Find the location of a sphere resting on 3 planes

Find the location of a sphere resting on 3 planes

The following basic description uses a 2D example, but the concept still applies in 3D.

Scenario - A sphere of known diameter rests on three planes.  Where is the actual center of the sphere?



A sphere resting on 3 planes will have exactly three points of contact.  One on each plane.  Even if the planes are out of position, tilted, or rotated, the sphere center is always exactly a sphere radius distance from the contact (tangent) point on the plane.



To determine the actual center of the sphere using CMM-Manager:
  1. Measure the 3 planes.
  2. Construct 3 planes, offset by the sphere radius.  Actual measured values will be used for the planes.


  1. Construct a line at the intersection of the first two constructed planes.


  1. Construct a point at the intersection of the constructed line and the constructed 3rd plane.  This is the center location of the sphere.


Here is a printed example of the code: