Fractals/Computer graphic techniques/2D/grid

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Digital Region Boundary Tracing--start point

The domain has been discretized into a mesh and then rasterized to the image


Image[edit]

Digital image

  • binary image ( 1-bit color)[1]
  • grayscale image
  • color image


grid[edit]

  • grid[2][3]
  • mesh
  • tiling
  • tesselation of the plane
    • Set partitions

Dimension[edit]

  • 2D
  • 3D
Elements of polygonal 3D mesh

Types[edit]

  • regular mesh = Structured grid = global grid ( finite differences)
    • a quadrilateral grid is most common in structured grids
      • quadratic
    • a triangular mesh
      • "the Coxeter-Freudenthal triangulation. It is constructed by dividing space using a uniform cubic grid and the triangulation is obtained by subdividing each cube." [4][5]
    • hexagonal
  • An unstructured = irregular grid, adaptive grid, local grid ( fast marching methods)
    • Quadtree Grid
    • BSP tree
    • A triangular surface mesh is always quick and easy to create. It is most common in unstructured grids.

tilings by regular polygons: regular (=structured ) grid

Pixel connectivity[edit]

Pixel connectivity in wikipedia

creating[edit]

coordinate system[edit]

In geometry, a coordinate system is a system which uses one or more numbers (= coordinates) to uniquely determine the position of a point in the space[7]

See also[edit]

references[edit]

  1. stackoverflow question: how-can-i-display-a-2d-binary-matrix-as-a-black-white-plot
  2. wikipedia: Regular_grid
  3. Stuttgart Visualization Course
  4. Image Segmentation Using Topologically Adaptable Surfaces by Tim McInerney and Demetri Terzopoulos. Published in the Proc. CVRMed'97, Grenoble, France, March, 1997.
  5. T-snakes: Topology adaptive snakes by Tim McInerney , Demetri Terzopoulos. Medical Image Analysis 4 (2000) 73–91
  6. gnuplot docs: grid
  7. wikipedia : coordinate system