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Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2
BigObject SubdivisionOfPoints<Scalar>
from application fan
The inhomogeneous variant of SubdivisionOfVectors
, similar to the derivation of PointConfiguration
from VectorConfiguration
.
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.
-
N_POINTS
- Type:
-
POINTS
The points of the configuration. Multiples allowed. Alias for property
VECTORS
.- Type:
Matrix<Scalar,NonSymmetric>
-
POLYHEDRAL_COMPLEX
The polyhedral complex induced by the cells of the subdivision.
- Type:
PolyhedralComplex<Scalar>
-
REGULAR
Whether the subdivision is regular, i.e. induced by a weight vector.
- Type:
-
TIGHT_SPAN
The tight span of the subdivision.
- Type:
PolyhedralComplex<Scalar>
-
UNIMODULAR
A subdivision is unimodular if it is a triangulation such that each maximal simplex has unit normalized volume.
- Type:
- Example:
Unit square, triangulated.
> $S = new SubdivisionOfPoints(POINTS=>cube(2,0)->VERTICES, WEIGHTS=>[0,0,0,1]); > print $S->UNIMODULAR true
- Example:
Unit 3-cube, triangulation induced by four compatible vertex splits.
> $S = new SubdivisionOfPoints(POINTS=>cube(3,0)->VERTICES, WEIGHTS=>[0,1,1,0,1,0,1,0]); > print $S->UNIMODULAR false
-
WEIGHTS
Vector assigning a weight to each point to get a regular subdivision.
- Type:
Vector<Scalar>
Visualization
These properties are for visualization.
-
POINT_LABELS
Unique names assigned to the
POINTS
. If specified, they are shown by visualization tools instead of point indices. Alias for propertyLABELS
.- Type:
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.
-
AMBIENT_DIM
Ambient dimension of the point configuration (without the homogenization coordinate). Similar to
AMBIENT_DIM
.
-
DIM
Affine dimension of the point configuration. Similar to
DIM
.
-
cell(Int i)
Returns the i-th cell of the complex as a
PointConfiguration
- Parameters:
Int
i
- Returns:
Visualization
These methods are for visualization.
-
VISUAL()
Visualizes the
SubdivisionOfPoints
.- Options:
- option list
geometric_options
- Returns: