טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentSteiner Dvir
SubjectExtraction of Topological Information and Calculation of
Global Parameterization of Genus-n Meshes
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Anath Fischer


Abstract

Reverse Engineering (RE) techniques are based on the following six stages: data acquisition, range image registration, mesh reconstruction, segmentation, parameterization and 3D surface reconstruction. Current RE surface reconstruction methods for freeform objects are based mainly on geometrical criteria, while topological factors are neglected. These RE surface reconstruction methods use a bottom-up approach based on local parameterization to reconstruct an object from a cloud of points to a dense mesh and finally to smooth connected patches. After the data has been acquired, the first step in RE is to reconstruct a triangular mesh. However, representing an object as a triangular mesh is not sufficient for most manufacturing and production processes. Algorithms for mesh manipulations use local information for reconstruction, which sometimes causes topological problems that might lead to parameterization difficulties and noisy surface behavior.

In this research, new algorithms were developed for extracting topological information from triangular meshes. In addition, the validity and benefits of using topological information for constructing top-down algorithms were investigated. The topological information explored is in the form of topological graphs, cut graphs and object generators. Identifying these generators automatically formed the basis for a new parameterization approach. Utilizing the topological information enabled us to develop a parameterization algorithm that constructs a unique parameterization surface which is dictated by the object topology. The algorithm is straightforward, does not suffer from distortions and is flexible in determining the properties of the mesh to be preserved in the parameterization. The parameterization algorithm proposed here is the first algorithm for genus-n objects that can handle genus‑n meshes while using nonsymmetrical weights.