**comp.graphics.algorithms**

## Subject: **Re: How to get angle and speed to reach a movable point**

staryon@gmail.com wrote:

> LetÂ´s consider that A is in (0,0) and B in (0,100). If B starts

> moving south they will meet eventually.

> Another example is the following. A is in (0,0) and B in (50,100). If B

> starts moving southwest, there will be a moment that it will be very

> close to A (it doesnÂ´t have to be 0,0)

> If A starts moving towards that direction even if its speed is slower,

> it will catch B.

> Does you algorithm include that condition?

No, as a matter of fact, it doesn't. That's because the equation

B'^2 + C'^2 = A'_max^2

is wrong --- there's no need for C' to be orthogonal to B'.

OK, second try.

(B - A) = t * (A' - B')

A'^2 = A'_max^2

t >= 0

t = min!

Isolate A' in the first equation, square and use the third equation,

and you get a quadratic equation in t:

(B'^2-A'_max^2)*t^2 + 2*t*(B-A).B' + (B-A)^2 = 0

Solve that, if possible, picking the smaller t if there are two

solutions. Substitute the result in the first equation, and you get

A'.

--

Hans-Bernhard Broeker (broeker@physik.rwth-aachen.de)

Even if all the snow were burnt, ashes would remain.

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