Sifted Disks. (6th May 2013)

• Record Type: Journal Article
• Authors: Ebeida, Mohamed S.; Mahmoud, Ahmed H.; Awad, Muhammad A.; Mohammed, Mohammed A.; Mitchell, Scott A.; Rand, Alexander; Owens, John D.
• Is Part Of: Computer graphics forum. Volume 32:Number 2(2013)Part 4
• Page Start: 509
• Page End: 518
• Publication Date: 2013-05-06
• Subjects: I.3.5 [Computing Methodologies]: Computer Graphics—Computational Geometry and Object Modeling; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12071
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract: We introduce the Sifted Disk technique for locally resampling a point cloud in order to reduce the number of points. Two neighboring points are removed and we attempt to find a single random point that is sufficient to replace them both. The resampling respects the original sizing function; In that sense it is not a coarsening. The angle and edge length guarantees of a Delaunay triangulation of the points are preserved. The sifted point cloud is still suitable for texture synthesis because the Fourier spectrum is largely unchanged. We provide an efficient algorithm, and demonstrate that sifting uniform Maximal Poisson‐disk Sampling (MPS) and Delaunay Refinement (DR) points reduces the number of points by about 25%, and achieves a density about 1/3 more than the theoretical minimum. We show two‐dimensional stippling and meshing applications to demonstrate the significance of the concept.