Here's a prototype I made for dividing a string into thirds. It will eventually end up inside a gen~ patch to control node placement on a waveguide string. The two sliders represent the nodes and the A, B, and C segments of the string are calculated from moving them. It seems to work fine but I thought for my own/everyone's amusement I'd see if any of the math/geometry geniuses could come up with a more elegant solution. What would really be interesting is an extensible solution that could be used for any amount of nodes. Not sure if that's even possible (not for me right now :-) )
PS - The overall string length is set at the constant 100 for ease of reading, but of course in the final patch I'll have a variable string length (in samples for the delay operators in gen~).