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Publications in Scientific Journals:

C. Jiang, C. Wang, F. Rist, J. Wallner, H. Pottmann:
"Quad-mesh based isometric mappings and developable surfaces";
ACM Transactions on Graphics, 39/4 (2020), 128; 1 - 13.



English abstract:
We discretize isometric mappings between surfaces as correspondences between checkerboard patterns derived from quad meshes. This method captures the degrees of freedom inherent in smooth isometries and enables a natural definition of discrete developable surfaces. This definition, which is remarkably simple, leads to a class of discrete developables which is much more flexible in applications than previous concepts of discrete developables. In this paper, we employ optimization to efficiently compute isometric map-pings, conformal mappings and isometric bending of surfaces. We perform geometric modeling of developables, including cutting, gluing and folding. The discrete mappings presented here have applications in both theory and practice: We propose a theory of curvatures derived from a discrete Gauss map as well as a construction of watertight CAD models consisting of developable spline surfaces.

Keywords:
CCS Concepts, Computing methodologies, Shape modeling, Optimization algorithms, discrete differential geometry, computer-aided design, computational fabrication, shape optimization, discrete isometry, developable surface, developable spline surface


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1145/3386569.3392430


Created from the Publication Database of the Vienna University of Technology.