Related papers: Local Surface Parameterizations via Smoothed Geode…
The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline…
We derive the implicit equations for certain parametric surfaces in three-dimensional projective space termed tensor product surfaces. Our method computes the implicit equation for such a surface based on the knowledge of the syzygies of…
Neural signed distance functions (SDFs) have shown powerful ability in fitting the shape geometry. However, inferring continuous signed distance fields from discrete unoriented point clouds still remains a challenge. The neural network…
Neural implicit functions have emerged as a powerful representation for surfaces in 3D. Such a function can encode a high quality surface with intricate details into the parameters of a deep neural network. However, optimizing for the…
Surface parameterization is widely used in computer graphics and geometry processing. It simplifies challenging tasks such as surface registrations, morphing, remeshing and texture mapping. In this paper, we present an efficient algorithm…
We propose a novel method for reconstructing explicit parameterized surfaces from Signed Distance Fields (SDFs), a widely used implicit neural representation (INR) for 3D surfaces. While traditional reconstruction methods like Marching…
This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…
Surface reconstruction is a fundamental problem in 3D graphics. In this paper, we propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in…
We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear…
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…
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 present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization…
We introduce a new implicit shape representation called Primary Ray-based Implicit Function (PRIF). In contrast to most existing approaches based on the signed distance function (SDF) which handles spatial locations, our representation…
Spatial data collected worldwide at a huge number of locations are frequently used in environmental and climate studies. Spatial modelling for this type of data presents both methodological and computational challenges. In this work we…
A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a spline-based representation of a…
Most genuine multi-sided surface representations depend on a 2D domain that enables a mapping between local parameters and global coordinates. The shape of this domain ranges from regular polygons to curved configurations, but the simple…
Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these…
Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…