Force Directed Near-Orthogonal Grid Generation on Surfaces
Single curved surfaces can always easily be covered by meshes that result into an equilateral and orthogonal grid when the surface is developed. On double curved surfaces, however, we can never find a mesh consisting of ‘squares on the surface’. Nevertheless, there is a need for ‘orthogonal and locally almost equilateral meshes’ on such surfaces in several fields, e.g., in architecture (fair and easy to build, increased rigidity) and computer graphics (undistorted mapping of textures, good tessellation for rendering purposes and also for aesthetical reasons). We present an iterative force-directed algorithm that is capable of optimizing given grids with rectangular topology and yields the task in an optimal way. It allows to cover arbitrary parametric double-curved surfaces with grids that are almost orthogonal and, optionally, locally have almost constant grid size in both directions.