Urban Settlement Spatial Analysis in Permanent Preservation Area of M’boicy Watershed River, Foz do Iguaçu City in Brazil

Irregular urban settlement increases environmental impacts, especially when these occupations occur in fragile location, as the environmental preservation areas. In these areas, also defined as Permanent Preservation Area (PPA), the presence of watersheds is common, which is the factor that increases the need of protecting them from anthropic actions. Those actions deteriorate the environment and mainly the watercourses. This research objective is to identify and estimate the environmental risks of M’Boyci watershed River PPA occupied areas by urban population. The risk analysis approach, at this PPA in Foz do Iguacu City in Brazil, is able to support public interventions in order to reestablish the PPA natural conditions. To reach this goal, it was necessary to use cartographical representation images, generated from digital orthophotos analyzed through free geographical information systems. The overlap and the contrast of geographical data related to preservation in urban areas show that urban occupation reaches almost 40% of the permanent preservation area. Complementarily, it is evidenced that the development of a risk map identifies PPA areas characterized by a greater concentration of irregular settlement, contributing to the planning process of residents, relocation actions and recovery of degraded areas.

Existence of invariant curves with prescribed frequency for degenerate area preserving mappings

We consider small perturbations of analytic non-twist area preserving mappings,and prove the existence of invariant curves with prescribed frequency by KAM iteration.Generally speaking,the frequency of invariant curve may undergo some drift,if the twist condition is not satisfied.But in this paper,we deal with a degenerate situation where the unperturbed rotation angle function r→w+r^(2n+1)is odd order degenerate at r=0,and prove the existence of invariant curve without any drift in its frequency.Furthermore,we give a more general theorem on the existence of invariant curves with prescribed frequency for non-twist area preserving mappings and discuss the case of degeneracy with various orders.

Topological Disk Mesh Morphing Based on Area-Preserving Parameterization

Mesh morphing is a technique which gradually deforms a mesh into another one. Mesh parameterization, a powerful tool adopted to establish the one-to-one correspondence map between different meshes, is of great importance in 3 D mesh morphing. However, current parameterization methods used in mesh morphing induce large area distortion, resulting in geometric information loss. In this paper, we propose a new morphing approach for topological disk meshes based on area-preserving parameterization. Conformal mapping and M？bius transformation are computed firstly as rough alignment. Then area preserving parameterization is computed via the discrete optimal mass transport map. Features are exactly aligned through radial basis functions. A surface remeshing scheme via Delaunay refinement algorithm is developed to create a new mesh connectivity. Experimental results demonstrate that the proposed method performs well and generates high-quality morphs.