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convexHullFormat mPower Reference Home

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


is an option for convexHull. It controls the format of the data object returned by convexHull which is itself an option list of the form:

	{
	vertices→list of vertices,
	vertexCoordinates→list of vertex coordinates,
	facets→list of facets,
	convexHullEdges→list of edges of convex hull,
	convexHullNeighboringVertices→list of neighboring vertices for each
		vertex of the convex hull,
	facetNormals→list of normal vectors to each facet of the convex hull
	}
       
Any given option is only returned if the corresponding option with the same name in convexHullFormat has a value of True.

The list of vertices is a list of integers {i1,i2,...} meaning that the i1th, i2th, etc, elements in the list of points input to convexHull form the convex hull. For two dimensional data, the list will be sorted as sequential vertices along the edge of a polygon if returnClosedRegion→True.

The list of vertex coordinates is a list of coordinates {{x1,y1,..},{x2,y2,..},..} that give the two- or three-dimensionals coordinates of the vertices that form the convex hull.

The list of facets is a list of the form {{i11,i12,..}, {i21,i22,..} where the kth facet is formed by points {ik1,ik2,..}. The indices are not sorted, i.e., they are not given sequentially around the facet. This option may only be requested for three-dimensional data.

The list of neighboring vertices for each vertex in the convex hull is a list of the form {{i1, {j11,j12,..} {i2, {j21,j22,..} ,..} where ik is an integer representing the kth vertex in the convex hull (meaning that it is the kth point supplied to convexHull), and jk1,jk2,.. are the indices of vertices in the convex hull for which there is a edge of the convex hull conected to vertex ik. This option may only be requested for three-dimensional data.

The list of facet normals is a list {{x1,y1,z1,offset1}, {x2,y2,z2,offset2},..} that give normal vectors for each vertex. Each {x,y,z} triple is a unit vector and each offset is the offset of the vector. The vectors point outward from the convex hull. The list of facet normals may only be requested for three-dimensional data.


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[20-Dec-2005]