Untitled in english

Author(s)

Marcelo Shimada

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Escola Politécnica (EP/BC)
• Defense date: 2002-04-08

Examining board members

Marcos de Sales Guerra Tsuzuki; Oswaldo Horikawa; Alexandre Kawano

• Advisor: Marcos de Sales Guerra Tsuzuki

Abstract

In this work, the use of interval arithmetic is considered to increase robustness of geometric classification algorithms in operations of solid modelling systems. The classification algorithms, also known as incidence tests, are important to keep the consistency between topology and solid geometry during the application of cut solid and boolean operations. A incidence test error, where values are compared, can damage the next steps of the cut solid and boolean operations algorithm and then make the solid inconsistent. The interval arithmetic incorporates approximation errors, so that, eliminates the need of defining a fixed tolerance to do the comparation between floating point numbers. However, it is not possible to directly convert the algorithms using floating point to algorithms using interval arithmetic, so that, there is a need of total reformulation of the algorithms. Another important item is the determination of intersection points that is done in cut solid and boolean operations, the use of interval arithmetic can result values with intervals with large dimensions, and this can cause fails in the algorithm of incidence tests. To deal with this fail, a correction based on the geometry is applied. So, this work will show the basic concepts of the interval arithmetic, the representation of geometric elements using interval arithmetic, the incidence tests, concepts of a B-Rep Solid Modeller and the algorithms for cut solid and boolean operations. (AU)