Linear geometric objects inside sphere test

[Ravana 101]

Hi All,

 

Say I want to check if some linear geom object (segment, tetrahedron,.. ) is fully inscribed by the sphere. 

 

I am thinking of testing if all the vertices of the linear object lies inside sphere and if so the object itself 

is inside the sphere. 

 

Is there a possibility that this test fails for linear objects?

 

Also, is there a fast algorithm to do this. 

 

Thank you.

 

Ravana

[Paradigm Shifter 5832]

All vertices inside will work for containment within any convex shape, which a sphere is so you are good to go.

 

The fastest method would be to test only vertices on the convex hull of the shape you are testing.

[Ravana 101]

even for concave objects this works, isnt it? basically if all the vertices are inside, you can not have a segment which goes from one vertice to the other making the object concave be outside sphere as the segments are linear.

[Paradigm Shifter 5832]

Yes, it works for objects which are concave being contained in a convex shape. (EDIT: just test the convex hull of the concave shape)

 

It DOESN'T work if you are testing a shape inside a concave shape though (e.g. a box in an L-shaped room, can cut the corner although all vertices are inside the L). It is the containing primitive which needs to be convex for the test to work, the contained shape can be anything.

Edited August 19, 2013 by Paradigm Shifter

[Ravana 101]

Yes. If the containing primitive is concave, the things are not the same. Thanks for the reply.