Slicker Algorithm is a way to determine the area of the n-sided polygon. This algorithm takes the y-direction pointing upwards as positive according to the mathematical conventions but according to computer systems where the positive y-direction is downwards, the most efficient way is to list the vertices counter-clockwise using the positive y-down coordinates which cancels out the two effects and in turn returns the positive area.
Example:
Input: Enter number of sides of the Polygon: 4
Enter the coordinates as : <x> <y>
0 0
1 0
1 1
0 1Output: The Area of Polygon with 4 points using Slicker Algorithm is: 1
Approach
Take no of sides and coordinates of n-sided polygon as an input from the user
Define function Area() which calculates the area with p as an argument as follows:
for i = 0 to (p.n-1)
j = (i + 1) % p.n;
calculate area += (p.p[i].x * p.p[j].y) - (p.p[j].x * p.p[i].y);
print total area as area/2
Note: Input points must take in order, Program will not work properly with points taken in random order.
Below is the implementation of the above program
Java
// Implement Slicker Algorithm that avoids// Triangulation to Find Area of a Polygonimport java.util.*;class Main { // defining the maximum no of sides for the Polygon static final int MAXSIDES = 200; static class Corner { double x, y; } static class Polygon { Corner p[] = new Corner[MAXSIDES]; int n; Polygon() { for (int i = 0; i < MAXSIDES; i++) p[i] = new Corner(); } } // calculating area with Slicker Algorithm static double area(Polygon p) { double total = 0; for (int i = 0; i < p.n; i++) { int j = (i + 1) % p.n; total += (p.p[i].x * p.p[j].y) - (p.p[j].x * p.p[i].y); } return total / 2; } static public void main(String[] args) { Polygon p = new Polygon(); Scanner sc = new Scanner(System.in); // Taking inputs from the user System.out.print( "Enter number of sides of the Polygon: "); p.n = sc.nextInt(); System.out.println( "Enter the coordinates as : <x> <y>"); // Taking the coordinates of each Corner for (int i = 0; i < p.n; i++) { p.p[i].x = sc.nextDouble(); p.p[i].y = sc.nextDouble(); } double area = area(p); if (area > 0) System.out.print( "The Area of Polygon with " + p.n + " points using Slicker Algorithm is : " + area); else System.out.print( "The Area of Polygon with " + p.n + " points using Slicker Algorithm is : " + (area * -1)); sc.close(); }} |
Output:
Time Complexity: O(N), Where N is the number of sides of the polygon.
Auxiliary Space: O(1) because constant array p of constant size 200 has been used
