Search results for " Geometry"

Computation of the topological type of a real Riemann surface

2012

We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$, namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the $\mathcal{A}$-cycles are invariant under the anti-holomorphic involution $\tau$.

Continuous reformulations and heuristics for the Euclidean travelling salesperson problem

2008

We consider continuous reformulations of the Euclidean travelling salesperson problem (TSP), based on certain clustering problem formulations. These reformulations allow us to apply a generalisation with perturbations of the Weiszfeld algorithm in an attempt to find local approximate solutions to the Euclidean TSP.

Equilibrium structure of LiCCH

2000

Efficiently using connectivity information between triangles in a mesh for real-time rendering

2004

Triangle meshes are the most popular standard model used to represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphics system. Taking advantage of the connectivity information between the triangles in a mesh dramatically diminishes the amount of information the graphics system must handle. Multiresolution Triangle Strips (MTS) represent a triangle mesh as a collection of multiresolution triangles strips. These strips are the basis of both the storage and the rendering stage. The coherence between the extraction of two levels of detail is used in the model in order to decrease the visualisation time.

Performance analysis of user-centric SBS deployment with load balancing in heterogeneous cellular networks: A Thomas cluster process approach

2020

Abstract In conventional heterogeneous cellular networks (HCNets), the locations of user equipments (UEs) and base stations (BSs) are modeled randomly using two different homogeneous Poisson point processes (PPPs). However, this might not be a suitable assumption in case of UE distribution because UE density is not uniform everywhere in HCNets. Keeping in view the existence of nonuniform UEs, the small base stations (SBSs) are assumed to be deployed in the areas with high UE density, which results in correlation between UEs and BS locations. In this paper, we analyse the performance of HCNets with nonuniform UE deployment containing a union of clustered and uniform UE sets. The clustered UE…

The geometry of surfaces in 4-space from a contact viewpoint

1995

We study the geometry of the surfaces embedded in ℝ4 through their generic contacts with hyperplanes. The inflection points on them are shown to be the umbilic points of their families of height functions. As a consequence we prove that any generic convexly embedded 2-sphere in ℝ4 has inflection points.

The Local Fractional Derivative of Fractal Curves

2008

Fractal curves described by iterated function system (IFS) are generally non-integer derivative. For that we use fractional derivative to investigate differentiability of this curves. We propose a method to calculate local fractional derivative of a curve from IFS property. Also we give some examples of IFS representing the slopes of the right and left half-tangent of the fractal curves.

Representation of NURBS surfaces by Controlled Iterated Functions System automata

2019

Iterated Function Systems (IFS) are a standard tool to generate fractal shapes. In a more general way, they can represent most of standard surfaces like Bézier or B-Spline surfaces known as self-similar surfaces. Controlled Iterated Function Systems (CIFS) are an extension of IFS based on automata. CIFS are basically multi-states IFS, they can handle all IFS shapes but can also manage multi self-similar shapes. For example CIFS can describe subdivision surfaces around extraordinary vertices whereas IFS cannot. Having a common CIFS formalism facilitates the development of generic methods to manage interactions (junctions, differences...) between objects of different natures.This work focuses…

2D virtual texture on 3D real object with coded structured light

2008

Augmented reality is used to improve color segmentation on human body or on precious no touch artifacts. We propose a technique to project a synthesized texture on real object without contact. Our technique can be used in medical or archaeological application. By projecting a suitable set of light patterns onto the surface of a 3D real object and by capturing images with a camera, a large number of correspondences can be found and the 3D points can be reconstructed. We aim to determine these points of correspondence between cameras and projector from a scene without explicit points and normals. We then project an adjusted texture onto the real object surface. We propose a global and automat…

Efficient Implementation of Multiresolution Triangle Strips

2002

Triangle meshes are currently the most popular standard modelto represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphic engine. It has been shown that using drawing primitives, such as triangle fans or strips, dramatically reduces the amount of information. Multiresolution Triangle Strips (MTS) uses the connectivity information to represent a mesh as a set of multiresolution triangles strips. These strips are the basis of both the storage and rendering stages. They allow the efficient management of a wide range of levels of detail. In this paper, we have taken advantage of the coherence property betwee…