4 research outputs found
Reconstruction of Orthogonal Polyhedra
In this thesis I study reconstruction of orthogonal polyhedral surfaces
and orthogonal polyhedra from partial information about their
boundaries. There are three main questions for which I provide novel
results. The first question is "Given the dual graph, facial angles and
edge lengths of an orthogonal polyhedral surface or polyhedron, is it
possible to reconstruct the dihedral angles?" The second question is
"Given the dual graph, dihedral angles and edge lengths of an
orthogonal polyhedral surface or polyhedron, is it possible to
reconstruct the facial angles?" The third question is "Given the
vertex coordinates of an orthogonal polyhedral surface or polyhedron, is
it possible to reconstruct the edges and faces, possibly after
rotating?"
For the first two questions, I show that the answer is "yes" for
genus-0 orthogonal polyhedra and polyhedral surfaces under some
restrictions, and provide linear time algorithms. For the third
question, I provide results and algorithms for orthogonally convex
polyhedra. Many related problems are studied as well
Conceptual free-form styling in virtual environments
This dissertation introduces the tools for designing complete models from scratch directly in a head-tracked, table-like virtual work environment. The models consist of free-form surfaces, and are constructed by drawing a network of curves directly in space. This is accomplished by using a tracked pen-like input device. Interactive deformation tools for curves and surfaces are proposed and are based on variational methods. By aligning the model with the left hand, editing is made possible with the right hand, corresponding to a natural distribution of tasks using both hands. Furthermore, in the emerging field of 3D interaction in virtual environments, particularly with regard to system control, this work uses novel methods to integrate system control tasks, such as selecting tools, and workflow of shape design. The aim of this work is to propose more suitable user interfaces to computersupported conceptual shape design applications. This would be beneficial since it is a field that lacks adequate support from standard desktop systems.Diese Dissertation beschreibtWerkzeuge zum Entwurf kompletter virtueller Modelle von Grund auf. Dies geschieht direkt in einer tischartigen, virtuellen Arbeitsumge-bung mit Hilfe von Tracking der Hände und der Kopfposition. Die Modelle sind aus Freiformlächen aufgebaut und werden als Netz von Kurven mit Hilfe eines getrack-ten, stiftartigen Eingabegerätes direkt im Raum gezeichnet. Es werden interaktive Deformationswerkzeuge für Kurven und Flächen vorgestellt, die auf Methoden des Variational Modeling basieren. Durch das Ausrichten des Modells mit der linken Hand wird das Editieren mit der rechten Hand erleichtert. Dies entspricht einer natürlichen Aufteilung von Aufgaben auf beide Hände. Zusätzlich stellt diese Arbeit neue Techniken für die 3D-Interaktion in virtuellen Umgebungen, insbesondere im Bereich Anwendungskontrolle, vor, die die Aufgabe der Werkzeugauswahl in den Arbeitsablauf der Formgestaltung integrieren.
Das Ziel dieser Arbeit ist es, besser geeignete Schnittstellen fĂĽr den computer-unterstĂĽtzten, konzeptionellen Formentwurf zur VerfĂĽgung zu stellen; ein Gebiet, fĂĽr das Standard-Desktop-Systeme wenig geeignete UnterstĂĽtzung bieten