Antialiased composition by coverage?

Question

Does anyone know of a graphics system which handles composition of multiple anti-aliased lines well?

I'm showing a dependency diagram and have a bunch of curves emanating from a point. These are drawn anti-aliased in the usual way, of blending partially covered pixels. So if two lines would occupy the same half of a pixel, the antialiasing blends it to 75% filled rather than 50% filled. With enough lines drawn on top of each other, the pixel blend clamps and you end up with aliased lines.

I know anti-grain geometry has algorithms for calculating blends which cater for lines which abut, and that oversampling might work, but are there any other approaches?

Answer 1

It sounds like you want a premade drawing library, which I do not know of.

However, to answer your question of knowing any approach that would work, you can consider a pixel to be a square. You can then approximate any shape that you draw as a polygon that intersects the pixel box. By clipping these polygons against the box of the pixel and against each other, you can get a very good estimate of the areas associated with each color that intersects the pixel for accurate antialiasing. This is, of course, very slow to calculate and is not suitable for interactive drawing.

Answer 2

Handling this form of line composition well is going to be slow (you have to consider all the lines that impinge upon each pixel using a deferred rendering approach). I doubt that there are many (if any) libraries out there that will do it for you.

The quickest and easiest method (and possibly the only realistic and cost effective solution for your case), which will work with virtually any drawing library would be to supersample it - draw to an offscreen bitmap at much higher resolution (e.g. 4 times wider and higher, with lines of 4 pixels width. Disable antialiasing when drawing this as it'll only slow it down) and then scale the result down with bilinear filtering. The main down-side is that it uses a lot of memory for the offscreen bitmap.

Answer 3

If you need an existing system that gets antialiased lines "visually correct", you might try using one of several existing RenderMan-compliant 3D renderers. The REYES algorithm, which many of these renderers use, works by breaking up primitives into micropolygons, then sampling them at several random point locations within each pixel. So even if you have a million lines collectively obscuring 50% of a pixel, the resulting image value will show roughly 50% coverage. (This is, for example, how the millions of antialiased hairs are drawn on characters in many animated movies.)

Of course, using a full-blown 3D renderer to draw 2D lines is like driving nails with a sledgehammer. You'd need a fairly pathological scenario for the 3D renderer to be any more efficient than simply supersampling with a traditional 2D renderer.