2009/03/10 by Leslie Greengard, Greengard, Leslie, Chris Stucchio +1
Computer Science · Engineering · #3D Shape Modeling and Analysis #Computational Geometry (cs.CG) #Digital Image Processing Techniques #F.2.2 #FOS: Computer and information sciences #I.3.5 #Image Processing and 3D Reconstruction #cs.CG
paper · pdf · doi:10.48550/arxiv.0903.1817
22 pages, 11 figures
arxiv created 2009/03/10 · openalex publication_date 2009/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Reconstructing a finite set of curves from an unordered set of sample points is a well studied topic. There has been less effort that considers how much better the reconstruction can be if tangential information is given as well. We show that if curves are separated from each other by a distance D, then the sampling rate need only be O(sqrt(D)) for error-free reconstruction. For the case of point data alone, O(D) sampling is required.