intracse - aspiration-5

5.Convex Hull

Problem Description

Computer graphics deals with representation of graphical constructs into mathematical models. A point is represented by its coordinates (x, y). One of very popular algorithm is called "convex hull" where you are given a set of points in a plane. You have to find a smaller set of points such that all the other points are inside this smaller set of points. See below image for a convex hull idea by imagining an elastic band which engulfs the set of points.

You can use any algorithm of your choice to solve the convex hull problem, though we will suggest an algorithm which uses divide and conquer technique. A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same (or related) type, until these become simple enough to be solved directly.

In divide and conquer algorithm for convex hull problem,

Divide the points into two equal sized sets L and R such that all points of L are to the left of the most leftmost points in R.
Recursively find the convex hull of L (left hull) and R (right hull).
Merge the left hull and the right hull to get the final hull. (Hint: merging may have to do with looking for the topmost points and the bottom most points in each hull).

Instructions to use Open PBT Client:

Specify the work directory path in the 'Work Directory Path' field. The path should correspond to your solution work directory.
Download the Support files by clicking the Get Support Files.
You will find the problem directories containing:
- problem.h file
- problem.c file

in your work directory.

Write your solution in .c file

Step 1:

In your Solution File:
Add a function struct convexhull* getConvex(int points[][2], int noofcoord).

Step 2:

Pass the following parameter to the function getConvex().

int points[][2] :points represents coordinates of the points in the set.
int noofcoord: noofcoord represents number of coordinates of the points.

Step 3:

Write the appropriate code for the given problem on below given Constraints.

Here you have to write a code for a very popular algorithm is called "convex hull" where you are given a set of points in a plane. You have to find a smaller set of points such that all the other points are inside this smaller set of points.
You can use any algorithm of your choice to solve the convex hull problem.
We will suggest an algorithm which uses divide and conquer technique.
In divide and conquer algorithm for convex hull problem,
Divide the points into two equal sized sets L and R such that all points of L are to the left of the most leftmost points in R.
Recursively find the convex hull of L (left hull) and R (right hull). Merge the left hull and the right hull to get the final hull. (Hint: merging may have to do with looking for the topmost points and the bottom most points in each hull)
In easy words you have to find the smallest bourdary around all the points.(where points should lie on the boundary or inside the boundary )
The Number of Coordinates should be greater than 3 else return NULL.
Please read the exapmle carefully.

The Prototype of the Function is :

struct convexhull* getConvex(int points[][2], int noofcoord); Where points represents coordinates of the points in the set, noofcoord represents number of coordinates of the points and the function returns the set of the points that makes the convex hull.

Constraint

The Number of Coordinates should be greater than 3 else return NULL.

Example 1

Input

double points[][2] = {{3,1},{2,3},{1,2},{3,2},{2,4},{4,3},{4,4},{5,2}};
int noofcoord = 8;

Output

The function getConvex returns {{3,1},{1,2},{2,4},{4,4},{5,2}}.

Explanation: The points {{3,1},{1,2},{2,4},{4,4},{5,2}} which forms the convex hull of the outer most points in which all other points present inside. Hence the function returns the position of these points.

Example 2

Input

double points[][2] = {{2,1},{2,2},{1,3},{3,3}};
int noofcoord = 4;

Output

The function getConvex returns {{2,1},{1,3},{3,3}}.

Example 3

Input

double points[][2] = {{2,1},{2,2}};
int noofcoord = 2;

Output

The function getConvex returns NULL.

For C solutions

Header File	:	convexhull.h
Function Name	:	struct convexhull* getConvex(int points[][2], int noofcoord)
Directory Name	:	convexhull
File Name	:	convexhull.c

For C++ solutions

Header File	:	convexhull.h
Class Name	:	ConvexHull
Function Name	:	struct convexhull* getConvex(int points[][2], int noofcoord)
Directory Name	:	convexhull
File Name	:	convexhull.cpp

General Instructions

*	The file / class names, functions, method signatures, header files to be used are mentioned in the problem statement. Do not use your own names or change the method signatures and fields. You can add any number of additional methods.
*	Do not forget to mention the file extension, either .c or .cpp as the case maybe.
*	For C solutions, change the value of "C_OR_CPP" macro in header file to 1 and for C++ solutions change the value to 2.
*	Incase of iostream.h specify as iostream only.