Search results for "triangle"
showing 10 items of 89 documents
An Henstock-Kurzweil type integral on a meausure metric space
2014
We consider an Henstock-Kurzweil type integral defined on a complete measure metric space $X=(X, d)$ endowed with a Radon measure $\mu$ and with a family $\F$ of ``intervals" that satisfies, besides usual conditions, the Vitali covering theorem. In particular, for such integral, we obtain extensions of the descriptive characterization of the classical Henstock-Kurzweil integral on the real line, in terms of $ACG_*$ functions and in terms of variational measures. Moreover we show that, besides the usual Henstock-Kurzweil integral on the real line, such integral includes also the dyadic Henstock-Kurzweil integral, the $GP$-integral and the $s$-HK integral. For this last integral we prove a be…
A comparison of local parametric C0 Bézier interpolants for triangular meshes
2011
Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C^0 curved shape schemes we are aware of, based on a reformulation of their original constr…
A Fuzzy Approach to the Role of Symmetry in Shape Formation: The Illusion of the Scalene Triangle
2009
The main purposes of this work are to demonstrate the role of directional symmetry as a second order principle that polarizes the perception of the shape and to show how this preference can be easily encoded in an algorithm using a fuzzy operator for symmetry detection. The role of grouping in influencing shape perception and the role of directional symmetry was demonstrated through small triangles that create a large triangle. The specific questions answered in the psychophysical experiments were the following: Can the grouping by similarity influence both the pointing and the shape of the small and the large isosceles triangles? Conversely, can the shape of the large triangle influence th…
Collision Orbits in the Isosceles Rectilinear Restricted Problem
1995
In the study of the Collinear Three-Body Problem, McGehee (1974) introduced a new set of coordinates which had the effect of blowing up the triple collision singularity. Subsequently, his method has been used to analyze some other collision or singularities. Recently, Wang (1986) introduced another transformation which differs from the McGehee’s coordinates in the fact that the blowing-up factor is now the potential function, U, instead of the moment of inertia, I. Meyer and Wang (1993) have applied this method to the Restricted Isosceles Three-body Problem with positive energy and Cors and Llibre (1994) to the hyperbolic restricted three-body problem. In this paper we study the singulariti…
Entropic measure of spatial disorder for systems of finite-sized objects
2000
We consider the relative configurational entropy per cell S_Delta as a measure of the degree of spatial disorder for systems of finite-sized objects. It is highly sensitive to deviations from the most spatially ordered reference configuration of the objects. When applied to a given binary image it provides the quantitatively correct results in comparison to its point object version. On examples of simple cluster configurations, two-dimensional Sierpinski carpets and population of interacting particles, the behaviour of S_Delta is compared with the normalized information entropy H' introduced by Van Siclen [Phys. Rev. E 56, (1997) 5211]. For the latter example, the additional middle-scale fe…
Inhomogeneity and complexity measures for spatial patterns
2002
In this work, we examine two different measures for inhomogeneity and complexity that are derived from non-extensive considerations à la Tsallis. Their performance is then tested on theoretically generated patterns. All measures are found to exhibit a most sensitive behaviour for Sierpinski carpets. The procedures here introduced provide us with new, powerful Tsallis’ tools for analysing the inhomogeneity and complexity of spatial patterns.
On bounds for total absolute curvature of surfaces in hyperbolic 3-space
2003
Abstract We construct examples of surfaces in hyperbolic space which do not satisfy the Chern–Lashof inequality (which holds for immersed surfaces in Euclidean space). To cite this article: R. Langevin, G. Solanes, C. R. Acad. Sci. Paris, Ser. I 336 (2003).
Detecting self-similarity in surface microstructures
2000
The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend on the kind of the carpet. These peaks point to the presence of self-similarity even for randomly perturbed initial fractal sets. This is also demonstrated for the model population of particles diffusing over the surface considered by Van Siclen, Phys. Rev. E 56 (1997) 5211. These results allow the subtle self-similarity traces to be explored.
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…
Els triangles amorosos i l'amor cast. Alguns paral·lelismes entre la novel·la grega antiga i ¨Tirant lo Blanc¨
2018
Malgrat la distància temporal, cultural i lingüística que separa el Tirant lo Blanch i la novel·la grega antiga, es poden establir paral·lelismes evidents en personatges, escenes i motius, pel que fa al tractament de l?amor. En el present article ens centrem en l?enamorament de la parella de protagonistes de la novel·la de Joanot Martorell i de la novel·la d?Aquil·les Taci, Leucipe i Clitofont (s. II dC), i en algunes fites pel que fa al progrés de la seva relació amorosa. A continuació, analitzem els personatges de l?emperadriu i la Viuda Reposada, amb el mirall de les dones adúlteres de les novel·les Leucipe i Clitofont i Etiòpiques, com a protagonistes dels respectius triangles amorosos…