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Topic: Center of ARC in Cartesian co-ordinates !!!
Replies: 2   Last Post: Feb 5, 1998 9:02 AM

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Alan Lipp

Posts: 41
Registered: 12/6/04
Re: Center of ARC in Cartesian co-ordinates !!!
Posted: Feb 2, 1998 10:41 AM
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> I am held up with a problem in playing with ARCS. I need to create ARC
> using a primitive which needs
> (i) arc center point and start and end points of the arc.
> But I am falling short of one inputs and that is the center point.
> I do have another input and that is the radius of the ARC.


If I understand your question you are trying to develop a procedure
ARC_3pt(startx,starty,midx,midy,endx,endy) and what you have to
work with are the two points (startx,starty), (endx,endy) and

If this is your problem then you need to come up with an additional
input because these five inputs do not uniquely determine an arc.
Here is an easy counter-example:

Suppose the starting point is (1, 0) the ending point is (0, 1) and the
radius is 1. One solution is the unit circle centered at the origin
which would output the midpoint of the arc (midx, midy) =
(1/sqrt(2), 1/sqrt(2)). But a second solution is the unit circle
centered at (1, 1). The two endpoints still determine a quarter
circle but now the arc's midpoint is (1-1/sqrt(2), 1-1/sqrt(2)).


Alan Lipp
Williston Northampton School
Easthampton, MA 01027

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