Bridges, String art, and Bezier Curves

[mistercow]

Incidentally, the "rotated parabola" representation of quadratic bezier curves can be extremely useful when writing highly optimized code, as it lends itself to closed form solutions in some situations where the parametric representation does not.

[tylerneylon]

Is there a place where I can read more about this? Like how to write code along these lines, and maybe how to understand why it works?

[akg]

The book "Architectural Geometry" http://www.amazon.com/gp/product/193449304X/103-2668819-9693... is a fantastic read with plenty of nice geometric insights.

[tylerneylon]

There's a generalization of this problem where we consider the set of all lines between (a, 0) and (0, b) with

||(a, b)||_p = 1

as in the Lp norm; and ask, what curve is produced (as their boundary) ?

And the answer has the nice form: The set of points (x,y) which satisfy

||(x, y)||_q = 1

where q = p / (p+1) [which can be written as 1/q - 1/p = 1.]

This is written up as the solution to a puzzle here:

http://fridaypuzzl.es/?p=187

and if you love puzzles, try to forget what you just read, and here is the puzzle:

http://fridaypuzzl.es/?p=180

[leeoniya]

reminds me of the exhibits at the Saint Louis Arch http://www.dzre.com/alex/slarch/ and http://www.sciencefriday.com/video/04/23/2009/how-the-arch-g...