Various related geometric concepts :
- Convex Hull :
- It's a polytope that encloses the point set S.
- Alpha-Ball :
- Alpha-ball b is an open ball with
radius alpha.
- e.g. 0-ball is a point and infinite ball is an open half
space.
- An alpha-ball is empty if intersection of b
with S is null.
- K-Simplex :
- The convex hull of any subset T
of S is a k-Simplex,
- if |T| = k+1
for 0 <= k <=3.
- Alpha-Exposed k-Simplices :
- For 0 <= k <= 2, a k-simplex
is said to be alpha-exposed if
- there is an empty alpha ball b
where T is the extension of S
- and the sphere or plane bounding b.
- Alpha-Shape :
- Alpha-Shape of S is a polytope
whose boundary consists of
- triangles in 2-Simplices, edges in 1-simplices and the
- vertices in 0-Simplices. It is not necessarily convex
and nor
- connected.
- Alpha-Hull :
- Complement of the union of all empty balls is the Alpha-Hull
- of surface. This is the formal counterpart of the styrofoam
- object we have been talking about.
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