Related papers: Smooth surface interpolation using patches with ra…
Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
Recovering high-quality surfaces from irregular point cloud is ill-posed unless strong geometric priors are available. We introduce an implicit self-prior approach that distills a shape-specific prior directly from the input point cloud…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
Problems involving approximation from scattered data where data is arranged quasi-uniformly have been treated by RBF methods for decades. Treating data with spatially varying density has not been investigated with the same intensity, and is…
We give a new method for calculating the cohomology of the normal bundles over rational varieties which are smooth projections of Veronese embeddings. The method can be used also when the projections are not smooth, in this case it provides…
This paper presents the symmetric wave interpolation method for stable global interpolation using readily available equidistant points. Its key achievement is the integration of the practical utility of such points with the numerical…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
We study the Bergman space interpolation problem of open Riemann surfaces obtained from a compact Riemann surface by removing a finite number of points. We equip such a surface with what we call an asymptotically flat conformal metric,…
We produce implicit equations for general biquadratic (order 2x2) B\'ezier triangle and quadrilateral surface patches and provide function evaluation code, using modern computing resources to exploit old algebraic construction techniques.
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface…
We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.
This paper presents some applications of using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain…
We present a semi-Lagrangian method for the numerical resolution of Vlasov-type equations on multi-patch meshes. Following N. Crouseilles et al. [A parallel Vlasov solver based on local cubic spline interpolation on patches. Journal of…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem. The problem is technically ill-posed, and becomes more difficult considering that various sensing…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method…