Solving an eqaution

#1 Posted: 4 years ago

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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 Posted: 4 years ago

Jean Giraud

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

#3 Posted: 4 years ago

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 Posted: 4 years ago

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 Posted: 4 years ago

Necronomicron

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Group: User

Sphere and cubic Bezier curve intersection points.sm (10 KiB) downloaded 90 time(s).

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 KiB) downloaded 90 time(s).

#6 Posted: 4 years ago

Oscar Campo

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Group: Moderator

Wrote
Please attach your Smath document.

Sphere and cubic Bezier curve intersection points.sm (10 KiB) downloaded 90 time(s).

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 KiB) downloaded 102 time(s).

#7 Posted: 4 years ago

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 Posted: 4 years ago

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 Posted: 4 years ago

Alvaro Diaz Falconi

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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 KiB) downloaded 92 time(s).

Best regards.
Alvaro.

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Oscar Campo 4 years ago

#10 Posted: 4 years ago

Necronomicron

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Group: User

Wrote

Wrote
Please attach your Smath document.

Sphere and cubic Bezier curve intersection points.sm (10 KiB) downloaded 90 time(s).

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 KiB) downloaded 102 time(s).

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 KiB) downloaded 93 time(s).

#11 Posted: 4 years ago

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 KiB) downloaded 93 time(s).

Please refer to Maxima plugin instructions, you can find here

#12 Posted: 4 years ago

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 KiB) downloaded 93 time(s).

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 KiB) downloaded 88 time(s).

#13 Posted: 4 years ago

Necronomicron

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

Sphere and cubic Bezier curve intersection points.sm (12 KiB) downloaded 96 time(s).

#14 Posted: 4 years ago

Oscar Campo

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

Sphere and cubic Bezier curve intersection points.sm (12 KiB) downloaded 96 time(s).

There is a missing "*"

#15 Posted: 4 years ago

Necronomicron

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Group: User

Wrote

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

Sphere and cubic Bezier curve intersection points.sm (12 KiB) downloaded 96 time(s).

There is a missing "*"

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

#16 Posted: 4 years ago

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 Posted: 4 years ago

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 Posted: 4 years ago

Alvaro Diaz Falconi

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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 Posted: 4 years ago

Jean Giraud

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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 KiB) downloaded 83 time(s).

#20 Posted: 4 years ago

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 4 years ago

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