TY - JOUR
T1 - Optimal development of doubly curved surfaces
AU - Yu, Guoxin
AU - Patrikalakis, Nicholas M.
AU - Maekawa, Takashi
N1 - Funding Information:
Funding for this research was obtained in part from the New Industry Research Organization (NIRO), and from the MIT Sea Grant and Department of Ocean Engineering. The authors thank Professor J.N. Tsitsiklis and the referees for their valuable comments.
PY - 2000/7
Y1 - 2000/7
N2 - This paper presents algorithms for optimal development (flattening) of a smooth continuous curved surface embedded in three-dimensional space into a planar shape. The development process is modeled by in-plane strain (stretching) from the curved surface to its planar development. The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming problem. Based on the strain distribution and the coefficients of the first fundamental form of the curved surface, another unconstrained nonlinear programming problem is solved to obtain the optimal developed planar shape. The convergence and complexity properties of our algorithms are analyzed theoretically and numerically. Examples show the effectiveness of the algorithms.
AB - This paper presents algorithms for optimal development (flattening) of a smooth continuous curved surface embedded in three-dimensional space into a planar shape. The development process is modeled by in-plane strain (stretching) from the curved surface to its planar development. The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming problem. Based on the strain distribution and the coefficients of the first fundamental form of the curved surface, another unconstrained nonlinear programming problem is solved to obtain the optimal developed planar shape. The convergence and complexity properties of our algorithms are analyzed theoretically and numerically. Examples show the effectiveness of the algorithms.
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U2 - 10.1016/S0167-8396(00)00017-0
DO - 10.1016/S0167-8396(00)00017-0
M3 - Article
AN - SCOPUS:0034230424
SN - 0167-8396
VL - 17
SP - 545
EP - 577
JO - Computer Aided Geometric Design
JF - Computer Aided Geometric Design
IS - 6
ER -