Using bezier curves effectively

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David Sudweeks's picture
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Using bezier curves effectively
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The same glyph done with curves whose handles extend [1] at 45° and 90° angles; and [2] the way that felt good at the time.

I'm new to digital type design. The above is in Illustrator. Could I get the advice of somebody with a lot of bezier curve experience on what works best for them? I'm open to even the most upbraiding comments, including 'Don't do it in Illustrator'. (Maybe you could do even better.) I took some time to create outlines of some famous type and look at it, but it seemed so full of anchor points.

Satya Rajpurohit's picture
Joined: 27 Jul 2006 - 3:31pm
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Illustrator is Fun, FontLab is Gun.

David Sudweeks's picture
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I'll give it a shot.

[edit: pardon the unintentional pun]

Mark Simonson's picture
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Generally, you want to use as few control points as possible. Too many points makes it hard to get a smooth, flowing line on a long curve. Too few points restricts the possible path the curve can follow.

If you are intending to create fonts, it's good to get into the habit of placing points at the "extrema" locations on curves, which are points that are on the extreme left, right, top, and bottom of a curve. On a circle, these would be at clock points 12, 3, 6, and 9. Another way to think of it is, if you put a rectangle around the curve just large enough for the curve to fit, the points where the curve touches the rectangle are the extrema points. Extrema points are mostly needed for hinting to work properly in fonts.

Jelmar Geertsma's picture
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> If you are intending to create fonts, it’s good to get into the habit of placing points at the “extrema” locations on curves,(...)

And try to keep the control handles mostly vertical and horizontal. There are exeptions, but for smooth curves, straight handles are important.

Also important; if there are two vectors with a curve in between, try to make both handles 'carry' the curve equally.

Blank's picture
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There’s an excellent chapter about this in Leslie Cabarga’s book The Logo, Font, and Lettering Bible.

Mark Simonson's picture
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> And try to keep the control handles mostly vertical and horizontal. There are exeptions, but for smooth curves, straight handles are important.

Right, by definition, if the points are on the extrema, the control handles will be either perfectly vertical or perfectly horizontal (assuming it's not a corner). Note that if you're just working in Illustrator or something similar, it doesn't generally matter.

Jelmar Geertsma's picture
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Yeah, but you can always pull one of them in another direction, especially in Illustrator. Which will result in bumpy curves.

James Montalbano's picture
Joined: 18 Jun 2003 - 11:00am
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I certainly agree with Mark about point placement, but the thing I find most interesting about the example is how lousy the resulting artwork looks. Whatever your philosophy of point placement is, the outlines created did follow the analog artwork with a fair degree of accuracy but the results are less than ideal. It may be what the analog artwork actually looks like, but in the realm of digital outlines, it disappoints. There is a difference between digital and analog art, and slavishly following an analog original, will not give you what you want.

But then again, most analog art is flawed, and deeply so, when it comes to translating it to digital outlines, and it relies on the skilled interpreter to render it in a pleasing form in the digital realm, regardless of what the analog original actually looks like.

James

Mark Simonson's picture
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Good point.

When I look back at my early bezier drawings I can't believe how bad I was, even though I was skilled at doing the same thing with traditional tools. The only cure seems to be time and practice.

Christopher Slye's picture
Joined: 5 Oct 2006 - 11:03am
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Good advice here, I'd say. I'll just elaborate a little:

Related to hinting benefit, having points at extrema also helps with design by making it easier to keep sidebearings and stem widths predictable. At some point during typeface development, you'll run into some reason to care about the bounding box of a glyph, and if it's being determined by a curve rather than a point, it will be difficult to adjust.

That being said, I've been told a few times that points at extrema are less useful in italic and script faces, because the stems are not vertical. (Of course there are still horizontal stems.) And there's no need to get overzealous about it in the small details. The rounded end of a protruding serif probably doesn't need an extra point there.

It helps to have a general understanding about how PostScript lines are drawn. Just like Mark, I'm a little embarrassed by some of the constructions I did ten years ago; back then I though of a single point and its two control handles as an element, whereas PostScript sees two points and the line and control handles in between as an element. If you can get a bit of that embedded in the back of your mind, you'll make better decisions about where to put things.

If you are designing multiple master outlines, all of this advice becomes more important. Having a simple, disciplined approach to outline construction will help with interpolations.

(You'll want to remove that overlapping path eventually, too -- but maybe you knew that already!)

