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Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models from hundreds of thousands of (noisy) two-dimensional…
The computation of the elastic shape registration of two simple surfaces in 3-dimensional space and therefore of the elastic shape distance between them has been investigated by Kurtek, Jermyn, et al. who have proposed algorithms to carry…
Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two…
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…
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…
Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…
Under conditions that prevent tangential intersection, we prove quadratic convergence of a projection algorithm for the feasibility problem of finding a point in the intersection of a smooth curve and line in $\mathbb{R}^2$. This nonconvex…
In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…
Understanding grain-surface processes is crucial to interpreting the chemistry of the ISM. However, accurate surface chemistry models are computationally expensive and are difficult to integrate with gas-phase simulations. A new…
Variational quantum algorithms provide a direct, physics-based approach to protein structure prediction, but their accuracy is limited by the coarse resolution of the energy landscapes generated on current noisy devices. We propose a hybrid…
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have non-trivial genus and…
The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
We introduce a new algorithm for computing the periods of a smooth complex projective hypersurface. The algorithm intertwine with a new method for computing an explicit basis of the singular homology of the hypersurface. It is based on…
This paper presents the methods that have participated in the SHREC 2021 contest on retrieval and classification of protein surfaces on the basis of their geometry and physicochemical properties. The goal of the contest is to assess the…
In this article, we study subloci of solvable curves in $\mathcal{M}_g$ which are contained in either a K3-surface or a quadric or a cubic surface. We give a bound on the dimension of such subloci. In the case of complete intersection genus…
Reconstructing surfaces from normals is a key component of photometric stereo. This work introduces an adaptive surface triangulation in the image domain and afterwards performs the normal integration on a triangle mesh. Our key insight is…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
Computing the envelope of deforming planar domains is a significant and challenging problem with a wide range of potential applications. We approximate the envelope using circular arc splines, curves that balance geometric flexibility and…