相关论文: Computational Geometry Column 38
We propose a new algorithm for curve skeleton computation which differs from previous algorithms by being based on the notion of local separators. The main benefits of this approach are that it is able to capture relatively fine details and…
We discuss recent progress in understanding the issues essential to the development of better cone jet algorithms.
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
Three-dimensional particle reconstruction with limited two-dimensional projections is an under-determined inverse problem that the exact solution is often difficult to be obtained. In general, approximate solutions can be obtained by…
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are…
A quadric in $\R P^3$ cuts a curve of degree 6 on a cubic surface in $\R P^3$. The papers classifies the nonsingular curves cut in this way on non-singular cubic surfaces up to homeomorphism. Two issues new in the study related to the first…
The paper presents the results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed…
This paper briefly reviews past milestones in the field of medical image reconstruction and describes some future directions. It is part of an overview paper on "open problems in signal processing" that will appear in IEEE Signal Processing…
We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of negative self-intersection C^2. The only known examples of…
Reconstructing a finite set of curves from an unordered set of sample points is a well studied topic. There has been less effort that considers how much better the reconstruction can be if tangential information is given as well. We show…
These are notes on some algebraic geometry of complex projective curves, together with an application to studying the contact curves in CP^3 and the null curves in the complex quadric Q^3 in CP^4, related by the well-known Klein…
ConicCurv is a new derivative-free algorithm to estimate the curvature of a plane curve from a sample of data points. It is based on a known tangent estimator method grounded on classic results of Projective Geometry and B\'ezier rational…
Some work in progress is announced, on the use of algebraic geometry, mostly concerning elliptic curve theory, to model turbulence. Attention is given to flows across the scales, on some convenient model space, and some current trials are…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
This paper documents and reviews the state of the art concerning computational models of construction grammar learning. It brings together prior work on the computational learning of form-meaning pairings, which has so far been studied in…
This is a survey paper: we discuss certain recent results, with some improvements. It will appear in the S. Cruz proceedings.
We demonstrate a new ultrafast pulse reconstruction modality which is somewhat reminiscent of frequency resolved optical gating but uses a modified setup and a conceptually different reconstruction algorithm that is derived from…
In the preprint cond-mat/0408050 M. V. Cheremisin noticed that some results (namely Fig. 4) of our recent work (cond-mat/0407364) have been taken from his paper cond-mat/0405176. As clear from the caption to Fig. 4 as well as from the text…
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been developed and has made significant contributions to medical…
In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We…