# Smoothness of Tunni curves

Posts: 186
While researching a curve optimization algorithm, I also examined Tunni curves for their smoothness. My findings may also be of interest to you. I have summarized them in the attached PDF.

• Posts: 352
Is there an "official" definition of what constitutes a Tunni curve anywhere?
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edited July 14
Yes! and video too (in Spanish)

Part 1) Eduardo's Introduction

Part 2) Theory

Part 3) As a FL5 plugin
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Thanks, Pablo!
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edited July 16
Tunni Lines are without doubt a great invention. I use Tunni Lines very often in FontLab 8. Incidentally, FontLab 8 has a similar function in Panel Node, which I also like very much. This function can also be applied to several letters at once in FontLab's edit-across-glyphs mode.
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In FontLab VI, 7, and 8 there is also the auto Tunni adjust: just double-click on the blue dotted line (the Tunni curve control). The line appears when your cursor is on its area.

• Posts: 1,110
edited July 17
This was interesting; a Tunni curve is just a special case of a Bezier curve, claimed to have superior aesthetic properties. And in looking that up, I found a reference to Hobby's curves; this refers to an algorithm for quickly producing a sequence of Bezier curves to pass through a series of points. However, continuity of curvature across those points is only approximate, not exact, although this would usually be invisible.
This inspired me to do a search for what I would be interested in, and I found that there were published mathematical papers on approximating conic sections with Bezier curves; some did so with fourth-order and sixth-order curves, but others used cubic and quadratic curves, which would be applicable to font formats.
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• Posts: 352
edited July 18
I think the normal “adjust” mode of my Curve EQ plugin (RoboFont/Glyphs) works with Tunni curves then, even if they are not called that in the UI.

Incidentally, John Hobby curves, as mentioned in Linus’ paper can also be used in Curve EQ.