All Questions
Tagged with packing-problem computational-geometry
16
questions
0
votes
2
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52
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Sum of fractions in the form $\frac{1}{n}$ from $\frac{1}{2^n}$ to $\frac{1}{3*2^{(n-1)} - 1}$ less than $\frac{1}{2}$?
https://mathoverflow.net/a/278290/501460
I've been trying to figure out why this works, and why the tiles don't go past the middle, considering all the squares together have an infinite side length.
...
- 3
1
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0
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237
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Packing maximum number of identical rectangles in a polygon
Given a 2D polygon, convex or nonconvex, maybe some holes (also small polygons) inside. How can we pack an (approximately) maximum number of identical rectangles in the polygon (the rectangle can not ...
- 61
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2
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841
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Volume of air in the box (packing problem)
Suppose I have a box with dimensions $L \times W \times H$.
What is the volume of air in the box, if I pack balls with radii $r$?
With increase of radius, does volume of air decrease?
- 2,319
1
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1
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87
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Up to 6 points spaced $r$ apart can fit on a rectangle of dimensions $(r,2r)$
Consider a rectangle of dimensions $(r,2r)$. Is it true that one can place only up to 6 points spaced at least $r$ apart from one another in or on the rectangle?
One can place the 6 points on the ...
- 1,279
1
vote
1
answer
240
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Nesting Problem: Randomly-Generated Rectangles In Series Within Larger Rectangle
How efficiently can randomly-generated rectangles be nested within a larger rectangle of defined width (say, 30”) and fairly long length, where each inner rectangle must be placed/nested permanently ...
- 11
5
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1
answer
958
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What's the maximum number of points at distance r or more inside a d-dimensional sphere of radius r?
We have a sphere of radius $r$ in a $d$-dimensional space. What is the maximum amount of points that I can fit inside the sphere such as the distance between any pair of points is at least $r$? And ...
- 63
1
vote
1
answer
699
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Smallest enclosing cylinder
I have a set of 3D points that approximately lie on a cylinder. This cylinder is straight and can be oriented in any direction. I would like to compute the minimal enclosing cylinder for the set; that ...
- 5,007
5
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199
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packing problem of semicircles into rectangle
I have problem. How can I get the maximum amount of semicircles (for example radius $35\;mm$) into rectangle $(485\times 185\:mm)$.
I found many articles about packing of circles but nothing about ...
- 51
1
vote
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292
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population of dots with normal distribution of pitch
I want to generate a plot that shows a rectangle populated with dots, where the dot-to-dot distance (pitch) distribution is a lognormal (or a gaussian). I want to be able to change the mean dot-to-dot ...
- 111
8
votes
2
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822
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Visual illustrations of circle packing theorem?
Circle packing theorem states:
For every connected simple planar graph G there is a circle packing in the plane whose intersection graph is (isomorphic to) G.
Paper Collins, Stephenson: A circle ...
- 16k
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votes
1
answer
119
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Packingof Spheres in 3D
I am looking to find out the size of the largest sphere , that can fit in the voids created by packing spheres ( hcp) of radius R.
user9591
2
votes
1
answer
942
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Circle Packing: Unsolved Problem in Geometry?
Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for non-...
- 9,666
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votes
1
answer
1k
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Radius of circle coverage of n circles in square packing configuration
Is there a reference about determining the minimum radius of a circle that would cover n circles of radius 1 that are in a square packing configuration ( see Wolfram's MathWorld packing packing ...
- 101
3
votes
1
answer
4k
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How many rectangles can fit in a polygon with n-sides?
I am trying to write an algorithm to solve a problem I have. I have a few ideas of what the algorithm might be like but I am posting to see if anyone else has a better more efficient solution or any ...
- 999
5
votes
1
answer
2k
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Circle Packing Algorithm
I have question related to circle-packing. The problem is to find the circle of minimum radius enclosing four non-overlapping circles of arbitrary radius. I have to write a program in C for this ...
