Friday, July 31, 2009

delaunayn

n-D Delaunay tessellation

Syntax

  • T = delaunayn(X)

Description

T = delaunayn(X) computes a set of simplices such that no data points of X are contained in any circumspheres of the simplices. The set of simplices forms the Delaunay tessellation. X is an m-by-n array representing m points in n-D space. T is a numt-by-(n+1) array where each row contains the indices into X of the vertices of the corresponding simplex.

Visualization

Plotting the output of delaunayn depends of the value of n:

  • You cannot plot delaunayn output for n > 3.

Example

This example generates an n-D Delaunay tessellation, where n = 3.

  • d = [-1 1];
    [x,y,z] = meshgrid(d,d,d); % A cube
    x = [x(:);0];
    y = [y(:);0];
    z = [z(:);0];
    % [x,y,z] are corners of a cube plus the center.
    X = [x(:) y(:) z(:)];
    Tes = delaunayn(X)

    Tes =
    9 1 5 6
    3 9 1 5
    2 9 1 6
    2 3 9 4
    2 3 9 1
    7 9 5 6
    7 3 9 5
    8 7 9 6
    8 2 9 6
    8 2 9 4
    8 3 9 4
    8 7 3 9

You can use tetramesh to visualize the tetrahedrons that form the corresponding simplex. camorbit rotates the camera position to provide a meaningful view of the figure.

  • tetramesh(Tes,X);camorbit(20,0)



Algorithm

delaunayn is based on Qhull [2],. It uses the Qhull joggle option ('QJ'). For information about qhull, see http://www.geom.umn.edu/software/qhull/. For copyright information, see http://www.geom.umn.edu/software/download/COPYING.html.

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