Related papers: Computational Geometry Column 38
Several recent SIGGRAPH papers on surface simplification are described.
Two results in "computational origami" are illustrated.
Curve reconstruction from unstructured points in a plane is a fundamental problem with many applications that has generated research interest for decades. Involved aspects like handling open, sharp, multiple and non-manifold outlines,…
We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures. These curvatures are invariant under the special Euclidean group and the equi-affine groups, respectively, and play an important…
A compendium of thirty previously published open problems in computational geometry is presented.
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
Open problems from the 15th Annual ACM Symposium on Computational Geometry.
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
The algorithm of Edelsbrunner for surface reconstruction by ``wrapping'' a set of points in R^3 is described.
This is a survey describing recents developments in enumerative geometry of curves on projective varieties. Various methods to arrive at results such as Kontsevich's formula for plane rational curves, or Caporaso-Harris's formula for plane…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
The recent result that n congruent balls in R^d have at most 4 distinct geometric permutations is described.
In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds. We prove that the minimal spanning tree, given a sufficiently dense sample, correctly reconstructs the smooth arcs and…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
Reconstructing the missing parts of a curve has been the subject of much computational research, with applications in image inpainting, object synthesis, etc. Different approaches for solving that problem are typically based on processes…
Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive…
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified treatment, complemented with several novel observations, may be…
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
An expository description of smooth cubic curves in the real or complex projective plane.