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BigObject PointConfiguration
The POINTS of an object of type PointConfiguration encode a not necessarily convex finite point set. The difference to a parent VectorConfiguration is that the points have homogeneous coordinates, i.e. they will be normalized to have first coordinate 1 without warning. derived from ['/polytope/objects/Geometry/VectorConfiguration'] specializations: {'PointConfiguration::ExactCoord': {'$text': ' A point configuration with an exact coordinate type, like Rational.\n'}}
Properties
Triangulation and volume
These properties collect information about triangulations of the object and properties usually computed from such, as the volume.
POLYTOPAL_SUBDIVISION
| Type | SimplicialComplex blabla |
| Description | Polytopal Subdivision of the point configuration |
POLYTOPAL_SUBDIVISION
| Type | SimplicialComplex blabla |
| Polytopal Subdivision of the point configuration |
POLYTOPAL_SUBDIVISION
| Type | SimplicialComplex blabla |
| Polytopal Subdivision of the point configuration |
POLYTOPAL_SUBDIVISION
| Type | SimplicialComplex blabla |
| Polytopal Subdivision of the point configuration |
POLYTOPAL_SUBDIVISION
| Type | SimplicialComplex blabla |
| Polytopal Subdivision of the point configuration |
- TRIANGULATION : /polytope/objects/PointConfiguration/properties/Triangulation and volume/TRIANGULATION
Some triangulation of the point configuration.
Visualization
These properties are for visualization.
- PIF_CYCLIC_NORMAL : /common/property_types/Basic Types/Array
VIF_CYCLIC_NORMAL of the CONVEX_HULL, but with the indices form POINTS instead of VERTICES
- POINT_LABELS : /common/property_types/Basic Types/Array
Unique names assigned to the POINTS. Alias for property LABELS.
Input property
These properties are for input only. They allow redundant information.
- POINTS : /common/property_types/Algebraic Types/Matrix
The points of the configuration. Multiples allowed. Alias for property VECTORS.
Geometry
These properties capture geometric information of the object. Geometric properties depend on geometric information of the object, like, e.g., vertices or facets.
- BARYCENTER : /common/property_types/Algebraic Types/Vector
The center of gravity of the point configuration.
- CONVEX : /common/property_types/Basic Types/Bool
True if the POINTS are in convex position.
- CONVEX_HULL : /polytope/objects/PointConfiguration/properties/Geometry/CONVEX_HULL
The polytope being the convex hull of the point configuration.
- VERTEX_POINT_MAP : /common/property_types/Basic Types/Array
Indices of VERTICES of the CONVEX_HULL as POINTS
- N_POINTS : /common/property_types/Basic Types/Int
Number of POINTS. Alias for property N_VECTORS.
- NON_VERTICES : /common/property_types/Set Types/Set
POINTS that are not VERTICES of the CONVEX_HULL
- MULTIPLE_POINTS : /common/property_types/Basic Types/Bool
Tells if multiple points exist. Alias for property MULTIPLE_VECTORS.
- FAR_POINTS : /common/property_types/Set Types/Set
Indices of POINTS that are rays.
- BOUNDED : /common/property_types/Basic Types/Bool
True if the point configuration is bounded.
- AFFINE_HULL : /common/property_types/Algebraic Types/Matrix
Dual basis of the affine hull of the point configuration
- CENTERED : /common/property_types/Basic Types/Bool
True if (1, 0, 0, …) is in the relative interior.
Symmetry
These properties capture information of the object that is concerned with the action of permutation groups.
- GROUP : /polytope/objects/PointConfiguration/properties/Symmetry/GROUP
Augmented subobject CONVEX_HULL.
- N_MAX_BOUNDARY_SIMPLICES : /common/property_types/Basic Types/Int
Tells the number of MAX_BOUNDARY_SIMPLICES
- SPLIT_COMPATIBILITY_GRAPH : /graph/objects/Combinatorics/Graph
Two SPLITS are compatible if the defining hyperplanes do not intersect in the interior of the point configuration. This defines a graph.