show/hide this revision's text 2 Added clarifications.

This is a problem that has been studied for a long time. I showed with my students Carol Gitlin and Vinita Subramanian, that there does not always exist a polyhedron that connects two arbitrary polygons in parallel slices. In other words, Daniel's hope to "simply [join] the 'corresponding' points in both 'slices' " cannot always be realized:

C. Gitlin, J. O'Rourke, V. Subramanian. "On reconstruction of polyhedra from parallel slices," International Journal of Computational Geometry & Applications, 6(1) 1996, 103-122.

These two polygons constitute a counterexample:
                      cex

There is a very nice summary of the early work, and a practical algorithm, in:

Gill Barequet, Daniel Shapiro, Ayellet Tal. "History Consideration in Reconstructing Polyhedral Surfaces from Parallel Slices." Proceedings of IEEE Visualization, 1996. (CiteSeer link)

Maybe look at this more recent work?:

Samir Akkouche, Eric Galin. "Implicit surface reconstruction from contours." The Visual Computer. August 2004, Volume 20, Issue 6, pp 392-401. (Springer link)


           Contours

show/hide this revision's text 1

This is a problem that has been studied for a long time. I showed with my students Carol Gitlin and Vinita Subramanian, that there does not always exist a polyhedron that connects two arbitrary polygons in parallel slices:

C. Gitlin, J. O'Rourke, V. Subramanian. "On reconstruction of polyhedra from parallel slices," International Journal of Computational Geometry & Applications, 6(1) 1996, 103-122.

                      cex

There is a very nice summary of the early work in:

Gill Barequet, Daniel Shapiro, Ayellet Tal. "History Consideration in Reconstructing Polyhedral Surfaces from Parallel Slices." Proceedings of IEEE Visualization, 1996. (CiteSeer link)

Maybe look at this more recent work?:

Samir Akkouche, Eric Galin. "Implicit surface reconstruction from contours." The Visual Computer. August 2004, Volume 20, Issue 6, pp 392-401. (Springer link)


           Contours