Extremal distance, harmonic measure and numerical conformal mapping

Geometric trajectory filtering via numerical conformal mapping

The paper studies the problem which we refer to as geometric trajectory filtering, where only trajectories that satisfy the local safety constraints are selected from a library of trajectories. The goal is to speed up primitive-based motion planning while still maintaining a relatively a large collection of motion primitives. One way to solve this problem is to obtain a proper (preferably smoot...

Extremal Length and Conformal Capacityo

Conformal Capacities and Extremal Metrics

For any non-compact Riemannian manifold M of dimension n ≥ 2 we previously defined a function λM : M×M → R+ = R+∪{+∞] only dependent on the conformal structure of M , and proved that for a class of manifolds containing all the proper subdomains of R, λ 1 n M was a distance on M [F1, F2]. The case of a domain G of R has been the object of several investigations leading to estimations of λG[V1, ....

Conformal mapping of some non-harmonic functions in transport theory

Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace’s equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in two dimensions. In physics, these include steady states of various nonlinear diffusion equations, the advection–diffusion equations for potential flows, and...

Accurate Circle Conngurations and Numerical Conformal Mapping in Polynomial Time

| According to a remarkable re-interpretation of a theorem of E.M. Andreev (1970) by W.P. Thurston (1982), there is a unique (up to inversive transformations) packing of interior-disjoint circles in the plane, whose contact graph is any given polyhedral graph G, and such that an analagous \dual" circle packing simultaneously exists, whose contact graph is the planar dual graph G , and such that...