f**n
发帖数: 155 | 1 Let's say there is an arbitrary shape in a 3D volume. How to fill the shape
using an ellipsoid with much smaller size? Additional constraints are:
1. The 3D shape must be fully covered. Overlap of ellipsoids are allowed.
2. The number of used ellipsoids is minimized.
Any thought?
Thanks! |
e***e
发帖数: 3872 | 2 interesting problem.
misfilling criteria? any regularity constraints on the volume?
i guess with a well regularized volume, you could apply some tricks like
spectrum analysis or ellipsoid decomposition.
shape
【在 f**n 的大作中提到】
: Let's say there is an arbitrary shape in a 3D volume. How to fill the shape
: using an ellipsoid with much smaller size? Additional constraints are:
: 1. The 3D shape must be fully covered. Overlap of ellipsoids are allowed.
: 2. The number of used ellipsoids is minimized.
: Any thought?
: Thanks!
|
f**n
发帖数: 155 | 3 It doesn't need to be a tight filling. That is to say the outside of the 3D
shape may also be covered, but the fewer the better.
How to apply spectrum analysis to this problem? |
e***e
发帖数: 3872 | 4 but still one formalization of the error and the regularity constrains is
necessary, i think.
3D
【在 f**n 的大作中提到】
: It doesn't need to be a tight filling. That is to say the outside of the 3D
: shape may also be covered, but the fewer the better.
: How to apply spectrum analysis to this problem?
|
f**n
发帖数: 155 | 5 Your right. One more condition, all the ellipsoids have the same orientation
besides size.
is
【在 e***e 的大作中提到】
: but still one formalization of the error and the regularity constrains is
: necessary, i think.
:
: 3D
|
e***e
发帖数: 3872 | 6 it's still problematic. but you could, for example, think of a solution
using PCA, taking a constructive solid geometry representation of the
shape under processing. the solution is then always a trade-off between
number of ellipsoids and the precision of coverage.
orientation
【在 f**n 的大作中提到】
: Your right. One more condition, all the ellipsoids have the same orientation
: besides size.
:
: is
|
