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Just for fun:

Re: Defining a sphere.

fun ended .......

Re: Defining a sphere.

Wow! Seems this is a popular thread! Anyone else try/gigure this out besides Grahame?

Re: Just for fun:

Man, this is funny, I'd forgotten I'd started this under a different name way back in the day. Interesting.

Re: Defining a sphere.

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




Re: Defining a sphere.

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.

Re: Defining a sphere.

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....

Re: Defining a sphere.

@FrankSSchiavone  we're gonna work on matching up profiles!   Watch Community announcements over next few months 😉

Re: Defining a sphere.

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!

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