Related papers: An algorithm that constructs irreducible triangula…
A surface automorphism is strongly irreducible if every essential simple closed curve in the surface has nontrivial geometric intersection with its image. We show that a three-manifold admits only finitely many inequivalent surface bundle…
An ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that each pair of points in a surface has a finite number of…
We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…
We explore the existence of irreducible and reducible arc-sections in an irreducible hypersurface singularity germ along finite projections. In particular we provide examples of irreducible isolated hypersurface singularities for which no…
A census is presented of all closed non-orientable 3-manifold triangulations formed from at most seven tetrahedra satisfying the additional constraints of minimality and P^2-irreducibility. The eight different 3-manifolds represented by…
We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can…
A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal, incompressible annuli are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible,…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
The ideal (tagged resp.) triangulation of bounded surface with marked points are associated with skew-symmetric (skew-symmetrizable) exchange matrices. An algo- rithm is established to decompose the graph associated to such matrix. There…
In the given paper the algorithm describing original and universal principles of a triangulation of a smooth molecular surface: solvent excluding solvent (SES), received by primary and secondary rolling, and solvent accessible surface (SAS)…
A {\em $1-$vertex triangulation} of an oriented compact surface $S$ of genus $g$ is an embedded graph $T\subset S$ with a unique vertex such that all connected components of $S\setminus T$ are triangles (adjacent to exactly 3 edges of $T$).…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
We propose a new geometric method of IR factorization in sector decomposition. The problem is converted into a set of problems in convex geometry. The latter problems are solved using algorithms in combinatorial geometry. This method…
Inspired by the seminal result that a graph and an associated rotation system uniquely determine the topology of a closed manifold, we propose a combinatorial method for reconstruction of surfaces from points. Our method constructs a…
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…
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded by…
There are many fundamental algorithmic problems on triangulated 3-manifolds whose complexities are unknown. Here we study the problem of finding a taut angle structure on a 3-manifold triangulation, whose existence has implications for both…
Tight triangulations are exotic, but highly regular objects in combinatorial topology. A triangulation is tight if all its piecewise linear embeddings into a Euclidean space are as convex as allowed by the topology of the underlying…