Related papers: Simple Methods to Represent Shapes with Sample Sph…
The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C^k, where k is an arbitrary integer.
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
We introduce a recursive procedure for computing the number of realizations of a minimally rigid graph on the sphere up to rotations. We accomplish this by combining two ingredients. The first is a framework that allows us to think of such…
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
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…
We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
We introduce a simple representation for isotropic spherical random fields and we discuss how it allows to discuss different notions of sparsity under isotropy. We also show how a suitable construction of sparse fields can mimic well the…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
Traditional explicit 3D representations, such as point clouds and meshes, demand significant storage to capture fine geometric details and require complex indexing systems for surface lookups, making functional representations an efficient,…
The paper describes a novel real-time algorithm for finding 3D geometric primitives (cylinders, cones and spheres) from 3D range data. In its core, it performs a fast model fitting with a model update in constant time (O(1)) for each new…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
A pair of rooted tangents -- defining a quantum triangle -- with an associated quantum wave of spin 1/2 is proposed as the primitive to represent and compute symmetry. Measures of the spin characterize how "isosceles" or how "degenerate"…
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by…
We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…
A fundamental challenge in text-to-3D face generation is achieving high-quality geometry. The core difficulty lies in the arbitrary and intricate distribution of vertices in 3D space, making it challenging for existing models to establish…