Differences

This shows you the differences between two versions of the page.

--- playground:playground [2019/03/01 15:59] – oroehrig
+++ playground:playground [2020/05/21 12:24] (current) – removed benmuell
@@ Line 1: / Line 1: @@
-====== BigObject PointConfiguration ======
- The [[/polytope/objects/PointConfiguration/properties/Input property/POINTS]] of an object of type PointConfiguration encode a not necessarily convex finite point set.
- The difference to a parent [[/polytope/objects/Geometry/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 ==
-kjsaf
-Polytopal Subdivision of the point configuration
-=== POLYTOPAL_SUBDIVISION ===
-oahf
-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
-    [[/polytope/objects/Polytope/properties/Visualization/VIF_CYCLIC_NORMAL]] of the [[/polytope/objects/PointConfiguration/properties/Geometry/CONVEX_HULL]], but with
- the indices form [[/polytope/objects/PointConfiguration/properties/Input property/POINTS]] instead of [[/polytope/objects/Polytope/properties/Geometry/VERTICES]]
-  * **POINT_LABELS** : /common/property_types/Basic Types/Array
-    Unique names assigned to the [[/polytope/objects/PointConfiguration/properties/Input property/POINTS]].
- Alias for property [[/polytope/objects/Geometry/VectorConfiguration/properties/Visualization/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 [[/polytope/objects/Geometry/VectorConfiguration/properties/Input 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 [[/polytope/objects/PointConfiguration/properties/Input property/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 [[/polytope/objects/Polytope/properties/Geometry/VERTICES]] of the [[/polytope/objects/PointConfiguration/properties/Geometry/CONVEX_HULL]] as [[/polytope/objects/PointConfiguration/properties/Input property/POINTS]]
-  * **N_POINTS** : /common/property_types/Basic Types/Int
-    Number of [[/polytope/objects/PointConfiguration/properties/Input property/POINTS]].
- Alias for property [[/polytope/objects/Geometry/VectorConfiguration/properties/Geometry/N_VECTORS]].
-  * **NON_VERTICES** : /common/property_types/Set Types/Set
-    [[/polytope/objects/PointConfiguration/properties/Input property/POINTS]] that are not [[/polytope/objects/Polytope/properties/Geometry/VERTICES]] of the [[/polytope/objects/PointConfiguration/properties/Geometry/CONVEX_HULL]]
-  * **MULTIPLE_POINTS** : /common/property_types/Basic Types/Bool
-    Tells if multiple points exist.
- Alias for property [[/polytope/objects/Geometry/VectorConfiguration/properties/Geometry/MULTIPLE_VECTORS]].
-  * **FAR_POINTS** : /common/property_types/Set Types/Set
-    Indices of [[/polytope/objects/PointConfiguration/properties/Input property/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 [[VectorConfiguration::GROUP
-=== Combinatorics ===
- These properties capture combinatorial information of the object.
- Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.
-  * **SIMPLEXITY_LOWER_BOUND** : /common/property_types/Basic Types/Int
-    A lower bound for the minimal number of simplices in a triangulation
-  * **MAX_BOUNDARY_SIMPLICES** : /common/property_types/Basic Types/Array
-    Tells the full-dimensional simplices on the boundary that contain no points except for the vertices.
-  * **MAX_INTERIOR_SIMPLICES** : /common/property_types/Basic Types/Array
-    Tells the full-dimensional simplices that contain no points except for the vertices.
-  * **N_MAX_INTERIOR_SIMPLICES** : /common/property_types/Basic Types/Int
-    Tells the number of MAX_INTERIOR_SIMPLICES
-  * **COCIRCUIT_EQUATIONS** : /common/property_types/Algebraic Types/SparseMatrix
-    Tells the cocircuit equations that hold for the configuration, one for each interior ridge
-  * **SPLITS** : /common/property_types/Algebraic Types/Matrix
-    The splits of the point configuration, i.e., hyperplanes cutting the configuration in
- two parts such that we have a regular subdivision.
-  * **INTERIOR_RIDGE_SIMPLICES** : /common/property_types/Basic Types/Array
-    Tells the number of codimension 1 simplices that are not on the boundary
-  * **GRAPH** : /graph/objects/Combinatorics/Graph
-    Graph of the point configuration.
- Two points are adjacent if they are neigbours in a edge of the [[/polytope/objects/PointConfiguration/properties/Geometry/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 [[/polytope/objects/PointConfiguration/properties/Combinatorics/SPLITS]] are compatible if the defining hyperplanes do not intersect in the
- interior of the point configuration.  This defines a graph.