TIL: premultiplied-alpha colors

Alpha is the measure of how translucent an object is. An alpha of 0.0 means the object is entirely transparent, an alpha of 1.0 means the object is entirely opaque, and an alpha in the middle means a fraction of the total light may passthrough the object. Traditionally, a color is represented by 4 constituent components: a red contribution, a green contribution, a blue contribution, and the alpha. When compositing two colors together, one on top of the other, the alpha acts as a modulus of the colors, indicating how much of the top color and how much of the bottom color contribute to the new composited color. The traditional compositing operation is as follows, where A is being composited over top B:


Alternatively, we may wish to premultiply the red, green, and blue components by the alpha:


With this representation we get a new compositing equation:

This new form is interesting for a couple reasons.

1. It is computationally more efficient. It requires one less vector multiplication.
2. It is a closed form. Compositing a premultiplied-alpha color over top a premultiplied-alpha color yields another premultiplied-alpha color. The same cannot be said of non-premultiplied-alpha colors. Compositing two non-premultiplied-alpha colors yields, interestingly, a premultiplied-alpha color.
3. When filtering (aka downsampling), it produces more visually accurate results. A picture is worth a thousands words.

And that's it. Premutliplied-alpha colors are nifty.

TIL: Alpha-to-coverage for order-independent transparency

Alpha-to-coverage is a computer graphics technique, supported by most (all?) modern GPUs, for rendering translucent multi-sampled anti-aliased primitives. Given an alpha value in the range of [0.0, 1.0] and N samples of color stored per pixel, the alpha channel will be discretized into a coverage-mask of the N samples. An alpha of 0 will generate an empty coverage-mask (no samples take on the new color), an alpha of 1 will result generate a full coverage-mask (all samples take on the new color), and values in between will generate a partial coverage-mask (between 1 and N-1 samples take on the new color).

It's not alpha-to-coverage itself that I learned today however, but rather it's implication; Alpha-to-coverage is a form of order-independent transparency! In the naïve case, one benefits from N-layers of transparency. I suppose this is the whole point of alpha-to-coverage, but I never put two-and-two together*.

* I blame my experience. Being a GPU driver engineer, but never a rendering engineer, I'm exposed to large cross-section of rendering techniques and low-level graphics implementation details, but never to the greater-picture of real-time rendering but by word of mouth and self-study.