Binary Space Partitioning (BSP)

Recursively divides the space into two parts until the leaf nodes satisfy the constraints such as minimum number of spatial objects in a partition.

BSP tree is a heirarchical subdivisions of n dimensional space into convex subspaces. The space is subdivided using hyperplanes passing through node.
Kd-trees and quad-trees have hyperplanes aligned with the coordinate axis while BSP tree has hyperplanes with any orientation.

How to run Binary Space Partitioning algorithm

You can change the parition parameters in extract_params_partitioning method of partition_params.hpp.
Paramters are volume of space (min_x, min_y, min_z, max_x, max_y, max_z) and bucket_size. You choose the volume of space based on the input spatial objects so that all the spatial objects are covered.
In the code, space volume is hard-coded as 0,0,0,50,50,50 for testObj.mbb as input and bucket_size as 4.
```
g++ -std=c++0x bsp_3d.cpp -o bsp
./bsp testObj.mbb
```

Sort Tile Recursive Partitioning (STR)

Sort Tile Recursive Partitioning : Partitioning using RTree from libSpatialIndex.

Hello World of libSpatialIndex C++ library

https://github.com/libspatialindex/libspatialindex/wiki/1.-Getting-Started

g++ -std=c++0x helloLibSpatial.cpp -lspatialindex_c -lspatialindex -o helloLibSpatial
./helloLibSpatial

How to run Sort Tile Partitioning algorithm

g++ -std=c++0x str_3d.cpp -lspatialindex_c -lspatialindex -o str
./str testObj.mbb

Visualizations with OpenGL (trials)

Hello World of OpenGL C++ library with installation instructions

http://www.linuxjournal.com/content/introduction-opengl-programming

Installation

apt-cache search opengl
sudo apt-get install freeglut3 freeglut3-dev libglew-dev
sudo apt-get install mesa-utils

Check your OpenGL installation
```
glxinfo | grep OpenGL
```
Draw Triangle and Circle as a HelloWorld program.
- Opens Triangle and Circle in two openGL windows.
```
g++ openGLHelloWorld.cpp -lglut -lGL -o hello
./hello
```

Draw Rotated Cube using OpenGL.

g++ openGLCube.cpp -lglut -lGL -lGLU -o cube
./cube

Visualizations in Matlab

After trying several things in OpenGL, I found stackoverflow links directing to Matlab. The APIs were simpler and easy to implement. So, I implemented the partitioning algorithm visualizations in Matlab and not in OpenGL.

Run simplecube.m

The visualizations are for both BSP and STR partitioning algorithms.

BSP

Input for BSP visualization is
- testObj.dat containing spatial MBBs
- boundingBoxBSP.dat has output partitioned MBBs.
  Output is a bounding box visualization. Check project report or bsp.png for the visualization.
STR

Input for STR visualization is
- testObj.dat containing spatial MBBs
- boundingBoxSTR.dat has output partitioned MBBs.
  Output is a bounding box visualization. Check project report or str.png for the visualization.