Re: Generalized Pursuit Curve Problem

From: pikalaw (tsang_at_cims.nyu.edu)
Date: 09/06/04 

Date: Mon, 06 Sep 2004 03:47:52 GMT

pikalaw wrote:
>
> Clearly, grad q != Q-P for -1 <= t <= 0.
>

Ooops, I made a mistake. Q *is* in the direction of P in your program:
        grad q = (2A, -2Bt) = 2(A, -Bt)
and
        P-Q = (-At, Bt^2) = -t(A, -Bt).
Since t is negative, these two are in the same direction.

So, you are right if Q does not begin at A. Of course, a simpler
counter-example is:
        Q starts at the position x=0, and
        P starts at A located at x=1 and goes the straight path toward B
located at x=2.
Clearly, the path of Q has length 2 while the path of P has length 1.

However, if Q does start at A, intuitively the Q's path cannot be longer
than P's. Of course, initially when both P and Q are at A, Q's
direction toward P is the zero vector and Q will not move until a later
time when P has left A.

-pikalaw

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