Computational Conformal Geometry Applied in Engineering Fields
International Congress of Chinese Mathematicians 2007 (Invited Talk)
Xianfeng Gu, Miao Jin, Junho Kim, and Shing-Tung Yau
Computational conformal geometry is an interdisciplinary
field, combining modern geometry theories from pure
mathematics with computational algorithms from computer
science.
Computational conformal geometry offers many powerful
tools to handle a broad range of geometric problems in
engineering fields. This work summarizes our research results
in the past years. We have introduced efficient and robust
algorithms for computing conformal structures of surfaces
acquired from the real life, which are based on harmonic maps,
holomorphic differential forms and surface Ricci flow. We have
applied conformal geometric algorithms in computer graphics,
computer vision, geometric modeling and medical imaging.