RE: [Algorithms] Nearest point on plane for 2D IK

[Steve W. <Ste...@im...>]

> -----Original Message-----
> From: Steve Wood 
> That's not the tangent yet because we need to move 
> that point in an arc around the sphere toward the 
> beginning of the ray by the same angle as

Oops!  Not that angle but 90 degrees minus that angle...darn KMart virtual
protractor!
Rockn-Roll

> described by the center of the sphere to the intersection of 
> the ray and the
> plane to the beginning of the ray.

> -----Original Message-----
> From: Steve Wood 
> Sent: Tuesday, August 29, 2000 4:15 PM
> To: 'gda...@li...'
> Subject: RE: [Algorithms] Nearest point on plane for 2D IK
> 
> 
> How about if you use the center of the sphere and the point 
> at the beginning
> of your ray to use as the normal for a plane passing through 
> the center of
> the sphere.  Calculate the intersection of the ray and that plane.
> Calculate the point that is the sphere's radius from it's 
> center along the
> line from the center of the sphere to the intersection of the 
> ray and the
> plane.  That's not the tangent yet because we need to move 
> that point in an
> arc around the sphere toward the beginning of the ray by the 
> same angle as
> described by the center of the sphere to the intersection of 
> the ray and the
> plane to the beginning of the ray.
> 
> Just using my virtual protractor and compass.
> 
> Rockn-Roll
> 
> > -----Original Message-----
> > From: David Kornmann [mailto:da...@ik...]
> > Sent: Tuesday, August 29, 2000 2:43 PM
> > To: gda...@li...
> > Subject: Re: [Algorithms] Nearest point on plane for 2D IK
> > 
> > 
> > 
> > 
> > 
> > > Hmmm ... surely what you want is to find the point on the 
> > line closest to
> > > the center of the sphere (easy to do) and then if that is 
> > less than R away
> > > from the center you have definite intersection, and proceed 
> > to compute the
> > > points at which the line intersects the sphere, and otherwise, you
> > > conveniently have a point which is in line with the nearest 
> > tangential point
> > > of the sphere, so you can easily find that tangential point.
> > 
> > Well, computing the point when the ray intersect with the 
> > sphere is not a big
> > deal.
> > The problem comes when the ray does not intersect:
> > 
> >  I am not looking for the closest surface point on the sphere 
> > then, but a point
> > that
> > can be described as follow:
> > 
> > - Take the plane defined with the ray and the center of the sphere.
> > - Rotate the ray around its origin and along the plane until 
> > it is tangent to
> > the sphere.
> > - Compute the tangetial point (easy).
> > 
> > That's what seems to me complicated and which needs to be 
> > very accurate.
> > 
> > Any idea?
> > 
> > Thanks.
> > 
> > David Kornmann.
> > --
> > 
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