Feature Based Visualization

In this thesis we applied powerful mathematical tools
such as
interval arithmetic for applications in computational
geometry,
visualization and computer graphics, leading to
robust, general and
e cient algorithms. We presented a completely novel
approach for
computing the arrangement of arbitrary implicit
planar curves and
performed ray casting of arbitrary implicit functions
by jointly
achieving, for the rst time, robustness, e ciency
and exibility.
Indeed we were able to render even the most di cult
implicits in
real-time with guaranteed topology and at high
resolution. We used
subdivision and interval arithmetic as
key-ingredients to guarantee
robustness. The presented framework is also
well-suited for
applications to large and unstructured data sets due
to the inherent
adaptivity of the techniques that are used. We also
approached the
topic of tensors by collaborating with mechanical
engineers on
comparative tensor visualization and provided them
with helpful
visualization paradigms to interpret the data.

Autorentext

Younis O. Hijazi, Ph.D. in computer science, University ofKaiserslautern, Germany. Post-doctoral researcher at the University of Strasbourg, France.

Klappentext

In this thesis we applied powerful mathematical toolssuch as interval arithmetic for applications in computationalgeometry, visualization and computer graphics, leading torobust, general and e cient algorithms. We presented a completely novelapproach for computing the arrangement of arbitrary implicitplanar curves and performed ray casting of arbitrary implicit functionsby jointly achieving, for the rst time, robustness, e ciencyand exibility. Indeed we were able to render even the most di cultimplicits in real-time with guaranteed topology and at highresolution. We used subdivision and interval arithmetic askey-ingredients to guarantee robustness. The presented framework is alsowell-suited for applications to large and unstructured data sets dueto the inherent adaptivity of the techniques that are used. We alsoapproached the topic of tensors by collaborating with mechanicalengineers on comparative tensor visualization and provided themwith helpful visualization paradigms to interpret the data.