>In addition, the fundamental reason scatterplots are bad, even with opacity, is essentially that opacity gives rise to an exponential relationship between overplotting and transparency.
can you elaborate on this, I don't see why it would not be linear.
>There exists an alternative solution, which is to use additive blending and an adaptive linear colorscale, from zero to maximum-overdraw. Unfortunately, at present there exists no data visualization toolkits which support this.
I think this _might_ be done in Mathematica, since Graphics objects can be manipulated symbolically, but I might be wrong.
It boils down to the (very reasonable) way alpha blending works. Alpha was originally designed to always lie between zero and one, which for compositing makes sense. For scatterplot colormapping, not so much:
If you create a plot with opacity alpha, and which puts N points on top of each other, the remaining 'transparency', that is, the resulting opacity is
1 - (1 - alpha)^N
This is an exponential, which has the unfortunate feature that it's flat for most of the regime, and then spikes in a relatively short scale. The spike is where we get color differentiation (different opacities get different colors). That's bad: color differentiation should be uniform across the scale.
I'm pretty certain Mathematica doesn't do this right either, because it's a pixel-based technique that requires frame buffer manipulation. Instead of rendering with the usual blending operation, you do everything with additive blending, compute the maximum overdraw, and then color-scale linearly.
can you elaborate on this, I don't see why it would not be linear.
>There exists an alternative solution, which is to use additive blending and an adaptive linear colorscale, from zero to maximum-overdraw. Unfortunately, at present there exists no data visualization toolkits which support this.
I think this _might_ be done in Mathematica, since Graphics objects can be manipulated symbolically, but I might be wrong.