Surface visualization via level curves and applications

Abstract

[en] This study intends to implement a 3-D surface representation via level curves. This way of representing surfaces requires a lot of previous work. Nevertheless, it is very useful when dealing with problems where it is important to know the points of the surface that are in each level cut. A general simulator has been implemented in order to be easily adapted to different problems. The program code has been structured in a way in which it can be used for different surfaces. The simulator has been applied to the representation of zero-velocity curves of the extended planar and circular restricted 3-body problem (XPCR3BP). This project aims to be as general as possible. However, some simplifications of the surface visualization via level curves problem have been taken into consideration in order to ease the programming purposes: the problem has been implemented only for simple closed curves; and the singular level curves associated to saddle points have been considered to be homoclinic.