Search results for "computational geometry"
showing 10 items of 139 documents
Computing the Arrangement of Circles on a Sphere, with Applications in Structural Biology
2009
International audience; Balls and spheres are the simplest modeling primitives after affine ones, which accounts for their ubiquitousness in Computer Science and Applied Mathematics. Amongst the many applications, we may cite their prevalence when it comes to modeling our ambient 3D space, or to handle molecular shapes using Van der Waals models. If most of the applications developed so far are based upon simple geometric tests between balls, in particular the intersection test, a number of applications would obviously benefit from finer pieces of information. Consider a sphere $S_0$ and a list of circles on it, each such circle stemming from the intersection between $S_0$ and another spher…
3D objects descriptors methods: Overview and trends
2017
International audience; Object recognition or object's category recognition under varying conditions is one of the most astonishing capabilities of human visual system. The scientists in computer vision have been trying for decades to reproduce this ability by implementing algorithms and providing computers with appropriate tools. Hence, several intelligent systems have been proposed. To act in this field, numerous approaches have been proposed. In this paper we present an overview of the current trend in 3D objects recognition and describe some representative state of the art methods, highlighting their limits and complexity.
CliffoSor: A Parallel Embedded Architecture for Geometric Algebra and Computer Graphics
2006
Geometric object representation and their transformations are the two key aspects in computer graphics applications. Traditionally, compute-intensive matrix calculations are involved to model and render 3D scenery. Geometric algebra (a.k.a. Clifford algebra) is gaining growing attention for its natural way to model geometric facts coupled with its being a powerful analytical tool for symbolic calculations. In this paper, the architecture of CliffoSor (Clifford Processor) is introduced. ClifforSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on an FPGA board is detailed. Initial test results show more …
Design of the CGAL Spherical Kernel and application to arrangements of circles on a sphere
2009
International audience; This paper presents a CGAL kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the mathematics underlying two non trivial predicates are presented. Second, the design of the kernel concept is developed, and the connexion between the mathematics and this design is established. In particular, we show how two different frameworks can be combined: one for the general setting, and one dedicated to the case where all the objects handled lie on a reference sphere. Finally, an assessment about the efficacy of the \sk\ is made through the calculation of the exact arrangement of circles on a sphere. On average …
Salient Spin Images: A Descriptor for 3D Object Recognition
2018
In the last decades a wide range of algorithms have been devoted to recognize 3D free-from objects under real conditions such as occlusions, clutters, rotation, scale and translation. Spin image is one of these algorithms known to be robust to rotation, translation, occlusions up to 70% and clutters up to 60%, but still suffer from scaling, resolution changes and it is time consuming. In this paper we present a novel approach based on spin images, called salient spin images (SSI). This method enhances spin images algorithm based on its limits. Particularly, it decreases significantly the complexity of the algorithm using DoG detector, it shows a higher performance due to the relevant locali…
Geometric Entropies of Mixing (EOM)
2005
Trigonometric and trigonometric-algebraic entropies are introduced. Regularity increases the entropy and the maximal entropy is shown to result when a regular $n$-gon is inscribed in a circle. A regular $n$-gon circumscribing a circle gives the largest entropy reduction, or the smallest change in entropy from the state of maximum entropy which occurs in the asymptotic infinite $n$ limit. EOM are shown to correspond to minimum perimeter and maximum area in the theory of convex bodies, and can be used in the prediction of new inequalities for convex sets. These expressions are shown to be related to the phase functions obtained from the WKB approximation for Bessel and Hermite functions.
Single chain magnet behaviour in an enantiopure chiral cobalt(II)–copper(II) one-dimensional compound
2010
The self-assembly of an enantiomerically pure, chiral dianionic oxamatocopper(II) complex with cobalt(II) ions leads to neutral oxamato-bridged heterobimetallic chains that combine chirality and slow magnetic relaxation, providing thus the first example of ‘‘chiral single chain magnets (CSCMs). Ruiz Garcia, Rafael, Rafael.Ruiz@uv.es ; Lloret Pastor, Francisco, Francisco.Lloret@uv.es
G1-Blend between a Differentiable Superquadric of Revolution and a Plane or a Sphere Using Dupin Cyclides
2008
In this article, we present a method to perform G1-continuous blends between a differentiable superquadric of revolution and a plane or a sphere using Dupin cyclides. These blends are patches delimited by four lines of curvature. They allow to avoid parameterization problems that may occur when parametric surfaces are used. Rational quadratic Bezier curves are used to approximate the principal circles of the Dupin cyclide blends and thus a complex 3D problem is now reduced to a simpler 2D problem. We present the necessary conditions to be satisfied to create the blending patches and illustrate our approach by a number of superellipsoid/plane and superellipsoid/sphere blending examples.
From A Medial Surface To A Mesh
2012
Medial surfaces are well-known and interesting surface skeletons. As such, they can describe the topology and the geometry of a 3D closed object. The link between an object and its medial surface is also intuitively understood by people. We want to exploit such skeletons to use them in applications like shape creation and shape deformation. For this purpose, we need to define medial surfaces as Shape Representation Models (SRMs). One of the very first task of a SRM is to offer a visualization of the shape it describes. However, achieving this with a medial surface remains a challenging problem. In this paper, we propose a method to build a mesh that approximates an object only described by …
Curvilinear constraints for free form deformations on subdivision surfaces
2010
This paper presents a method to deform a subdivision surface with curvilinear constraints. It combines an intuitive free form deformation with a Loop subdivision algorithm. The main advantage of this method of deformation is that it uses only vertices of an object and satisfies the geometrical constraints provided by the user. It permits us to control the final shape of the deformed object, defining the range (i.e. the impact) of the deformation before applying it. The deformation takes into account the Loop properties to follow the subdivision scheme, allowing the user to fix some curvilinear constraints at the subdivision level he works on and to render the final object at the level he wa…