Math Is Fun Forum

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Circle in a 3D space

The goal is to draw a circle which turns around one of its chords.
I had an idea to define a plane with a base point on a circle's chord and a normal vector, then turn the vector.... But while I can imagine this graphically I am completely stuck in the algebraic part.
Or am I thinking in the wrong direction completely?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circle in a 3D space

hi White_Owl

I'm not clear about what you want from this.  See diagram below.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Circle in a 3D space

No, what you draw is a moving center of a circle in the same plane as the original circle.

I need something like this. I can draw a circle C1 using

But now I need to draw the circle with a center in C2, but in a different plane. The original plane and the new one intersect along the chord AB.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circle in a 3D space

OK. I understand now.

So the chord is forever fixed. 

So would you like the equation for the circle at different rotations?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Re: Circle in a 3D space

Well, I would not say that the chord is forever fixed

OK, let me think out loud:
We can define a plane by three points. Let's say the first one is defined by points (C1, A, B) and the second one by (C2, A, B). So basically I need a formula of a circle which goes through points A and B, and have a center in the point C1.
For the the plane we can use formula ax+by+cz+d=0, so for the plane we have a set:

It would give us a, b, c, and d.
Each point of the circle also is a member of the same plane and at the same time the distance between it and a center is fixed.
So we should add to the previous set of three formulas two more:

And this should give us a circle in any arbitrary plane defined by three points....
Is this correct or did I made a mistake somewhere?

Now the question is how to simplify it into more usable formulas.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Circle in a 3D space

If you mean tge intersection of the grtapjs of those two equations,then I think that is right.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circle in a 3D space

Yes that looks ok but

Now the question is how to simplify it into more usable formulas.

That may be tough. 

I'll give it some thought.  hope you're not in a great hurry. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Circle in a 3D space

Maybe it can be simplified using parametrization?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.