Ph.D Thesis | |

Ph.D Student | Surazhsky Tatiana |
---|---|

Subject | Matching and Morphing Freeform Surfaces |

Department | Department of Applied Mathematics |

Supervisor | PROF. Gershon Elber |

In this work, we examine different
aspects of continuous deformations

that can be applied to the freeform rational curves and surfaces.

One very popular type of such deformations is known as metamorphosis

or morphing.

Morphing, also known as metamorphosis, is the gradual and continuous

transformation of one shape into another. The morphing problem

has been investigated in many contexts, e.g., morphing

of two-dimensional images, polygons, polylines and freeform curves, while

in three dimensions polyhedra and even the volumetric models have been

considered.

The metamorphosis process is characterized by two steps and we study

them both. The first one tries to find a correspondence (matching)

between features of the two prescribed shapes. The second stage

attempts to find trajectories that the intermediate shapes traverse

through, during the morphing process. These trajectories continuously

transform the initial shape into the final shape. We aim at defining

a completely automatic algorithm that finds a good looking and

intuitive metamorphosis sequence.

In our work we present several new methods for the deformations of

freeform curves and surfaces. We present a new matching technique

for the freeform surfaces, using the resemblance of the normal vector

fields, and a new algorithm to solve the interpolation part of the

metamorphosis problem for freeform curves and surfaces using curvature

interpolation.

One more interesting deformation technique presented in this research

effort is text deformation following the shape of the given

freeform curve or surface. The key stage of our method is a symbolic

composition of the embedded geometry and the warping surface. Several

interesting applications of text deformation technique are described

in this work. Among them one can find an arbitrary layout of text

along a freeform parametric curve, text animation and an artistic

surface rendering.