https://github.com/ivanfratric/polypartition

Tiny Polygon Partitioning and Triangulation Library
https://github.com/ivanfratric/polypartition

Last synced: about 1 month ago
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Tiny Polygon Partitioning and Triangulation Library

• Host: GitHub
• URL: https://github.com/ivanfratric/polypartition
• Owner: ivanfratric
• License: mit
• Created: 2015-05-03T11:16:10.000Z (over 9 years ago)
• Default Branch: master
• Last Pushed: 2024-07-27T08:03:23.000Z (5 months ago)
• Last Synced: 2024-08-02T07:19:16.040Z (4 months ago)
• Language: C++
• Homepage:
• Size: 156 KB
• Stars: 631
• Watchers: 28
• Forks: 113
• Open Issues: 11
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

Awesome Lists containing this project

• awesome-game-engine-dev - PolyPartition - 2D polygon partitioning and triangulation. (Libraries / C++)
• AwesomeCppGameDev - polypartition

README

        
#### PolyPartition

PolyPartition is a lightweight C++ library for polygon partition

and triangulation. PolyPartition implements multiple algorithms

for both convex partitioning and triangulation. Different

algorithms produce different quality of results (and their

complexity varies accordingly). The implemented methods/algorithms

with their advantages and disadvantages are outlined below.

For input parameters and return values see method declarations

in `polypartition.h`. All methods require that the input polygons

are not self-intersecting, are defined in the correct vertex order

(counter-clockwise for non-holes, clockwise for holes), and any holes

must be explicitly marked as holes (you can use `SetHole(true)`).

Polygon vertices can easily be ordered correctly by

calling `TPPLPoly::SetOrientation` method.

Input polygon:

![images/test_input.png](images/test_input.png)

#### Triangulation by ear clipping

Method: `TPPLPartition::Triangulate_EC`

Time/Space complexity: `O(n^2)/O(n)`

Supports holes: Yes, by calling `TPPLPartition::RemoveHoles`.

Quality of solution: Satisfactory in most cases.

Example:

![images/tri_ec.png](images/tri_ec.png)

#### Optimal triangulation in terms of edge length using dynamic programming algorithm

Method: `TPPLPartition::Triangulate_OPT`

Time/Space complexity: `O(n^3)/O(n^2)`

Supports holes: No. You could call `TPPLPartition::RemoveHoles` prior

to calling `TPPLPartition::Triangulate_OPT`, but the solution would no

longer be optimal, thus defeating the purpose.

Quality of solution: Optimal in terms of minimal edge length.

Example:

![images/tri_opt.png](images/tri_opt.png)

#### Triangulation by partition into monotone polygons

Method: `TPPLPartition::Triangulate_MONO`

Time/Space complexity: `O(n*log(n))/O(n)`

Supports holes: Yes, by design

Quality of solution: Poor. Many thin triangles are created in most cases.

Example:

![images/tri_mono.png](images/tri_mono.png)

#### Convex partition using Hertel-Mehlhorn algorithm

Method: `TPPLPartition::ConvexPartition_HM`

Time/Space complexity: `O(n^2)/O(n)`

Supports holes: Yes, by calling `TPPLPartition::RemoveHoles`.

Quality of solution: At most four times the minimum number of convex

polygons is created. However, in practice it works much better

than that and often gives optimal partition.

Example:

![images/conv_hm.png](images/conv_hm.png)

#### Optimal convex partition using dynamic programming algorithm by Keil and Snoeyink

Method: `TPPLPartition::ConvexPartition_OPT`

Time/Space complexity: `O(n^3)/O(n^3)`

Supports holes: No. You could call `TPPLPartition::RemoveHoles`

prior to calling `TPPLPartition::Triangulate_OPT`, but the solution

would no longer be optimal, thus defeating the purpose.

Quality of solution: Optimal. A minimum number of convex polygons is produced.

Example:

![images/conv_opt.png](images/conv_opt.png)