vlax-curve-getParam..... functions. What are they?

Rakesh Rao

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Nov 26, 2001, 12:11:35 AM11/26/01

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Can someone explain what is the meaning of the "parameter" in the
function (vlax-curve-getParamAtPoint curve-obj point)

I cannot find any explanation for this.

I tested this on various curves like lines, polylines, arcs etc and it
seems to give stuff like length, angle etc. It is nowhere documented
(atleast I could not find it ) about what this means and how it works.

Any info is welcome. Thanks

- Rakesh Rao

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Vladimir Nesterovsky

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Nov 26, 2001, 9:12:20 PM11/26/01

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Imagine you have a function x = x(u), for u @ [0,1]
(... u belongs to interval from 0 to 1). Say, x = sin(u) or
x = cos(u) or whatever. Then we'll call this u a parameter,
in a sense that for each its value (which belongs to some
region of values, called the function's definition region)
we can find the function's value. Now imagine you
have two such functions,
x = cos(u)
y = sin(u), u @ [0, 2*pi]

For any u value in the definition region we can find the two
corresponding values, x and y; so if we'd put the point (x y)
for each u on the screen, we'd get a curve - a parametric
curve. In our case, a circle.

Any curve type entity in AutoCAD has some underlying
parameterization defined arbitrarily by programmers.
Which exactly was chosen will show up in two aspects ---
the parameter range (start and end parameter value) and
the placement of points on curve corresponding to the
uniformly spaced parameter values.

For instance, the above parameterization
(coincidentally used also for circles by ACAD) dictates
the parameter range from 0 to 2*pi and even distribution
of points along the circle for evenly spaced parameters,
but there exist another parameterization(s) for circles, one
having a parameter range from minus- to plus-infinity
(agreeably not a practical choice). The points for it of course
won't be spaced equally at all.

For ACAD's choice of parameterization for polylines and
circles the points will be equidistantly distributed along the
curve, for ellipses and splines they will be placed more densely
on more curved segments of the curve and more sparsely
along straighter segments.

--
Vlad http://vnestr.tripod.com/
(define (list . args) args)

Rakesh Rao <rakes...@vsnl.net> wrote in message
news:3C01CF07...@vsnl.net...

>
> Can someone explain what is the meaning of the "parameter" in the
> function (vlax-curve-getParamAtPoint curve-obj point)
>
> I cannot find any explanation for this.
>
> I tested this on various curves like lines, polylines, arcs etc and it
> seems to give stuff like length, angle etc. It is nowhere documented
> (atleast I could not find it ) about what this means and how it works.

> [.....]

Rakesh Rao

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Nov 28, 2001, 7:06:26 AM11/28/01

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Vladimir,

Thanks for the fundamental insights. You sure are good at maths.

Rakesh

Vladimir Nesterovsky wrote:

--

Jim Short

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Nov 28, 2001, 8:14:39 AM11/28/01

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Vlad,
A lovely explanation probable not found anywhere else. Thanks!
Can mention a practical use for this function?
Jim

"Vladimir Nesterovsky" <vne...@netvision.net.il> wrote in message
news:DFB53B6134BC1BFE...@in.WebX.maYIadrTaRb...

Jon Fleming

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Nov 29, 2001, 7:22:46 AM11/29/01

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Parameterized curves and their parameters are exceptionally useful when
calculating intersections and perpendiculars and extensions and the like.

jrf
Member of the Autodesk Discussion Forum Moderator Program
Please do not email questions unless you wish to hire my services

In article <C73550103F99F13A...@in.WebX.maYIadrTaRb>, Jim Short
wrote:

Achim Dabrunz

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Nov 30, 2001, 4:08:58 AM11/30/01

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"Vladimir Nesterovsky" <vne...@netvision.net.il> wrote:

>Any curve type entity in AutoCAD has some underlying
>parameterization defined arbitrarily by programmers.
>Which exactly was chosen will show up in two aspects ---
>the parameter range (start and end parameter value) and
>the placement of points on curve corresponding to the
>uniformly spaced parameter values.

A question: Where I can find a documentation of the
curve-parameterizations used by Autodesk? -or- Do you know the
parameterization they use?

Achim Dabrunz