Related papers: A procedural framework and mathematical analysis f…
Collision detection is one of the most time-consuming operations during motion planning. Thus, there is an increasing interest in exploring machine learning techniques to speed up collision detection and sampling-based motion planning. A…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…
This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. This dissertation systematically trailblazes a novel volumetric modeling framework to…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
Visual recognition of material boundaries in transparent vessels is valuable for numerous applications. Such recognition is essential for estimation of fill-level, volume and phase-boundaries as well as for tracking of such chemical…
Analyzing and identifying the shortcomings of current subdivision methods for finding intersections of rays with fibers defined by the surface of a circular contour swept along a B\'ezier curve, we present a new algorithm that improves…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
Motion planning in modified environments is a challenging task, as it compounds the innate difficulty of the motion planning problem with a changing environment. This renders some algorithmic methods such as probabilistic roadmaps less…
We present a real-time algorithm that finds the Penetration Depth (PD) between general polygonal models based on iterative and local optimization techniques. Given an in-collision configuration of an object in configuration space, we find…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
This paper discusses improvements to the numerical robustness of the algorithm described in Kasper Fauerby's "Improved Collision Detection and Response." The algorithm addresses a common collision detection query: a moving sphere or…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
The present work proposes an approach for fluid-solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable…