Many manufacturing processes involve wrapping a sheet of material over a surface. This paper focuses on wrappings where there is free movement of the sheets and the surfaces are almost developable. The approach is predominantly geometric and the key issues are the definition of almost developable surfaces and the distinction between flattening and unwrapping algorithms. There is an industrial case study to construct the pattern shape for a ceramic pot decoration.
HoschekJ.PottmannH.Interpolation and approximation with developable B-spline surfaces. In Mathematical methods for curves and surfaces (Ed. DaehlenM.LycheT.SchumakerL. L.) 1995, pp. 255–264 (Vanderbilt University Press, NA).
ShimadaT.TadaY.Development of a curved surface using a finite element method. In Proceedings of 1st Conference on Computer-aided optimum design of structures (Ed. BrebbiaC.A.HernadexS.) 1989, pp. 23–30 (Springer-Verlag).
15.
ShimadaT.TadaY.Approximate transformation of an arbitrary curved surface into a plane using dynamic programming. Comput. Aided Des., 1991, 23, 153–159.
16.
ZhangQ.-L.LuoX.-Q.Finite element method for developing arbitrary surfaces to flattened forms. Finite Elements in Analysis Des., 2003, 39, 977–984.
17.
McCartneyJ.HindsB. K.SeowB. L.The flattening of triangulated surfaces incorporating darts and gussets. Comput. Aided Des., 1999, 31, 249–260.
18.
WangC. C. L.SmithS. S.-F.YuenM. M. F.Surface flattening based on energy model. Comput. Aided Des., 2002, 34(11), 823–833.
19.
AzariadisP.AspragathosN.Design of plane developments of doubly curved surfaces. Comput. Aided Des., 1997, 29(10), 675–686.
20.
AzariadisP.AspragathosN.An evolutionary algorithm for generating planar developments of arbitrarily curved surfaces. Comput. in Industry, 2002, 47, 357–368.
21.
BarnhillR. E.Coons' patches and convex combinations. In Fundamental developments of computer-aided geometric modeling (Ed. PieglP.), 1993, pp. 135–163 (Academic Press).