Related papers: Generating Large Convex Polytopes Directly on Poin…

Approximating collision-free space is fundamental to robot planning in complex environments. Convex geometric representations, such as polytopes and ellipsoids, are widely employed due to their structural properties, which can be easily…

Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and rigid body dynamics simulations. We…

We describe a uniformly fast algorithm for generating points \vec{x} uniformly in a hypercube with the restriction that the difference between each pair of coordinates is bounded. We discuss the quality of the algorithm in the sense of its…

In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…

We propose a method to generate 3D shapes using point clouds. Given a point-cloud representation of a 3D shape, our method builds a kd-tree to spatially partition the points. This orders them consistently across all shapes, resulting in…

In this paper, we present a novel deep method to reconstruct a point cloud of an object from a single still image. Prior arts in the field struggle to reconstruct an accurate and scalable 3D model due to either the inefficient and expensive…

Learning to generate 3D point clouds without 3D supervision is an important but challenging problem. Current solutions leverage various differentiable renderers to project the generated 3D point clouds onto a 2D image plane, and train deep…

The visible capability is critical in many robot applications, such as inspection and surveillance, etc. Without the assurance of the visibility to targets, some tasks end up not being complete or even failing. In this paper, we propose a…

Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve…

We propose an online iterative algorithm to optimize a convex cover to under-approximate the free space for autonomous navigation to delineate Safe Flight Corridors (SFC). The convex cover consists of a set of polytopes such that the union…

In this paper, we propose an effective point cloud generation method, which can generate multi-resolution point clouds of the same shape from a latent vector. Specifically, we develop a novel progressive deconvolution network with the…

This work proposes a general-purpose, fully-convolutional network architecture for efficiently processing large-scale 3D data. One striking characteristic of our approach is its ability to process unorganized 3D representations such as…

Conventional methods of 3D object generative modeling learn volumetric predictions using deep networks with 3D convolutional operations, which are direct analogies to classical 2D ones. However, these methods are computationally wasteful in…

Fast and accurate 3D shape generation from point clouds is essential for applications in robotics, AR/VR, and digital content creation. We introduce ConTiCoM-3D, a continuous-time consistency model that synthesizes 3D shapes directly in…

While recent work on text-conditional 3D object generation has shown promising results, the state-of-the-art methods typically require multiple GPU-hours to produce a single sample. This is in stark contrast to state-of-the-art generative…

A generative model for high-fidelity point clouds is of great importance in synthesizing 3d environments for applications such as autonomous driving and robotics. Despite the recent success of deep generative models for 2d images, it is…

Many computations in robotics can be dramatically accelerated if the robot configuration space is described as a collection of simple sets. For example, recently developed motion planners rely on a convex decomposition of the free space to…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…

Mechanical metamaterials enable precise control over structural properties, but their design method remains challenging due to their complex structure. Although additive manufacturing has expanded geometric freedom, navigating this vast and…