In this paper we exploit redundant information in geodesic distance fields for a quick approximation of all-pair distances. Starting with geodesic distance fields of equally distributed landmarks we analyze the lower and upper bound resulting from the triangle inequality and show that both bounds converge reasonably fast to the original distance field. The lower bound has itself a bounded relat...

An algorithm is presented for computing geodesic furthest neighbors for all the vertices of a simple polygon, where geodesic denotes the fact that distance between two points of the polygon is defined as the length of an Euclidean shortest path connecting them within the polygon. The algorithm runs in O(n log n) time and uses O(n) space; n being the number of vertices of the polygon. As a corol...

Less than 10% of Minnesota’s hardwood forests remain after heavy logging in the 19 and early 20 centuries. In order to ensure that this ecosystem continues to be a part of Minnesota’s natural history, forest managers have begun practicing active and passive restoration. The composition of a remnant forest, planted forest, and an adjacent old-field in the St. Olaf College Natural Lands, was anal...

The distance between two objects is an important problem in CAGD, CAD and CG etc. It will be presented in this paper that a simple and quick method to estimate the distance between a point and a Bezier curve on a Bezier surface. Keywords—Geodesic-like curve, distance, projection, Bezier.

In this paper we consider positively 1-homogeneous supremal functionals of the type F (u) := supΩ f(x,∇u(x)). We prove that the relaxation F̄ is a difference quotient, that is F̄ (u) = RF (u) := sup x,y∈Ω, x6=y u(x)− u(y) dF (x, y) for every u ∈ W (Ω), where dF is a geodesic distance associated to F . Moreover we prove that the closure of the class of 1-homogeneous supremal functionals with respe...

Relationships between composition of secondary vegetation and environment were studied in central North Island, New Zealand. A classification procedure was used to identify broad compositional groups which included forest, broadleaved scrub, shrub-fernland, sclerophyllous scrub and shrubland, and tussock-shrubland. Generalised additive models (GAMs) were used to examine relationships between sp...

In this note we will construct an example of a quasi-geodesic in the Te-ichm uller space of a surface with the following instability property: Theorem For any hyperbolic surface S whose Teichm uller space T (S) has dimension at least 4, there is a bi-innnite quasi-geodesic L in T (S) such that 1. L projects to a compact part of the moduli space M(S), but 2. L does not lie in a bounded neighborh...

In this paper, we propose a numerical strategy to define a multiscale analysis for color and multicomponent images based on the representation of data on a graph. Our approach consists in computing the graph of an image using the psychovisual information and analysing it by using the spectral graph wavelet transform. We suggest introducing color dimension into the computation of the weights of ...

We exhibit examples of sub-Riemannian metrics with integrable geodesic flows and positive topological entropy. Introduction Consider a distribution on a manifold M, i.e. subbundle of the tangent bundle Π ⊂ TM . Non-holonomic Riemannian metric is a Riemannian metric g ∈ SΠ on this bundle. We call the pair (Π, g) sub-Riemannian structure. A curve γ : [0, 1] → M is called horizontal if γ̇ is a sect...