# Fractals/Computer graphic techniques/2D/grid

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

## ImageEdit

Digital image

- binary image ( 1-bit color)
^{[1]} - grayscale image
- color image

# gridEdit

- grid
^{[2]}^{[3]}^{[4]} - mesh
- tiling
- tesselation of the plane
- Set partitions

- Lattice

## DimensionEdit

- 2D
- 3D

## TypesEdit

- regular mesh = Structured grid = global grid ( finite differences)
- a quadrilateral grid is most common in structured grids
- quadratic = rectangular mesh

- 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."
^{[5]}^{[6]}

- "the Coxeter-Freudenthal triangulation. It is constructed by dividing space using a uniform cubic grid and the triangulation is obtained by subdividing each cube."
- hexagonal

- a quadrilateral grid is most common in structured grids
- 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 connectivityEdit

Pixel connectivity in wikipedia

## creatingEdit

- gnuplot
^{[7]}

# coordinate systemEdit

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^{[8]}

# See alsoEdit

- 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
- dimension-aware rasterising
^{[9]}

- dimension-aware rasterising

# referencesEdit

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