https://github.com/muellan/packing
benchmark solutions for selected packing problems: circle, rectangle, cube, cuboid, polygon packings
https://github.com/muellan/packing
circle-packing-algorithm circles cubes packing packing-algorithm packing-algorithms packing-benchmarks rectangle-packing rectangles sphere-packing spheres
Last synced: 3 months ago
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benchmark solutions for selected packing problems: circle, rectangle, cube, cuboid, polygon packings
- Host: GitHub
- URL: https://github.com/muellan/packing
- Owner: muellan
- License: other
- Created: 2015-10-27T14:41:21.000Z (over 9 years ago)
- Default Branch: master
- Last Pushed: 2018-06-05T13:19:46.000Z (about 7 years ago)
- Last Synced: 2025-01-27T11:49:57.042Z (5 months ago)
- Topics: circle-packing-algorithm, circles, cubes, packing, packing-algorithm, packing-algorithms, packing-benchmarks, rectangle-packing, rectangles, sphere-packing, spheres
- Homepage:
- Size: 141 MB
- Stars: 30
- Watchers: 3
- Forks: 4
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# AM Packing Benchmarks
This repository contains my personal (putative/quasi-optimum) solutions for many packing problem benchmark instances.
Some of the solutions are also listed on Eckard Specht's excellent website www.packomania.com. He has nice pictures, shortest tours of the items and a contact analysis for each packing. Note that he uses a different file format and normalizes most of the container sizes to 1.
You should also have a look at http://www2.stetson.edu/~efriedma/packing.html.
See below for a list of all benchmarks, tables of all the symbols used, etc.
#### Repository Structure
```
container_type
scenario_type
{overview images}
{benchmark result lists}
item_shape_distribution
{result packing files}
```
#### Conventions
* items : objects to be packed
* container : object(s) enclosing the items
* n : number of items
* i : item index in range [1,n]
* i = 0 : container index
* Containers are centered at the global origin and aligned to the coordinate system axes.
* Symbols referring to container properties start with an uppercase letter.
#### Scenario / Folder Names
* find smallest container for a set of items:
"min-ContainerType(ItemType)"
* find legal arrangement of items in a rigid container:
"ContainerType(ItemType)"
## Inventory
| Scenario | Description |
| -------------------------------- | ----------------------------------------------------------- |
| min-Circle(Circle) | circles in smallest enclosing circle |
| min-Circle(ConvexRegularPolygon) | convex regular polygon in smallest enclosing circle |
| min-Square(Circle) | circles in smallest enclosing square |
| min-Square(Square) | freely rotatable squares in smallest enclosing square |
| min-Square(ConvexRegularPolygon) | convex regular polygon in smallest enclosing square |
| min-Rectangle(Circle) | circles in smallest enclosing rectangle |
| min-Rectangle(RectangleAA) | axis-oriented rectangles in smallest enclosing rectangle |
| min-Rectangle(Rectangle) | freely rotatable rectangles in smallest enclosing rectangle |
| min-Sphere(Sphere) | spheres in smallest enclosing sphere |
| min-Cube(Sphere) | spheres in smallest enclosing cube |
| min-Cuboid(Sphere) | spheres in smallest enclosing cuboid |
| min-Cube(Cube) | cubes in smallest enclosing cube |
| min-Cube(CubeAA) | axis-aligned cubes in smallest enclosing cube |
| min-Cuboid(Cuboid) | cuboids in smallest cuboid |
| min-Sphere4d(Sphere4d) | 4d hyperspheres in smallest enclosing 4d hypersphere |
| min-Sphere5d(Sphere5d) | 5d hyperspheres in smallest enclosing 5d hypersphere |
### 2D Benchmark Instances
| Container Type | Item Type | Item Shape Distribution | n | |
| ----------------- | --------------- | ------------------------- | ------- | ----------------------------- |
