Funny this conversation was from 10 years ago.... hahaha.
you only need 2 points if you already know it's a sphere.
All axes that are perpendicular to the surface of a sphere will go through the center of that sphere.
Since all axes go through the center, then any 2 will intersect at the center.
Therefore, you only need 2 such points to define 2 such axes to find the center.
Then you can measure from that intersecting point to either of the 2 points on the surface, and you will have your radius.
However in order to define a sphere from points, you'd need 4 points.
Of course, not just any 4 points, you'd need 4 points that are not all coplanar, or colinear, or coincident.
It won't work if any 3 points lie on a line, or if all 4 are co-planar, or if any of the points are coincident.
2 points define a line
or a point if they are coincident.
3 points define a plane unless they all lie on the same line
or a line if they are all colinear
4 points define a sphere
or a plane if they are all coplanar
of a line if they are all colinear
I disagree. With only 2 points you cannot establish the normal (to surface) for the axiis thru those 2 points. If I give you 2, or even 3 point coordinates in 3D space, you cannot tell me the radius, it takes 4.
Still disagree. Even if you KNOW it's a sphere, with only 2 points, you don't know the vector the axis takes thru each point. You could cross the axiis at any point on a plane and the point created would only tell you the radius of a CIRCLE with that centerpoint. Change the angle of the axiis, and you'd get just another circle with a different radius. Even with 3 points, unless you knew the angles of the axiis, you could have any number of spherical radii. It takes the fourth point.
Model it up and see. 😉
Funny, I've been on here working at any number of companies, this is originally my thread, but I can't combine all my posts under a single name. Ah well....
@FrankSSchiavone we're gonna work on matching up profiles! Watch Community announcements over next few months 😉
That would be cool, I'd like to combine them all, I think I have at least 3 profiles here over the years.
What I REALLY want is my photo album back!