Finding if two sphere's intersect method

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Discussion Overview

The discussion revolves around the method for determining whether two spheres intersect based on their centers and radii. Participants explore the conditions under which spheres intersect, touching on both theoretical and mathematical reasoning.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant proposes a method involving the centers and radii of two spheres to determine intersection.
  • Another participant points out that the initial assumption of equal radii may not hold in general cases and clarifies that the distance between the centers must be compared to the sum of the radii for intersection.
  • A later reply acknowledges the oversight regarding the assumption of equal radii but maintains that the method needs adjustment for general cases.
  • Another participant asserts that even with equal radii, the correct condition for intersection is that the distance between centers must be less than or equal to twice the common radius.

Areas of Agreement / Disagreement

Participants express disagreement regarding the initial method proposed, with multiple competing views on the correct conditions for intersection. The discussion remains unresolved as participants refine their understanding of the criteria involved.

Contextual Notes

Limitations include the initial assumption of equal radii and the need for clarification on the conditions for intersection, particularly regarding the distance between centers and the sum of the radii.

SanEng02
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Hi I was just curious if this method of solving whether or not two spheres intersect is a viable method that will give me the correct answer. Say if I am given the two equations of the sphere's is it viable to:
  • Find the centre and radius of each sphere.
  • Find the magnitude of the distance of the line between the sphere's centres
  • If (magnitude distance of line) > radius they do not intersect, if (magnitude distance of the line) ≤ radius they do intersect.
From what I'm reading in the book and my notes, I think this should work.

Thanks in advance!
 
Last edited:
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SanEng02 said:
  • If (magnitude distance of line) > radius they do not intersect, if (magnitude distance of the line) ≤ radius they do intersect.
Almost. Two points:
  1. You assume that the spheres have the same radii. In the general case, they might not.
  2. Assume that the spheres just barely touch. Then the distance from the center of each sphere to the touching point is equal to the radius of that sphere ∴ The distance between the centers is equal to the sum of the radii. Therefore, if the distance between the centers is less than the sum of the radii, the spheres will intersect.
 
Svein said:
Almost. Two points:
  1. You assume that the spheres have the same radii. In the general case, they might not.
  2. Assume that the spheres just barely touch. Then the distance from the center of each sphere to the touching point is equal to the radius of that sphere ∴ The distance between the centers is equal to the sum of the radii. Therefore, if the distance between the centers is less than the sum of the radii, the spheres will intersect.

In this case the radii were the same but I forgot to mention that but I knew I was missing something. Thanks!
 
Even in that case, your statement was wrong. Given two spheres of equal radii, they will intersect if and only if the distance between their centers is less than or equal to two times their common radius.
 
Right, that makes even more sense thanks!
 

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