Interpolating ?

RachelR's picture

Hi all

This might sound like a strange but what is interpolating and how is it used in type design. I keep reading articles with it mentioned but I'm not completely sure what it is.

Rr

William Berkson's picture

As I understood from a presentation by Thomas Phinney, it is essentially producing a new glyph that averages the distances between points on two related glyphs--they need to have the same start point and number of nodes. The interpolation doesn't just have to be a 50/50 average, but can be 90/10 or whatever you want. You can also extrapolate.

There are two things most available for doing this, the MM technology in FontLab, and Superpolator, which has additional capacities.

Your can read more here (scroll about half way down the thread):

http://typophile.com/node/39965

blank's picture

William gave a good simple answer, for the complex details read this PDF:
http://www.adobe.com/devnet/font/pdfs/5091.Design_MM_Fonts.pdf

Also, take a look at the Superpolator site:
http://superpolator.com/

William Berkson's picture

The Adobe document James links to is really good. I got it some time ago. In talking with Lucas de Groot after a lecture of his, he recommended it as a kind of hidden treasure on type design written by "Slimbach himself."

Tim Ahrens's picture

Hi Rachel,

Interpolation is essentially the same as creating a mix drink:

To create your cocktail (c) you would typically pour in a certain quantity (q) of drink 1 (d1) and then fill up the rest of the glass (1-q) with drink 2 (d2).
So: GinTonic = q Gin + (1-q) Tonic.

Interpolation of fonts works in exactly the same way. Even the formula is the same, only it is applied to the node coordinates. You mix two flavours and what you get in the end is something that, ideally, feels like somewhere in between. Unfortunately, extra light mixed with extrabold does not feel the same as a real regular just like water plus brandy does not taste like wine even though it may have the same "weight". I hope this analogy helps to understand the issue.

William Berkson's picture

Thanks, Tim. Cheers!

ps Interpolation also scales the handles, right?

dezcom's picture

yes.

ChrisL

Nick Shinn's picture

FontLab > Tools > Blend Fonts...

RachelR's picture

So Interpolation is the process of creating a medium weight from a Light and a bold weights ?

Miss Tiffany's picture

Non-type designer interruption:

But from what I know and see interpolation doesn't produce the final result, just as extrapolation to get a bolder or thinner weight doesn't. So many fonts I see where the designer doesn't complete the process by fine-tuning after the fact. Not doing so renders the font completely useless to users.

End of Non-type designer interruption.

dezcom's picture

"So Interpolation is the process of creating a medium weight from a Light and a bold weights ?"

In a way, yes, but it is not just limited to changes in weight. Slant is another derivation but that gets trickier. You can have a slanted font and an upright font and interpolate something in-between but you must have compatible outlines to work with.

Interpolation is finding an intermediate step between to known axis extremes with compatible outlines. Extrapolation is attempting to determine an instance which is beyond either of the known extremes and projecting what it might look like if the same rules were followed as with interpolation. With extrapolation, the odds of failure to make a reasonable image is higher and that failure rate grows with the greater distance beyond the known axis increases. If I attempt to create an instance of semi-bold between the known forms of light and bold, I have quite a good chance of success with minimal correction. If I try to determine an instance of an extra-bold from those same 2 light and bold known originals, my success rate will be somewhat less. Then, if I use the same pair to try to determine an extra black instance, my odds of success become even less likely and I will surely need much adjustment to make a tolerable looking Extra Black. As Tiffany said, fine tuning is important. With extrapolation the tuning is more than fine and requires much work. There is a point of diminishing returns where the corrections overcome the value in extrapolation.

ChrisL

William Berkson's picture

Tiffany, I think the math of interpolation is such that interpolation generally gives better shapes than do automatic bolding routines. That's because you've already designed the extremes by eye to match, and the so the intermediates in effect already have a lot of the adjustments already programmed in. I'm sure Tim can explain it better, but I think the point is right--it explains Chris's success with interpolating and having relatively minimal adjustments.

Nick Shinn's picture

So Interpolation is the process of creating a medium weight from a Light and a bold weights ?

Yes. Which is why it makes sense to create the extreme weights in a type family first, and interpolate all the others from these.
In particular, the Thin in a sans serif is a good starting point, as all you have to do is draw a path and apply a stroke width.

dezcom's picture

"Interpolation is finding an intermediate step between to known axis extremes"

I meant to say:

"Interpolation is finding an intermediate step between TWO (or more) known axis extremes"

I dare not fix my original post or it would move to the bottom and screw up the whole thread.

ChrisL

Miss Tiffany's picture

Oh. William I wasn't advocating automatic bolding at all. Ech. This could be me showing my ignorance to most of the process. I shouldn't have interrupted. Continue. I'm learning.

William Berkson's picture

Tiffany, I didn't express myself well, as I wasn't thinking of eg when Word does an autobold.

I was thinking actually of when you use the FontLab interpolation tool to get a bold. Somehow always requires a lot of fixing, even though it's not totally mechanical--you choose what points to extend, and do x and y passes separately. But interpolation between two weights seems by report--I haven't done it yet--to give pretty clean results.

It just occurred to me: Rachel were you maybe asking about the interpolation tool in Font Lab, rather than interpolating between two weights? That is explained, sort of, in John Hudson's wiki on small caps from caps.

I admit I don't fully understand the rules operating in that tool. Sometimes it seem to go around corners and sometime not. I've used it anyway, just seeing what works by trial and error.

RachelR's picture

Thanks for your help explaining - I think I understand now.

On another related topic what are your recommendations for drawing a bolder weight from say a thin weight. Nick mentoned drawing a thin weight and then adding a stroke to obtain bolder weight - is this the process most people use ?