Stefan Seifert's picture
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>There is a difference between digital and analog art, and slavishly following an analog original, will not give you what you want.

Oh yes, there is a great difference!
And in the first time in the history of human culture people are convinced to have found something within the computers and beziér curves that could equal or even do better than analog form like the one we see in the nature before our feet (as long there will be left some) We can’t and never will. Dante even before Renaissance age did know that.
Analog form will always be superior to any kind of mathematical constructed curve because it reflects the face of god and his creation.
I design digital typefaces for 15 years now and I still love to do it. But that doesn’t change what has to be said about it.

;-)
Stefan

David Sudweeks's picture
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Thanks to all for your helpful advice. In any of the past projects I've done, it's just taken a lot of work. I'll keep working. Here's a (in my opinion, improved and not so clumsy-looking) version of the same glyph. Outlines are of the glyph without and with points at the extrema. I did have a lot of trouble doing an outline with just horizontal and vertical handles. I guess the main reason why I reject it is just because of the /ax/es/ of the glyphs in this case. I know I'm a novice. I have spent hundreds of hours with bezier curves, (not tens of thousands as you probably have) but it feels wrong to try to do that (in this specific case).

The last outline I decided to throw in for conversation. It's Hoefler Text's italic Q. I noticed the points at the extrema, but what interest me are the many points that just seem unnecessary. Is that how it was drawn, or were those added in later for some reason?

Mark Simonson's picture
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The reason there are so many points on the Hoefler Text Q is that it is a TrueType font outline converted to PostScript bezier curves. TrueType does not use the same kind of curves as PostScript, so when you convert to outlines in a program like Illustrator, you get roughly twice as many points.

paul d hunt's picture
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Q. I noticed the points at the extrema, but what interest me are the many points that just seem unnecessary. Is that how it was drawn, or were those added in later for some reason?

it's hard to tell. in what software program were you checking this outline?
what was the font format of the font in question?
what are your FontLab import settings?

these all make a difference.

Ben Mitchell's picture
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I have a question too, if i may join it in here to the discussion. I am just starting with some software called Font Creator, which allows as few or as many control points (circles) as you like between the start and end-points (squares).

My letter 'e', for example, is here so you can see what i mean. Is this going to create problems too? Is Font Creator a very bad programme?

(I know some of the curves are not smooth; I'm still working on it)

Would I be better using Illustrator/something else?

Thank you!

David Sudweeks's picture
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Bendy,
That depends on what you'd like to accomplish. I'm just playing around in Illustrator right now. This work is eventually for a logotype, so I'm not worried about many of the things that would otherwise concern me regarding font creation. FontLab is the voiced tool of choice for the vast majority of the Typophile community.

Tim Daly's picture
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One of the benefits of using as few points as possible is, that once the points are positioned, one can drag the curve (rather than moving the arms of one or two point[s]), I’ve found that keeping to x and y axes makes life simpler, although this doesn’t always prove possible.

Tim

Satya Rajpurohit's picture
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I find myself not caring too much about the extrema as long as I am in the design process. For example, I could design an italic "o" with just two points for each contour placed at the point where the stroke should be the thinnest. By doing this it is much easier to change the curves without having always to adjust several points at once.
After the design is finished I insert points at the extrema and delete the other points. This is very easy in FontLab since it tries to keep the curve the same when you add and delete points. Unfortunately that's not the case in Illustrator.

Ben Mitchell's picture
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Thanks for your comments. I'm not of course a professional font designer so don't necessarily need high-power software and Font Creator seems to do most things I need so far.

My real concern was whether to use quadratic, cubic or more complicated curves, and if this might cause problems on other platforms. I do now see the benefit of fewer points and of keeping them at extrema.

William Berkson's picture
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>That being said, I’ve been told a few times that points at extrema are less useful in italic and script faces, because the stems are not vertical. (Of course there are still horizontal stems.) And there’s no need to get overzealous about it in the small details. The rounded end of a protruding serif probably doesn’t need an extra point there.

This is an important cautionary note, I think, as it shows there are other approaches that may be helpful, depending on what you are drawing. It is often helpful to the drawing process to have points on curves only at extrema, with horizontal and vertical handles. But sometimes it helps the design process, particularly in an italic, not to do this. And even in the final outline, these are not a requirement for auto-hinting in in Type 1 or CFF in every situation either, as Christopher points out.

