Solving an eqaution

#1 Publicado: 15/9/2021 10:22:58

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Hello!
I have an equation (sphere and cubic Bézier curve intersection points): B(t) ⋅ B(t) = r², where dot means vector dot product.
B(t) is a cubic Bézier curve:
B(t) = (1 − t)³ ⋅ P0 + 3t ⋅ (1 − t)² ⋅ P1 + 3t² ⋅ (1 − t) ⋅ P2 + t³ ⋅ P3, 0 ≤ t ≤ 1
P0, P1, P2, P3 are some known points, к is some known value too.
Is it possible to solve this using SMath while keeping constants as letters?

#2 Publicado: 15/9/2021 11:08:25

Jean Giraud

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Please attach your Smath document.
Bézier/Hermite ... lot in Smath.
Cheers ... Jean.

#3 Publicado: 15/9/2021 11:49:13

Necronomicron

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Wrote
Please attach your Smath document.
Bézier/Hermite ... lot in Smath.
Cheers ... Jean.

https://ru.smath.com/cloud/sheet/ao2a4mLPSz
Well, not much in there, I don't know how to write the equation in it. I am new to SMath, and used only MathCAD a few times, like, 13-14 years ago...

#4 Publicado: 15/9/2021 12:19:37

Oscar Campo

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Wrote

Wrote
Please attach your Smath document.
Bézier/Hermite ... lot in Smath.
Cheers ... Jean.

https://ru.smath.com/cloud/sheet/ao2a4mLPSz
Well, not much in there, I don't know how to write the equation in it. I am new to SMath, and used only MathCAD a few times, like, 13-14 years ago...

"Error. There is no Worksheet found."

Please upload your sm file to any cloud service a share the link

Regards,

Oscar

#5 Publicado: 15/9/2021 12:24:03

Necronomicron

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Sphere and cubic Bezier curve intersection points.sm (10,28 KiB) descargado 1265 vez(es).

Wrote

Wrote

Wrote
Please attach your Smath document.
Bézier/Hermite ... lot in Smath.
Cheers ... Jean.

https://ru.smath.com/cloud/sheet/ao2a4mLPSz
Well, not much in there, I don't know how to write the equation in it. I am new to SMath, and used only MathCAD a few times, like, 13-14 years ago...

"Error. There is no Worksheet found."

Please upload your sm file to any cloud service a share the link

Regards,

Oscar

Sphere and cubic Bezier curve intersection points.sm (10,28 KiB) descargado 1265 vez(es).

#6 Publicado: 15/9/2021 13:00:26

Oscar Campo

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Wrote
Please attach your Smath document.

Sphere and cubic Bezier curve intersection points.sm (10,28 KiB) descargado 1265 vez(es).

You must use Symbolic evaluation to solve your equation, additionally, you can use some plugin for this task (in my case I used the Maxima plugin).
Please see attached file:

Sphere and Cubic.sm (215,02 KiB) descargado 1249 vez(es).

#7 Publicado: 15/9/2021 14:21:28

overlord

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All those kind of symbolic solvings require either Maxima or Maple plugin as far as I know.
Every other smath solvers [solve(), roots(), FindRoot(), al_nleqsolve(), etc] are numerical solvers.
Could someone correct this statement if it is not true?

Regards

#8 Publicado: 15/9/2021 14:33:35

Oscar Campo

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Wrote
All those kind of symbolic solvings require either Maxima or Maple plugin as far as I know.
Every other smath solvers [solve(), Roots(), al_nleqsolve(), etc] are numerical solvers.
Could someone correct this statement if it is not true?

Regards

yes, that's correct, you can check the description of solve(), roots(), al_nleqsolve(), etc on the Interactive SMath Handbook

#9 Publicado: 15/9/2021 20:57:18

Alvaro

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Hi. In the attached how to solve the problem numerically. Notice that B(t) must to be defined using vectorize, because SMath don't expand the scalar by vector products.

Sphere and Cubic.sm (8,86 KiB) descargado 1205 vez(es).

Best regards.
Alvaro.

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Oscar Campo 15/9/2021 21:07:00

#10 Publicado: 16/9/2021 6:43:49

Necronomicron

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Wrote

Wrote
Please attach your Smath document.

