# polypartition

**Repository Path**: cpkg/polypartition

## Basic Information

- **Project Name**: polypartition
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2022-03-30
- **Last Updated**: 2022-03-30

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## 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)