Related papers: Algorithms for geometrical operations with NURBS s…
This paper proposes fast and novel methods to jointly estimate the target's unknown 3D shape and dynamics. Measurements are noisy and sparsely distributed 3D points from a light detection and ranging (LiDAR) sensor. The methods utilize…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity given new mesh surfaces. Using surfaces that represent geological boundaries, the objectives are to identify areas…
The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We…
The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…
We present an algorithm of clustering of many-dimensional objects, where only the distances between objects are used. Centers of classes are found with the aid of neuron-like procedure with lateral inhibition. The result of clustering does…
A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
We propose a neural network-based approach for collision detection with deformable objects. Unlike previous approaches based on bounding volume hierarchies, our neural approach does not require an update of the spatial data structure when…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
Genetic algorithms are modeled after the biological evolutionary processes that use natural selection to select the best species to survive. They are heuristics based and low cost to compute. Genetic algorithms use selection, crossover, and…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
The immersed isogeometric Boundary Element Method is presented and applied to the simulation of underground excavations. Nonuniform rational B-splines (NURBS) are used for the accurate definition of complex geometries with few parameters.…
In this work we address the complexity problem of the isogeometric Boundary Element Method by proposing a collocation scheme for practical problems in linear elasticity and the application of hierarchical matrices. For mixed boundary value…
In this paper, we present an easy to use sketch-based interface to extract geometries and generate affordance files from 3D point clouds for robot-object interaction tasks. Using our system, even novice users can perform robot task planning…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Boundary representations (B-reps) using Non-Uniform Rational B-splines (NURBS) are the de facto standard used in CAD, but their utility in deep learning-based approaches is not well researched. We propose a differentiable NURBS module to…
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…