Your task is to implement **KD-tree** data structure for efficient lookup in huge set of planar
short line segments. Think hard about **optimal tree building** (set of line segments is static, you will
be able to balance a tree easily) and about **the ray-pass algorithm** itself. Each ray-pass instance
(query) is defined by: *ray origin*, *ray direction* and *maximal number of intersections*.
Query results will be returned in form of line segment handles, intersections have to be sorted
from the closest one to the farthest one (in the sense of ray direction).

Your algorithms should count various statistics: number of intersections, number of ray-box tests, etc. (see below). These numbers will be used in a result table comparing all the handed-in solutions.

It is recommended to test the algorithms on **very large input sets** (10^{7} lines or more).
Your methods should be universal and robust!

**WinForms-based application** is ready to test efficiency and correctness of your kd-tree implementation
by generating arbitrary number of short lines (deterministic but uneven distribution based on
the Lorentz attractor,
Paul Bourke page).
Your tree-building code is invoked and after this building phase
a required set of queries is performed. Results are optionally presented in graphical form, a
simple hashcode-based fingerprint is computed for checking correctness of the results.
Elapsed time and counter-based statistics are presented as well.

Statistics which will be used to assess your solution:

- number of atomic geometric tests
**"ray vs. line segment"** - number of bounding-box tests
**"ray vs. box"** - number of
**"heap-operations"**; only operations with the**O(log N)**complexity are relevant - time spent in tree initialization (building phase) in seconds
- total time of all ray-set queries (in seconds)

You are obliged to provide the first three statistics (see the **GetStatistics()** function)!

You have to use the ** 008kdtree** project from the
grcis repository.
A WinForms-based application is ready, user can modify size of input set,
number of queries, random-seed, etc.
Your implementation will be in the

You have to implement this simple API:

- builds the new kd-tree from the scratch. Set of line-segments is passed in the**BuildTree()**`segments`argument- one ray vs. set query. Result set of size**RayIntersect()**`K`(or smaller if there were not enough intersections) is returned in order from nearest to farthest one- retrieves accumulated statistics (ray vs. segment tests, ray vs. box tests, heap operations). Internal counters should be reset by this call**GetStatistics()**

**Ray vs. line-segment intersection:** use provided function ` RaySegment2D()`.

Data size | Random seed | Query size | HASH | INTERSECTIONS |
---|---|---|---|---|

1000000 | 7 | 100 | E5DA3BAB292F8020 | 15138 |

1000000 | 12 | 200 | D29B8AF580E85624 | 31162 |

5000000 | 144 | 200 | 9B155E1F59FE5FE | 33306 |

Due to: **20. 12. 2015**

Base: **25 points** (functional code, 100% correct intersections!),
bonus points for very good efficiency

Visual Studio project: ** 008kdtree**.

Modify and submit the file: `KDTree.cs`

Not yet.

Copyright (C) 2005-2015 J.Pelikán, last change: 2015-11-19 21:51:45 +0100 (Thu, 19 Nov 2015)