// A program that plots a picture of a function of two variables.
// The name 'wallpapr.cc' is from Dewdney's Sceintific American
// article on the "Wallpaper Program".  You can have a lot of fun
// with similar programs producing various patterns and pictures
// Version3, started  March 7th 2000 by RJB
/* Algorithm
   For each row in turn
       For each column in turn
           Ouput a symbol to represent the value of a function at that point
       Repeat with next column
       output end of line
   Repeat with next row
*/
#include <iostream>
using namespace std;  // added December 13th 2007

int F(int x, int y, int z)// The function to be displayed
{
	return (x*x + y*y - z*z) * ( x - y ) * ( x + y) ;
	// or try the following:
	//return (x*x + y*y - z*z) ;
}

int main()
{
	const int N = 20;//height and width of grid in characters
	const int H = N/2; // Largest(Highest) coordinate value
	const int L = 1+H-N; // Smallest(Lowest) cordinate value
		// The range L,L+1,...,0,1,...,H has exactly N integers
		// and 0 is as close to the middle as it can get.

	const int z=9;  //height of the zero level in the surface

	int x, y; //coordinates of a point in the x><y plane
	for( y = H;  y >= L;  y-- )//For each row in turn y=H, H-1, H-2, ...,L+1, L
	{//draw a row of picture elements(pixels) with the same y cordinate

		cout << "\t"; // output a "tab" character

		for( x = L; x <= H; x++ )//For each column in turn x=L,L+1, L+2, ... H-1, H
		{// draw the pixel (x,y)
			const int Fxyz = F(x,y,z);

			if( x == 0 and y == 0 ) 
				cout << "0";
			else if( Fxyz > 0 ) 
				cout <<"+";
			else if( Fxyz == 0 ) 
				cout <<".";
			else // Fxyz < 0
				cout<<"-";
		}

		cout << endl; //end of the line

	}
	//end of the grid

	return 0;

}