surface fitting approach for tensile membranes design - Tecnun

Many methods for surface fitting are implemented to obtain the control net from a cloud of points.[ROG89] and [PIE00] describe in detail the technique.Once the parametric surface is calculated, the designer can obtain the position at any point of themembrane surface, not only at the nodes used for calculating the equilibrium shape.Not many points are needed to generate a smooth surface. In the example shown in Figure 5, a smoothsurface is obtained from an initial grid of 3x3 by interpolation. The designer that manipulates the modelcan easily drag and drop a vertex of the membrane in real time. Many shapes can be obtained, and theuser has the feeling that the membrane is being moving in real time while dragging any point of thestructure by means of the mouse.In Table 1 and Figure 6, computational times for calculating the equilibrium shape and surface fittingare shown.Grid Size Method Time (seconds) Nodes Bars3x3 Force Density 0.033 16 245x5 Force Density 0.049 36 607x7 Force Density 0.061 64 1129x9 Force Density 0.100 100 1803x3 Non-Linear 0.039 16 245x5 Non-Linear 0.078 36 607x7 Non-Linear 0.152 64 1129x9 Non-Linear 0.402 100 180Table 1. Computational times for different grid sizes and formfinding methods.0.450.40.350.3Seconds0.250.20.15Force DensityNon Linear0.10.0503x3 5x5 7x7 9x9Grid SizeFigure 6. Computational times for different grid sizes and formfinding methods.