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

In this work 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. The present 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 make a method efficient in practice. The method is illustrated by building several free form surfaces from a triangular mesh.