# 3d Circle calcalations???

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Okay, I've realy hit rock bottom over here. The problem is: I've got a normalized vector and a point. from those two I should be able to get a surface that is vertical to the normalized vector and that contains the point (This should be easy but I dont remember how to do it...). After this was achieved I need to take the point and the surface and use two more things I have: a radius and an angle. I need to take the point and pretend it's the center of a circle (on the surface) whose radius is known, then I need to take the angle and find the relevant point on the circle arc. If you wonder about the angle - where should 0 degrees be located, than you should know it doesn't matter, all that matters that from 0 to 360 a complete circle will be calculated. That is more than I can manage with my humble mind. I would realy appreciate any help. Thanks, Asaf Polturak, Israel

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It sounds like you need an 'orthonormal basis' function.

To construct a circle in 3-space you need a coordinate system. You already have the origin (the point) and an axis, call it z (the normalized vector). You need to find two additional vectors, x and y, which form an orthonormal basis with z. One way to do this is as follows:

1. Cross z and the world axis with which it is least aligned
2. Normalize the result to get x
3. Cross z and x to get y

You can now simply iterate from 0 to 2pi by some delta. The circle vertices are then of the form:

p + cos(t) * x * r + sin(t) * y * r

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I didn't understand completly.

first of all to be on the safe side, cross product of two vectors is

(x1,y1,z1) * (x2,y2,z2) = x1*x2 + y1*y2 + z1*z2

Is that correct?

"Cross z and the world axis with which it is least aligned" - what does that mean? what world axis?

thanks

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Quote:
 first of all to be on the safe side, cross product of two vectors is(x1,y1,z1) * (x2,y2,z2) = x1*x2 + y1*y2 + z1*z2Is that correct?
That's the dot product. Google 'cross product' to find the correct form.
Quote:
 "Cross z and the world axis with which it is least aligned" - what does that mean? what world axis?
By world axis I mean the cardinal basis vectors, (1,0,0), (0,1,0), and (0,0,1). The world axis with which a vector is least aligned is the one that it is 'least parallel to', or alternately 'most perpendicular to'. The least-aligned world axis corresponds to the component of the vector with the smallest absolute value.

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