ANN: Rolling graphics

[Eric Chatonet]

Hi Jim,

Amazing!
Jump is very impressive: seems very natural (path, friction, rotation 
speed).
Bravo from Paris.

Le 12 mai 05, à 16:43, Jim Hurley a écrit :

> To see this stack, run this from the message box:
>
> go url "http://home.infostations.net/jhurley/Rolling.rev"
>
> (DO NOT CLICK ON THE LINK.)
>
> Warning: This is of importance only to those interested in 
> programmable graphics.
>
> As an offshoot of something else I was working on, I needed a way to 
> set a disk rolling down a curve without slipping. I ran into some 
> interesting problems.
>
> The curve I chose was a bezier line because I needed to be able to 
> change the shape easily. But when I used the points of the bezier 
> graphic, the motion of the rolling disk was herky-jerky, as some 
> points exhibiting retrograde motion, i.e. fall *up* hill-see the first 
> card on the stack.
>
> The origin of the problem turned out to be round-off errors in setting 
> the points of the bezier graphic line. Run Rev will only accept whole 
> numbers for graphic points. It will accept fractional points for the 
> loc of objects, e.g.100.88, 200.33, but not for graphic points. (If 
> you would like to see this changed, vote for bugzilla 356) So it is 
> necessary to round off the calculated line coordinates to whole 
> numbers. (Run Rev doesn't round location sites; it truncates them.)
>
> To illustrate the difficulty this causes, imagine you need the slope 
> of the line at some point. (I need this slope so that I can position 
> the disk so that the slope of the disk and the curve are the same at 
> the point of contact.)  To get the slope you compare two adjacent 
> points on the curve; say the calculated points are:
>
> 9.500001, 10
>  and
> 11.4999,11
>
> If you round these points for the graphic point, then dx = 11 - 10 = 
> 1, and dy = 1, so that the slope, dy/dx is 1.
>
>
> If you use the calculated  values, dx = 2 (approx.) and dy = 1, so 
> that the slope is .0.5
>
> Big difference. 100% error. (This problem *increases* as the number of 
> line points increases.)
>
> So I went back to the program defining the bezier curve and, beside 
> the rounded points for the graphic display of the curve, I also 
> created a set of "customPoints" for the curve; these are the actual 
> calculated points derived from the bezier formula. Notice the 
> substantial difference in performance-card one.
>
> There is talk of Run Rev including bezier curves in a future release. 
> This will be great, but for some applications you might need the 
> precise, calculated points and not just the rounded graphic points.
>
> It might be nice if Run Rev were to include these calculated 
> coordinates as the graphic points-but displayed, of course, only the 
> rounded values-but this would entail a bit of overhead. If these 
> calculated points were included, the command: put the points of 
> graphic "myBezier" would list the full precision with which Run Rev 
> performs calculations. (What is this, by the way? I couldn't find it 
> in the docs.)
>
>  And there is a fix; namely: calculate the points and put them in a 
> custom property of the curve. To do this you will need the positions 
> of the bezier handles. Complicated if there are multiple bezier 
> controls.
>
> More than you wanted to know.
>
> Jim

Eric Chatonet.
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