The conformal model of Geometric Algebra suggests an intimate connection between mathematics and perception, in particular in the handling of the problem of infinity. The observed properties of phenomenal perspective suggest an extension to Hestenes’ conformal mapping by adding a second conformal stage that maps the infinity of external reality to a finite double conformal map. Mathematics Subj...

In order to compare and integrate brain data more effectively, data from multiple subjects are typically mapped into a canonical space. One method to do this is to conformally map cortical surfaces to the sphere. It is well known that any genus zero Riemann surface can be mapped conformally to a sphere. Cortical surface is a genus zero surface. Therefore, conformal mapping offers a convenient m...

Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obtain a diffeomorphism between shapes that minimizes angular distortion. Conformal registrations are beneficial since it preserves the local geometry well. However, when landmark constraints are enforced, conformal mappi...

Comparing the location and size of functional brain activity across subjects is difficult due to individual differences in folding patterns and functional foci are often buried within cortical sulci. Cortical flat mapping is a tool which can address these problems by taking advantage of the two-dimensional sheet topology of the cortical surface. Flat mappings of the cortex assist in simplifying...

The flow field, velocity and pressure coefficient distribution of some 2-D ideal flows are presented. Conformal mapping is used to simulate two-dimensional ideal flow for a variety of complex internal and external configurations, based on the numerical integration of Schwarz-Christoffel transformation. The advantages of this method are simplicity and high accuracy. The method presented in this ...

Abstract. In this paper we investigate theoretically an approximation technique for avoiding the crowding phenomenon in numerical conformal mapping. The method applies to conformal maps from rectangles to "long quadrilaterals," i.e., Jordan domains bounded by two parallel straight lines and two Jordan arcs, where the two arcs are far apart. We require that these maps take the four corners of th...

In this paper we proposed the estimation of the characteristic impedance, effect of dispersion, and the effective dielectric constant of Coplanar Waveguide (CPW) using conformal mapping theory and performances are analyzed. Numerically efficient and accurate formulae based on the conformal mapping method for the analysis of coplanar waveguide structures are presented. The analysis formulas for ...

The self-organization model with a conformal-mapping adaptation is studied in this work. This model is designed to provide conformal transformation to meet the conformality requirement in biological morphology and geometrical surface mapping. This model spans the network field in the input space where topological conformality is preserved. The converged network provides not only the organized c...