Innovations in conformal mapping continue to extend this classical technique to more complicated configurations, and surveys of the various techniques available are given in Ref. [7] and Ref. [1]. Some specific recommendations of techniques and tools are given in Ref. [7]. Conformal systems have advantage the of introducing the fewest additional terms in transformed partial differential equatio...

Cortical flattening algorithms are becoming more widely used to assist in visualizing the convoluted cortical gray matter sheet of the brain. Metric-based approaches are the most common but suffer from high distortions. Conformal, or angle-based algorithms, are supported by a comprehensive mathematical theory. The conformal approach that uses circle packings is versatile in the manipulation and...

Locations and patterns of functional brain activity in humans are difficult to compare across subjects because of differences in cortical folding and functional foci are often buried within cortical sulci. Unfolding a cortical surface via flat mapping has become a key method for facilitating the recognition of new structural and functional relationships. Mathematical and other issues involved i...

We answer a question raised by M. Chuaqui, P. Duren, and B. Osgood by showing that a conformal mapping of a simply connected domain cannot take two circles onto two proper ellipses. The goal of this note is to prove the following. Proposition 1. Let Ω be a simply connected domain on C = C ∪ {∞} containing circles (on C) C1 and C2, C1 = C2. Let f be a conformal mapping from Ω into C. If f maps e...

Few analytical techniques are better known to students of applied mathematics than conformal mapping. It is the classical method for solving problems in continuum mechanics, electrostatics, and other fields involving the two-dimensional Laplace and Poisson equations. To employ the method, one needs an explicit mapping function from some standard domain— such as the unit disk or upper half plane...

We describe a method to compute conformal parameterizations with a natural boundary based on a simple differentiable expression measuring angles between edges by using complex numbers. The method can be adapted to preserve metric properties or map textures with constrained positions. Some illustrations are shown to assess the efficiency of the algorithms.

Conformal (Same form or shape) mapping is an important technique used in complex analysis and has many applications in different physical situations.If the function is harmonic (ie it satisfies Laplace’s equation∇f = 0 )then the transformation of such functions via conformal mapping is also harmonic. So equations pertaining to any field that can be represented by a potential function (all conse...

This paper presents a method to construct a smooth seamless conformal surface for the genus-0 manifold. The method is developed for the conformal self-organizing map [10]. The constructed surface is both piecewise smooth and continuous. The mapping between the model surface and the sphere surface is one-to-one and onto. We show experiments in surface reconstruction and texture mapping.

We investigate the interface dynamics in Laplacian growth model, using the conformal mapping technique. Starting from the governing equation obtained by B.Shraiman and D.Bensimon, we derive intergro-differential evolution equation of interphase dynamics. It is shown that such representation of the conformal mapping technique is convenient for computer simulations of the quasi-stationary Stefan ...