float signed_triangle_area(int ax, int ay, int bx, int by, int cx, int cy) {
    return 0.5*((by-ay)*(bx+ax) + (cy-by)*(cx+bx) + (ay-cy)*(ax+cx));
}

void triangle(int ax, int ay, int bx, int by, int cx, int cy,  TGAColor color) {
    int bbminx = min(min(ax, bx), cx); // bounding box for the triangle
    int bbminy = min(min(ay, by), cy); // defined by its top left and bottom right corners
    int bbmaxx = max(max(ax, bx), cx);
    int bbmaxy = max(max(ay, by), cy);
    float total_area = signed_triangle_area(ax, ay, bx, by, cx, cy);

    for (int x=bbminx; x<=bbmaxx; x++) {
        for (int y=bbminy; y<=bbmaxy; y++) {
            float alpha = signed_triangle_area(x, y, bx, by, cx, cy) / total_area;
            float beta  = signed_triangle_area(x, y, cx, cy, ax, ay) / total_area;
            float gamma = signed_triangle_area(x, y, ax, ay, bx, by) / total_area;
            if (alpha<0 || beta<0 || gamma<0) continue; // negative barycentric coordinate => the pixel is outside the triangle
            PutPixel(x, y, color);
        }
    }
}               
    

x = X/Z
y = Y/Z