Related papers: Manifold-based B-splines on unstructured meshes
We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially consider 1D spline spaces of arbitrary degree spanned over…
Observations made in continuous time are often irregular and contain the missing values across different channels. One approach to handle the missing data is imputing it using splines, by fitting the piecewise polynomials to the observed…
A novel approach to unstructured quadrilateral mesh generation for planar domains is presented. Away from irregular vertices, the resulting meshes have the properties of nearly conformal grids. The technique is based on a theoretical…
Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct…
In computer-aided design (CAD), the ability to "reverse engineer" the modeling steps used to create 3D shapes is a long-sought-after goal. This process can be decomposed into two sub-problems: converting an input mesh or point cloud into a…
Crowd-sourced mapping offers a scalable alternative to creating maps using traditional survey vehicles. Yet, existing methods either rely on prior high-definition (HD) maps or neglect uncertainties in the map fusion. In this work, we…
The stable and unstable manifolds of an invariant set of a piecewise-smooth map are themselves piecewise-smooth. Consequently, as parameters of a piecewise-smooth map are varied, an invariant set can develop a homoclinic connection when its…
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. In our former work, we have…
While the common environment representation in structure from motion is given by a sparse point cloud, the community has also investigated the use of lines to better enforce the inherent regularities in man-made surroundings. Following the…
Choosing the right representation for geometry is crucial for making 3D models compatible with existing applications. Focusing on piecewise-smooth man-made shapes, we propose a new representation that is usable in conventional CAD modeling…
Reliable estimation and approximation of probability density functions is fundamental for their further processing. However, their specific properties, i.e. scale invariance and relative scale, prevent the use of standard methods of spline…
We present a new method for the interpolation of given data points and associated normals with surface parametric patches with rational normal fields. We give some arguments why a dual approach is the most convenient for these surfaces,…
By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly…
We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they…
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…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
Univariate pseudo-splines are a generalization of uniform B-splines and interpolatory $2n$-point subdivision schemes. Each pseudo-spline is characterized as the subdivision scheme with least possible support among all schemes with specific…
We present a prior for manifold structured data, such as surfaces of 3D shapes, where deep neural networks are adopted to reconstruct a target shape using gradient descent starting from a random initialization. We show that surfaces…
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant…