# ivanfratric/polypartition

Tiny Polygon Partitioning and Triangulation Library
Switch branches/tags
Nothing to show
ivanfratric Merge pull request #32 from julienjpk/master
`Added simple polygon validity checks.`
Latest commit 4921a9b Sep 1, 2018
 Failed to load latest commit information. images May 25, 2011 src Aug 31, 2018 test May 4, 2014 README.md Apr 16, 2017

#### 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, and are defined in the correct vertex order (conter-clockwise for non-holes, clockwise for holes). Polygon vertices can easily be ordered correctly by calling `TPPLPoly::SetOrientation` method.

#### 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:

#### 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:

#### 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:

#### 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:

#### 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: