Ph.D Thesis

Ph.D StudentSurazhsky Tatiana
SubjectMatching and Morphing Freeform Surfaces
DepartmentDepartment 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

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

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.