Finding intersections of contours in 3D
- To: mathgroup at smc.vnet.net
- Subject: [mg34078] Finding intersections of contours in 3D
- From: "Bram Platel" <b.platel at stud.tue.nl>
- Date: Wed, 1 May 2002 08:01:09 -0400 (EDT)
- Organization: Eindhoven University of Technology, The Netherlands
- Sender: owner-wri-mathgroup at wolfram.com
I want to find intersections of the surfaces of two contour plots in 3D. For example I have contours of a 3D data set where the derivative to X is 0, and I have contours of a 3D data set where the derivative to Y is zero. Then I would like to find the intersections of these contours (so I find curves where dX=dY=0). I have read an article by Steven Wilkinson about finding intersections of surfaces, but he uses a sort of numerical solver (to use his method the equations of the surfaces must be known), so I cannot use it for 3D contours (where the equations of the surfaces are not known). The only way to do it I can think of is using Mathematica's output of ListContourPlot3D (which are coordinates of Polygons) and then find (with a clever algorithm) the intersections of these little polygons. Does someone have experience with this, or an idea on how to implement this?