Fractals/Computer graphic techniques/2D/grid

thumb|right|Digital Region Boundary Tracing--start point The domain has been discretized into a mesh and then rasterized to the image Image Digital image binary image ( 1-bit color)stackoverflow question: how-can-i-display-a-2d-binary-matrix-as-a-black-white-plot grayscale image color image grid gridwikipedia: Regular_gridStuttgart Visualization Course Amit Patel : gridsin game programminglog polar graph paper by Claude tiling tesselation of the plane Set partitions Lattice Mesh checkerboard see also: ruler axis Dimension 2D 3D thumb|right|Elements of polygonal 3D mesh Types classify grids is by their basic grid elements:Three-Dimensional Mesh Generation for Device and Process Simulation by Johann Cervenka 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 Coxeter-Freudenthal triangulation. It is constructed by dividing space using a uniform cubic grid and the triangulation is obtained by subdividing each cube." 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 hexagonal 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 tilings by regular polygons: regular (=structured ) grid triangulation 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 Applications 350px|Finite Element Analysis solution of a fluid flow problem 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. 260px230px230pxSierra Nevada terrain map2D triangular mesh2D 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 Pixel connectivity in wikipedia creating gnuplot gnuplot docs: grid mesh 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 (n-gons) Software openmesh - A generic and efficient polygon mesh data structure ( C++) meshlab paraview The Polygon Mesh Processing Library is a modern C++ open-source library for processing and visualizing polygon surface meshes. demo VCG The Visualization and Computer Graphics Library (VCG for short) is a open source portable C++ templated library for manipulation, processing and displaying with OpenGL of triangle and tetrahedral meshes meshio input/output for many mesh formats in python mesh pro commercial Mesh generation in wikipedia coordinate system 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 spacewikipedia : coordinate system See also 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 dimension-aware rasterising dimension-aware-rasterising by TGlad plane decomposition tiling robert heaton : wavefunction-collapse-algorithm references