Hello-

Does anyone have any input on how to extrude a 2d polygon along a 2d path?  

I can't quite figure the vector maths...  

I want to extrude an arbitrary polygon along any arbitrary 2d path..  So a circle extruded along a line becomes a cylinder.  Or, a circle extruded along a circle becomes a torus.

The straight line case is easy, and I already have that working fine..  Its the arbitrary path that is proving tricky..

like this?

http://supercoldmilk.com/ac3dplug/extpath_scale.html

(there's code there. it's c++ and a bit dense but...)

Ardor3D seems to be a java library that makes that possible
http://www.ardor3d.com/

http://ardor3d.com/release/0.5/javadoc/ardor3d-core/com/ardor3d/scenegraph/shape/Extrusion.html

Hey guys- thanks for the replies and links!

The supercoldmilk stuff is very close to what I'm trying to do, and the source code is fairly readable..  GLE pretty much does exactly what I need also, but I want to write my own- as this is only step one in the effect I'm going for..  

I will look into this more and keep you posted.  In the meantime I am trying to find a pseudocode/explanation of what exactly needs to happen vector wise..  

Thats interesting, what exactly is Pmatrix for? Its new to me. couldnt find any good documentation. But looks like i should take a closer look at it.

the question "what is a matrix" is a bit too broad to cover here, google "linear algebra" for example.

however, in this context, it's ok to imagine a matrix as a set of of 3 orthogonal axes, like a little miniature coordinate system that you can control, and that's capable of transforming points INTO that coordinate system.

you'd typically start with an identity matrix, that corresponds exactly to the default x/y/z axes.  So if you were to transform the point <1,2,3> you'd get the same point <1,2,3> back.

however, if you translate the matrix along z by 5 units, that same point would then be transformed to <1,2,8>.   corresponding things happen when you scale or rotate the matrix then transform the original point - the resulting point is now translated/scale/rotated to match the current state of the matrix.

if you were to connect the results from transforming that point a number of times you'd get a line of some sort, roughly describing the "path" that the matrix has "travelled". (particularly if the point you're transforming is <0,0,0> then each point is the origin of where the matrix "was" at that moment)

if you instead had a SET of points describing a "shape" (say an approximated circle) you could repeatedly translate/rotate/scale the matrix and transform those points to create an extruded mesh of points (and then probably draw tris or quads between subsequent sets), turning that flat "circle" into a cylinder or other twisted tube-like form.  (the exact form will depend on what transforms are applied to the matrix)

imagine repeatedly transforming the matrix with "translate by 1 unit along z, rotate by 10 degrees around x" - after 36 iterations of that the matrix would have travelled in a circle.  if you had been transforming a set of points (flat x/y's on the z=0 plane) that represented a circle, the result would be a mesh describing a torus.  if there had additionally been some translation along y (or, more properly, some rotation around x, to give y "inclination"), then the result would be a mesh describing a helix (which you can just imagine as a torus that has been "pulled apart", and you could continue rotating/translating to extend the helix further)  add in some scaling, and you can "taper" it as well.

..do it over and over and over again with variations, and you might get something like this:


hth

Ahh, thanks Dave-

That's a nice clean solution.  I like how you converted to spherical coords.. That was one thing I didn't think of that should help with the twisting problems I was having.   Thanks!!