Question

GIFT WRAPPING ALGORITHM OF JARVIS MARCH In mathematics, the convex hull of a set of points is the smallest convex set that contains these points. The convex hull may be visualized as the shape enclosed by a rubber band stretched around these points (see the figure below). In your first homework, you are going to compute the convex hull of a set of given points in a separate file (input.txt). For the given set of 14 points below, you can find the 7 points on the right most column, through which the convex hull passes SET of 14 Points: Points on the convex hull: 0.09 0.42 0.19 0.19 0.62 0.18 0.95 0.59 1.00 0.77 0.50 1.00 0.18 0.81 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.09 0.42 0.19 0.19 0.18 0.81 0.24 0.57 0.33 0.62 0.39 0.79 0.50 1.00 0.50 0.40 0.60 0.60 0.62 0.18 0.70 0.35 0.95 0.59 1.00 0.77 0.94 0.76 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 The algorithmic problem of finding the convex hull of a finite set of points in the plane or other low dimensional Euclidean spaces is one of the fundamental problems of computational geometry There are different algorithms to compute the convex hull of a set of points, however, you are asked to use the gift wrapping algorithm of Jarvis March

Answer 1

#include<stdio.h>
#include<math.h>
#include<stdlib.h>
#define pi 3.14159
typedef struct v1
{
int x, y;
}vertex;
vertex p0;
int process_vertices( int n, vertex *v)
{
int i;
for(i=0;i<n;i++) scanf(" %d %d",&v[i].x,&v[i].y);
return n;
}
void swap(vertex *v1, vertex *v2)
{
vertex temp = *v1;
*v1 = *v2;
*v2 = temp;
}
int orientation(vertex p, vertex q, vertex r)
{
int val = (int)(q.y - p.y) * (r.x - q.x) - ( int)(q.x - p.x) * (r.y - q.y);
if (val == 0) return 0;
return (val > 0)? 1: 2;
}
int distSq(vertex p1, vertex p2)
{
return (int)(p1.x - p2.x)*(p1.x - p2.x) + ( int)(p1.y - p2.y)*(p1.y - p2.y);
}
int compare(const void *vp1, const void *vp2)
{
vertex *p1 = (vertex *)vp1;
vertex *p2 = (vertex *)vp2;

int o = orientation(p0, *p1, *p2);
if (o == 0)
return (distSq(p0, *p2) >= distSq(p0, *p1))? -1 : 1;

return (o == 2)? -1: 1;
}
vertex * Convex_Hull(vertex *v, int *count)
{
int n = *count, ymin = v[0].y, min = 0, i,m;vertex *stack;
for(i = 1; i < n; i++)
{
if((v[i].y < ymin) || ((v[i].y == ymin) && (v[i].x < v[min].x)))
{
ymin = v[i].y;
min = i;
}
}
swap(&v[0], &v[min]);
p0 = v[0];
if(n > 1)
qsort(&v[1], n - 1, sizeof(vertex), compare);
m = 1;
for(i = 1; i < n; i++)
{
while((i < n - 1) && orientation(v[0], v[i], v[i + 1]) == 0)
i++;
v[m++] = v[i];
}
*count = n = m;
if(n < 3)
return v;
stack = (vertex *)malloc(n * sizeof(vertex));
stack[0] = v[0];
stack[1] = v[1];
stack[2] = v[2];
m = 2;
for(i = 3; i < n; i++)
{
while(orientation(stack[m-1], stack[m], v[i]) != 2)
m--;
stack[++m] = v[i];
}
*count = n = ++m;
free(v);
return stack;
}

int main()
{
int t, n, i,count;

vertex *v;

scanf("%d", &n);

v = (vertex *)malloc( n * sizeof(vertex));
count = process_vertices(n, v);

v = Convex_Hull(v, &count);
for(i=0;i<count;i++)
   printf("%d %d\n",v[i].x,v[i].y);

return 0;
}
/* run this code in online c compiler.*/