
Journal for Geometry and Graphics 14 (2010), No. 2, 135145 Copyright Heldermann Verlag 2010 Force Directed NearOrthogonal Grid Generation on Surfaces Franz Gruber Dept. of Geometry, University of Applied Arts, OskarKokoschkaPlatz 2, 1010 Vienna, Austria franz.gruber@uniak.ac.at Guenter Wallner Dept. of Geometry, University of Applied Arts, OskarKokoschkaPlatz 2, 1010 Vienna, Austria Georg Glaeser Dept. of Geometry, University of Applied Arts, OskarKokoschkaPlatz 2, 1010 Vienna, Austria 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 forcedirected 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 doublecurved surfaces with grids that are almost orthogonal and, optionally, locally have almost constant grid size in both directions. Keywords: Orthogonal grids, grid generation, force directed algorithm. MSC: 5304; 53A05, 68U05 [ Fulltextpdf (1436 KB)] for subscribers only. 