comp.graphics.algorithms

Subject: Re: Plotting non overlapping rectangles

"Dave Eberly" wrote in message
> "Stephen Brown" wrote in message
> news:-6KdnfK1q7zBnv_Z4p2dnA@comcast.com...
>
>> What I need to do is calculate the coordinates of a point C, along the
>> line AB and just outside the fixed rectangle. When I construct a
>> rectangle around the line CB using the same offsets as before, I want the
>> resulting rectangle to touch but not overlap the fixed rectangle.
>
> Let D = B - A. The point C = A + t*D for some t > 0.
> The line containing C and perpendicular to D has the
> property that it contains one or two of the fixed
> rectangle's vertices, the other vertices "behind" the
> line.
>
> Let V[i], 0 <= i <= 3, be the vertices of the fixed
> rectangle. Determine the index k for which
> Dot(D,V[k]-A) is a maximum. The vertex V[k] is
> an extreme vertex of the rectangle in the direction D.
> The point C = A + Dot(D,V[k]-A)*D.

I may be reading it wrong, but this solution doesn't appear to take into
consideration the width of the rectangle around line CB?

Steve