delaunayTriangulation | mPower Reference Home |

delaunayTriangulation[{{x1,y1},{x2,y2}, ...}, options] computes the Delaunay Triangulation using qhull (qdelaunay). It returns an option list as specified by the value of the option delaunayFormat. If any of the options in delaunayFormat are False the the corresponding portion of the return value of delaunayTriangulation is not returned.

Options for delaunayTriangulation:

traceqhull→False - if True, messages will be printed summarizing the data and execution process.

delaunayFormat→ list of options describing the type of output requsted.

keepDelaunayFiles→False: if True, temporary files created during the interface with qhull (the input and output files of qdelaunay) are not deleted.

The value returned by delaunayTriangulation has the format:{ edges→{{iwhere:_{1},j_{1}},{i_{2},j_{2}},..} edgeCoordinates→ {{{x_{11},y_{11},z_{11}},{x_{12},y_{12},z_{12}}}, {{x_{21},y_{21},z_{21}},{x_{22},y_{22},z_{22}}},..} regions→{{i_{11},i_{12},...},{i_{21},i_{22},...},...} regionCoordinates→ {{{x_{11},y_{11},z_{11}},{x_{12},y_{12},z_{12}},...}, {{x_{21},y_{21},z_{21}},{x_{22},y_{22},z_{22}},...},...} statistics→{mean, median, standard-deviation} }

The edges pairs {i_{k},j_{k}} are pairs of integers indicating that
the Delaunay Triangulation of the points contains an edge connecting the points i_{k},j_{k}. The edges are listed with the first index smaller than the second index and in increasing numerical order.

The list of edgeCoordinates give the Cartesian Coordinates of the edges in the same order as in edges.

The list of regions give the indices of the points defining each region in the Delaunay Triangulation. The points in the regions are not ordered, i.e, one can not assume that one traverses the edge of the polygon sequentially. [ In 2D the polygons are triangles, so this comment does not apply.]

The list of regionCoordinates gives the coordinates of the points defining each region in the Delaunay Triangulation.

The statistics give the average, median, and standard deviation of the lengths of the edges in the Delaunay Triangulation.

Example

See also:

[23-Dec-2005]