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- Re: Defining a sphere.

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Jun 19, 2007
03:50 PM

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Jun 19, 2007
03:50 PM

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

Jun 20, 2007
09:27 AM

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Jun 20, 2007
09:27 AM

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

Jun 20, 2007
10:48 AM

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Jun 20, 2007
10:48 AM

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

Jun 20, 2007
11:18 AM

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Jun 20, 2007
11:18 AM

"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

Jun 20, 2007
12:33 PM

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Jun 20, 2007
12:33 PM

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.

Jun 20, 2007
12:50 PM

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Jun 20, 2007
12:50 PM

"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.

Jun 20, 2007
12:56 PM

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Jun 20, 2007
12:56 PM

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.

Jun 20, 2007
01:02 PM

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Jun 20, 2007
01:02 PM

"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.

Jun 20, 2007
01:04 PM

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Jun 20, 2007
01:04 PM

"Grahame Ward" wrote:

Jul 04, 2007
04:38 AM

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Jul 04, 2007
04:38 AM

Great fun

Jul 11, 2007
12:07 AM

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Jul 11, 2007
12:07 AM

fun ended .......

Jul 13, 2007
09:29 AM

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Jul 13, 2007
09:29 AM

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

Mar 12, 2012
09:45 AM

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Mar 12, 2012
09:45 AM

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

Apr 07, 2017
12:59 PM

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Apr 07, 2017
12:59 PM

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

Jun 22, 2018
01:55 PM

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Jun 22, 2018
01:55 PM

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.

Sep 05, 2018
06:34 PM

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Sep 05, 2018
06:34 PM

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....

Oct 18, 2018
07:41 PM

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Oct 18, 2018
07:41 PM

@Patriot_1776 we're gonna work on matching up profiles! Watch Community announcements over next few months 😉

Oct 30, 2018
01:39 PM

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Oct 30, 2018
01:39 PM

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!