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LiDAR-based SLAM is a core technology for autonomous vehicles and robots. One key contribution of this work to 3D LiDAR SLAM and localization is a fierce defense of view-based maps (pose graphs with time-stamped sensor readings) as the…
In this paper, we present a simple yet effective formulation called Coverage Axis for 3D shape skeletonization. Inspired by the set cover problem, our key idea is to cover all the surface points using as few inside medial balls as possible.…
In this paper, we discuss the mechanics and planning algorithms to slide an object on a horizontal planar surface via frictional patch contact made with its top surface. Here, we propose an asymmetric dual limit surface model to determine…
The most important aim in tool path generation methods is to increase the machining efficiency by minimizing the total length of tool paths while the error is kept under a prescribed tolerance. This can be achieved by determining the moving…
This paper studies 3D LiDAR mapping with a focus on developing an updatable and localizable map representation that enables continuity, compactness and consistency in 3D maps. Traditional LiDAR Simultaneous Localization and Mapping (SLAM)…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
We introduce a family of boundary conditions and point constraints for conformal immersions that increase the controllability of surfaces defined as minimizers of conformal variational problems. Our free boundary conditions fix the metric…
The rapid development of autonomous driving and mobile mapping calls for off-the-shelf LiDAR SLAM solutions that are adaptive to LiDARs of different specifications on various complex scenarios. To this end, we propose MULLS, an efficient,…
This paper provides a novel approach to stitching surface images of rotationally symmetric parts. It presents a process pipeline that uses a feature-based stitching approach to create a distortion-free and true-to-life image from a video…
We present methods for analyzing and designing cylindrical electromagnetic metasurfaces with non-circular cross sections based on conformal transformations. It can be difficult to treat surfaces with non-canonical geometries since they…
Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation.…
Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
We propose a novel optimization framework for computing the medial axis transform that simultaneously preserves the medial structure and ensures high medial mesh quality. The medial structure, consisting of interconnected sheets, seams, and…
We propose a novel 3D shape correspondence method based on the iterative alignment of so-called smooth shells. Smooth shells define a series of coarse-to-fine shape approximations designed to work well with multiscale algorithms. The main…
Adaptable, low-cost, coils designed by carefully selecting the arrangements and geometries of simple primitive units are used to generate magnetic fields for diverse applications. These extend from magnetic resonance and fundamental physics…
The main contribution of this paper is a new submap joining based approach for solving large-scale Simultaneous Localization and Mapping (SLAM) problems. Each local submap is independently built using the local information through solving a…