Search results for "subdivision"
showing 10 items of 52 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…
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…
The PCHIP subdivision scheme
2016
In this paper we propose and analyze a nonlinear subdivision scheme based on the monotononicity-preserving third order Hermite-type interpolatory technique implemented in the PCHIP package in Matlab. We prove the convergence and the stability of the PCHIP nonlinear subdivision process by employing a novel technique based on the study of the generalized Jacobian of the first difference scheme. MTM2011-22741
Annihilation Operators for Exponential Spaces in Subdivision
2022
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.
On new means with interesting practical applications: Generalized power means
2021
Means of positive numbers appear in many applications and have been a traditional matter of study. In this work, we focus on defining a new mean of two positive values with some properties which are essential in applications, ranging from subdivision and multiresolution schemes to the numerical solution of conservation laws. In particular, three main properties are crucial—in essence, the ideas of these properties are roughly the following: to stay close to the minimum of the two values when the two arguments are far away from each other, to be quite similar to the arithmetic mean of the two values when they are similar and to satisfy a Lipchitz condition. We present new means with these pr…
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…
Multiresolution Analysis for Irregular Meshes
2003
International audience; The concept of multiresolution analysis applied to irregular meshes has become more and more important. Previous contributions proposed a variety of methods using simplification and/or subdivision algorithms to build a mesh pyramid. In this paper, we propose a multiresolution analysis framework for irregular meshes with attributes. Our framework is based on simplification and subdivision algorithms to build a mesh pyramid. We introduce a surface relaxation operator that allows to build a non-uniform subdivision for a low computational cost. Furthermore, we generalize the relaxationoperator to attributes such as color, texture, temperature, etc. The attribute analysis…
Calcul direct d'une tesselation de la surface limite pour les schémas de subdivision uniformes
2017
International audience; Le peu d'utilisation des surfaces de subdivision dans les systèmes CAO est principalement lié au fait que la surface est le plus souvent seulement approchée par des niveaux de raffinement successifs, ce qui induit un manque de pré-cision. De plus, il est difficile d'intégrer la représentation des surfaces de subdivision dans le noyau géométrique (ensemble de primitives et d'outils) des applications CAO. C'est dans ce but que nous décrirons un formalisme général de construction de surfaces de subdivision basé sur les Systèmes Itérés de Fonctions. Le principal apport est que toutes les surfaces de subdivision classiques sont gérées de la même manière quel que soit le s…
Conceptualization for intended action: A dynamic model
2023
Concepts are the building blocks of higher-order cognition and consciousness. Building on Conceptual Spaces Theory (CST) and proceeding from the assumption that concepts are inherently dynamic, this paper provides historical context to and significantly elaborates the previously offered Iterative Subdivision Model (ISDM) with the goal of pushing it toward empirical testability. The paper describes how agents in continuous interaction with their environment adopt an intentional orientation, estimate the utility of the concept(s) applicable to action in the current context, engage in practical action, and adopt any new concepts that emerge: a largely pre-intellectual cycle that repeats essent…
Splines Computation by Subdivision
2015
In this chapter, fast stable algorithms are presented, which compute splines’ values at dyadic and triadic rational points starting from their samples at integer grid points. The algorithms are implemented by the causal-anticausal recursive filtering of initial data samples, which is followed by iterated application of FIR filters. Extension of the algorithms to the multidimensional case is straightforward. A natural application of the presented subdivision algorithms is for upsampling of signals and images. A few upsampling examples are provided.