The hedgehog is a noble beast; he keeps the garden clear Of slugs and snails and other pests throughout the temperate year. Just after dusk you’ll see him on his customary beat Hunting Lumbricus terrestris or some other juicy treat. Although he’s not the biggest or the fastest or most…
A bit of Pythagoras
Given Pythagorean triples that satisfy the Diophantine equation: a² + b² = c² where a, b and c share no common factors, one of a and b must be odd, the other must be even, and c is always odd. First, note that squares of even numbers are always divisible…
Even more on ellipses and splines
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…