
Developable Surfaces
Developable surfaces can be unfolded to the plane without stretching or tearing.


Y. Liu, H. Pottmann, J. Wallner, Y.L. Yang, and W. Wang.
Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graphics 25/3 (2006), 681689, Proc. SIGGRAPH.
Developable surfaces can be unfolded to the plane without stretching or tearing. This property makes them important for several applications in manufacturing. Geometric optimisation of meshes consisting of convex planar quadrilaterals combined with subdivision is an effective tool for modelling developable surfaces.


H. Pottmann and J. Wallner. Approximation algorithms for developable surfaces. Comput. Aided Geom. Design 16 (1999), 539556.
By its dual representation, a developable surface can be viewed as a curve of dual projective 3space. After introducing an appropriate metric in the dual space and restricting ourselves to special parametrisations of the surfaces involved, we derive linear approximation algorithms for developable NURBS surfaces, including multiscale approximations. Special attention is paid to controlling the curve of regression.


H.Y. Chen, I.K. Lee, S. Leopoldseder, H. Pottmann, T. Randrup, and J. Wallner.
On surface approximation using developable surfaces.
Graph. Models Img. Processing 61 (1999), 110124.
We introduce a method for approximating a given surface by a developable surface. It will be either a G^{1} surface consisting of pieces of cones or cylinders of revolution or a G^{r} NURBS developable surface. Our algorithm will also deal properly with the problems of reverse engineering and produce robust approximation of given scattered data. The presented technique can be applied in computer aided manufacturing, e.g. in ship building.


Publications

Y. Liu, H. Pottmann, J. Wallner, Y.L. Yang, and W. Wang.
Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graphics 25/3 (2006), 681689, Proc. SIGGRAPH.

H. Pottmann and J. Wallner. Approximation algorithms for developable surfaces. Comput. Aided Geom. Design 16 (1999), 539556.
[Zbl], [MR].

H.Y. Chen, I.K. Lee, S. Leopoldseder, H. Pottmann, T. Randrup, and J. Wallner.
On surface approximation using developable surfaces.
Graph. Models Img. Processing 61 (1999), 110124.
[Zbl].

H. Dirnböck and H. Stachel.
The development of the oloid.
J. Geom. Graphics 1 (1997), 105118.
[Zbl], [MR].



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Hellmuth Stachel
Johannes Wallner
Discrete Differential Geometry
Nonlinear Subdivision
Geometric Spline Theory
Geometric Tolerancing
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