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 is conservative (points outside the zero isosurface are guaranteed to be outside the surface), accurate and efficient to evaluate for all the above data types. This, in combination with its ability to smooth sparsely sampled data, like point clouds, enhances typical graphics tasks such as sphere tracing and enables new applications such as direct, co-dimensional rigid body simulation using unprocessed lidar data.