Generation of quadrilateral meshes from triangular data with resulting smooth surface reconstruction

A new method for surface reconstruction from an initial triangular mesh is introduced. The method transforms the mesh to a quadrilateral one and then builds a smooth surface on top of it. This approach is efficient for large collections of triangular patches, including difficult situations such as sharp junctions and n-patch vertices. During the reconstruction process, the number of mesh elements is considerably reduced. The possibility of parallel computation makes the method efficient in practice. The method is illustrated by building several free-form surfaces from a triangular mesh