Research On Recognition And Reconstruction Of Developable Surfaces

Developable surface is a kind of curved surface with special geometrical properties. Because of its property that can be expanded to the plane region without being stretched and cut out, developable surface is a good mathematical model for paper, wood, metal plate, etc. On the basis of developable surface or approximate developable surface that was represented by triangular mesh model, around the exhibition of model, recognition of developable region on curved surface and reconstruction of developable surface were studied in this paper. Finally, a new method for automatic recognition and reconstruction of developable surface was presented.For the recognition of developable region, according to the shape and the normal of curved surfaces which approximating to a plane, this paper established the adjacent relations of planes. With the help of adjacent relationship, different developable regions of model were recognized automatically. By this new method,the characteristic curves of developable surfaces were calculated correctly, and the curved surface was divided reasonably into some developable regions.In the part of model reconstruction, the initial control mesh was obtained on the basis of the representation of plane approximation firstly. By using the Gauss Newton iterative method, the control mesh was optimized, and B spline fitting developable surface of various developable regions were developed. When the optimization was finished, the discrete grid model of developable surface could be constructed with the help of rulings sampling from B spline developable surface.Finally, by the intersection and the boundary clipping operation of the curved surface, seamless meshes of reconstructed developable surfaces were obtained.In the method proposed in this paper, the recognition and reconstruction of the surface didn’t need to use the parametric representation of the original model or the unfolding form in the plane of curved surface. This method is capable of dealing with the developable surface model with creases and the piecewise developable surface model that can not be unfolded to the plane. For the model with unobvious characteristics or data missing, this method can also get good reconstruction results.At the end of this paper, the effectiveness of this new method was demonstrated by several examples, and the time efficiency of each step of the algorithm was analyzed in detail.