Projet de thèse en Mathématiques et Informatique
Sous la direction de Stefanie Hahmann.
Thèses en préparation à l'Université Grenoble Alpes en cotutelle avec l'Universiti Sains Malaysia , dans le cadre de Mathématiques, Sciences et technologies de l'information, Informatique , en partenariat avec LJK - Laboratoire Jean Kuntzmann (laboratoire) et de EVASION (equipe de recherche) depuis le 01-03-2012 .
Geometric Modeling is the branch of Computer Science concerned with the efficient acquisition, representation, manipulation, reconstruction and analysis of 3-dimensional geometry on a computer. In many problems from science and engineering, it is an important requirement that design and reconstruction techniques produce curves and surfaces that are smooth and represent physical reality as closely as possible. In this thesis different aspects of smooth design of free form surfaces will be developed. A first part of the thesis will be concerned with the construction of tangent plane continuous (G1) smooth surface. When dealing with surfaces of arbitrary topology, a particular problem arises when an arbitrary number of patches joint with G1 continuity at a commen vertex. This problem is known as “vertex consistency problem”. Several solutions exist already in literature. However, several method do not always work for control polyhedral with arbitrary topology. We intent to improve these methods by developing new conditions of G1 continuity, which will work for quadrilateral faces. The surfaces are modeled by converting the control points to Bezier points for each patch by using blending matrices which are constructed from bicubic B-spline blending functions. The second part of the thesis will deal with reconstruction of smooth surfaces with quasi-developable surfaces. This particular class of surfaces is very important when simulating deformable but non-extensible surface, e.g. metal sheet, clothes. While many works exist on reconstructing surfaces from point clouds, we aim to study the possibility to reconstruct surfaces from boundary information only.
Modeling smooth surfaces of arbitrary topology
Geometric Modeling is the branch of Computer Science concerned with the efficient acquisition, representation, manipulation, reconstruction and analysis of 3-dimensional geometry on a computer. In many problems from science and engineering, it is an important requirement that design and reconstruction techniques produce curves and surfaces that are smooth and represent physical reality as closely as possible. In this thesis different aspects of smooth design of free form surfaces will be developed. A first part of the thesis will be concerned with the construction of tangent plane continuous (G1) smooth surface. When dealing with surfaces of arbitrary topology, a particular problem arises when an arbitrary number of patches joint with G1 continuity at a commen vertex. This problem is known as “vertex consistency problem”. Several solutions exist already in literature. This research will be conducted at USM University. During my 12 months-stay in France research on the second part will be conducted. This second part of the thesis will deal with reconstruction of smooth surfaces with quasi-developable surfaces. This particular class of surfaces is very important when simulating deformable but non-extensible surface, e.g. metal sheet, clothes. While many works exist on reconstructing surfaces from point clouds, we aim to study the possibility to reconstruct surfaces from boundary information only.