@article{21253,
  abstract     = {We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n - 1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.},
  author       = {Pach, János and Saghafian, Morteza and Schnider, Patrick},
  issn         = {0925-7721},
  journal      = {Computational Geometry},
  publisher    = {Elsevier},
  title        = {{Decomposition of geometric graphs into star-forests}},
  doi          = {10.1016/j.comgeo.2025.102186},
  volume       = {129},
  year         = {2025},
}

@article{8317,
  abstract     = {When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special “basic” holes guarantee foldability.},
  author       = {Aichholzer, Oswin and Akitaya, Hugo A. and Cheung, Kenneth C. and Demaine, Erik D. and Demaine, Martin L. and Fekete, Sándor P. and Kleist, Linda and Kostitsyna, Irina and Löffler, Maarten and Masárová, Zuzana and Mundilova, Klara and Schmidt, Christiane},
  issn         = {1879-081X},
  journal      = {Computational Geometry: Theory and Applications},
  publisher    = {Elsevier},
  title        = {{Folding polyominoes with holes into a cube}},
  doi          = {10.1016/j.comgeo.2020.101700},
  volume       = {93},
  year         = {2021},
}

@article{793,
  abstract     = {Let P be a finite point set in the plane. A cordinary triangle in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P . Motivated by a question of Erdös, and answering a question of de Zeeuw, we prove that there exists a constant c > 0such that P contains a c-ordinary triangle, provided that P is not contained in the union of two lines. Furthermore, the number of c-ordinary triangles in P is Ω(| P |). },
  author       = {Fulek, Radoslav and Mojarrad, Hossein and Naszódi, Márton and Solymosi, József and Stich, Sebastian and Szedlák, May},
  issn         = {0925-7721},
  journal      = {Computational Geometry: Theory and Applications},
  pages        = {28 -- 31},
  publisher    = {Elsevier},
  title        = {{On the existence of ordinary triangles}},
  doi          = {10.1016/j.comgeo.2017.07.002},
  volume       = {66},
  year         = {2017},
}

@article{4001,
  abstract     = {The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes. The technical part of this paper focuses on the second task: the specification of a deformation mixing two or more shapes in continuously changing proportions. (C) 2001 Elsevier Science B.V All rights reserved.},
  author       = {Cheng, Ho and Edelsbrunner, Herbert and Fu, Ping},
  issn         = {0925-7721},
  journal      = {Computational Geometry: Theory and Applications},
  number       = {2-3},
  pages        = {191 -- 204},
  publisher    = {Elsevier},
  title        = {{Shape space from deformation}},
  doi          = {10.1016/S0925-7721(01)00021-9},
  volume       = {19},
  year         = {2001},
}

@article{4002,
  abstract     = {Shape deformation refers to the continuous change of one geometric object to another. We develop a software tool for planning, analyzing and visualizing deformations between two shapes in R-2. The deformation is generated automatically without any user intervention or specification of feature correspondences. A unique property of the tool is the explicit availability of a two-dimensional shape space, which can be used for designing the deformation either automatically by following constraints and objectives or manually by drawing deformation paths.},
  author       = {Cheng, Siu and Edelsbrunner, Herbert and Fu, Ping and Lam, Ka},
  issn         = {0925-7721},
  journal      = {Computational Geometry: Theory and Applications},
  number       = {2-3},
  pages        = {205 -- 218},
  publisher    = {Elsevier},
  title        = {{Design and analysis of planar shape deformation}},
  doi          = {10.1016/S0925-7721(01)00020-7},
  volume       = {19},
  year         = {2001},
}

@article{4018,
  abstract     = {Given a subspace X subset of or equal to R-d and a finite set S subset of or equal to R-d, we introduce the Delaunay complex, D-X, restricted by X. Its simplices are spanned by subsets T subset of or equal to S for which the common intersection of Voronoi cells meets X in a non-empty set. By the nerve theorem, boolean OR D-X and X are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for boolean OR D-X and X be homeomorphic.},
  author       = {Edelsbrunner, Herbert and Shah, Nimish},
  issn         = {0925-7721},
  journal      = {International Journal of Computational Geometry & Applications},
  number       = {4},
  pages        = {365 -- 378},
  publisher    = {World Scientific Publishing},
  title        = {{Triangulating topological spaces}},
  doi          = {10.1142/S0218195997000223},
  volume       = {7},
  year         = {1997},
}

@article{4021,
  abstract     = {A homeomorphism from R-2 to itself distorts metric quantities, such as distance and area. We describe an algorithm that constructs homeomorphisms with prescribed area distortion. Such homeomorphisms can be used to generate cartograms, which are geographic maps purposely distorted so their area distributions reflects a variable different from area, as for example population density. The algorithm generates the homeomorphism through a sequence of local piecewise linear homeomorphic changes. Sample results produced by the preliminary implementation of the method are included.},
  author       = {Edelsbrunner, Herbert and Waupotitsch, Roman},
  issn         = {0925-7721},
  journal      = {Computational Geometry: Theory and Applications},
  number       = {5-6},
  pages        = {343 -- 360},
  publisher    = {Elsevier},
  title        = {{A combinatorial approach to cartograms}},
  doi          = {10.1016/S0925-7721(96)00006-5},
  volume       = {7},
  year         = {1997},
}

@article{3581,
  abstract     = {A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. In this paper we address the problem of estimating how many such cuts arc always sufficient. We also consider a few related algorithmic and combinatorial geometry problems. For example, we demonstrate that n lines in space can be sorted in randomized expected time O(n4’st’), provided that they define no cycle. We also prove an 0(n7’4) upper bound on the number of points in space so that there are n lines with the property that for each point there are at least three noncoplanar lines that contain it. },
  author       = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Pollack, Richard and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack},
  issn         = {0925-7721},
  journal      = {Computational Geometry: Theory and Applications},
  number       = {6},
  pages        = {305 -- 323},
  publisher    = {Elsevier},
  title        = {{Counting and cutting cycles of lines and rods in space}},
  doi          = {10.1016/0925-7721(92)90009-H},
  volume       = {1},
  year         = {1992},
}