Sphere and cubic Bezier curve intersection points.sm (10,28 KiB) descargado 1265 vez(es).

You must use Symbolic evaluation to solve your equation, additionally, you can use some plugin for this task (in my case I used the Maxima plugin).
Please see attached file:

Sphere and Cubic.sm (215,02 KiB) descargado 1249 vez(es).

There is missing «²» after second parentheses in your file. And I downloaded SMath and Maxima, but when I open your file, I get an error: «Cannot find maxima.bat».

Sphere and cubic Bezier curve intersection points.sm (3,77 KiB) descargado 1290 vez(es).

#11 Publicado: 16/9/2021 7:33:52

Oscar Campo

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Wrote

...

There is missing «²» after second parentheses in your file. And I downloaded SMath and Maxima, but when I open your file, I get an error: «Cannot find maxima.bat».

Sphere and cubic Bezier curve intersection points.sm (3,77 KiB) descargado 1290 vez(es).

Please refer to Maxima plugin instructions, you can find here

#12 Publicado: 16/9/2021 8:18:04

Necronomicron

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Wrote

Wrote

...

There is missing «²» after second parentheses in your file. And I downloaded SMath and Maxima, but when I open your file, I get an error: «Cannot find maxima.bat».

Sphere and cubic Bezier curve intersection points.sm (3,77 KiB) descargado 1290 vez(es).

Please refer to Maxima plugin instructions, you can find here

OK, I've fixed the error, but now it says: «r is undefined». Sorry, it's really hard to understand what to do and I can't find any proper docs about it...

Sphere and cubic Bezier curve intersection points.sm (4,62 KiB) descargado 1263 vez(es).

#13 Publicado: 16/9/2021 8:43:30

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I really don't get what's wrong now...

Sphere and cubic Bezier curve intersection points.sm (12,04 KiB) descargado 1290 vez(es).

#14 Publicado: 16/9/2021 9:40:26

Oscar Campo

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I really don't get what's wrong now...

Sphere and cubic Bezier curve intersection points.sm (12,04 KiB) descargado 1290 vez(es).

There is a missing "*"

#15 Publicado: 16/9/2021 11:07:40

Necronomicron

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Wrote

Wrote
I really don't get what's wrong now...

Sphere and cubic Bezier curve intersection points.sm (12,04 KiB) descargado 1290 vez(es).

There is a missing "*"

Thank you! But what should I do with «r is undefined»? 🤔

#16 Publicado: 16/9/2021 11:12:25

Oscar Campo

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Are you sure you are using the option "Symbolic Optimization"?

You must right-click over your equation, then choose Optimization-Symbolic

#17 Publicado: 16/9/2021 11:40:06

Necronomicron

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Are you sure you are using the option "Symbolic Optimization"?

You must right-click over your equation, then choose Optimization-Symbolic

Thank you very much! It worked! However, the roots are so long... Not sure I can use them... Thanks anyway! 😊

#18 Publicado: 16/9/2021 14:52:16

Alvaro

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Hi. Notice that P0, ..., P3 are vectors with 3 components, not scalars. You can't get the distance with B(t).B(t) using P's as scalars.

Best regards.
Alvaro.

#19 Publicado: 16/9/2021 20:16:44

Jean Giraud

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Wrote
I have an equation (sphere and cubic BÃ©zier curve intersection points):

Didn't see the sphere ?
Bézier is a 2 D plot
I don't understand your project, will leave.
You can project Bézier as surface plot on the sphere,
at this point, all 'N' are roots.
Enjoy/ignore ... Jean.

Page6 Bezier.sm (30,64 KiB) descargado 1465 vez(es).

#20 Publicado: 16/9/2021 21:20:45

overlord

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Wrote
Didn't see the sphere ?
Bézier is a 2 D plot
I don't understand your project, will leave.
You can project Bézier as surface plot on the sphere,
at this point, all 'N' are roots.
Enjoy/ignore ... Jean.

Not related with topic. Nice example to Bezier however no relation with question.
Seeing Bezier in question doesn't mean you can search your files and post your first match Bezier example.

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fedeghi 17/9/2021 3:24:00

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