Interactive Design of Developable Surfaces

被引：107

作者：

Tang, Chengcheng ^{[1
]}

Bo, Pengbo ^{[1
,2
,5
]}

Wallner, Johannes ^{[3
]}

Pottmann, Helmut ^{[1
,4
]}

机构：

[1] King Abdullah Univ Sci & Technol, Jeddah 239556900, Saudi Arabia

[2] Harbin Inst Technol, Harbin, Peoples R China

[3] Graz Univ Technol, Kopernikusgasse 24, A-8010 Graz, Austria

[4] Vienna Univ Technol, Wiedner Hauptstr 8-10-104, A-1040 Vienna, Austria

[5] Harbin Inst Technol Weihai, 2 West Wenhua Rd, Shandong 264209, Peoples R China

来源：

ACM TRANSACTIONS ON GRAPHICS | 2016年 / 35卷 / 02期

基金：

中国国家自然科学基金; 奥地利科学基金会;

关键词：

Interactive design; computational differential geometry; developable surface; spline surface; origami; curved folding; isometric deformation; digital reconstruction; constraint solving; BEZIER; CURVATURE; MESHES;

D O I：

10.1145/2832906

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We present a new approach to geometric modeling with developable surfaces and the design of curved-creased origami. We represent developables as splines and express the nonlinear conditions relating to developability and curved folds as quadratic equations. This allows us to utilize a constraint solver, which may be described as energy-guided projection onto the constraint manifold, and which is fast enough for interactive modeling. Further, a combined primal-dual surface representation enables us to robustly and quickly solve approximation problems.

引用

页数：12

共 44 条

[1]

[Anonymous], 1978, A Practical Guide to Splines

[2]

[Anonymous], 1976, Differential Geometry of Curves and Surfaces

[3] A simple algorithm for designing developable Bezier surfaces [J].

Aumann, G .

COMPUTER AIDED GEOMETRIC DESIGN, 2003, 20 (8-9) :601-619

[4] Interpolation with developable Bezier patches [J].

Aumann, Guenter .

Computer Aided Geometric Design, 1991, 8 (05) :409-420

[5] DESIGN OF DEVELOPABLE SURFACES USING DUALITY BETWEEN PLANE AND POINT GEOMETRIES [J].

BODDULURI, RMC ;

RAVANI, B .

COMPUTER-AIDED DESIGN, 1993, 25 (10) :621-632

[6]

Chen DR, 2002, PROG NAT SCI-MATER, V12, P383

[7] A fully geometric approach for developable cloth deformation simulation [J].

Chen, Ming ;

Tang, Kai .

VISUAL COMPUTER, 2010, 26 (6-8) :853-863

[8]

Chu C-H, 2004, P DETC, V1, P431, DOI 10.1115/DETC2004-57257

[9] Developable Bezier patches:: properties and design [J].

Chu, CH ;

Séquin, CH .

COMPUTER-AIDED DESIGN, 2002, 34 (07) :511-527

[10]

Demaine ED, 2011, ORIGAMI(5): FIFTH INTERNATIONAL MEETING OF ORIGAMI SCIENCE, MATHEMATICS, AND EDUCATION, P39

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