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Constructing developable surfaces by wrapping cones and cylinders

Affiliation:	1. School of Automation, Nanjing University of Science and Technology, Nanjing, PR China;2. Institute of Food Crops, Jiangsu Academy of Agricultural Sciences, Nanjing, PR China;3. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, PR China;4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, Nanjing, PR China;1. Department of Mathematics, Technion, Israel;2. Department of Computer Science, Technion, Israel;1. Istanbul Technical University, Turkey;2. Chuo University, Japan;3. The University of Tokyo, Japan;1. State Key Lab of CAD&CG, Zhejiang University, Hangzhou, 310027, China;2. University of Science and Technology of China, Hefei, 230026, China

Abstract:	We model developable surfaces by wrapping a planar figure around cones and cylinders. Complicated developables can be constructed by successive mappings using cones and cylinders of different sizes and shapes. We also propose an intuitive control mechanism, which allows a user to select an arbitrary point on the planar figure and move it to a new position. Numerical techniques are then used to find a cone or cylinder that produces the required mapping. Several examples demonstrate the effectiveness of our technique.

Keywords:	Developable surface Cone Cylinder Direct manipulation Paper bending
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