Basics of Coordinate Metrology
Unit 5:  Geometric Combinations - Intersection

Step 5 of 8
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Intersection Line (e.g. cylinder axis, etc.) Plane Circle Cylinder Sphere
Plane
A line and a plane intersect
  • in a point if the line is not parallel to the plane
  • in the line itself if the line is on the plane
  • not at all if the line is parallel to the plane above or below the plane.
The intersection of two planes is a line.
Exception: If the planes are parallel, there is no intersection!
A circle and a plane intersect
  • in two points if the perpendicular distance of the circle center from the plane is smaller than the circle radius. 
  • a point if the perpendicular distance of the circle center from the plane is equal to the circle radius. 
  • in no point if the perpendicular distance of the circle center from the plane is greater than the circle radius. 
The intersection of a plane and a cylinder is in general an ellipse.

In the special case that the cylinder axis is exactly perpendicular to the plane is the intersection a circle.

In the special case that the cylinder axis is parallel to the plane the intersection result are two lines.
A sphere and a plane intersect
  • in a circle if the perpendicular distance of the sphere center from the plane is smaller than the sphere radius. 
  • not at all if the perpendicular distance of the sphere center from the plane is greater than the sphere radius.