Search results for " graph"
showing 10 items of 1277 documents
Iterative construction of Dupin cyclides characteristic circles using non-stationary Iterated Function Systems (IFS)
2012
International audience; A Dupin cyclide can be defined, in two different ways, as the envelope of an one-parameter family of oriented spheres. Each family of spheres can be seen as a conic in the space of spheres. In this paper, we propose an algorithm to compute a characteristic circle of a Dupin cyclide from a point and the tangent at this point in the space of spheres. Then, we propose iterative algorithms (in the space of spheres) to compute (in 3D space) some characteristic circles of a Dupin cyclide which blends two particular canal surfaces. As a singular point of a Dupin cyclide is a point at infinity in the space of spheres, we use the massic points defined by J.C. Fiorot. As we su…
Chevalley cohomology for aerial Kontsevich graphs
2013
Let $T_{\operatorname{poly}}(\mathbb{R}^d)$ denote the space of skew-symmetric polyvector fields on $\mathbb{R}^d$, turned into a graded Lie algebra by means of the Schouten bracket. Our aim is to explore the cohomology of this Lie algebra, with coefficients in the adjoint representation, arising from cochains defined by linear combination of aerial Kontsevich graphs. We prove that this cohomology is localized at the space of graphs without any isolated vertex, any "hand" or any "foot". As an application, we explicitly compute the cohomology of the "ascending graphs" quotient complex.
Dirichlet approximation and universal Dirichlet series
2016
We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical results of Runge, Mergelyan and Vitushkin. We also strengthen the notion of universal Dirichlet series.
Dupin Cyclide Blends Between Quadric Surfaces for Shape Modeling
2004
We introduce a novel method to define Dupin cyclide blends between quadric primitives. Dupin cyclides are nonspherical algebraic surfaces discovered by French mathematician Pierre-Charles Dupin at the beginning of the 19th century. As a Dupin cyclide can be fully characterized by its principal circles, we have focussed our study on how to determine principal circles tangent to both quadrics being blended. This ensures that the Dupin cyclide we are constructing constitutes aG 1 blend. We use the Rational Quadratic Bezier Curve (RQBC) representation of circular arcs to model the principal circles, so the construction of each circle is reduced to the determination of the three control points o…
Dupin cyclide blends between non-natural quadrics of revolution and concrete shape modeling applications
2014
Abstract In this work, we focus on the blending of two quadrics of revolution by two patches of Dupin cyclides. We propose an algorithm for the blending of non-natural quadrics of revolution by decomposing the blending operation into two complementary sub-blendings, each of which is a Dupin cyclide-based blending between one of the two quadrics and a circular cylinder, thus enabling the direct computation of the two Dupin cyclide patches and offering better flexibility for shape composition. Our approach uses rational quadric Bezier curves to model the relevant arcs of the principal circles of Dupin cyclides. It is quite general and we have successfully used it for the blending of several n…
An isoperimetric type problem for primitive Pythagorean hodograph curves
2012
An isoperimetric type problem for primitive Pythagorean hodograph curves is studied. We show how to compute, for each possible degree, the Pythagorean hodograph curve of a given perimeter enclosing the greatest area. We also discuss the existence and construction of smooth solutions, obtaining a relationship with an interesting sequence of Appell polynomials.
An annihilator-based strategy for the automatic detection of exponential polynomial spaces in subdivision
2021
Abstract Exponential polynomials are essential in subdivision for the reconstruction of specific families of curves and surfaces, such as conic sections and quadric surfaces. It is well known that if a linear subdivision scheme is able to reproduce a certain space of exponential polynomials, then it must be level-dependent, with rules depending on the frequencies (and eventual multiplicities) defining the considered space. This work discusses a general strategy that exploits annihilating operators to locally detect those frequencies directly from the given data and therefore to choose the correct subdivision rule to be applied. This is intended as a first step towards the construction of se…
Introducing a novel mesh following technique for approximation-free robotic tool path trajectories
2017
Abstract Modern tools for designing and manufacturing of large components with complex geometries allow more flexible production with reduced cycle times. This is achieved through a combination of traditional subtractive approaches and new additive manufacturing processes. The problem of generating optimum tool-paths to perform specific actions (e.g. part manufacturing or inspection) on curved surface samples, through numerical control machinery or robotic manipulators, will be increasingly encountered. Part variability often precludes using original design CAD data directly for toolpath generation (especially for composite materials), instead surface mapping software is often used to gener…
Gray coding cubic planar maps
2016
International audience; The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize beta-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps. (C) 2015 Elsevier B.V. All rights reserved.
Demo: Co-simulation of UAVs with INTO-CPS and PVSio-web
2018
This demo shows our ongoing work on the co-simulation of co-operative Unmanned Aerial Vehicles (UAVs). The work is based on the INTO-CPS co-simulation engine, which adopts the widely accepted Functional Mockup Interface (FMI) standard for co-simulation, and the PVSioweb prototyping tool, that extends a system simulator based on the PVS logic language with a web-based graphical interface. Simple scenarios of Quadcopters with assigned different tasks, such as rendez-vous and space coverage, are shown. We assumed a linearized dynamic model for Quadcopters formalized in OpenModelica, and a linearized set of equations for the flight control module written in C language. The co-ordination algorit…