Applying Isotropic Fractional-Rational Curves Toward Surface Modeling: New Insights from the Applied Mathematics Perspective

Abstract

Given curves or points, one of the problems that have been documented in the recent past entails building smooth surfaces. The problem is pronounced due to computer technology and industry developments. Initially, zero Gaussian curvature shells and minimal surfaces were used. These surfaces relied on isotropic analytic curves. However, consumer properties restrict these curves. Hence, there is a growing need to steer expansions in surface shaping. In response to this trend, this paper proposed a technique for surface construction based on the role of isotropic fractional-rational curves. In the framework, the building of surfaces involved the use of flat orthogonal and isothermal grids, a process governed by the Weierstrass technique. Indeed, the latter approach was adopted due to the associated trend of demanding minimal surfaces.