I've been waiting for the smoke to clear on the battlefield... :-P

"clipka" <nomail@nomail> wrote:

> Are you familiar with calculus?
>
> Exact alignment would mean that the current direction would be the tangent to
> the spline at the current position.

>
> To compute a tangent to an arbitrary curve defined as f(t) (the value of which
> in this case is a vector), you need the derivative f'(t) of that function,
> which is defined as:
>
>     f'(t) = lim(d->0) [f(t+d)-f(t)]/d
>
> which is to say, take two *infinitesimally* close points on the function, and
> divide the difference between the function values by the difference between
> the function parameters.

Yes, completely understood. (It's been ...*awhile*...since I took a calculus
course, and I'm certainly NO expert.) I guess, in the context of the math
discussions here, what I'm looking for IS finding the 'limit' at
delta-*something* = 0. But I see the difficulties (I think!)
>
> As you will see, although this is an exact mathematical definition, it doesn't
> work with d = 0 because you'd get 0/0, which is nonsense.

That piques my curiosity. I thought calculus was the 'prime tool' for getting
that exact tangent. So, do I understand that POV-Ray can't actually calculate
that?  (Sorry if my ignornace is showing.)

But more prosaically, my original question--a rather naive one, as I see
now--was really about the *idea* of being able to set Foresight to zero. As a
way for the macro to 'make better sense' to the user. Of course, I do now see
the practical difficulties involved.  (Here's a REALLY goofball idea: Maybe,
'behind the scenes' in the macro, there could be a little 'hidden' addition of
..001 or something, so that when Foresight IS set to zero, the equations will
still have a little number to work with.)  Silly, I know. Even stupid! :-O  And
not even good coding practice, I would assume.

KW

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