Syntax
Description
TES = delaunay3(x,y,z)
returns an array TES
, each row of which contains the indices of the points in (x,y,z)
that make up a tetrahedron in the tessellation of (x,y,z)
. TES
is a numtes
-by-4
array where numtes
is the number of facets in the tessellation. x
, y
, and z
are vectors of equal length. If the original data points are collinear or x
, y
, and z
define an insufficient number of points, the triangles cannot be computed and delaunay3
returns an empty matrix.
Visualization
Use tetramesh
to plot delaunay3
output. tetramesh
displays the tetrahedrons defined in TES
as mesh. tetramesh
uses the default tranparency parameter value 'FaceAlpha' = 0.9
.
Example
This example generates a 3-D Delaunay tessellation, then uses tetramesh
to plot the tetrahedrons that form the corresponding simplex. camorbit
rotates the camera position to provide a meaningful view of the figure.
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.
Tes = delaunay3(x,y,z)
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
X = [x(:) y(:) z(:)];
tetramesh(Tes,X);camorbit(20,0)
Algorithm
delaunay3
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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