Fractals/Computer graphic techniques/2D/grid
The domain has been discretized into a mesh and then rasterized to the image
Image Edit
Digital image
 binary image ( 1bit color)^{[1]}
 grayscale image
 color image

binary ( 1 bit) image

8bit grayscale image

24bit color image
grid Edit
 grid^{[2]}^{[3]}^{[4]}^{[5]}
 tiling
 tesselation of the plane
 Set partitions
 Lattice
 Mesh
 checkerboard
see aslo:
 ruler
 axis
Dimension Edit
 2D
 3D
Types Edit
classify grids is by their basic grid elements:^{[6]}
 regular mesh = Structured grid = global grid ( finite differences)
 a quadrilateral grid is most common in structured grids
 quadratic = rectangular mesh
 a triangular mesh : triangles are one of the most basic and standard ways to draw all kinds of meshes and shapes
 "the CoxeterFreudenthal triangulation. It is constructed by dividing space using a uniform cubic grid and the triangulation is obtained by subdividing each cube." ^{[7]}^{[8]}
 hexagonal
 a quadrilateral grid is most common in structured grids
 An unstructured = irregular grid, adaptive grid, local grid ( fast marching methods). Grid Refinement = Adaptive Meshes
 Quadtree Grid
 BSP tree
 A triangular surface mesh is always quick and easy to create. It is most common in unstructured grids.
 Spatially adaptive Fibonacci grids

Basic 2D Cell Shapes

Basic 3D Cell Shapes
tilings by regular polygons: regular (=structured ) grid

triangular: the CoxeterFreudenthal triangulation

quadratic

Hexagonal tiling
triangulation Edit
 Surface_triangulation
 Category:Triangulation_(geometry) in commons
 Category:Triangulation_(geometry) in wikipedia
 Delaunay_triangulation in wikibooks
 CONREC A Contouring Subroutine Written by Paul Bourke July 1987 ( using triangulation)  surface represented as a regular triangular mesh
 delaunator  A really fast JavaScript library for Delaunay triangulation of 2D points

Illustration of a dolphin, represented with triangles.


Applications Edit
 For morphing images the Delaunay triangulation provides a 'good' way to create a triangular mesh from points that are going to be moved. Each triangle can be distorted in a simple way, leading to a complex 'morphing' distortion of the overall image. In the example of morphing shown, the triangular shapes are distorted from one image to the next, so for example the hair in the first image is distorted to fit the hair in the second. At the same time as that happens, the colours 'cross fade' from one colour to another so the grey cross fades to brown.
Sierra Nevada terrain map  2D triangular mesh  2D solution calculated from mesh 
 For modelling terrain or other objects given a set of sample points, the Delaunay triangulation gives a nice set of triangles to use as polygons in the model. In particular, the Delaunay triangulation avoids narrow triangles (as they have large circumcircles compared to their area).
 Delaunay triangulations are used in many other applications where a shape has to be divided up into triangles. Analysis of stresses and strains in structures is often done using a triangular mesh. In the analysis shown above, more points are put in the area of most interest to get a finer more detailed analysis in that area. That's also what we do when morphing images  we put more points where we want most control over the fine details of the morphing. If you want to change a frown into a smile, put more points around the mouth so you can change the shape more easily.
Pixel connectivity Edit
Pixel connectivity in wikipedia

Square 4 connectivity

Square 8 connectivity

Hexagonal 6 connectivity
creating Edit
 gnuplot ^{[9]}
mesh Edit
A mesh is a representation of a larger geometric domain by smaller discrete cells.
Types by cells:
 polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object.
 The faces usually consist of triangles (triangle mesh)
 quadrilaterals (quads)
 simple convex polygons (ngons)
Software
 openmesh  A generic and efficient polygon mesh data structure ( C++)
 meshlab
 paraview
 The Polygon Mesh Processing Library is a modern C++ opensource library for processing and visualizing polygon surface meshes. demo
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^{[10]}
See also Edit
 Tessellation is the process of partitioning space into a set of smaller polygons.
 commons:Category:Mesh in computer graphics
 wikipedia: Grid cell topology
 Pathfinding
 Triangle strip is a series of connected triangles, sharing vertices, allowing for more efficient memory usage for computer graphics.
 transformations
 rasterisation
 dimensionaware rasterising ^{[11]}
 plane decomposition
 tiling
references Edit
 ↑ stackoverflow question: howcanidisplaya2dbinarymatrixasablackwhiteplot
 ↑ wikipedia: Regular_grid
 ↑ Stuttgart Visualization Course
 ↑ Amit Patel : gridsin game programming
 ↑ log polar graph paper by Claude
 ↑ ThreeDimensional Mesh Generation for Device and Process Simulation by Johann Cervenka
 ↑ Image Segmentation Using Topologically Adaptable Surfaces by Tim McInerney and Demetri Terzopoulos. Published in the Proc. CVRMed'97, Grenoble, France, March, 1997.
 ↑ Tsnakes: Topology adaptive snakes by Tim McInerney , Demetri Terzopoulos. Medical Image Analysis 4 (2000) 73–91
 ↑ gnuplot docs: grid
 ↑ wikipedia : coordinate system
 ↑ dimensionawarerasterising by TGlad