How to get the length of paths in an given font/character

Question

I wan't create some LED-rope text, using some script font, like the following:

For this I need somewhat estimate the needed length of the LED-rope for the given letter (or combinations of letters).

Some more info:

• The font will be TTF or FT2.
• I could manage some programs in perl using the FreeType library, eg. read some properties of the character in the font-file - if this helps.
• Also could install Inkscape (Illustrator open-source alternative) or even could use Illustrator at my friend - if any of this tools could help.

Looking for some suggestions how to measure the length of paths in the given font for the particular character (or whole text).

I don't need exact precision, (see the purpose above) and looking for the solution as simple as possible, but I haven't any idea how even approach this problem. :(

Of course, I always could print the text and buy some inexpensive curve runner, but would be better to have some computer-based solution. :)

Ps: I'm not fully sure that this is the right place to ask such question, if not - I will delete it, but please suggest some better place.

Answer 1

The way I would approach this is to get the outline curves of the font and then break each one down into some fixed number of steps (like, say, 100), and make a series of very small straight lines.

So if you've got some bezier curve, you loop t from 0 to 1 in 100 steps and plug it into the equation:

double x = calculateBezier(0.0, c0.x, c1.x, c2.x, c3.x);
double y = calculateBezier(0.0, c0.y, c1.y, c2.y, c3.y);
double dist = 0.0;
for (double t = 0.01; t <= 1.0; t+= 0.01)
{
    double nextX = calculateBezier(t, c0.x, c1.x, c2.x, c3.x);
    double nextY = calculateBezier(t, c0.y, c1.y, c2.y, c3.y);
    double nextDist = sqrt((nextX - x) * (nextX - x) + (nextY - y) * (nextY - y));
    dist += nextDist;
}

Where calculateBezier() is a function that calculates a point on a bezier curve given the parameter t and control points c0 through c3:

double calculateBezier(double t, double c0, double c1, double c2, double c3)
{
    double t1 = 1.0 - t;

    return (t1 * t1 * t1) * c0 + 3.0 * (t1 * t1) * c1 + 
            3.0 * t1 * (t * t) * c2 + (t * t * t) * c3;
}

And just add the distances of each part of the curve until you're out of curves.

Note that this assumes cubic bezier curves. For quadratic, the calculateBezier function would calculate a quadratic one (like described here).

Answer 2

I decided to solve the LED-rope problem using Inkscape as:

• enter the wanted text into the Inkscape
• set the color of the text to yellow
• add new layer above the text and lock the text layer
• in the new layer, manually draw over the letters my own wanted bezier path(s)
• and finally use the tool in Extensions -> Visualise Path -> Measure Path... - this adds the length of the given bezier path into the drawing as text.

The reason why:

I studied a bit the ttf-font structure (the whole new world for me). This blog entry and this Reference manual helped a lot understanding the following (rough) basics.

• the given glyph (character) is composed from many closed paths, e.g. the letter O is composed from two paths (outer circle and the inner circle).
• the paths are stored in the font file as pairs of x-y coordinates
• so it isn't so hard to calculate the length of each path from the given coordinates.
• but - in such way I will get the lengths of the all outlines. Creating the outlines using the LED-rope it could be even interesting and also it is used at many examples, (like bellow), but this isn't what I want - I want a simple path(s) - as in the image in the question.
• getting such simple path from the font's many outlines would need some tracing and approximation and other complicated math, which is definitely outside of my area of interest.
• therefore (for me) would be much easier just manually create the simple path's and measure their length in the Inkscape.

Also,

• if someone want the length of the font's outlines, it is easily doable
• just need break apart the text into characters
• transform the (font) objects into the strokes
• and use the Measure path... tool