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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.
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.