Interpolating and meshing 3D surface grids

In the boundary representation (B-Rep) model, a three-dimensional (3D) surface is de ned by a set of ‘simpler surfaces’ called ‘patches’. Although there are many di erent ways to specify a patch, a common case is that of a 4-sided patch represented by a structured grid of points. For instance, this kind of data can easily be obtained from a CAD system, as it is the mapping of regularly spaced points in a rectangular parametric domain. It can also be obtained from some particular 3D scanning devices. Non-rectangular topologies may also be encountered, for instance the 3-sided patch which can be considered as a degenerate case of the 4-sided patch (one side being of zero length). In this paper, we use the Coons method to build a surface interpolating the vertices of such a grid. The continuity of this parameterization makes it suitable for our indirect approach to surface meshing, which is generally based on the generation of an anisotropic mesh in the parametric space. Moreover, the indirect approach has been extended to the construction of anisotropic geometric surface meshes in 3D space, allowing an accurate geometric representation of the surface with a minimal number of elements. Several examples demonstrate the capabilities of this method