Related papers: Robust Numerical Integration on Curved Polyhedra B…

The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…

We present an algorithm which computes a cylindrical algebraic decomposition of a semialgebraic set using projection sets computed for each cell separately. Such local projection sets can be significantly smaller than the global projection…

The need for efficient normal integration methods is driven by several computer vision tasks such as shape-from-shading, photometric stereo, deflectometry, etc. In the first part of this survey, we select the most important properties that…

A method is presented for constructing closed surfaces out of Euclidean polygons with infinitely many segment identifications along the boundary. The metric on the quotient is identified. A sufficient condition is presented which guarantees…

Solving geometric tasks involving point clouds by using machine learning is a challenging problem. Standard feed-forward neural networks combine linear or, if the bias parameter is included, affine layers and activation functions. Their…

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…

In numerical integration, cubature methods are effective, especially when the integrands can be well-approximated by known test functions, such as polynomials. However, the construction of cubature formulas has not generally been known, and…

Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in…

The folding of paper, hide, and woven fabric has been used for millennia to achieve enhanced articulation, curvature, and visual appeal for intrinsically flat, two-dimensional materials. For graphene, an ideal two-dimensional material,…

This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…

Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions. The different graph models used within the irregular…

We analyze the problem of folding one polyhedron, viewed as a metric graph of its edges, into the shape of another, similar to 1D origami. We find such foldings between all pairs of Platonic solids and prove corresponding lower bounds,…

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…

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…

Previous multi-view normal integration methods typically sample a single ray per pixel, without considering the spatial area covered by each pixel, which varies with camera intrinsics and the camera-to-object distance. Consequently, when…

From a scalar field defined at the corner of a cube, an isosurface can be extracted using the Marching Cube algorithm. The isosurface separates the cell into two or more partial cells. A similar situation arises when an material interface…

Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in $d$-space into constant-complexity subcells. In this paper, we settle in the affirmative a few long-standing open…

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…

In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…