Set of balls (or even better blobs) enclosing a 3d set of points

Set of balls (or even better blobs) enclosing a 3d set of points

Post by Marc Sokolows » Fri, 18 Aug 1995 04:00:00



        Hi all,

        I am sure this is a nice linear programming problem. The set of 3d
points defines a certain volume, and we can disregard the points that end up
being inside this volume.... now how to choose a close to optimal
combination of balls filling this volume to the fullest (say limiting the
miniumum size a ball can have). Also is there a way to use blobs, so that
the surface can be smoother between the shere and shaped by both positive or
negative forces???
        Anyway, I posted an article earlier about triangulation, but I don't
think it will work for my model.... so I am turning to sheres now! So I will
be glad if somebody could tell me if an a;lgorithm exists so that given a
set of 3d points listed by their coordinates
x1 y1 z1
x2 y2 z2
...
xn yn zn

we get a set of balls
x1 y1 z1 d1
x2 y2 z2 d2
...
xm ym zm dm

where xyz is the center and d the diameter
or even better
x1 y1 z1 d1 f1
...
where f is the "force" field so that the volume defined by the set of points
is best approximated by thos spheres (or blobs)...

                        TIA,

                                        Marc
--
"Error #132: Cannot exit from Windows, try the door"
                Edouard Shtrutsrup, "Jokes only programmers can understand"
Marc Sokolowski

 
 
 

1. Set of balls (or even better blobs) enclosing a 3d set of points

        Hi all,

        I am sure this is a nice linear programming problem. The set of 3d
points defines a certain volume, and we can disregard the points that end up
being inside this volume.... now how to choose a close to optimal
combination of balls filling this volume to the fullest (say limiting the
miniumum size a ball can have). Also is there a way to use blobs, so that
the surface can be smoother between the shere and shaped by both positive or
negative forces???
        Anyway, I posted an article earlier about triangulation, but I don't
think it will work for my model.... so I am turning to sheres now! So I will
be glad if somebody could tell me if an a;lgorithm exists so that given a
set of 3d points listed by their coordinates
x1 y1 z1
x2 y2 z2
...
xn yn zn

we get a set of balls
x1 y1 z1 d1
x2 y2 z2 d2
...
xm ym zm dm

where xyz is the center and d the diameter
or even better
x1 y1 z1 d1 f1
...
where f is the "force" field so that the volume defined by the set of points
is best approximated by thos spheres (or blobs)...

                        TIA,

                                        Marc
--
"Error #132: Cannot exit from Windows, try the door"
                Edouard Shtrutsrup, "Jokes only programmers can understand"
Marc Sokolowski

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