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.
@article{Madan:2022:smoothdists,
author = {Madan, Abhishek and Levin, David I.W.},
title = {Fast Evaluation of Smooth Distance Constraints on Co-Dimensional Geometry},
journal = {ACM Trans. Graph.},
volume = {41},
number = {4},
year = {2022},
publisher = {ACM}
}
This research has been funded by in part by NSERC Discovery (RGPIN-2017–05524), Connaught Fund (503114), Ontario Early Researchers Award (ER19–15–034), Gifts from Adobe Research and Autodesk, and the Canada Research Chairs Program.
The authors would like to thank Hsueh-Ti Derek Liu, Silvia Sellán, Ty Trusty, Yixin Chen, and Honglin Chen for proofreading, and Silvia Sellán and Ty Trusty for help in figure rendering. The motorcycle, deer, and octopus models are from the Thingi10K dataset; the bunny is from the Stanford 3D Scanning Repository; the city lidar point cloud is from the Toronto-3D dataset; and the terrain point cloud is from OpenTopography.