Related papers: A more robust multiparameter conformal mapping met…
It has long been clear that the conformal bootstrap is associated with a rich geometry. In this paper we undertake a systematic exploration of this geometric structure as an object of study in its own right. We study conformal blocks for…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
Multi-mobile robot systems show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging…
Shape assembly composes complex shapes geometries by arranging simple part geometries and has wide applications in autonomous robotic assembly and CAD modeling. Existing works focus on geometry reasoning and neglect the actual physical…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for…
In this study, the multiple solutions of Nonlinear Coupled Constitutive Relation (NCCR) model are firstly observed and a way for identifying the physical solution is proposed. The NCCR model proposed by Myong is constructed from the…
We propose a novel method for parameterizations of triangle meshes by finding an optimal quasiconformal map that minimizes an energy consisting of a relative entropy term and a quasiconformal term. By prescribing a prior probability measure…
Numerous applications require the simultaneous redistribution of the irradiance and phase of a laser beam. The beam shape is thereby determined by the respective application. An elegant way to control the irradiance and phase at the same…
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…
Biharmonic and conformal-biharmonic maps are two fourth-order generalizations of the well-studied notion of harmonic maps in Riemannian geometry. In this article we consider maps into the Euclidean sphere and investigate a geometric…
We propose a novel optimization algorithm for continuous functions using geodesics and contours under conformal mapping.The algorithm can find multiple optima by first following a geodesic curve to a local optimum then traveling to the next…
The Coherence Length Diagram and the related maps have been shown to represent a useful tool for image analysis. Setting threshold parameters is one of the most important issues when dealing with such applications, as they affect both the…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It is well known that there exists a unique Riemann conformal…
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated surfaces are…