Fast Evaluation of Smooth Distance Constraints on Co-Dimensional Geometry

TL;DR

This paper introduces a fast, smooth distance evaluation method for various geometric data types, enabling real-time applications like lidar-based rigid body simulation by approximating true distances efficiently and reliably.

Contribution

It develops a novel approach combining LogSumExp, blending weights, and Barnes-Hut acceleration for accurate, conservative distance approximation across multiple geometric representations.

Findings

Method is efficient and accurate for point clouds, meshes, and their combinations.

Ensures conservative distance estimates outside the zero isosurface.

Facilitates direct simulation from unprocessed lidar data.

Abstract

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.