M.Sc Student | Yakersberg Evgeny |
---|---|

Subject | Morphing between Geometric Shapes using a Straight-Skeleton- Based Interpolation |

Department | Department of Computer Science |

Supervisor | Professor Gill Barequet |

In
this thesis we design and implement a 2-dimensional morphing technique between
polygonal shapes, based on a 3-dimensional surface interpolation between them.
A shape may consist of several non-intersecting contours (each one is a simple
polygon), possibly nested within each other. A major challenge of this problem
is morphing between shapes having different geometries and topologies. Our
approach involves surface reconstruction (or interpolation) between the source
and target shapes, and then extraction of intermediate slices. This is
accomplished by *slicing* the solid object bounded from below and above by
the original shapes embedded in parallel planes, and by the interpolated
surface between the two planes. Using a dense-enough series of intermediate
planes, the resulting sequence of slices can be used for visualizing the
morphing between the original shapes. Our approach is naturally extended to the
general case of *n* parallel polygonal shapes, for *n>2*.

The
solid objects constructed by the interpolation often have irregular boundaries
and sharp dihedral angles between faces. This is not always suitable for the
reconstructed object, and it often creates disappointing artifacts in the
morphing process. We propose a subdivision smoothing scheme, which is adopted
from a spline subdivision scheme. In order to make this scheme operate on a set
of 2D parallel cross-sections, we define the *straight skeleton average*,
and base the subdivision scheme on this average.