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.

Square grid
100 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
9 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
16 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
25 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
36 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
49 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
64 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
81 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)

Lattice points
100 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
9 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
16 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
25 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
36 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
49 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
64 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
81 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)

Points inside a square
10 points

Objective: min (sum of surface area)
20 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
30 points
Objective: min (sum of surface area)
40 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
50 points
Objective: min (sum of surface area)
60 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
70 points
Objective: min (sum of surface area)
80 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
90 points
Objective: min (sum of surface area)
100 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
110 points
Objective: min (sum of surface area)
120 points
Objective: min (sum of surface area)
130 points
Objective: min (sum of surface area)
140 points
Objective: min (sum of surface area)
150 points
Objective: min (sum of surface area)
160 points
Objective: min (sum of surface area)
170 points
Objective: min (sum of surface area)
180 points
Objective: min (sum of surface area)
200 points
Objective: min (sum of surface area)
220 points
Objective: min (sum of surface area)
240 points
Objective: min (sum of surface area)
260 points
Objective: min (sum of surface area)
280 points
Objective: min (sum of surface area)
300 points
Objective: min (sum of surface area)
320 points
Objective: min (sum of surface area)

Cyclic polytope
10 points

Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
20 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
30 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)
40 points
Objective: min (maximum aspect ratio)
Objective: min (sum of surface area)


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