Discrete Differential Operators and Geometry Processing

technologies within the last decade have
enabled the creation of complex digital models
from real-world objects. The field of geometry
processing concerns the representation, analysis,
manipulation, and optimization of the resulting
geometric data. The findings in this field are
of importance for many industrial applications,
for example in the automotive industry and architecture.

Fundamental to geometry processing is an understanding
of geometric properties of the shapes to be processed.
Since these are discrete and not smooth manifolds,
they lie out of the realm of classical differential
geometry. Discrete differential geometry develops
notions and concepts that describe geometric properties
of discrete manifolds in analogy to the smooth theory.
Concepts developed in this field form a basis for many
algorithms in geometry processing.

In this talk, we discuss the construction of discrete
differential operators, their convergence properties,
and recent advances in surface editing and spacetime
control of deformable objects.