HGeometry provides some basic geometry types, and geometric algorithms and data structures for them. The main two focusses are: (1) Strong type safety, and (2) implementations of geometric algorithms and data structures with good asymptotic running time guarantees. Design choices showing these aspects are for example:

- we provide a data type
`Point d r`

parameterized by a type-level natural number`d`

, representing d-dimensional points (in all cases our type parameter`r`

represents the (numeric) type for the (real)-numbers):

- the vertices of a
`PolyLine d p r`

are stored in a`Data.LSeq`

which enforces that a polyline is a proper polyline, and thus has at least two vertices.

Please note that aspect (2), implementing good algorithms, is much work in progress. Only a few algorithms have been implemented, some of which could use some improvements. Currently, HGeometry provides the following algorithms:

- two \(O(n \log n)\) time algorithms for convex hull in \(\mathbb{R}^2\): the typical Graham scan, and a divide and conqueror algorithm,
- an \(O(n)\) expected time algorithm for smallest enclosing disk in \(\mathbb{R}^2\),
- the well-known Douglas Peucker polyline line simplification algorithm,
- an \(O(n \log n)\) time algorithm for computing the Delaunay triangulation (using divide and conqueror).
- an \(O(n \log n)\) time algorithm for computing the Euclidean Minimum Spanning Tree (EMST), based on computing the Delaunay Triangulation.
- an \(O(\log^2 n)\) time algorithm to find extremal points and tangents on/to a convex polygon.
- An optimal \(O(n+m)\) time algorithm to compute the Minkowski sum of two convex polygons.
- An \(O(1/\varepsilon^dn\log n)\) time algorithm for constructing a Well-Separated pair decomposition.
- The classic (optimal) (O(nn)) time divide and conquer algorithm to compute the closest pair among a set of (n) points in (^2).

It also has some geometric data structures. In particular, HGeometry contans an implementation of

- A one dimensional Segment Tree. The base tree is static.
- A one dimensional Interval Tree. The base tree is static.
- A KD-Tree. The base tree is static.

HGeometry also includes a datastructure/data type for planar graphs. In particular, it has a `EdgeOracleâ€™ data structure, that can be built in \(O(n)\) time that can test if the graph contains an edge in constant time.

Current work is on implementing tools for efficient polygon intersection and map overlay.

The easiest way to get HGeometry is from Hackage. The source code for HGeometry can be found on github.

See github.