Model Fabrication

19 Figure 11: Computer model of an f16 (left) and assembled out of heavy paper (right). 150 Table 1: Diierent models layout construction times. piecewise developable surfaces. However, the introduced approach allows one to construct a piecewise developable surface approximation to an arbitrary freefrom surface, with tolerance control. Throughout this paper, it was implicitly assumed that the material thickness is negligible. Unfortunately, this is not always the case and compensating for the distortion that can result is a future research topic. In addition, extending this methodology to support stretching and tearing, should be investigated. Not only will that enable dealing with arbitrary surfaces (which cannot be exactly decomposed into piecewise developable surfaces) but this algorithm may then support the ability to handle fabric and other anisotropic materials. 18 Figure 9: Computer models (left) and assembled out of heavy paper (right). Figure 10: Computer model of a teapot (left) and assembled out of heavy paper (right). and 11 show more complex models having several trimmed surfaces. Table 1 provides some timing results for the model decomposition and layout computation. Tests were run on a SGI4D 240 GTX (R3000 25MHz Risc machine). All tests are measured in seconds. 5 Conclusion This paper introduces a new approach to and provides a working algorithm for automating the decomposition and subsequent speciication and layout of freeform models into developable components. Not every freeform surface can be exactly represented using 17 Figure 8: A helicopter model (top left) laid out (bottom) and assembled (top right). projection with the cross sections of the developable surfaces, and the assembled piece. Figure 9 shows several models laid out using these techniques and then assembled from heavy paper. Each developable surface was cut from paper and folded into its 3-space shape. Paper connecting stubs were used to hold and keep the pieces together. More complex models can be created using Boolean operations when the model is a union or intersection of several freeform surfaces. The layouts of the trimming curves of these surfaces are also computed, in a way similar to the ruled surface layouts. Figures 10 16 Figure 7: Trimming curves should be laid out with the ruled surfaces. bilinear surface the u direction is also assumed to be of constant speed and the exact location is then interpolated from the at bilinear four corner points. Finally, since the developable surface representation is only an approximation, it may be …