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mauro sacchetto
Posts: **267**

Which is the most efficient way to design a curve, so that it is symmetrical, harmonious? Are there basic criteria to be met?

I enclose an example of what I mean here by "curve"

Thank you

Thank you

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## Comments

30948461The facetious answer is: yes, there exists a mathematical description of an efficient, pleasing curve that you describe. The challenge is to find a point on a given ellipse such that the curve of the ellipse is tangent to a given straight line. The mathematics are actually more complicated than you would think, but a full derivation is given in Knuth’s 1980 article “The Letter S” (Mathematical Intelligencer 2:114-122).

The reason this is facetious is that nobody ever designs curves like this, because type design is not a matter of mathematical logic. The true test of whether a design is right is whether or not it looks right, and learning whether or not it looks right is far more useful than learning the algorithms that ought to make it look right.

The serious answer is the one James gave you.

1,7011,0061,259163That said, let's get right to the issue. OK, so you've drawn a glyph using digital vector points. You're looking at it and you notice a few spots where the inside curves are not working exactly well with the outside curves and overall movement. Ok, so how do you quickly make the adjustment to the overall curve in that location without adjusting the vector point itself or the support shift handles around it. I'm not saying you cannot do it that way, just that it's difficult to do.

Realize that most times the shape is not awful, just slightly off. Better to focus first on where the spot is bad. Then, use FontLab "Knife Tool (3)" and click on the before and after the bad spot. try to be careful and not change the original curve while you are placing these two additional curve points to the overall curve (keep a copy of the glyph in the background Mask area). If you slightly are changing the shape "undo" until you add these two new points on either side of the curve without altering the original overall shape. Now you can delete the extreme vector point on the bad spot, keeping the 2 support vector points you've just added to the curve. If you've done this correctly, you will immediately see the bad shape improve. If not to your satisfaction, play with the handles (of the 2 added points)... pulling one out which seems more obvious to your eyes. If not that one..."undo" try the other handle of the second added point. If the shape finally looks good now, go to the menu and select "nodes at Expremes". Done. You can try to delete the added perious 2 points to make this adjustment, but sometimes you will need to keep them to keep the improved shape. That's it!

You can try this technique on bad curves at extremes, or anywhere along a curve. Same principals apply. It just takes some practice. After awhile anyone can get really good at this.

I'm attaching 2 visuals to illustrate this all clearly.

Here is a figure "eight" I was working on. I see that the inside of the top inside curves look a bit flat on the inside extremes of the curve.

So, see the adjustment I made as indicated in my discussions above.

I added the 2 RED new vectors on either side of the bad spots. Then, deleted the original extreme points. And, had the application create new extreme points. I still had to adjust one of the 2 support points (on the right inside upper spot on curve) to get the overall shape just right. But, this was the general technique I used.

I always leave the original shape (in the background Mask layer) so that I can visualize the adjustments I've made.

If you decide to try this, please let me know how this works for you.

If needed, you can contact me directly at [email protected] with your problem glyphs and I'll make the adjustments for you in FontLab and send you back your data as a learning exercise.

Good luck, I hope this helps. —Alex

2674631,679626267626I woke up like thiskind of way). I wonder whether there were glottal stops in original (pre-digital) Garamonds.323So I believe he might have been asking the recurring more specific question as well, are there methods to arrange my control points and handles in the most correct way? I admit I have never dug deeply for this.

Here’s an old thread with suggestions: https://typedrawers.com/discussion/967/beziers (some links no longer work).

948626267463That, and lots of RMX's Harmonizer tool.

323In the last case, the question goes directly to your reply. Otherwise, since you have already obtained the desired curve, it’s a matter of redrawing it with the curves, and thus the question becomes both technical and of getting accustomed to them, as you said.

459I get much better results when placing nodes at “corners”. I mean as if I drew a Bezier circle and rotated it 45 deg. Something like:

If I try to do this with nodes at extremas, I always end up having frustratingly ugly shapes

I use the FontLab 7 node sliding (Shift-Alt-drag) to get a node to a position where the angle of the handles makes visual sense (often at the point of highest and lowest contrast). I can get sensible shapes then. The longer the handles the better.

Once I’ve drawn something, I copy to mask and “Clean Up”. Then I get “technically correct” curves with nodes at extremas, but that means that something is lost — somehow those resulting curves no longer “create” the shape, merely “describe” it.

1,259625459626somehow, differs from what you expected.