Draw rectangles, circles or arbitrary polygons in a m x n matrix

Question

I want to simulate the flow around objects in two dimensions. Therefore I wrote a program in C which uses the Navier-Stokes equations to describe the motion of fluids. Now I cam

Answer 1

There might be more efficient ways of doing this, but here's one way.

Define a function in C using the equation of the polygon you wish to draw. The function is defined such that it accepts a point coordinates, and returns whether the point lies inside the polygon or not. For example, for a circle, the function could accept the point (x,y), the centre (x0,y0), and the radius r, and return (x-x0)^2 + (y-y0)^2 - r^2 < 0. Let this function be f.

Determine the bounding box rectangle of the polygon, if possible, or else, the smallest rectangle you can determine which completely encloses the polygon. This will give you a rectangular matrix.

Now, iterate over the points in the rectangular matrix. For each point, call the function you previously defined. Assign the coordinate a 1 if it returns True, and 0 if it returns False. This will construct the polygon.

Suppose you want to draw a circle with centre (x0,y0), radius r, then you can use:

int f(int i, int j, int x0, int y0, int r)
{
    return pow((i-x0),2) + pow((j-y0),2) - pow(r,2) < 0;        
}


for(int i = x0-r; i <= x0 + r; i++)
{
    for(int j = y0-r; j <= y0 + r; j++)
    {
        if(f(i,j,x0,y0,r))
        {
            M[i][j] = 1;
        }
        else
        {
            M[i][j] = 0;
        }
    }
}