this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

Introduction Line integral convolution (LIC) is a flow-driven texture generation method that has become one of the best-known and most commonly used techniques in computer graphics for visualizing 2D flow, or flow over a surface in 3D. The popularity of LIC as a tool for 3D flow visualization, or the depiction of flow through a volume, has been relatively limited in contrast, however, primarily...

* Correspondence: [email protected] Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan Full list of author information is available at the end of the article Abstract In this investigation, motivated from Breaz study, we introduce a new family of integral operator using famous convolution technique. We also apply this newly defined operator for investigating some inte...

of memory and disk space become more accessible, demands for more effective visualization methods that can analyze large-scale numerical data also continue to grow. Among many problems that are faced by visualization researchers, how to effectively visualize numerical vector field data is one of the most challenging research subjects. In 1993, Cabral and Leedom proposed an innovative approach c...

An error analysis of Runge-Kutta convolution quadrature is presented for a class of nonsectorial operators whose Laplace transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ0 and a polynomial bound O(s 1) there, the stronger polynomial bound O(s2) in convex sectors of the form | arg s| ≤ π/2 − θ < π/2 for θ > 0. The order of convergence of the Runge-Kutt...

In this lecture we will discuss how line integral convolution can be generalized to depict vector fields defined on surfaces in 3D. The surfaces are assumed to be topologically equivalent to a 2D plane – at least in a local neighbourhood. In principle, any 2D imaging technique can be applied to such a surface as well. In particular, it is possible to map standard 2D LIC images onto the surface ...

Flow visualization has been a very attractive field within visualization research for a long time already. Usually huge datasets need to be processed, which often consist of multi-variate data with a really large number of sample locations, often arranged in multiple time-steps. Recently, the ever increasing performance of computers again has become a driving factor for a new boom in flow visua...

We present a visualization method that for three-dimensional tensor fields based on the idea of a stretched or compressed piece of fabric used as a “texture” for a two-dimensional surfaces. The texture parameters as the fabric density reflect the physical properties of the tensor field. This method is especially appropriate for the visualization of stress and strain tensor fields that play an i...

Stereo PIV datasets have three dimensional information over a plane, from which multiple quantities can be derived at each point. The task of visualizing these different parameters simultaneously is challenging, and this inhibits our ability to analyze and derive firm conclusions about the physics of the flow. Presently, the common approach is to view each parameter separately in different imag...