I've programmed drawing tools for graph images and am experiencing a problem with the coordinates of an Ellipse on a graph with a Log Y axis.

It's quite easy to work out the Y Axis coordinates for other primitive objects such as Line, Rectangle & etc:

y1 = ((viewHeight - stPoint.Y + topMargin) / (viewHeight) * (maxY - minY) + minY);
y2 = ((viewHeight - endPoint.Y + topMargin) / (viewHeight) * (maxY - minY) + minY);

if (isLogYAxis)
   y1 = Math.Exp(y1);
   y2 = Math.Exp(y2);

Here is an example showing the Epilog generated for a Circle and a Rectangle I've drawn:

enter image description here

Epilog -> {{RGBColor[1,0.2196,1], Circle[{AbsoluteTime@{1991,03,09} + ((AbsoluteTime@{1996,04,28} - AbsoluteTime@{1991,03,09}) / 2),Log@40},    
{(AbsoluteTime@{1996,04,28} - AbsoluteTime@{1991,03,09}) / 2,Log@60}]},

{EdgeForm[Directive[Thick, RGBColor[0.6157,0.6,0.7922]]], Transparent, Rectangle[{AbsoluteTime@{1986,03,26},Log@60},{AbsoluteTime@{1990,12,15},Log@40}]}}

When I execute this command the Ellipse's Y axis is out of proportion, see:

enter image description here

I want to be able to plug in Log@40 and Log@60 for both the Rectangle and Circle and get the same results.

I've made a basic example to demonstrate this.

LogPlot[x^x, {x, 1, 5}, 
 Epilog -> {{RGBColor[0, 0, 0], 
    Circle[{2, [email protected]}, {1, [email protected]}]}}]

Seeing the radius from the ellipse's centre to its top (2000) will be a different size from its centre to its bottom (approx 50), is it even possible to draw a Ellipse on a LogY Graph as I've described?

enter image description here


@Artes thank you for pointing me in the right direction, I've tried all sorts of things using this formula Plot[Exp[y /. Solve[x^2 + y^2 == 1, y]], {x, -1, 1}] without luck.

In the last screenshot I've put red squares around the [email protected] and [email protected] does anybody know what formula's I would have to change these too in order to get a circle with Log Height of about 5?

If it makes any difference I have the MinY and MaxY Log scale:

MinY = 3.6888794541139363
MaxY = 4.941642422609304


1 Answer 1


If you want to draw an ellipse on top of a LogPlot by specifying the left, right, top and bottom of the ellipse:

ellipse1[l_, r_, t_, b_] :=
 Circle[{(r + l)/2, (Log[t] + Log[b])/2}, {(r - l)/2, (Log[t] - Log[b])/2}]

LogPlot[x^x, {x, 1, 5}, Epilog -> {Black, ellipse1[2, 4, 5, 500]}]

enter image description here

If you want to show a truly elliptical region distorted by the log scale on the y axis:

ellipse2[l_, r_, t_, b_] := 
 Cases[ParametricPlot[{(r + l)/2 + (r - l) Cos[a]/2, 
    Log[(t + b)/2 + (t - b) Sin[a]/2]}, {a, 0, 2 Pi}], _Line, -1]

LogPlot[x^x, {x, 1, 5}, Epilog -> {Black, ellipse2[2, 4, 5, 500]}]

enter image description here

  • 1
    $\begingroup$ Thank you SO much! Your xkcd-style graph answer is also a favorite of mine. $\endgroup$
    – WolframFan
    Commented Jun 17, 2013 at 22:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.