Attention: Maths ahead! Non-geeks may prefer to avoid the equations, and just look at the pretty colors instead.

Previously, on Jacek Writes: our hero introduced the topic of smoothly blending between two colors algorithmically.

Last time, I defined an equation for blending linearly between two color vectors a and b as time, t, increases from 0 to 1:

line(t, a, b) = a + t * (b - a)

After a little algebra, we can rewrite that function as:

line(t, a, b) = (1-t)(a) + bt

Linear blending looks just fine for blending between two colors, as demonstrated above. Starting from the left, we progress from red to blue, passing through magenta and purples. Looks pretty good, right?

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I wrote a post about “section radius” recently, which involved drawing curves with a discreet number of anchor points. The application there was a more robust replacement for the Taper attribute of prims. Of course, the usefulness of using a curve instead of one or two numbers is not limited to Taper alone—there are innumerable other uses for them, completely aside from the Object attributes.

One of my backburner obsessions for the past few months has been color. (No surprise there, given that I’m currently enrolled in a color theory class, I suppose.) In particular and with regard to SL, two aspects have been on my mind. The first is using a base color as input to an algorithm to generate related colors (lighter tint, darker shade, blue-shifted, red-shifted, visual complement…). The second is blending between two colors in a smooth and visual appealing fashion.

This is where curves come in.

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I didn’t conciously realize this when I first started writing here, but my feature requests have a very specific agenda. To put it succinctly:

I want Second Life to be more like a high-level 3D modelling application.

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