Also I think there is a problem of too much digital type looking alike, and sometimes looking a bit sterile. Putting in intermediate points creates more challenge in getting smooth curves, but it also can give curves a more warm and organic look. I think trying both ways--with and without intermediate points--is often a good idea.

On cubic vs quadratic curves, my impression is that almost everybody initially designs with cubic beziers, and then converts if they are doing True Type. But I may be wrong about that.

Randy Jones's picture
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It is easier to see the benefit of designing with extrema in Fontlab vs Illustrator. That's because even though both are vector-based programs, Fontlab's vectors have resolution dependence (ie points and handles can only be on integer numbers). The equivalent in Illustrator would be designing with "snap to grid" turned on, and a fine grid. When I moved into Fontlab this was one of the most frustrating things (and sometimes still is). But, it does help you keep your design consistent and often it helps me create smoother curves than I would in illustrator. Now I finalize all logos in FL too.

I also agree will Bill that beziers can dull your creativity. Straight stems and crisp corners are the mode by defualt because of the tool. To combat this, sometimes I'll go for a session in illustrator, or rough in a design using short straight segments, and then convert to curves using FL's fantastic line to curve tool. For an example of a roughed design see ye old type battle 12. http://bigcartel.typophile.com/battle12

BRING BACK THE TYPE BATTLE. I'm getting too productive at work.

R

Jelmar Geertsma's picture
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what happened to type battles anyway?

Randy Jones's picture
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Should have said David, your second G is looking much better, but still has some issues. In an effort to be helpful:

One problem I have when sketching a script with a pencil is that there's a big difference between a pencil and a quill/brush/steel pointed pen etc. The difference is that those instruments produce thicks and thins regularly depending on how you hold, twist and form your letters. To replicate it well with a pencil requires an intimate understanding of those details. In your example (like mine often are) the ductus is somewhat confused.

For example, the following might be two ways to construct your G (green or purple). Depending on what the tool is, that could mean a bunch of different things. Stroke 1 could be entirely thin or include a thick if the tool allows for contrast on the upstroke by applying pressure (such as steel pointed pen -- see Edwardian Script). Whatever rules you set for yourself, stick to them. I'm no expert with scripts, so everyone please chime in here.

Just looking at the quality of the curves themselves, there are some lumps and kinks. I will say it's hard to tell from a gif at this size. In general on the down strokes I would move the weight lower in the curve. This makes sense as you think about pulling the instument down the page adding weight. Watch out for wide-narrow-wide sections where it should be smooth (the little waist marks in green). The other thing is that some of the cuves happen too tight, or not smoothly enough (marked with a green corner). Lastly, watch your intersections. Here you have medium thickness crossing medium (a no-no). In general, thicks cross thins. Thins can cross thins, but never thicks crossing thicks (or almost thicks crossing almost thicks :-) There are probably exceptions, but in general this is true.

Hope that helps, or at least coaxes out better advice :-) You've chosen an ambitious project. Digital scripts are EXTREMELY tricky on the designer and their beziers. Especially so with thin ones like this since it's often harder to tell what is wrong. Good luck!

Randy

EDIT: one last thing. If you can, check pages 180-196 of Doyald Young's excellent FONTS & LOGOS. His is a script master and offers several nuggets there.

David Sudweeks's picture
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Randy, that's super helpful.

Endre Berentzen's picture
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I second that David, thanks Randy! This is a really good thread guys:-)

David Berlow's picture
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"(You’ll want to remove that overlapping path eventually, too — but maybe you knew that already!)"

Why should overlaps be removed?

"The reason there are so many points on the Hoefler Text Q is that it is a TrueType font outline converted to PostScript bezier curves."

I'm certain that it is a PostScript outline converted to TrueType.

The other two things no one mentioned here, or I missed, that might be helpful, are: that the drawing of the shapes without the points on extrema is common. Left this way, non-extreme contours remain fine at high resolutions.

And, that anything less than high res and extrema-d contours become required (hinted or not) because of the general effects of scaling. The illustration below shows two perfect circles with that one difference (above). Then, (below), scaled to 1%, and back up again.

The left bottom "circle" is in fact "better", regardless of the fact that it is also more easily hinted. :-)

Cheers!

