cc wrote:

> I wanted accelleration and smooth steering-angle change.   So I worked on a

If all you want is a nice movie, why not start with the given
shape of the curve and the location as a function of time,
and then get the angles etc. by differentiation?

>     cos( sin(x) )  dx

Looks like something with a Bessel function to me. Are you sure
you want to use this?

If yes, try Gradstein/Ryshik or Abramowitz/Stegun (the first one
is a great collection of integrals ant other stuff, the second
has mostly definitions, but has all of them correct (it is
something like an ANSI standard about higher functions)).

Yet another way to do it would be to integrate numerically -- just
hack a Runge-Kutta using POV's macros.

Ralf

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> I haven't looked at the whole thing yet, but I can tell you that this
> part at least is incorrect.  If the front wheels are parallel, their
> axes will never intersect.  In fact when you turn, one or both wheels
> will skid just a little.

That is why cars use trapezoidal steering mechanisms.

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I am just wondering, what exactly does integration do? Several people have tried
unsuccessfully to explain it to me. I believe something to do with area under a
curve? Just tell me what the input represents and what the output represents,
that's all I really want to know.

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David Fontaine <dav### [at] faricynet> wrote in message
news:3887B189.DE2796FE@faricy.net...
> I am just wondering, what exactly does integration do? Several people have
tried
> unsuccessfully to explain it to me. I believe something to do with area
under a
> curve? Just tell me what the input represents and what the output
represents,
> that's all I really want to know.

input: a bunch of things to be added up, with a certain weight for each.
An example is the average. You add up all of them but weight
them by 1/(number of things).  average of a, b, and c is
a/3 +b/3+c/3.
Usually the term 'integration' is used when the things to
be added for a continuum of values. Thats why integration is
considered 'calculus'.
Say you want to know how a planet is going to revolve around its sun.
The force of gravity on the planet is not usually constant because the
planet
can go from one distance from its sun to other distances. To find out where
it will be tomorrow, you could 'move' it (on paper) in little increments
calculating the forces on it anew for each second, using its new position
and new forces. You are actually adding up all these effects, second
after second. But since it is more accurate to consider time as a
continuum, you really should add up a continuum of miniscule
effects. That is, you 'integrate' the effects

output: the sum

oh yeah, 'the area under the curve' explanation comes from finding the
area under a curve by adding up a bunch of rectangular regions (for
which you know that area=length X width) areas

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>I haven't looked at the whole thing yet, but I can tell you that this
>part at least is incorrect.  If the front wheels are parallel, their
>axes will never intersect.  In fact when you turn, one or both wheels
>will skid just a little.
>
>--

I used to have a radio controlled car which would turn the inside-wheel more
than the outside wheel.  Whether it did it perfectly is another story...   I
haven't done anything on my own to find out if real cars are that way too
but I hope that they are...

    -Charles

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I don't know what trapezoidal steering mechanisms do...   Do they do what I
was talking about... about rotating the wheel on the inside of the turn at a
steeper angle than the wheel on the outside?
    -Charles


David Fontaine wrote in message <3887B0B0.FCC0429F@faricy.net>...
>> I haven't looked at the whole thing yet, but I can tell you that this
>> part at least is incorrect.  If the front wheels are parallel, their
>> axes will never intersect.  In fact when you turn, one or both wheels
>> will skid just a little.
>
>That is why cars use trapezoidal steering mechanisms.
>
>--
>Homepage: http://www.faricy.net/~davidf/
>___     ______________________________
> | \     |_       <dav### [at] faricynet>
> |_/avid |ontaine      <ICQ 55354965>
>
>

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> I don't know what trapezoidal steering mechanisms do...   Do they do what I
> was talking about... about rotating the wheel on the inside of the turn at a
> steeper angle than the wheel on the outside?

Yep!

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Homepage: http://www.faricy.net/~davidf/
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 | \     |_       <dav### [at] faricynet>
 |_/avid |ontaine      <ICQ 55354965>

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Wow!   I'm still new to the idea of getting so many responses so quickly.
Thanks everybody :)

I think there was one thing that I should clarify regarding my original
post.  The system I have now IS able to handle continuous steering-wheel
movement via small incremental changes in steering-angle.    Those
incremental changes add up to a lot of number crunching during parse time.
For movements that leave the steering wheel in one position, we're just
dealing with arks and it's not too difficult.  One or two of my earlier
tests animations involved a steering-angle which went instantly from 45
degrees left to 45 degrees right to instantly straight...... physically
impossible yes, but easy to work with.  :-)

It was after that that I added the sweeping steering-angle movements and the
accelleration and the scripting and all that...    Here's where it's a
choice of working with arcs, and crunching away at a lot of them... or
(sigh) calculus.

-Charles

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> input: a bunch of things to be added up, with a certain weight for each.
> An example is the average. You add up all of them but weight
> them by 1/(number of things).  average of a, b, and c is
> a/3 +b/3+c/3.
> Usually the term 'integration' is used when the things to
> be added for a continuum of values. Thats why integration is
> considered 'calculus'.
> Say you want to know how a planet is going to revolve around its sun.
> The force of gravity on the planet is not usually constant because the
> planet
> can go from one distance from its sun to other distances. To find out where
> it will be tomorrow, you could 'move' it (on paper) in little increments
> calculating the forces on it anew for each second, using its new position
> and new forces. You are actually adding up all these effects, second
> after second. But since it is more accurate to consider time as a
> continuum, you really should add up a continuum of miniscule
> effects. That is, you 'integrate' the effects
>
> output: the sum
>
> oh yeah, 'the area under the curve' explanation comes from finding the
> area under a curve by adding up a bunch of rectangular regions (for
> which you know that area=length X width) areas

Okay, I sort of follow al this, but integral outputs a function, right? What's
the different x-values of the function represent? And what would be the point of
finding the average of all points in a planet's orbit? it'd just be the center
of the ellipse

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Thanks for the tip :)

What exactly is a Bessel function?    And no... I'm not sure about anything
regarding this :)

When I was searching for the integrals (and I'm not that experienced) I was
trying to find ways to simplify the integral I started with into something I
knew what to do with... and I tried to integrate simpler [looking] integrals
which had something in common with the original.   integral of: cos( sin(x)
dx  was one of the latter.

The other thing I wanted to ask you is where I can find out information
about Gradstein/Ryshik and Abramowitz/Stegun.  I'm very much a novice. :)

-Charles

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