Intersecção de segmentos de reta em domínio discreto

• Grant number: 12/19196-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2013
• End date: January 31, 2014
• Field of knowledge: Engineering - Mechanical Engineering
• Principal Investigator: Marcos de Sales Guerra Tsuzuki
• Grantee: Marcel Lourenço de Luna
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The segments of the line have already been studied under various aspects in the mathematics field, like vector analysis and numerical analysis. A common problem in that field is the determination of the intersection between two or more line segments. It is known that the comparison among floating-point numbers through a tolerance is not transitive. For this reason, robust geometric algorithms do not use floating-point, but the integer representation. Determining the intersection among segments of line in a discrete domain is even more complex. Particularly, in this research, it is shown that the actual methods for determining the intersection among line segments in a discrete domain are not commutative. In this research project, a new representation will be proposed such that the intersection among line segments becomes commutative.(AU)