We present a new analysis of finite element methods for partial differential equations over curved domains. In many applications, change variables translates physical Poisson problem domain into parametric polytopal domain. Whilst this greatly simplifies the geometry and numerical implementations, coordinate transformation typically features only low regularity. problem, manifests as rough coef...

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consis...

It has been found that disoriented children could use geometric information in combination with landmark information to reorient themselves in large but not in small experimental spaces. We tested domestic chicks in the same task and found that they were able to conjoin geometric and nongeometric (landmark) information to reorient themselves in both the large and the small space used. Moreover,...

Abstract Today’s typical application of geometric morphometrics to a quantitative comparison organismal anatomies begins by standardizing samples homologously labelled point configurations for location, orientation, and scale, then renders the ensuing comparisons graphically thin-plate spline as applied group averages, principal components, regression predictions, or canonical variates. The sca...

One of the most active research area in the watermarking community is the research in dealing with geometric distortion. The geometric distortion problem has two aspects, namely its effect on watermark detectability and its effect on the perceptual quality of the watermarked data. Most research in this area has been concentrated on addressing the first aspect of the problem, and research on obj...

This paper studies the creation of schematic maps from traditional vector-based, carto-graphic information. An algorithm is proposed to modify positions of lines in the original input map with the goal of producing as output a schematic map that meets certain geometric and aesthetic criteria. Special emphasis is placed here on preserving topological structure of features during this transformat...