Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
C++ Program to Implement Jarvis March to Find the Convex Hull
Jarvis March algorithm is used to detect the corner points of a convex hull from a given set of data points.
Starting from left most point of the data set, we keep the points in the convex hull by anti-clockwise rotation. From a current point, we can choose the next point by checking the orientations of those points from current point. When the angle is largest, the point is chosen. After completing all points, when the next point is the start point, stop the algorithm.
Input: Set of points: {(-7,8), (-4,6), (2,6), (6,4), (8,6), (7,-2), (4,-6), (8,-7),(0,0), (3,-2),(6,-10),(0,-6),(-9,-5),(-8,-2),(-8,0),(-10,3),(-2,2),(-10,4)}
Output: Boundary points of convex hull are:
(-9, -5) (6, -10) (8, -7) (8, 6) (-7, 8) (-10, 4) (-10, 3)Algorithm
findConvexHull(points, n)
Input: The points, number of points.
Output: Corner points of convex hull.
Begin start := points[0] for each point i, do if points[i].x < start.x, then // get the left most point start := points[i] done current := start add start point to the result set. define colPts set to store collinear points while true, do //start an infinite loop next := points[i] for all points i except 0th point, do if points[i] = current, then skip the next part, go for next iteration val := cross product of current, next, points[i] if val > 0, then next := points[i] clear the colPts array else if cal = 0, then if next is closer to current than points[i], then add next in the colPts next := points[i] else add points[i] in the colPts done add all items in the colPts into the result if next = start, then break the loop insert next into the result current := next done return result End
Example Code
#include<iostream>
#include<set>
#include<vector>
using namespace std;
struct point { //define points for 2d plane
int x, y;
bool operator==(point p2) {
if(x == p2.x && y == p2.y)
return 1;
return 0;
}
bool operator<(const point &p2)const { //dummy compare function used to sort in set
return true;
}
};
int crossProduct(point a, point b, point c) { //finds the place of c from ab vector
int y1 = a.y - b.y;
int y2 = a.y - c.y;
int x1 = a.x - b.x;
int x2 = a.x - c.x;
return y2*x1 - y1*x2; //if result < 0, c in the left, > 0, c in the right, = 0, a,b,c are collinear
}
int distance(point a, point b, point c) {
int y1 = a.y - b.y;
int y2 = a.y - c.y;
int x1 = a.x - b.x;
int x2 = a.x - c.x;
int item1 = (y1*y1 + x1*x1);
int item2 = (y2*y2 + x2*x2);
if(item1 == item2)
return 0; //when b and c are in same distance from a
else if(item1 < item2)
return -1; //when b is closer to a
return 1; //when c is closer to a
}
set<point> findConvexHull(point points[], int n) {
point start = points[0];
for(int i = 1; i<n; i++) { //find the left most point for starting
if(points[i].x < start.x)
start = points[i];
}
point current = start;
set<point> result; //set is used to avoid entry of duplicate points
result.insert(start);
vector<point> *collinearPoints = new vector<point>;
while(true) {
point nextTarget = points[0];
for(int i = 1; i<n; i++) {
if(points[i] == current) //when selected point is current point, ignore rest part
continue;
int val = crossProduct(current, nextTarget, points[i]);
if(val > 0) { //when ith point is on the left side
nextTarget = points[i];
collinearPoints = new vector<point>; //reset collinear points
}else if(val == 0) { //if three points are collinear
if(distance(current, nextTarget, points[i]) < 0) { //add closer one to collinear list
collinearPoints->push_back(nextTarget);
nextTarget = points[i];
}else{
collinearPoints->push_back(points[i]); //when ith point is closer or same as nextTarget
}
}
}
vector<point>::iterator it;
for(it = collinearPoints->begin(); it != collinearPoints->end(); it++) {
result.insert(*it); //add allpoints in collinear points to result set
}
if(nextTarget == start) //when next point is start it means, the area covered
break;
result.insert(nextTarget);
current = nextTarget;
}
return result;
}
int main() {
point points[] = {{-7,8},{-4,6},{2,6},{6,4},{8,6},{7,-2},{4,-6},{8,-7},{0,0},
{3,-2},{6,-10},{0,-6},{-9,-5},{-8,-2},{-8,0},{-10,3},{-2,2},{-10,4}};
int n = 18;
set<point> result;
result = findConvexHull(points, n);
cout << "Boundary points of convex hull are: "<<endl;
set<point>::iterator it;
for(it = result.begin(); it!=result.end(); it++)
cout << "(" << it->x << ", " <<it->y <<") ";
}Output
Boundary points of convex hull are: (-9, -5) (6, -10) (8, -7) (8, 6) (-7, 8) (-10, 4) (-10, 3)
Updated on: 30-Jul-2019
808 Views
Advertisements