This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== BigObject SubdivisionOfPoints<Scalar> ====== //from application [[..:fan|fan]]//\\ \\ The inhomogeneous variant of ''[[..:fan:SubdivisionOfVectors |SubdivisionOfVectors]]'', similar to the derivation of ''[[..:polytope:PointConfiguration |PointConfiguration]]'' from ''[[..:polytope:VectorConfiguration |VectorConfiguration]]''. ? Type Parameters: :: ''Scalar'': default: ''[[..:common#Rational |Rational]]'' ? derived from: : ''[[..:fan:SubdivisionOfVectors |SubdivisionOfVectors]]'' ? Example: :: To produce a regular subdivision of the vertices of a square: :: <code perl> > $c=new SubdivisionOfPoints(POINTS=>polytope::cube(2)->VERTICES,WEIGHTS=>[0,0,0,1]); > print $c->MAXIMAL_CELLS; {0 1 2} {1 2 3} </code> ===== Properties ===== ==== Geometry ==== These properties capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets. ---- {{anchor:n_points:}} ? **''N_POINTS''** :: The number of ''[[..:fan:SubdivisionOfPoints#POINTS |POINTS]]'' in the configuration. Alias for property ''[[..:fan:SubdivisionOfVectors#N_VECTORS |N_VECTORS]]''. ? Type: :''[[..:common#Int |Int]]'' ---- {{anchor:points:}} ? **''POINTS''** :: The points of the configuration. Multiples allowed. Alias for property ''[[..:fan:SubdivisionOfVectors#VECTORS |VECTORS]]''. ? Type: :''[[..:common#Matrix |Matrix]]<Scalar,[[..:common#NonSymmetric |NonSymmetric]]>'' ---- {{anchor:polyhedral_complex:}} ? **''POLYHEDRAL_COMPLEX''** :: The polyhedral complex induced by the cells of the subdivision. ? Type: :''[[..:fan:PolyhedralComplex |PolyhedralComplex]]<Scalar>'' ---- {{anchor:regular:}} ? **''REGULAR''** :: Whether the subdivision is regular, i.e. induced by a weight vector. ? Type: :''[[..:common#Bool |Bool]]'' ---- {{anchor:tight_span:}} ? **''TIGHT_SPAN''** :: The tight span of the subdivision. ? Type: :''[[..:fan:PolyhedralComplex |PolyhedralComplex]]<Scalar>'' ---- {{anchor:unimodular:}} ? **''UNIMODULAR''** :: A subdivision is unimodular if it is a triangulation such that each maximal simplex has unit normalized volume. ? Type: :''[[..:common#Bool |Bool]]'' ? Example: :: Unit square, triangulated. :: <code perl> > $S = new SubdivisionOfPoints(POINTS=>cube(2,0)->VERTICES, WEIGHTS=>[0,0,0,1]); > print $S->UNIMODULAR true </code> ? Example: :: Unit 3-cube, triangulation induced by four compatible vertex splits. :: <code perl> > $S = new SubdivisionOfPoints(POINTS=>cube(3,0)->VERTICES, WEIGHTS=>[0,1,1,0,1,0,1,0]); > print $S->UNIMODULAR false </code> ---- {{anchor:weights:}} ? **''WEIGHTS''** :: Vector assigning a weight to each point to get a regular subdivision. ? Type: :''[[..:common#Vector |Vector]]<Scalar>'' ---- ==== Visualization ==== These properties are for visualization. ---- {{anchor:point_labels:}} ? **''POINT_LABELS''** :: Unique names assigned to the ''[[..:fan:SubdivisionOfPoints#POINTS |POINTS]]''. If specified, they are shown by visualization tools instead of point indices. Alias for property ''[[..:fan:SubdivisionOfVectors#LABELS |LABELS]]''. ? Type: :''[[..:common#Array |Array]]<[[..:common#String |String]]>'' ---- ===== Methods ===== ==== Geometry ==== These methods capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets. ---- {{anchor:ambient_dim:}} ? **''AMBIENT_DIM''** :: Ambient dimension of the point configuration (without the homogenization coordinate). Similar to ''[[..:polytope:PointConfiguration#AMBIENT_DIM |AMBIENT_DIM]]''. ---- {{anchor:dim:}} ? **''DIM''** :: Affine dimension of the point configuration. Similar to ''[[..:polytope:PointConfiguration#DIM |DIM]]''. ---- {{anchor:cell:}} ? **''cell([[..:common#Int |Int]] i)''** :: Returns the //i//-th cell of the complex as a ''[[..:polytope:PointConfiguration |PointConfiguration]]'' ? Parameters: :: ''[[..:common#Int |Int]]'' ''i'' ? Returns: :''[[..:polytope:PointConfiguration |PointConfiguration]]'' ---- ==== Visualization ==== These methods are for visualization. ---- {{anchor:visual:}} ? **''VISUAL()''** :: Visualizes the ''[[..:fan:SubdivisionOfPoints |SubdivisionOfPoints]]''. ? Options: : option list ''[[..:common#geometric_options |geometric_options]]'' ? Returns: :''[[..:fan:Visual_PolyhedralFan |Visual::PolyhedralFan]]'' ---- documentation/latest/fan/subdivisionofpoints.txt Last modified: 2023/11/06 10:57by 127.0.0.1