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Just for fun:

ptc-1181807
Newbie

Just for fun:

You are handed a sphere and asked to find the radius. How many data points are required to find the radius, how would you then derive the radius from them and find the location of the radius relative to those points in Pro/E?
17 REPLIES 17

RE: Just for fun:

Man, you guys are no fun at all....... Am I posting things no one even wants to think about?

Defining a sphere.

if one thinks about a 3-legged milking stool which will fit onto any surface or sphere, it follows that 4 points are needed to define a sphere

Re: Defining a sphere.

"Richard Alcock" wrote:

if one thinks about a 3-legged milking stool which will fit onto any surface or sphere, it follows that 4 points are needed to define a sphere

Re: Defining a sphere.

Make a datum plane thru pts 1,2,3. Then sketch a circle thru the 3 pts on the datum plane. Uh... sketch a point at the center of the circle? Uh... make an axis thu the point normal to the datum plane? Do the same with another combination of the the 4 points, like say 2,3,4. where the axes intersect is the center of the circle. Maybe.

Re: Defining a sphere.

"Grahame Ward" wrote:

Make a datum plane thru pts 1,2,3. Then sketch a circle thru the 3 pts on the datum plane. Uh... sketch a point at the center of the circle? Uh... make an axis thu the point normal to the datum plane? Do the same with another combination of the the 4 points, like say 2,3,4. where the axes intersect is the center of the circle. Maybe.

Re: Defining a sphere.

Definitely make it a Guinness! Yes, I'd put a line from the perimeter to the center of the circle too. That would be apparent if I was doing it on Pro rather than in my head.

Re: Defining a sphere.

"Grahame Ward" wrote:

Definitely make it a Guinness! Yes, I'd put a line from the perimeter to the center of the circle too. That would be apparent if I was doing it on Pro rather than in my head.

Re: Defining a sphere.

"Grahame Ward" wrote:

Definitely make it a Guinness! Yes, I'd put a line from the perimeter to the center of the circle too. That would be apparent if I was doing it on Pro rather than in my head.

Re: Defining a sphere.

Great 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.

@Patriot_1776  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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