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
{i_{1},i_{2},...} meaning that the i1^{th}, i2^{th}, 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
{{x_{1},y_{1},..},{x_{2},y_{2},..},..} 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 {{i_{11},i_{12},..},
{i_{21},i_{22},..} where the k^{th} facet is formed by points
{i_{k1},i_{k2},..}. 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
{{i_{1}, {j_{11},j_{12},..}
{i_{2}, {j_{21},j_{22},..}
,..}
where i_{k} is an integer representing the k^{th} vertex in the convex hull (meaning
that it is the k^{th} point supplied to convexHull), and
j_{k1},j_{k2},.. are the indices of vertices in the convex hull for which there is a edge of the convex hull conected to
vertex i_{k}. This option may only be requested for three-dimensional data.

The list of facet normals is a list {{x_{1},y_{1},z_{1},offset_{1}},
{x_{2},y_{2},z_{2},offset_{2}},..} 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.

[20-Dec-2005]