Find the Intersection of Three Planes

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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This is not a hard problem but the construction can get messy if you're not careful. The biggest single problem is keeping all the lines separated in your mind. It's also critically important to make sure you are drawing intersections through the correct points. It can be very easy to mismatch contours. Using different colors for different elevations may help.

We have already seen how to find the intersection of two planes. If we add a third plane, it will intersect each of the other two. If we call the planes A, B, and C, there will be three intersection lines: A-B, B-C, and A-C, and they will all intersect at a common point.

The only difficulty is determining the elevation of the intersection, and that can be done by interpolating between structure contours.

Example

 1. Given this bed cut by a dike and a fault, find where all three planes intersect. 2. Structure contours for two planes have been constructed and the intersection line plotted. 3. Structure contours for the third plane are plotted. 4. The remaining two intersections are plotted. Interpolate between contours to find the elevation (1030 m).

Remember:

• All three intersection lines for each pair of planes must cross at a single point.
• You can pick any pair of contours to interpolate the elevation of the intersection. The interpolated elevation must agree with the structure contours on all three planes. It's a good idea to cross-check by interpolating between all three enclosing pairs of contours.

Created 5 January 1999, Last Update 31 January 2012
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