相关论文: Symmetries of discrete curves and point clouds via…
We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…
The aim of this paper is to find an optimal matching between manifold-valued curves, and thereby adequately compare their shapes, seen as equivalent classes with respect to the action of reparameterization. Using a canonical decomposition…
In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in $\mathbb{R}^{2}$. The main idea is to smooth the parametrization of the curve by…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a…
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
Establishing a consistent normal orientation for point clouds is a notoriously difficult problem in geometry processing, requiring attention to both local and global shape characteristics. The normal direction of a point is a function of…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
This paper describes a new algorithm for determining all discrete contact symmetries of any differential equation whose Lie contact symmetries are known. The method is constructive and is easy to use. It is based upon the observation that…
Discrete point cloud objects lack sufficient shape descriptors of 3D geometries. In this paper, we present a novel method for aggregating hypothetical curves in point clouds. Sequences of connected points (curves) are initially grouped by…
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…
Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex…
Let $\mathcal C$ be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfaces $P(x,y,z)=Q(x,y,z)=0$…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
We introduce a novel formulation for geometry on discrete points. It is based on a universal differential calculus, which gives a geometric description of a discrete set by the algebra of functions. We expand this mathematical framework so…
Point cloud is an important type of 3D representation. However, directly applying convolutions on point clouds is challenging due to the sparse, irregular and unordered data structure. In this paper, we propose a novel Interpolated…
Orienting surface normals correctly and consistently is a fundamental problem in geometry processing. Applications such as visualization, feature detection, and geometry reconstruction often rely on the availability of correctly oriented…
The methods of approximation, regularization and smoothing of trigonometric interpolation splines are considered in the paper. It is shown that trigonometric splines can be considered from two points of view - as a trigonometric Fourier…
A new effective solution to the problem of Hermite $G^1$ interpolation with a clothoid curve is here proposed, that is a clothoid that interpolates two given points in a plane with assigned unit tangent vectors. The interpolation problem is…