IP-based Triangulation of a Point Configuration in 3D


Some examples:
The applets are developed using JDK1.1, and you should use Netscape4.0+patch for JDK1.1, MS-IE4.0, or HotJava 1.1.

Dodecahedron

Objective: min (cardinality)
Objective: max (cardinality)

Icosidodecahedron

Objective: min (cardinality)
Objective: max (cardinality)

Truncated Octahedron

Objective: min (cardinality)
Objective: max (cardinality)

Square grid
8 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
Objective: max (cardinality)
12 points
Objective: min (cardinality)
Objective: max (cardinality)
16 points
Objective: min (cardinality)
Objective: max (cardinality)
18 points
Objective: min (cardinality)
Objective: max (cardinality)
20 points
Objective: min (cardinality)
Objective: max (cardinality)
24 points
Objective: min (cardinality)
Objective: max (cardinality)
27 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
36 points
Objective: min (cardinality)
48 points
Objective: min (cardinality)

Lattice points
8 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
27 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)

Points inside a cube
10 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
Objective: max (cardinality)
Objective: min (maximum solid angle)
Objective: min (maximum circumscribed sphere)
Objective: min (maximum minimum-enclosing sphere)
20 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
Objective: max (cardinality)
30 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
40 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
50 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
60 points
Objective: min (sum of surface area)

Points on a cylinder face
10 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
Objective: min (maximum solid angle)
Objective: min (maximum circumscribed sphere)
Objective: min (maximum minimum-enclosing sphere)
20 points
Objective: min (sum of surface area)
Objective: min (cardinality)
30 points
Objective: min (maximum aspect ratio)

Cyclic polytope
5 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
6 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
7 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
8 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
9 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
10 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
Objective: max (cardinality)
20 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
Objective: max (cardinality)
30 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)
40 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
Objective: min (cardinality)


If you have some questions or comments, please send e-mail to
tajima@trl.ibm.co.jp
or
akira@is.s.u-tokyo.ac.jp