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The idea of resolution and beziers being used in the same scentence is probably odd to most Illustrator-only folks. Perform the same 100 > 1 > 100 in Illustrator, and there will be no difference (or almost none). David's example above is great to show the resolution limitations of Fontlab and fonts in general. But it should also be said that anytime vectors are viewed, they're quantized into pixels or toner flakes etc. Blow up a scan of a print and the curves looked tweeked too, but less so, if there are points at the extrema. And there's the rub.

Randy

Christopher Slye's picture
Joined: 5 Oct 2006 - 11:03am
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Why should overlaps be removed?

Because PostScript prefers it. I am not mentally equipped to get into a discussion of how today's various rasterizers behave, but there are plenty of past examples of trouble caused by overlapping paths, reversed paths, and other PostScript oddities. For example, some rasterizers will show a filled, overlapping section as unfilled.

The Adobe Type 1 Font Format says:

3.6 Overlapping Paths
A single closed outline should not intersect itself ...

Kyle Hildebrant's picture
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This is a great thread. Thanks all who have been contributing.

Stefan Seifert's picture
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>Also I think there is a problem of too much digital type looking alike, and sometimes looking a bit sterile. Putting in intermediate points creates more challenge in getting smooth curves, but it also can give curves a more warm and organic look. I think trying both ways—with and without intermediate points—is often a good idea.

Thanks William!!!!!

Stefan

David Berlow's picture
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"Why should overlaps be removed?"
"Because PostScript prefers it"
I think you mean, some PostScript requires it, so all PostScript prefers it.
I guess I agree with the points on extrema to an extreme, and that's the rub.
When people here say "points on extrema" what's really meant, is that the extreme extent of a glyphs curve has an on-curve point and two colinear off-curve points. This makes scaling a relative breeze, as rounding effects the trio of points identically (in one dimension at least). When removing overlap introduces quads of points (or worse, think Ø), that must round in two dimensions to an implied but not specified line, degrading under the stress of resolution and or reproduction is sure thing. Palatino Linotype on the Mac, "&" below 20 pt on screen is a pretty good example.

Cheers!

David Berlow's picture
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"Perform the same 100 > 1 > 100 in Illustrator, and there will be no difference (or almost none)."
I know, but on the other hand, if you view an 8.5.x11 page at actual size in Illustrator, it'll never, or almost never actually be so.

Your choice, draw with no relationship to the reality of scaling, or actually think about the fonts being produced by the outline....by lookin; at em! :)

Cheers!

Christopher Slye's picture
Joined: 5 Oct 2006 - 11:03am
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I think you mean, some PostScript requires it, so all PostScript prefers it.

Yeah, that was just my way of saying it without being too dogmatic. I couldn't say it would always be a problem, but the T1 spec seems to want it that way, and at least at Adobe we'd consider it a bug.

This business of "grid-fitting" points (i.e. integer values) is an interesting topic. If one is going to work on a font and do a lot of scaling, then there is a case to be made for doing it in Fontographer or Illustrator, where shapes can be transformed a lot without the cumulative rounding errors. But it's worth pointing out -- because I've encountered people here and there who miss it -- that the outlines will be rounded to integer coordinates in the final font. That's the advantage of FontLab; it's more WYSIWYG.

Fábio Duarte Martins's picture
Joined: 23 Nov 2005 - 10:27am
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Well, if it's still of some use, here's this:
http://learn.scannerlicker.net/2014/04/16/bezier-curves-and-type-design-...

Cheers!

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I'll add my two cents to this.

I agree with Rob O Font, (26 Sept 2007 5:51 AM), when he said "drawing of the shapes without the points on extrema is common. Left this way, non-extreme contours remain fine at high resolutions. "

I'm not a professional graphics designer, nor do I design fonts for a living. I experiment with typography as a hobby, using archaic applications and techniques. I don't have Illustrator. I do have FontLab Studio5, but I prefer to use one of their other products, ScanFont 3, which only works with Windows operating systems prior to Vista. I draw my glyphs as monochrome bitmaps in MS Paint.

In my latest font, I used the monochrome source images from a previous font I'd made named Outstanding, (2012), based on an 1874 design originally called Light Shade, (AKA NightShade, in Solotype Catalog of 4,147 Display Typefaces, page 17). This alphabet has previously been digitalized as NigelsadeSH by Soft Horizons, (1993), very poorly by James Fordyce as Shadowed Serif, (1994), by Character as CameoAntique, (2011).

I create fonts by modifying photographs or artwork. I created Outstanding by scaling the large .jpg images available here: http://bigletters.org/big-decorative-vintage-letters.html
manually tracing them to two colours, composed for monochrome, as source graphics to import into my font editor.

