טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentShlafman Shimon
SubjectThree Dimensional Metamorphosis by Surface
Decomposition
DepartmentDepartment of Electrical Engineering
Supervisor Professor Ayellet Tal


Abstract

Metamorphosis is the gradual transformation of a source object through intermediate objects into a target objects. Metamorphosis of three-dimensional polyhedral surfaces has been a lively topic of research for many years. To generate a pleasing morph sequence, it is usually required to find a good correspondence between the surfaces before an interpolation is applied.

            A common approach for finding a correspondence between two given polyhedra is to look for a common embedding of their topologies (i.e., their one-skeleton graphs). This is done by projecting the models onto a common parameterization domain, merging their one-skeleton graphs in this domain, and projecting the merged topology back to the original models.

This general approach has a couple of drawbacks. First, fine correspondence is hard to achieve since the projection is global. Second, it is necessary to assume that the input models either genus-zero or disk-like polyhedral surfaces, for the above algorithm to be applicable.

In this work, we describe an algorithm for establishing a correspondence for metamorphosis of polyhedral models, that gets over both shortcomings. The algorithm is based on decomposing the input models into their inherent components. A full correspondence is found for each pair of compatible patches, while taking care to preserve continuity across the boundaries.

The main idea that underlies our scheme is that given a model, its components and the way they relate to each other characterize this model and portray its distinctive features. Thus, it is important to morph the meaningful components of the models to each other.

We describe a new parameterization scheme, which embeds cylinder-like patches onto an ideal cylinder. The latter algorithm avoids distortions and well maintains the symmetry of the patches due to its divide-and-conquer nature. We also review and compare some well-known embedding algorithms for disk-like patches.