potticus

Hey there,

I need to write an algorithm that will do the following (sounds oh so simple now, but I just can't get it :P):

for a specified point with known co-ordinates, find out whether this point lies within a particular volume.

Sounds pretty simple, but I can't find a path that'll make it work! My volume is described by a path function (an equation of any sorts, most probably cubic spline interpolation but for the same of the algorithm, anything will do to start with), and then a cross-sectional area which is swept along perpendicular to this line.

My problem is, that I could easily find out whether the point sits on the line, but once i start including the volume constraint, i get totally lost. to start with, I don't know how to fully define the volume, as with a curved path, it's not a simple, single equation definition.

once the volume is defined (if ever!), i also have problems as I can't just check if the point is within the cross-section for that given x-co-ordinate, as with the curved path, if I look at it in slices, the cross-section changes.

once i've got a methodolgy defined, i'm looking to code a routine in python to do all of this automatically (however, i might just start in matlab for now, but that's not really the issue at the forefront).

It's not particularly easy to describe, but if someone thinks they might be able to help, i'd appreciate it enormously! I guess if someone already knows of some existing code that can do the same job, that would be even better :) You'd really be digging me out of a hole, i'm going round in circles and not getting anywhere!

Thanks very much,
(a very mathed-out) potticus

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