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convexHull[{{x1,y1,..},{x2,y2,..},..}, options] calculates the convex hull of a set of points using qhull.

The first argument to convexHull is a list of point coordinates, in either two- or three-dimensions.

The return value is an option list whose elements are controlled by the option convexHullFormat. For example if

convexHullFormat→{vertices→True,vertexCoordinates→True},...}

Then the return value of convexHull will be:

{vertices→{i1,i2,i3,...},
 vertexCoordinates→{{vx1,vy1,..}, {vx2,vy2,..},..},...}

where i1,i2,i3,... are integers identifying vertices (as the i1^th,i2^th,...) point; and {vx1,vy1,...},... are the two- or three-dimensional coordinates of the vertices.

Options for convexHull:

traceqhull→False - if this is True then a debug error trace is turned on.

keepQhullFiles→False - temporary files used during the interface with qHull are normally deleted immediately after use. If keepQhullFiles→True then these files are kept.

convexHullFormat→
   {vertices→True,
   vertexCoordinates→True,
   facets→False,
   returnClosedRegion→True,
   convexHullEdges→ False,
   convexHullNeighboringVertices→False,
   facetNormals→False}

The following figures illustrate the concepts. Click on any of the figures to see a larger view; the example notebook illustrates how to generate these figures. A set of points Convex hull, with vertices highlighted. Convex hull

Example

• View in html
• Mathematica Notebook

See Also:

• delaunayTriangulation
• voronoiDiagram