions, such as heat-related phenomena, into video games with complex and customizable shapes.