I'd like to know what type of path the curved text commonly seen in logos takes. For example, consider the following logos (all pulled of a recent Google search):

enter image description here enter image description here enter image description here

Part of each logo is curved. In each case it appears that the curve is not along the path of a circle. It looks like it could be either a parabola or a hyperbolic sine, though I can't tell by eye. Presumably they used some graphic design software that rendered the image, so a correct answer can cite the practices of common software to achieve this effect.

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    have you tried placing these logos in Illustrator and trace an ellipse along the text's baseline? They look like ellipsoids to me. Those are some really bad logos, by the way... – Vincent Feb 28 '13 at 15:37
  • @Bakabaka Agreed about the logos, but they sufficed to illustrate the question. I'm writing a small piece of custom software on Linux, and I don't have access to Illustrator. This is more of a general question of graphic design about the shapes of these paths. Ugly or not, they are quite common. – Hooked Feb 28 '13 at 15:40
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    I believe these are actually following circles. – occulus Feb 28 '13 at 16:27

The paths used in the three logos you show are created using an ellipse tool. Circles are obviously constrained ellipses.

Note that in all the examples shown, the ellipsis' minor and major axes are larger than the extents of the final image. If you drew a line from the base of the first letter to the base of the last letter, that line would be a chord of the ellipse, not an axis.

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  • So do you mean they are circular or non-circular? – occulus Feb 28 '13 at 16:27
  • @occulus All circles are ellipses, but not all ellipses are circles. He is saying that the path is elliptical, which for some cases is circular. – Hooked Feb 28 '13 at 16:32
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    An ellipse is a closed curve which is symmetrical around BOTH the horizontal and vertical axes. In simpler terms: if you fold it in half along an axis, if both halves are identical, they are symmetrical. A circle is a special ellipse where the horizontal and vertical axes are the same length. – horatio Feb 28 '13 at 17:09
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    @horatio Your math teacher is currently standing up and cheering. :) – Lauren-Clear-Monica-Ipsum Feb 28 '13 at 17:56
  • She was frowning most of the time: would you believe I failed all four quarters of 10th grade geometry, but got a 96 on the final exam? – horatio Feb 28 '13 at 18:07

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