Fast Evaluation of Smooth Distance Constraints on Co-Dimensional Geometry

We present a new method for computing a smooth minimum distance function based on the LogSumExp function for point clouds, edge meshes, triangle meshes, and combinations of all three. We derive blending weights and a modified Barnes-Hut acceleration approach that ensure our method approximates the true distance, and is conservative (points outside the zero isosurface are guaranteed to be outside the surface) and efficient to evaluate for all the above data types. This, in combination with its ability to smooth sparsely sampled and noisy data, like point clouds, shortens the gap between data acquisition and simulation, and thereby enables new applications such as direct, co-dimensional rigid body simulation using unprocessed lidar data.

Automated summary

This paper presents a new method for computing a smooth minimum distance function for point clouds, edge meshes, and triangle meshes. The method introduces blending weights and an improved acceleration approach to accurately approximate the true distance and evaluate efficiently. It also has the capability to handle sparsely sampled and noisy data, bridging the gap between data acquisition and simulation and enabling new applications such as direct, co-dimensional rigid body simulation using unprocessed lidar data.