It's wonderful to see someone dive into this as deep. A simpler way to understand the complexity might be to try designing your own font.
Pick up a book on type and start up Fontforge, and off you go.
Be careful though, make an early choice if you are going with 3rd order curves or 2nd order (Bezier) curves.
Going through TeXbook and MetaFont books by DEK is also a brilliant way to learn about all this, with note that they do have an explicit
bitmap step in.
One correction though:
Without it, you wouldn't be reading this right now.
Computers started with bitmap fonts of different pixel sizes. Your console terminal in Linux is still using that, and nothing stops you from using them ("Fixed" has large Unicode coverage and is usually preinstalled) elsewhere too.
So no, none of this tech is necessary for us to read text on computer screens.
Fascinating read. Font rendering perfectly encapsulates the conflict between continuous mathematical curves and discrete pixel grids.
I run into similar 'quantization' challenges when building generative design systems in Python. Sometimes a mathematically 'perfect' alignment on the grid looks optically wrong to the human eye. The anti-aliasing logic described here is a great mental model for handling those edge cases.
Not OP, but white text on black (especially at 100% contrast) is harder to read than black text on white. Monospace is harder to read than natural-width text. Large passages of text with both features is fatiguing to read.
Black text on white background with no backlight is easier to read. Think black text on paper.
When it comes to computer screens, usually set too bright to accommodate varying ambient lightning conditions throughout the day/year, it's not as simple, and I am not sure there is a study to confirm it.
And even if so, any individual's case might be different.
I'm working on my own text editor and have ventured into font rendering as well. The main thing to understand about fonts and font rendering is that they are just bitmap images and the program just puts them together with simple XY+WH from a pre-rendered square image(square because GPUs like squares), called atlas, which in CSS would be called a sprite. It's really that simple.
Header-only libs can help avoiding the troubles and complexity of linker setup. This might be even more important on Windows, which this lib "explicitly support".
short answer, because C/C++ sucks. To work around how bad C/C++ sucks people put the entire implementation into one file. That way, there's less question of how you need to integrate it into your project.
In more modern langauges, this is a solved problem and it's easy to use other people code. In C/C++, it's not. As a relavant example, try using FreeType in your C/C++ project, make sure your solution compiles on Linxu, and Mac, and Windows (and ideally other platforms)
>> As a relavant example, try using FreeType in your C/C++ project, make sure your solution compiles on Linxu, and Mac, and Windows (and ideally other platforms)
This was interesting, thanks. Was hoping to see a bit more about type hinting, but there's already a lot here.
A question about efficiency: IIUC, in your initial bitmap rastering implementation, you process a row of target bitmap pixels at once, accumulating a winding number count to know whether the pen should be up or down at each x position. It sounds like you are solving for t given the known x and y positions on every curve segment at every target pixel, and then checking whether t is in the valid range [0, 1). Is that right?
Because if so, I think you could avoid doing most of this computation by using an active edge list. Basically, in an initial step, compute bounds on the y extents of each curve segment -- upper bounds for the max y, lower bounds for the min y. (The max and min y values of all 3 points work fine for these, since a quadratic Bezier curve is fully inside the triangle they form.) For each of the two extents of each curve segment, add a (y position, reference to curve segment, isMin) triple to an array -- so twice as many array elements as curve segments. Then sort the array by y position. Now during the outer rendering loop that steps through increasing y positions, you can maintain an index in this list that steps forward whenever the next element crosses the new y value: Whenever this new element has isMin=true, add the corresponding curve segment to the set of "active segments" that you will solve for; whenever it's false, remove it from this set. This way, you never need to solve for t on the "inactive segments" that you know are bounded out on the y axis, which is probably most of them.
If I understood you correctly, this might be an issue if you have multiple strokes (so multiple mins and maxes that you need to stay within) on a row of pixels (think all strokes of an N).
Thanks, I've bookmarked an article recently that I thought was about that, but haven't read it yet. Your explanation lays a very good foundation to understand that technique.
Pick up a book on type and start up Fontforge, and off you go.
Be careful though, make an early choice if you are going with 3rd order curves or 2nd order (Bezier) curves.
Going through TeXbook and MetaFont books by DEK is also a brilliant way to learn about all this, with note that they do have an explicit bitmap step in.
One correction though:
Computers started with bitmap fonts of different pixel sizes. Your console terminal in Linux is still using that, and nothing stops you from using them ("Fixed" has large Unicode coverage and is usually preinstalled) elsewhere too.So no, none of this tech is necessary for us to read text on computer screens.
I run into similar 'quantization' challenges when building generative design systems in Python. Sometimes a mathematically 'perfect' alignment on the grid looks optically wrong to the human eye. The anti-aliasing logic described here is a great mental model for handling those edge cases.
When it comes to computer screens, usually set too bright to accommodate varying ambient lightning conditions throughout the day/year, it's not as simple, and I am not sure there is a study to confirm it.
And even if so, any individual's case might be different.
not my experience (I prefer not to be flashbanged), but sure
In more modern langauges, this is a solved problem and it's easy to use other people code. In C/C++, it's not. As a relavant example, try using FreeType in your C/C++ project, make sure your solution compiles on Linxu, and Mac, and Windows (and ideally other platforms)
find_package(Freetype REQUIRED)
target_link_libraries(myproject PRIVATE Freetype::Freetype)
A question about efficiency: IIUC, in your initial bitmap rastering implementation, you process a row of target bitmap pixels at once, accumulating a winding number count to know whether the pen should be up or down at each x position. It sounds like you are solving for t given the known x and y positions on every curve segment at every target pixel, and then checking whether t is in the valid range [0, 1). Is that right?
Because if so, I think you could avoid doing most of this computation by using an active edge list. Basically, in an initial step, compute bounds on the y extents of each curve segment -- upper bounds for the max y, lower bounds for the min y. (The max and min y values of all 3 points work fine for these, since a quadratic Bezier curve is fully inside the triangle they form.) For each of the two extents of each curve segment, add a (y position, reference to curve segment, isMin) triple to an array -- so twice as many array elements as curve segments. Then sort the array by y position. Now during the outer rendering loop that steps through increasing y positions, you can maintain an index in this list that steps forward whenever the next element crosses the new y value: Whenever this new element has isMin=true, add the corresponding curve segment to the set of "active segments" that you will solve for; whenever it's false, remove it from this set. This way, you never need to solve for t on the "inactive segments" that you know are bounded out on the y axis, which is probably most of them.