Helmut Pottmann - Quad-mesh based mappings between surfaces

Helmut Pottmann, KAUST We discretize mappings between surfaces as correspondences between checkerboard patterns derived from quad meshes. This method captures the degrees of freedom inherent in smooth maps and provides a very simple and efficient computational approach to important types of maps such as conformal or isometric maps. In particular, it enables a natural definition of discrete developable surfaces which is much more flexible in applications than previous concepts of discrete developable surfaces. We discuss geometric modeling of developable surfaces, including cutting, gluing and folding, and present a construction of watertight CAD models consisting of developable spline surfaces. Moreover, we outline further applications of quad-mesh based maps in architectural geometry and computational fabrication.