Source graphic for S:
http://s26.postimg.org/6tmbl81q1/big_vintage_letters_s3_24b_778_24b_280_edit5_fin.png

After completing Outstanding, (a decent font, by freeware standards), I was displeased with the results. I liked the concept, but I thought the rendering of the alphabet design was poor, and the letters were much too wide for practical use.

I started by reducing the width of the Outstanding source graphics by 20%, without changing the height:

Source graphic of S from Cabbagetown:

http://s26.postimg.org/vo5tfamk9/big_vintage_letters_s3_edit5_final_80_mc.png

My 'raw' vector looked like this:

http://s26.postimg.org/h7ik0px2x/raw_S_vector.png

At this point, I begin to 'sculpt' the vector, by removing all nodes that are not necessary to hold the contour shape in place. I also make alterations to the design in the font editor, by manipulating the positions of the remaining nodes and control handles.

My final design is almost entirely based on Cartesian geometry, in the sense that the majority of the nodes and handles end up aligned with each other, in vertical, horizontal, and diagonal directions. This screen capture of the final edit:

http://s26.postimg.org/ejvef8gqh/S_133q8_vector.png

shows nodes in green, light blue, and red, with handles in yellow. The purple lines show horizontal and vertical alignments. The majority of the nodes at lower left and upper right have diagonal alignment with each other. Only 36 nodes are used to create the glyph.

I get really smooth outlines at enormous point sizes:

http://s26.postimg.org/6sa32xn7d/S_133r3_288_pt.png

I haven't figured out why the alignments occur, (this process is being used for the first time), but every glyph has them:

K from Cabbagetown, modified slightly since this screen cap was made:

http://s26.postimg.org/g6rle5juh/K_129i9_vector.png

I think of the vector as a malleable shape that evolves as it becomes more efficient and structured. The end result almost has more in common with chemical engineering than with graphic design, but I have to play to my strengths. I barely passed art class in high school, but I had completed all available math courses shortly after by fifteenth birthday.

I don't advocate that anyone abandon Illustrator to adopt MS Paint, but I do feel that the glyph on the Illustrator drawing board is just the first step in creating a fully realized vector.

Rather than placing nodes on the extrema, I remove the nodes that are not on or near the natural curvatures that I want to have. The curved dome on top of the S is created by the placement of two control handles on two specific horizontal planes. If I move either or both handles vertically, a flat spot will be created on top. If I move either or both horizontally, the curve on top will remain, but its position will change. This is, by no means, easier to do than the 'by the book' method of placing nodes at North, South, East and West, which guarantees a flat spot at each location, which no one will notice, provided that the text is small enough, or it is displayed in an app that hides small errors with smoothing.

Thomas Phinney's picture
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There are two different things here: one is doing the initial drawing with nodes wherever seems best for drawing and editing; the other is where nodes are placed on the final output font.

My take is that not having nodes at extrema will result in poor rendering on screen in many Windows rasterizers.

(EDITED to correct missing “not”)

Martin Silvertant's picture
Joined: 31 Dec 2009 - 11:51pm
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I've never heard of that. So should nodes at extreme be avoided, or what are you doing differently to guarantee proper rendering?

Also, can someone tell me what you consider to be the great benefit of doing your design in FontLab Studio? I sometimes do slight modifications in FontLab but haven't gotten used to it as a standard design program. I do my typefaces in Illustrator and then drag the design into FontLab. In Illustrator working with guides is easier to me, and I can zoom in further into the design to fix details.

My first attempt at a serif typeface years ago was rather disastrous, I believe I spent over 120 hours on it and I learned tremendously, but in the end I realized my way of handling nodes was very bad, and if I wanted to use the design at all I probably had to re-do each letter. I never actually tested what effect this way of handling nodes has. Can someone tell me what would happen to the first design David Sudweeks posted here? Does anyone have examples of the effect of handling diagonal beziers?

Fábio Duarte Martins's picture
Joined: 23 Nov 2005 - 10:27am
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My take is that having nodes at extrema will result in poor rendering on screen in many Windows rasterizers.

Thomas: please explain this, my eyebrows are twitching in very odd ways.

Craig Eliason's picture
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I'm almost positive he meant to write "NOT having nodes at extrema..."

Thomas Phinney's picture
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Indeed I did. Fixed now. Eek.