Rr

John Hudson's picture

It just occurred to me: Rachel were you maybe asking about the interpolation tool in Font Lab

I also wondered that, but the basic principle of interpolation is the same: for any two or more elements in a design space it it possible to interpolate intermediate elements. So, for example, one can interpolate between two weights of a typeface design to derive a new weight (as in a Multiple Master font), or one can interpolate a section of an outline or even a single node relative to changes in the position of other sections or nodes (the latter is what FontLab's 'Interpolate Nodes' tool does).

dezcom's picture

Here are 2 quick samples. There was no adjustment made before or after so the results are not as good as could be.
The first example shows a range with 2 axii, regular and bold. Between them (on the 2nd line marked demibold) is an interpolation with some need of fixing but still tolerable as a beginning point. The last line, as extrabold, is extrapolated and obviously in need of much more fixing. It looks better than it really is onscreen in low rez but don't let that fool you.
The second image is a blowup of the "a" from the extrabold extrapolation. Notice where the curves have flipped on eachother and caused overlaps? This example is not even extreme It is only 50% above the axis. If I went to Extra Black, it would look far worse. This is as far as FontLab will go though so I can't show you the really bad one.

ChrisL

Goran Soderstrom's picture

This is as far as FontLab will go though so I can’t show you the really bad one.

In fact, there is no limitation in FontLab. Try and type any number above 1500 or below -500 in the field, and you see that you indeed can produce the really bad ones :)

dezcom's picture

Thanks, Goran. I didn't know that before. Not that I will ever really use anything so far beyond except to show how ugly it can get :-)

ChrisL

Nick Shinn's picture

Rachel, no, you have to draw the bold. But I would say, draw the Extra Bold.
Why don't you try interpolating Helvetica 25 and 95, and see if you get 55? Or 35 and 75.
That will give you an idea of how effective working with extremes can be.

Goran Soderstrom's picture

Not that I will ever really use anything so far beyond except to show how ugly it can get :-)

Sometimes it can however work rather fine if you really plan how you place your points and handles. A corner for instance, like your example above doesnt have to be distorted that way if you place the nodes more carefully in the masters.

dezcom's picture

Goran,
I didn't even try to make my masters compatible, I was hoping for even worse results to show as an example. I rarely trust anything that seems too automatic anyway so I tend to pretty much redraw every extrapolated glyph. Nice to know I could push it further than I thought though. Thanks Goran.

ChrisL

blokland's picture

Perhaps it is interesting to know that with the in basis more than 30 years old Ikarus V4 interpolation module one can interpolate (more or less) corresponding letterforms with totally different numbers of IK points.

To illustrate this, I have made an interpolation (50%) between DTL Argo Regular and DTL Fleischmann Display Regular on our Ikarus system running under X11 (which we use for some functionality currently not available in FM).

Goran Soderstrom's picture

Interesting.

Would that also be of better quality in the bezier curves than if you did the same in FontLab?

dezcom's picture

Glad to see Ikarus can still fly.

ChrisL

Bendy's picture

I was interested in how effective FontLab would be at interpolating, and tried using it on a font I've recently started. You can see the pdf at www.typophile.com/node/37639. It's the one called Eternal Sample, where I've started from the Regular and Extrabold and interpolated the three weights in between. I hadn't touched the results, so that gives an idea exactly how good it is. There's one glitch on the semibold y, but otherwise just needs fine tuning. I didn't purposefully place nodes knowing how that would affect interpolation.
The font has now gone in a different direction so I'll redo these at some point.

blokland's picture

‘Would that also be of better quality in the bezier curves than if you did the same in FontLab?’

Actually I was not aware of the fact that one could do the same in another application.

If the IK marks are placed correctly on the contour(s), the conversion to Bezier splines will be adequate too.

Goran Soderstrom's picture

Yes, you can, but the result needs a lot(!) of fixing. Your example looks more clean to me.

blokland's picture

‘[...] Would that also be of better quality in the bezier curves than if you did the same in FontLab? [...]’

In the example the word was made within a glyph slot with the ‘Set Text’ option in IkarusMaster. The IK data was directly converted to Bezier curves with the default tolerance setting.

‘[...] Yes, you can, but the result needs a lot(!) of fixing. Your example looks more clean to me. [...]’

Also in this example ‘some’ cleaning has to be done. At the other hand one has to be careful not to consider functionality as identical if the outcome of an in basis comparable process is clearly different.

dezcom's picture

It looks like the fitting of splines to match a curve is something like we used to do in the old days when using assorted french curves and a ruling pen to try to draw a particular curve.

ChrisL

Rob O. Font's picture

That's why, when we began using Ikarus, and later tools, we started by digitizing our french curves, (and our scales). :)

"adding a stroke to obtain bolder weight - is this the process most people use ?"

FontLab is unkind to the original, sacred, points of a digitization, when "bolding" or "stroking" is used. To avoid the process of tediously having to go back through a sacred digitization, now polluted, to look 'under' every point, pan and zoom repeatedly in a hunt for FontLabs destructive ways, for me at least, is usually more time consuming than a careful, manual, bolding, or blackening, if in the end, blending, or interpolation, is required.

Cheers!

dezcom's picture

The old saying "There is no such thing as a free lunch" comes to mind. If something can be done as easily as a push of a button, the odds are, it will do as much harm as good. The bigger the amount of bolding, the worse the mess will be to correct. If you must use the automatic feature, just paste it in the mask layer and make your drawing fresh in the glyph window. Feel free to ignore 95% of what the auto bold thing did. As David said above, the mess is mischievous and sneaky. It is kind of like buying a Rollex from a street vendor in Manhattan. It seems like a sweet deal untill the next day :-)

ChrisL

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