Wow. You lost me quickly with all that math. Good luck building your theory.

Bill DeWitt wrote:

> SamuelT. <STB### [at] aolcom> wrote :
> > Bill, I don't think I understand your
> > question fully.
>
>     Actually you probably do, maybe even better than I do myself 8-) I am
> notorious for running out questions before I know enough to ask questions
> which could receive informative answers.
>
>     I think Chris's answer while certainly true and exactly what I asked
> for, is maybe one step too basic for me to understand all at once.
>
>     But I'm getting there. The following is a little long and may be
> tedious, but if someone could check me on it I would be grateful...
>
>     Using the example "function(x+1.0)", going in the x direction, starting
> at x=(-1.0), all points get the value 1.0 added to them. So at x=(-1.0), the
> point equals 0.0 (less than the threshold of 1.0), then it moves right to
> the middle, where x usually equals 0.0 but now equals 1.0, at that point,
> all points are greater than the threshold and so aren't shown. (if x > 0.0
> then Point > 1.0)
>
>     Using that way of talking about it, the example
> function{ (sin(x*3)+y)+y }" (parenthesis added for emphasis) and starting
> from the inmost set of parenthesis(x*3), all x values are tripled. So you
> get a similar effect as above, with one third the bounding box filled with
> points whose values are greater than 1.0 and so are not shown. (if x > 0.333
> then Point > 1.0)
>
>     Then finding the sine of (x*3) you get values which start at -1.0 and
> smoothly go to +1.0 then back to -1.0. This gives all points within the
> bounding box a value of 1.0 or less and so all points are shown ( If you
> drop the threshold below 1.0, you can see where the value of sin(x*3) is
> greater than the threshold but never gets above 1.0 ).
>
>     Adding y to the above begins to show the sine curve because at the
> bottom of the bounding box where y is -1.0, adding y to it makes it -2.0, in
> the middle height, where it is y=0, nothing is added to nothing. But for all
> values of y which are greater than 0, y now equals twice as much as before.
>
>     So the area where previously, x -almost- made it above 1.0, is now goes
> just over 1.0 (where y>0) and is excluded by the threshold. Further up, as Y
> gets exponentially greater, it becomes easier for x to be greater than 1.0
> so the area that is excluded becomes wider, giving the look of a sine curve.
>
>     Finally, adding y again flattens the curve even more, bringing all of
> it's height into the bounding box. Adding more and more y makes flatter and
> flatter waves.
>
>     And I finally figured out that the doubling effect of abs and sqr are
> because a negative number times a positive number equals a positive
> number...
>
>     All this makes sense to me. Which is either a sign that I am finally
> getting a grasp on the whole thing or that I am way wrong. I don't know if
> my math skills will go much further since I almost broke a blood vessel
> trying to get this far, but if someone can confirm that I am right about
> this, I'll consider this a working theory...
>
> > Chris Huff wrote:
> >
> > > It is "show all points where the function is equal to the threshold."
> > > Bounding and clipping shapes will alter it if the surface is not totally
> > > contained in the bounding shape.
> >
> > --
> > Samuel Benge
> >
> > E-Mail: STB### [at] aolcom
> > Website: http://members.aol.com/stbenge
> >
> > "Ni!"
> >
> >

--
Samuel Benge

E-Mail: STB### [at] aolcom
Website: http://members.aol.com/stbenge

"Ni!"

Post a reply to this message