Hello everyone!
I have difficulty plotting the function c which depends on the derivatives of two functions which in turn depend on the parameter t.
Could anyone help me? This in the smath file.. curvatura.sm (11,36 KiB) scaricato 1639 volta(e).
Thank you so much

Wrote

Hello everyone!
I have difficulty plotting the function c which depends on the derivatives of two functions which in turn depend on the parameter t...

Maybe this is what you want...



... and the .sm file: curvatura1.sm (9,4 KiB) scaricato 1686 volta(e).

Wrote

Could anyone help me ?

To plot both systems ... Jean

curvatura.sm (11,63 KiB) scaricato 1798 volta(e).
Maths Tangent.sm (91,95 KiB) scaricato 1691 volta(e).

thank you very much for your help, I hope I have no more problems

Wrote

thank you very much for your help, I hope I have no more problems

You´re welcome.
It's okay to ask, because you express the need to know. It is better to ask than keep silence

Thank you very much for the availability.
But I need more help.
How can I draw the tangent line to the equation in parametric form?
this is the file … curvatura2.sm (12,5 KiB) scaricato 1727 volta(e).

Hi Ale. Here, some ways.

curvatura3.sm (25,1 KiB) scaricato 1686 volta(e).
curvatura4.sm (20,83 KiB) scaricato 1675 volta(e).

Best regards.
Alvaro

Wrote

Thank you very much for the availability.
But I need more help.
How can I draw the tangent line to the equation in parametric form?

For the Tangent over C(t), it will follow the scalar rules
of the document Tangent.sm posted before.
The Tangent over the parabola is another business.
Smath does not derive linterp(x) as it is NOT a function
only an interpolation. This project and lot more are
rescued via Infinitesimal Analysis [dates back before CAS].
For that particular typical user point of tangency, OK.
You may want to experiment more .
Don't mind to see noisy curvature [disabled in collapsed].
Chers ... Jean.



curvatura2 Copy.sm (30,56 KiB) scaricato 1667 volta(e).

Thanks for the answers.
But if I wanted to find the tangent to the curve when the parameter t changes, how should I do?

Wrote

Thanks for the answers.
But if I wanted to find the tangent to the curve when the parameter t changes, how should I do?

Do you mean the envelope, all the tangents for the range en T?

curvatura5 - envelope.sm (23,64 KiB) scaricato 1554 volta(e).



Best regars.
Alvaro.

Wrote

Hi Ale. Here, some ways.

Thanks Alvaro ... superb/saved ... Jean

Ellipse otherwise from complex.

Circle Complex [Ellipse ROT].sm (13,86 KiB) scaricato 1484 volta(e).

Your project has been refactored strictly on discrete.
OK, you have functions but life is from collected data.
Collected data are always noisy from the quantization,
a small amount of Gaussian Ksmooth is often sufficient.
Ksmooth being applied before cinterp
As exemplified, cinterp is the best interpolator for
a clean curvature plot from infinitesimal maths.
I don't understand what your were attempting c(t) last module.
Please, don't hesitate for more.
Cheers ... Jean

Maths Tangent Data Set Copy.sm (36,61 KiB) scaricato 1646 volta(e).

Wrote

Your project has been refactored strictly on discrete.
O

.... more maths are coming:
cumulative integration, arc length
derivative you already have it from last attachment.

Thank you very much for the help, I appreciate it very much.
I hope to be able to continue alone.
kind regards

Wrote

Thank you very much for the help, I appreciate it very much.
I hope to be able to continue alone.
kind regards

Your project now all done, based on discrete collected data,
collected data that you will have to smooth [not offered].
Smoothing is a large Engineering tool box !
I hope to be able to continue alone.
Let's see the continued adventure.
Cheers ... Jean

Maths Tangent Data Set.sm (60,84 KiB) scaricato 1627 volta(e).

Hello Alvaro, Is graphing a tangent line as exhibited in "curature3.sm" only available for a plot/function in parametric form, i.e. is this available for a cartesian plot/function?

I welcome your review and look forward to your reply.

Sincerely,

Norm

Hi Norm. You can parametrize f(x) as {x(t)=t, y(t)=f(t)} and substitute in the formulas x'(t)=1, x''(t)=0, x(t) -> x and y(t) -> y(x).

curvatura3 - Cartesian.sm (40,25 KiB) scaricato 1686 volta(e).

Best regards.
Alvaro.

Thanks Alvaro! As always, great examples to work with!

Sincerely,

Norm