Cubic Bézier Curves

I spent some time solving equations for evaluating points along a cubic Bézier curve. What I find particularly elegant about Bézier curves is that they can be calculated with recursive/nested linear interpolations. It gets 100 geek points just for the phrases “recursive” and “linear interpolation” — it also wins my appreciation for how comparatively simple it is to solve by hand!

I had come up with an equation a while back for doing this same task, but it wasn’t as tight as it could be. For one thing, it required evaluating the coefficients for each curve every time a point was evaluated.

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Ambient Wildlife and Bouldered Paths

Lately, I’ve been thinking a lot about sound, color, and abstract artificial life. No doubt that this most recent bout is directly tied to my recent purchase of Electroplankton (the best, albeit only, $60 I’ve spent on Ebay), but all three are recurring themes that have been agitating my brain for years.

Wouldn’t it be wonderful to play with colorful creatures that scamper around and make musical sounds as they jump and chase each other? It sounds like the love child of Brian Eno and Will Wright, to be sure.

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