Honestly, they’re incredibly interesting. Anyway, I’ll skip straight to the pièce de résistance: This is a 4-curve cubic Bézier spline modulated onto an ellipse. The ellipse [a=4, b=3] is at an angle of π/4. C1 continuity of the complete curve is preserved. The flickr set tells the story of how…
On the Benefits of Showering
From time to time when I’m perplexed Or by a tricky problem vexed; A cipher that just will not yield But keeps its mystery concealed, I find I have a last resort Before cerebral fuel runs short: I open up the bathroom door And step onto the tiled floor. The…
Ellipses & Splines again
After some code cleanup and generalisation, I can now modulate whole splines onto ellipses and onto splines themselves. Here is my simple 4-bezier spline modulated onto an ellipse: And onto itself: Repeatedly modulating a spline onto itself while varying the frequency parameter leads to some interesting and fractal patterns. Nice.
Wish-it-was two-factor authentication
In order to print out a tax form, I’ve just had to go through some silly security question rigmarole with my online bank. The wish-it-was two-factor authentication is getting quite out of hand these days. They are really desperate to give the appearance of security. In addition to displaying a…
On Being, and Raising, a Gifted Child
[apologies to my LJ readers for the lack of cut] Lately I’ve been reading books on gifted children: how to identify them; how to deal with them; what to expect as a parent. Is mini-Elbeno gifted? Without wanting to sound like a competitive parent, and properly considering that it’s still…
LA Moments
Heading west on Sunset (that winding bit just north of the Los Angeles Country Club), when a charcoal grey Lamborghini Murcielago pulls out just ahead of me. Nice. It made a lovely sound and went from zero to 40 in about 2 seconds. Really expensive cars tend to actually be…
Splines and modulation
My efforts to equally subdivide a curve along its length have, in part, been leading to this. First, I extended the sampling to work with splines (made up of cubic Bézier curves with c1 continuity). This shot shows 4 curves put together to form a spline: Next, I wrote some…
And it was done
Since I already had the binary search and interpolation code, it was just a matter of writing different samplers for ellipses and Bézier curves. ;; make a sampler function for a bezier curve (defun make-bezier-sampler (p0 p1 p2 p3) (lambda (k) (decasteljau p0 p1 p2 p3 k))) ;; make a…
More on ellipses
I think I will use the same method as I do for Bézier curves to step along the circumference. Another generalisation I had to make from the circle code is with respect to the normal. For a circle of radius r, centred on the origin, and parameterised by angle θ,…
On ellipses
Having conquered equidistant spacing along a Bézier curve, my thoughts now turn to the same problem for an ellipse. I have solved the problem for a circle of course, which is a special case of an ellipse. One would think that going from a circle to an ellipse would be…