In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points. They were first defined by Edelsbrunner, Kirkpatrick & Seidel (1983). The alpha-shape associated with a set of points is a generalization of the concept of the convex hull, i.e.…
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Alpha shape topic overview
The analysis highlights Characters, Characterization and Alpha complex as prominent areas in the source structure around Alpha shape.
Related topics
20
Source areas
4
Connected nodes
24
Extracted relationships
55
Concept neighborhoods
11
Bridge connections
24
What this topic covers Research coverage
Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.
Alpha complex · 6 topics
Characterization · 5 topics
Examples · 5 topics
Overview · 4 topics
Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Suggested research paths
A focused starting point derived from the topic graph, ranked independently of the source article order.
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.
Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
How Alpha shape connects Entity context
Entity context groups extracted connections by relationship type. Counts show recurrence in the analyzed source; the examples are research signals, not claims about importance.
The extracted context around Alpha shape shows recurring relationship patterns in the source. For example, Alpha shape → Akkiraju, Alpha, Bangalore, Berlin, Comput, David, Edelsbrunner, Facello, Foundations, Fu, Geom, Herbert, IEEE Transactions, In Proc, Information Theory, Internat, Kirkpatrick, Lecture Notes, Minneapolis, MR Another extracted example is Alpha shape → Alpha Shapes, Ask, But Were Afraid, CGAL, Complex, Computational Geometry Algorithms LibraryAlpha, Description, Duke UniversityEverything You Always, GUDHI, Hulls, Know About Alpha Shapes, Louis, RDescription, Robert Pless, Shapes, St, Wanted, Washington University, Weighted. Use these groups to spot repeated connection types before inspecting the individual relationships.
Relationships are represented as Subject → Predicate → Object triples. Confidence describes extraction strength, not the real-world importance of a relationship; lower-confidence rows may be contextual rather than explicit.
TTTA extracted 55 structured relationships around Alpha shape. Examples in this analysis include Alpha shape → is a → convex hull and Alpha shape → related to Alpha complex → Alpha. The table shows each extracted connection, where it came from and its confidence.
Subject
Predicate
Object
Confidence
Src
Alpha shape
is a
convex hull
0.90
text
Alpha shape
related to Alpha complex
Alpha
0.60
section
Alpha shape
related to Alpha complex
Delaunay
0.60
section
Alpha shape
related to Alpha complex
Each
0.60
section
Alpha shape
related to Alpha complex
For
0.60
section
Alpha shape
related to Alpha complex
The
0.60
section
Alpha shape
related to External links
Alpha Shapes
0.60
section
Alpha shape
related to External links
CGAL
0.60
section
Alpha shape
related to External links
Computational Geometry Algorithms LibraryAlpha
0.60
section
Alpha shape
related to External links
Complex
0.60
section
Alpha shape
related to External links
GUDHI
0.60
section
Alpha shape
related to External links
Description
0.60
section
No triples extracted yet.
Related concept clusters Concept neighborhoods
Concept neighborhoods group terms that sit near one another in the extracted graph. They are useful for discovering adjacent language and context, but proximity does not by itself imply a factual relationship.
The concept neighborhoods around Alpha shape bring nearby vocabulary together. In this analysis, examples include Displaystyle, Set and Shapes. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
Alpha shape
Displaystyle
Set
Shapes
Shape
-complex
Alpha-shape
Complex
Point
Points
Finite
Associated
Closely
alpha shape
Displaystyle
Set
Shapes
Shape
-complex
Alpha-shape
Complex
Point
Points
Finite
Associated
Closely
alpha complex
Displaystyle
Number
Real
Set
Shapes
-complex
Shape
Alpha-shape
Complex
Point
Points
Finite
simplicial complex
Number
Real
Displaystyle
-complex
Computational
Concept
Disk
Edges
Formed
Generalized
Geometry
Radius
čech complex
Number
Real
Displaystyle
-complex
Computational
Concept
Disk
Edges
Formed
Generalized
Geometry
Radius
edelsbrunner, kirkpatrick & seidel (1983)
Seidel
Kirkpatrick
Plane
Shape
First
Related
Two
Points
Software
-complex
Set
Shapes
delaunay triangulation
Delaunay
Triangulation
Closely
Edge
Related
Radius
Associated
Point
Shapes
Set
Alpha
computational geometry
Geometry
Plane
Finite
Associated
Complex
Shapes
Alpha
Points
Shape
Set
Connections between topic areas Semantic bridges
Semantic bridges connect parts of the graph that would otherwise be more separate. A bridge is a structural signal in this analysis, not a claim that the two topic areas are equivalent.
For Alpha shape, one of the stronger structural bridges in this analysis connects Alpha shape with Alpha complex. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.
Alpha shape
Nodes25
Edges24
Triples55
Avg. degree1.92
Density0.08
Components1
Source & methodology
TTTA analyzes the structure around Alpha shape to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Characters, Characterization & Alpha complex, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
