# 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