Please help! Probably simple curve problem has me stymied :/

Curve Problem.skp (103.4 KB)

Just as a circle most efficenlty encloses a volume,
and an arc joins point (where possible) most simply, smoothly, and with the greatest radius,
I need a tool/way to join my 6 endpoints that don’t fall along an arc.

I’ve drawn a series of (4) tangential curves but they only relate to the tangent(s) next to them.
They don’t collectively, recusively align with eachother to create the smoothest possible overall curve.
I’ve also drawn a variety of curves (Catmull, Courbette, cubic Bezier, & F-Spline) but they’re all too 'hollow in the outer quarters and look ‘lumpy’.

I’m sure there’s a simple answer but it’s been trial and erroring me to death on and off for about a year :confused: Thank you for your time and considderation of my request.

Perhaps you could share the SKP file of what you have already? Or at least the part with the layout for the curve.

You keep talking about arcs but it seems that you need a non-circular curve instead.

It sounds to me as if one of the tools in the Bezier Spline extension would do the trick. You can get it from Sketchucation.


Bezier spline gets pretty close. Could be made closer with a little more attention.

Not easily but I can upload it.
Curve Problem.skp (103.5 KB)

Thank you David R, got it.
I’ll infer that you maually manipulated the points.
Good job but I can’t guestimate here.
I need a geomartically accurate solution and to be able at accurately get the resultant area.

I have no idea what “geomartically” means but to draw and soften any curve is easy with INKSCAPE. Export from there as DXF.

This is a cubic Bezier with 20 edges per section (original lines and curve deleted so you can get the area).

Curve Problem.skp (104.8 KB)

You didn’t indicate that you need the area under the curve. If you had, I’d have given you that information. Besides, I was only giving you an example and as I noted, I didn’t spend much time on the curve.

This statement doesn’t have a unique answer - it depends on what you mean by “geometrically accurate”. There are lots of ways to fit a curve through a sequence of sample points.

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It doesn’t seem quite reasonable to postulate a need for geometrically accurate curves and then assign the task to a program that doesn’t even create curves in the first place.

You should probably select a tool for your task that is at least theoretically capable of performing it.

-Gully

Incidentally, I hope you have a good editor lined up to review your patent application.

I appreciate your input miller, slbaumgartner, DavidR, and Gully_Foyle. Thank you all.
You’re all making good points and I see I need to communicate better.


Just as a circle most efficenlty encloses a volume,
and an arc joins point (where possible) most simply, smoothly, and with the greatest radius,
I need a tool/way to join my 6 endpoints that don’t fall along an arc.

In the example and attached file, you may see the curves I’ve tried are too hollow in the outer quarters,
leaving a ‘lump’ at the outermost point
(with the possible exception of the Courbette curve that is also the most asymmetric).
None of them comes up with the same results,
and none even has the same last half and first half!?
I appreciate the suggestion slbaumgartner; the cubic Bezier is one of the ones I tried.
I appreciate the suggestion Gully, thanks.

Curve Problem 2.skp (107.0 KB)

Curve Problem 3.skp (152.4 KB)

I went back and recreated and rechecked my curve of sequential tangents.
Not only are both sides the same, it looks like it actually might be the right solution.
Thoughts?

http://extensions.sketchup.com/en/content/curve-maker contains SUPERELLIPSE, a curve what looks a little bit like Yours

Edit: Sorry, I wrote this before I checked it - NO SUPERELLIPSE, it´s more like a normal ellipse.

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Steve: usually “looking right” can mislead. For curve fitting or interpolation one wants some type of quantitative measure of “how good”. A correlation coefficient at least .95 may be an acceptable goal for you. Unfortunately Su does not have a true cubic spline interpolator for you to compare but, there are some on the net so you could check your data with one of those? However they will not be accurate / usable at the end points.

I appreciate you suggestion Miller.

Thanks.

I appreciate your information mac7595.

I did a search for ‘true cubic spline tool’ but don’t know enough about it to use any of the information I saw. Would you mind giving me any further advice?

When you mention tool I assume you mean for SU. I have not seen one for SU. Fredo calls some of his Bezier plugins splines but, they are not what I was thinking. and he even mentions that in foot note in his use manual. Many hits show up when you do a internet search. Some even have on line calculators you can use to check the arcs you have drawn to see how good the fit is.I do not know what your end goal is so cannot comment. If it is to use the data you have and then interpolate between points to get other points cubic spline may be of use to you??

brill… nearly thought i had an anwer to a problem I had …done inkscape drawing saved as a.dxf but can’t seem to import it into sketch up …is this a feature of pro or am I just missing somethin hhhhh
cheers

I used Google SketchUp 8 when I did this Export/Import of DXF with a free plugin.
http://sketchucation.com/pluginstore?listtype=1&author=0&category=0&search=dxf&submit=%3F

But I am not shure - it could be SU 2014

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Hi mac7595,

I’m sorry for my delay in responding.

I do mean for SU.

I am using it for a an outboard hull profile but don’t have a ship design program ($).

I’ve looked for an online calculator. But I don’t understand how I could get anything useful back into SU. Still reading :confused: