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Article

Modeling Developable Folds on a Strip

[+] Author and Article Information
Kai Tang

Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, N.T., Hong Kong

Charlie C. L. Wang

Department of Automation and Computer-Aided Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

J. Comput. Inf. Sci. Eng 5(1), 35-47 (Mar 14, 2005) (13 pages) doi:10.1115/1.1804206 History: Received April 21, 2004; Revised August 05, 2004; Online March 14, 2005
Copyright © 2005 by ASME
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Figures

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Wrinkled surfaces: (a) a spherical mold of thick leather, and (b) a crumpled square of paper
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Developable wrinkle strip design in footwear: (a) shoe with a wrinkled strip; (b) carving a strip for wrinkle design
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Two C1 continuous curves linked by two line segments
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Developable vs non-developable ruled surfaces interpolating the same directrices: (a) non-developable; (b) developable
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Two BBTs with different local-convexity of a same strip
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Bending energy calculation
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Example I: (a) the input curves; (b) validity matrix of BBT; (c) shaded result of Min_Folding_BBT; (d) shaded result of Min_Dist_BBT; (e) mesh result of Min_Folding_BBT; (f ) mesh result of Min_Dist_BBT; (g) flattened 2D shape of Min_Folding_BBT result; (h) flattened 2D shape of Min_Dist_BBT result; (i) bending energy distribution comparison, where BBT is the curve of Min_Folding_BBT and SET represents the curve of Min_Dist_BBT
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Example II: (a) the input curves; (b) validity matrix of BBT; (c) shaded result of Min_Folding_BBT; (d) shaded result of Min_Dist_BBT; (e) mesh result of Min_Folding_BBT; (f ) mesh result of Min_Dist_BBT; (g) flattened 2D shape of Min_Folding_BBT; (h) flattened 2D shape of Min_Dist_BBT; (i) bending energy distribution comparison
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Example III: (a) the input curves; (b) validity matrix of BBT; (c) shaded result of Min_Folding_BBT; (d) shaded result of Min_Dist_BBT; (e) mesh result of Min_Folding_BBT; (f ) mesh result of Min_Dist_BBT; (g) flattened 2D shape of Min_Folding_BBT; (h) flattened 2D shape of Min_Dist_BBT; (i) bending energy distribution comparison
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Example IV: with vs without a priori rulings: (a) the input curves; (b) shaded result without a priori edges; (c) shaded result with additional a priori edges; (d) mesh result without a priori edges; (e) mesh result with additional a priori edges; (f ) validity matrix without a priori edges; (g) validity matrix with additional a priori edges; (h) flattened 2D shape without a priori edges; (i) flattened 2D shape with additional a priori edges; (j) bending energy distribution comparison, where r-BBT represents the curve of BBT with priori rulings
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Example V: (a) the input curves; (b) validity matrix of BBT; (c) shaded result of Min_Folding_BBT; (d) shaded result of Min_Dist_BBT; (e) mesh result of Min_Folding_BBT; (f ) mesh result of Min_Dist_BBT; (g) flattened 2D shape of Min_Folding_BBT; (h) flattened 2D shape of Min_Dist_BBT; (i) bending energy distribution comparison.
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Example VI: Comparison between the minimum vs the maximum bending criterion: (a) the result from the minimum bending criterion; (b) the result from the maximum bending criterion; (c) bending energy distribution comparison    
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Example VII: Shoe surface wrinkle design based on Min_Folding_BBT: (a) the input curves; (b) the shaded result of Min_Folding_BBT; (c) the original shoe upper surface; (d) wrinkled upper combined by (b) and (c).
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Valid list of movements

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