abstract 103

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

103

Detection and coverage of polygonal curves derived from vertical faults present on discontinuous surfaces (Research Paper)

Ramón Antonio Abancin Ospina, Martha Ximena Dávalos Villegas, Janneth del Rocío Morocho Yaucán.

The detection of discontinuities of a function $f(x,y)$ is the first step in problems of approximation of surfaces with strong variations (non-regular or discontinuous functions). This situation can be found in an important number of applications in concrete situations, such as modeling in Geology, and the reconstruction of medical or satellite images, among others. The purpose of this work is to present a methodology to detect and cover the set of discontinuities in explicit non-regular functions, from a set of N sparse Lagrangian data, $(\xi_j, f(\xi_j))$, with j in {1,2,..., N}, coming from a function explicitly defined as z=f(x,y). The proposed approach consists of the detection and approximation of a discontinuity set, and then the construction of a covering over that set. Results are presented for the detection and covering of polygonal curves derived from vertical faults present in discontinuous surfaces, using a scattered dataset of Lagrange type as input information. As a conclusion we obtain that the proposed methodology will open a way to define non-regular functional spaces, flexible enough to be adapted to the necessary requirements for the approximation of discontinuous surfaces.

Keywords: Irregular data; irregulars surfaces; detection of fault; vertical faults; covering of polygonal curves.

Cite this paper:

Abancin R.A., Dávalos M.X., Morocho J.R.

Detection and coverage of polygonal curves derived from vertical faults present on discontinuous surfaces,

Bull. Comput. Appl. Math. (Bull CompAMa),

Vol. 12, No.2 pp.xx-xx, 2024.