[A83] Re: The shape of a cord
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[A83] Re: The shape of a cord
> Not quite sure I understand, do you want to know how much
cord it will
> take to make a parabola-shaped cord go 5 feet from (x1,
y1) to (x2, y2)
> and still touch (x3, y3)?
Let's go through it again. We are in two dimensions.
I have a cord of known length and given the coordinates of
its endpoints, I'd like to find approximate its shape
with a parabola. To set up the equation for this
parabola, I need a third point, whose x coordinate
is also fixed to the average of the other two x
values. Some ASCII art:
Q(x2,y2)
P(x1,y1) /
\ /
\ / <--- the length of this parabola segment
\__/ is l
R(x3,y3)
We know x1, y1, x2, y2, l, and we fix x3 to be
(x1+x2)/2. Question: how much is y3? Normally there
should be two solutions, if l is greater than
the distance of P and Q, but let that not disturb
us for now, we are clever enough to choose the
right one if we have both. :)
PG
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