Algorithms

xNew=x*cos(alpha)+y*sin(alpha);
yNew=-x*sin)alpha)+y*cos(alpha);

widNew=wid*abs(cos(alpha))+hei*abs(sin(alpha));
heiNew=wid*abs(sin(alpha))+hei*abs(cos(alpha));

new_width  = abs( width * cos(alpha) + height * sin(alpha))
new_height = abs(-width * sin(alpha) + height * cos(alpha))

rotated_x =  x * cos(alpha) + y * sin(alpha)
rotated_y = -x * sin(alpha) + y * cos(alpha)

new_height = abs(-width * sin(alpha) + height * cos(alpha))

abs(-width * sin(alpha)) + abs(height * cos(alpha))
    ^
    |
    +- This is the minus that you are talking about, I suppose

abs(-x * sqrt(2) / 2 + x * sqrt(2) / 2)

abs(-x * a + x * a)

abs(0)

for x = 0 to xmax
  for y = 0 to ymax
    if (CI(x,y) > CI(x-1,y) || CI(x,y) > CI(x+1,y) || CI(x,y) > CI(x,y-1) || CI(x,y) > CI(x,y+1))
      set_line_colour(x,y);

int CI(int x, int y) 
{
  return (int)(altitude[x,y] / contour_interval);
}