Spline creation tangentlenght calculation

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On 17/03/2010 at 15:49, xxxxxxxx wrote:

User Information:
Cinema 4D Version:   11.027 
Platform:   Windows  ;   
Language(s) :     C++  ;

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Hy i write a plugin where i create a Spline connecting circles of different size as well as including their part in the new Spline too.
Till yet i have all needed Points for my Spline but when it comes to the Tangents of those Points the Bezier-Curve is still giving me a headache.
From normal circles i found that all 4 (90° to each other) Points have the Tangentlength of 0.415*Radius .. but if you cut the circle somewhere those values change ...

Can someone tell me how to calculate the lenght please ... the formula would be great ... perhaps there is already a way to get that ...

My idea yet is that it might be related to the arc of the circle but how to go on from there?

Thanks for any suggestions,
Patrick

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On 18/03/2010 at 05:44, xxxxxxxx wrote:

EDIT: wrong information

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On 18/03/2010 at 15:32, xxxxxxxx wrote:

Thanks for the diagram, it definitely gave me something to think and try, but i still can't figure out how the tangents in a circle on the 4 main points are recalculated if you cut somewhere through it. You know just look at a converted (circle) Spline-Object in Point-Mode and then Cut it somewhere with the 4 points selected, you will see that the tangents around get shortened. So in my situation i need to find a solution based on the angle of the arc between my points and calculate the right tangentlenght to make it fit to a circular shape.

Sorry, but as far as i was able to set in values in your formula and compare it, it would not explain to me the change of the already existing tangents like i mentioned before.

Those changes i can only think are related on the length of the arc or in that case position on the bezier-curve.

It would be great to know how Cinema is dealing with that special case (Circle <=> Bezier-Curve). Perhaps a part of calculation behind the Operation "Cut" which would be used for manual construction.

Thanks for your time and any help you can give,
Patrick

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On 18/03/2010 at 16:49, xxxxxxxx wrote:

Ok so far i figured out that the result always differs from the results in Cinema if you use that formuar.

BUT!

If you use a arc and play around with the radius and look at the resulting 5 points and those tangents ... it's always a 1/x of 90° multiplied with those magical 0.415 * Radius.

Means if you use to split a 90° arc (Radius 100) into 2 45° segments you get 4 tangents in there with 20.75 length each. Going to 3 30° Segments it's just the same (the 90° 41.5 tangent is divided through 1/3 giving 13.833333333 )

I guess i can use that, but my original question and interest is still not satified

I would say i just take the angle inside my arc and in relation to 90° i calculate the tangents.
Seriously, that was a brain-drainer .. lol .. but thanks to the hint ... even if it is not what i will use .. it helped me to find a solution.

Therefor thank you very much Matthias and keep up the good work

Problem should be solved for me with that ... else "i'll be back"
Patrick

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On 19/03/2010 at 02:48, xxxxxxxx wrote:

Sorry, I made a mistake. Reading up on Bezier curves shows that the matter is more complicated. It involves so called "magic numbers".

Please check following links:

Approximation of a cubic Bezier curveand vice versa

cubic spline & Bezier curves library

cheers,
Matthias

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On 19/03/2010 at 10:04, xxxxxxxx wrote:

Thanks for the reply and of cause for the helpfull links.

The solution i found is working fine for me as long as the angle of the arc between the points is within 90°. I will look in the material and try to find an easy way to come around that limitation too ... perhaps by adding just another point and reducing the angle under 90° again

Thanks and cheers
Patrick