| min-Circle | Circle | r(i) = 1 | 1 - 600 | |
| min-Circle | Circle | r(i) = i | 1 - 200 | "Al Zimmermann's contest set" |
| min-Circle | Circle | r(i) = i ^ (+1/2) | 5 - 100 | |
| min-Circle | Circle | r(i) = i ^ (-1/2) | 5 - 100 | |
| min-Circle | Circle | r(i) = i ^ (-2/3) | 5 - 100 | |
| min-Circle | Circle | r(i) = i ^ (-1/5) | 5 - 100 | |
| min-Circle | RegularTriangle | r(i) = 1 | 2 - 100 | |
| min-Circle | RegularTriangle | r(i) = i | 2 - 100 | |
| min-Circle | RegularPentagon | r(i) = 1 | 2 - 100 | |
| min-Circle | RegularPentagon | r(i) = i | 2 - 100 | |
| min-Circle | RegularHexagon | r(i) = 1 | 2 - 100 | |
| min-Circle | RegularHexagon | r(i) = i | 2 - 100 | |
| min-Circle | RegularOctagon | r(i) = 1 | 2 - 100 | |
| min-Circle | RegularOctagon | r(i) = i | 2 - 100 | |
| min-Square | Circle | r(i) = 1 | 1 - 100 | |
| min-Square | Circle | r(i) = i | 1 - 100 | |
| min-Square | Circle | r(i) = i ^ (+1/2) | 5 - 100 | |
| min-Square | Circle | r(i) = i ^ (-1/2) | 5 - 100 | |
| min-Square | Square | h(i) = 1 | 1 - 100 | |
| min-Square | Square | h(i) = i | 1 - 100 | |
| min-Square | RegularTriangle | r(i) = 1 | 2 - 100 | |
| min-Square | RegularTriangle | r(i) = i | 2 - 100 | |
| min-Square | RegularPentagon | r(i) = 1 | 2 - 100 | |
| min-Square | RegularPentagon | r(i) = i | 2 - 100 | |
| min-Square | RegularHexagon | r(i) = 1 | 2 - 100 | |
| min-Square | RegularHexagon | r(i) = i | 2 - 100 | |
| min-Square | RegularOctagon | r(i) = 1 | 2 - 100 | |
| min-Square | RegularOctagon | r(i) = i | 2 - 100 | |
| min-Rectangle | Circle | r(i) = 1 | 1 - 100 | |
| min-Rectangle | Circle | r(i) = i | 1 - 100 | |
| min-Rectangle | RetangleAA | hx(i)=i, hy(i)=0.750·i | 1 - 100 | |
| min-Rectangle | RetangleAA | hx(i)=i, hy(i)=0.500·i | 1 - 100 | |
| min-Rectangle | RetangleAA | hx(i)=i, hy(i)=0.250·i | 1 - 100 | |
| min-Rectangle | RetangleAA | hx(i)=i, hy(i)=0.125·i | 1 - 100 | |
| min-Rectangle | Rectangle | hx(i)=i, hy(i)=0.750·i | 1 - 100 | |
| min-Rectangle | Rectangle | hx(i)=i, hy(i)=0.500·i | 1 - 100 | |
| min-Rectangle | Rectangle | hx(i)=i, hy(i)=0.250·i | 1 - 100 | |
| min-Rectangle | Rectangle | hx(i)=i, hy(i)=0.125·i | 1 - 100 | |
### 3D Benchmark Instances
| Container Type | Item Type | Item Shape Distribution | n | |
| -------------- | ---------- | -------------------------------------- | ------- | ------------------- |
| min-Sphere | Sphere | r(i) = 1 | 1 - 100 | |
| min-Sphere | Sphere | r(i) = i | 1 - 100 | |
| min-Cube | Sphere | r(i) = 1 | 1 - 100 | |
| min-Cube | Sphere | r(i) = i | 1 - 100 | |
| min-Cube | Cube | h(i) = 1 | 1 - 100 | |
| min-Cube | Cube | h(i) = i | 1 - 100 | |
| min-Cube | CubeAA | h(i) = 1 | 1 - 100 | |
| min-Cube | CubeAA | h(i) = i | 1 - 100 | |
| min-Cuboid | Sphere | r(i) = 1 | 1 - 100 | |
| min-Cuboid | Sphere | r(i) = i | 1 - 100 | |
| min-Cuboid | Cuboid | hx(i)=i, hy(i)=0.75·i, hz(i)=0.5·i | 2 - 100 | "boxes" 4 x 3 x 2 |
| min-Cuboid | Cuboid | hx(i)=i, hy(i)=0.5·i, hz(i)=0.25·i | 2 - 100 | "bricks" 4 x 2 x 1 |
| min-Cuboid | Cuboid | hx(i)=i, hy(i)=0.5·i, hz(i)=0.1·i | 2 - 100 | "plates" 10 x 5 x 1 |
| min-Cuboid | Cuboid | hx(i)=i, hy(i)=0.125·i, hz(i)=0.125·i | 2 - 100 | "poles" 8 x 1 x 1 |
| min-Cuboid | Cuboid | AM cuboid set 1 | 2 - 100 | |
### 4D & 5D Benchmark Instances
| Container Type | Item Type | Item Shape Distribution | n |
| -------------- | ---------- | ------------------------ | ----------------------- |
| min-Sphere4d | Sphere4d | r(i) = i | 10, 20, 30, 40, 50, 100 |
| min-Sphere5d | Sphere5d | r(i) = i | 10, 20, 30, 40, 50, 100 |
## File Format
* the encoding is ASCII, multibyte characters must not be used
* line endings are expected to be LF only
* whitespace apart from LF does not have any semantic meaning other than separating numbers or identifier texts
### Packing File Format (.pac)
```
#PACKING
#CONTAINER
1
#CONTENT
...
```
### Packing Input File Format (.shp)
```
...
```
#### Entity Specification
* ```entity-specification``` : ```shape-specification``` ```placing```
* ```placing``` : ```position``` ```orientation``` ```scaling```
* ```position``` : ```center coordinates x, y, z, a, b, ...```
* ```orientation``` : ```angle between local and global x-axis``` or ```unit quaternion```
* ```scaling``` : ```scaling factors sx, sy, sz, sa, sb, ...```
#### Shape Specification
| symbol | description |
| -------- | --------------------- |
| ```r``` | radius |
| ```h``` | half length |
| ```l``` | full length |
| ```hx``` | half length on axis x |
| ```lx``` | full length on axis x |
#### Shape Placing
| symbol | description |
| ----------------- | ---------------------------------------- |
| ```x```, ```y```, ```z```, ... | x,y,z...-coordinate of the local origin |
| ```p``` | angle(local x, global x), counter-clockwise in radians |
| ```qw qx qy qz``` | orientation unit quaternion (qw: scalar part) |
| ```sx```, ```sy```, ```sz```, ... | scaling along x,y,z...-axis |
#### Simple 2D Entity Types
| type | description | specification |
| --------------- | ---------------------------- | --------------- |
| Circle | circle | ```r``` ```x y``` |
| SquareAA | axis-aligned square | ```h``` ```x y``` |
| Square | freely rotatable square | ```h``` ```x y``` ```p``` |
| RectangleAA | axis-aligned rectangle | ```hx hy``` ```x y``` |
| Rectangle | freely rotatable rectangle | ```hx hy``` ```x y``` ```p``` |
| RegularTriangle | freely rotatable regular triangle | ```r``` ```x y``` ```p``` |
| RegularPentagon | freely rotatable regular pentagon | ```r``` ```x y``` ```p``` |
| RegularHexagon | freely rotatable regular hexagon | ```r``` ```x y``` ```p``` |
| RegularOctagon | freely rotatable regular octagon | ```r``` ```x y``` ```p``` |
| Capsule2d | rectangle with semicircular caps | ```r h``` ```x y``` ```p``` |
#### Simple 3D Entity Types
| type | description | specification |
| --------------- | ---------------------------- | --------------- |
| Sphere | sphere | ```r``` ```x y z``` |
| CubeAA | axis-aligned cube | ```h``` ```x y z``` |
| Cube | freely rotatable cube | ```h``` ```x y z``` ```qw qx qy qz``` |
| CuboidAA | axis-aligned cuboid | ```hx hy hz``` ```x y z``` |
| Cuboid | freely rotatable cuboid | ```hx hy hz``` ```x y z``` ```qw qx qy qz``` |
| RegularTetrahedron | regular tetrahedron | ```r``` ```x y z``` ```qw qx qy qz``` |
| Capsule | cylinder with hemispherical caps | ```r h``` ```x y z``` ```qw qx qy qz``` |
#### Simple Entity Types (more than 3 dimensions)
| type | description | specification |
| --------------- | ---------------------------- | --------------- |
| HyperSphere4d | 4-dimensional sphere | ```r``` ```x y z a ``` |
| HyperSphere5d | 5-dimensional sphere | ```r``` ```x y z a b``` |
#### Complex Entity Types
* Polygon: planar, closed and possibly non-convex polygon with m points and m edges (orientation: ccw)
```
...
x y p
```
* TriangleCompound: collection of triangles "triangle soup"
```
...
x y z qw qx qy qz
```
#### Special Entity Types
| type | description | specification |
| ------------ | ---------------------------- | --------------- |
| $file | name of .shp file | ```filename``` |
| $file // $placing | name of .shp file and transformation | ```filename``` // ```placing``` |
### Examples
* A packing solution file for the min-Circle(Circle) problem:
```
#PACKING
#CONTAINER
Circle
1
5 0 0
#CONTENT
Circle
3
1 1 3
2 3 0
3 -2 0
```
* A packing file that references 3 .shp files containing some polygons:
```
#PACKING
#CONTAINER
RectangleAA
1
100 200 0 0
#CONTENT
$file // $placing
3
singlePolygon1.shp // -10.5 6.7 12.34
singlePolygon2.shp // 0.0 0.0 10
manyPolygons.shp // 12.4 -23 270
```
* A .shp file specifying two 4-sided polygons:
```
Polygon
2
4
0.0 0.0
5.0 0.0
5.0 4.0
6.0 0.0
1.023 -0.34
4
0.0 0.0
5.0 0.0
5.0 5.0
5.0 0.0
-12.2 4.5
```