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        riddles >> cs >> to make 2 circles on 2 different planes intersect 
        
(Message started by: sarojini on Aug 6^th, 2014, 4:27am)

Title: to make 2 circles on 2 different planes intersect
Post by sarojini on Aug 6^th, 2014, 4:27am

Hi All,

If I've two circles on two different planes in 3D space, given centers, radii of circles and two plane equations. The two planes are perpendicular to xy plane.
1. How to check if two circles intersect or not
2. If they are not intersecting how to make them intersect by adjusting the radii and the plane angle theta(angle of plane with y axis clockwise direction).

Please let me know if my question is not clear.

Regards,
Sarojini.

Title: Re: to make 2 circles on 2 different planes inters
Post by singhar on Nov 20^th, 2014, 11:39pm

If I understand the problem correctly, you can solve this by taking the projections of the circles on the x-y plane. The projections will be two simple line segments of length equal to the diameter of the circles, the mid-point of which will correspond to the projection of the centers.

The planes containing the circles will be projected as lines on x-y plane. These lines need to intersect, otherwise the circles will never intersect.

Find the intersection of the planes on x-y plane. The distance from the projected center to the point of intersection of the planes is one part of the displacement one has to do to get the circles intersect.

The second part can be done by similar projection on to one of the planes containing a circle. The projection will be an ellipse. The distance from the end of the diameter of one circle to the corresponding end of the minor axis of the ellipse (as a result of projecting a circle) is the second distance you have to slide the circle.