I have read the book "Computer Graphics with Open GL" (Hearn, Fourth Edition) recently. However, when I read the midpoint ellipse algorithm, the following example in the book is confusing me:

For region 2, the initial point is $(x_0,y_0) = (7,3)$ and the initial decision parameter is $$p2_0 = f_{\text{ellipse}}\Big(7 + \frac{1}{2}, 2 \Big) = -151$$

in which $f_{\text{ellipse}}(x,y) = r^2_y x^2 + r^2_x y^2 - r^2_x r^2_y$.

When I fed the value into the formula mentioned above, eventually, I get -23. Therefore, is the result given in this example wrong?

  • 1
    $\begingroup$ I transcribed your screenshots into text as it's easier to search than images. Welcome to CS.SE! :-) $\endgroup$
    – Juho
    Commented Dec 28, 2019 at 8:56
  • $\begingroup$ You forgot to supply the values of $r_x,r_y$. $\endgroup$
    – user16034
    Commented Feb 7, 2023 at 8:45

1 Answer 1


I've got a test tomorrow and just happened to come across this question today. I think the answer given might be incorrect and -23 is the correct value the equation returns. Just to cross-check, are the consecutive decision parameter values 361 and 297? Irrespective, the values are such that the coordinates generated would be identical.

  • $\begingroup$ This is not an answer, move it to a comment. $\endgroup$
    – user16034
    Commented Jun 8, 2023 at 12:18

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