Search results for "Computer Science::Graphics"
showing 10 items of 67 documents
A general 4th-order PDE method to generate Bézier surfaces from the boundary
2006
In this paper we present a method for generating Bezier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bezier surfaces whereby we studied the Bezier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bezier solutions of the Euler-Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourth-order operators for which Bezier solutions exist and hence we show that such operators can be utilised to generate Bezier surfaces from the boundary information. As part of this work we present a general method…
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…
Visualization of Large Terrain Using Non-restricted Quadtree Triangulations
2004
This paper presents a set of new techniques oriented towards the real-time visualization of large terrains. These techniques are mainly focused on semi-regular triangulations of non-restricted quadtree terrain representations. Despite the fact that the paper shows that triangulations based on non-restricted quadtrees are as simple and efficient as those based on restricted quadtrees, the new triangulations avoid discontinuity problems among the boundaries of different patches without the need for tree balancing and extra triangles addition. Another important feature of the proposed triangulation is that it incorporates an efficient method for building triangle strips and triangle fans for t…
Non-periodic Discrete Splines
2015
Discrete Splines with different spans were introduced in Sect. 3.3.1. This chapter focuses on a special case of discrete splines whose spans are powers of 2. These splines are discussed in more detail. The Zak transform provides an integral representation of such splines. Discrete exponential splines are introduced. Generators of the discrete-spline spaces are described whose properties are similar to properties of polynomial-spline spaces generators. Interpolating discrete splines provide efficient tools for upsampling 1D and 2D signals. An algorithm for explicit computation of discrete splines is described.
Reversing arrows: Duality
2021
What do you get reversing all arrows? The drawing ‘Duality’ is an homage to mirrors, classical art themes, and abstract mathematics.I’m looking for beauty in the arts and beauty in science. It’s a ...
"Table 5" of "Measurements of differential cross sections of $Z /\gamma^\ast$+jets+X events in proton anti-proton collisions at $\sqrt{s}$=1.96 TeV"
2009
PT distribution of the third jet in events with three or more jets with additional constraints on the electrons.
"Table 6" of "Measurements of differential cross sections of $Z /\gamma^\ast$+jets+X events in proton anti-proton collisions at $\sqrt{s}$=1.96 TeV"
2009
PT distribution of the third jet in events with three or more jets.
Polynomial Spline-Wavelets
2015
This chapter presents wavelets in the spaces of polynomial splines. The wavelets’ design is based on the Zak transform, which provides an integral representation of spline-wavelets. The exponential wavelets which participate in the integral representation are counterparts of the exponential splines that were introduced in Chap. 4. Fast algorithms for the wavelet transforms of splines are presented. Generators of spline-wavelet spaces are described, such as the B-wavelets and their duals and the Battle-Lemarie wavelets whose shifts form orthonormal bases of the spline-wavelet spaces.
Joining primal/dual subdivision surfaces
2012
International audience; In this article we study the problem of constructing an intermediate surface between two other surfaces defined by different iterative construction processes. This problem is formalised with Boundary Controlled Iterated Function System model. The formalism allows us to distinguish between subdivision of the topology and subdivision of the mesh. Although our method can be applied to surfaces with quadrangular topology subdivision, it can be used with any mesh subdivision (primal scheme, dual scheme or other.) Conditions that guarantee continuity of the intermediate surface determine the structure of subdivision matrices. Depending on the nature of the initial surfaces…
Robustness of texture parameters for color texture analysis
2006
This article proposes to deal with noisy and variable size color textures. It also proposes to deal with quantization methods and to see how such methods change final results. The method we use to analyze the robustness of the textures consists of an auto-classification of modified textures. Texture parameters are computed for a set of original texture samples and stored into a database. Such a database is created for each quantization method. Textures from the set of original samples are then modified, eventually quantized and classified according to classes determined from a precomputed database. A classification is considered incorrect if the original texture is not retrieved. This metho…