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lvl10720-Turquoise
20-Turquoise
March 24, 2025
Solved

Fill Surface the Curve ?

  Hello Everyone,

From:

Fill_Surface_Curve.PNG

  How to Fill Surface the Blue Curve ?

  Thanks in advance for your time and help.

  Regards.

Werner_E
Werner_EAnswer
25-Diamond I
March 25, 2025

You can do the same thing by showing the parameter lines for constant t-values. These are straight lines.

So we now clearly recognise the two sets of straight lines on this HP surface (hyperbolic paraboloid), which is therefore a two-fold ruled surface.

Paraboloid - Wikipedia

Ruled surface - Wikipedia

ani2.gif

BTW. the equation of this surface in kartesian coordinates is z(x,y):=x*y.

This said you could also parametrise this surface that way:

Werner_E_0-1742886569194.png

 

But, at the risk of repeating myself, this HP surface is just one of an infinite number of possible surfaces... 😉

Here is a last one, a cone:

Werner_E_0-1742916137100.png

 

 

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11 replies

Werner_E
Werner_E25-Diamond I
25-Diamond I
March 24, 2025

You would first have to define a surface function.

A surface is not defined just by the surrounding curve.

You may ask for the minimal surface but I guess this would turn into a hard job to do...    Minimal surface - Wikipedia

 

I don't know which kind of surface Mathcad is creating when you do a surface plot of S - do you know it? 😉

 

Here are three out an infinite number of possible surfaces which includes your curve:

Werner_E_0-1742856833519.png

 

 

 

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lvl10720-TurquoiseAuthor
20-Turquoise
March 25, 2025
@Werner_E wrote:

Here are three out an infinite number of possible surfaces which includes your curve:

 Many thanks, Werner. 🙄 🤔 😊. I guess it seems an infinite number of possible surfaces which DOES NOT includes the question's request :

 

I.png

II.PNG

III.png

(view in My Videos)

 

Best Regards.

 

 

 

 

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Werner_E
Werner_E25-Diamond I
25-Diamond I
March 25, 2025
@lvl107 wrote:
I guess it seems an infinite number of possible surfaces which DOES NOT includes the question's request :

Nonetheless an infinite number of surfaces does - three examples were given. Thats simply because your "request" only was " How to Fill Surface the Blue Curve ?" This did not make much sense anyway as a simple curve does not define a surface. That said any surface containing your curve can be seen as a solution to your request. If you had a specific surface in mind you should  have had to say so clearly.

 

BTW, I don't think that what you posted now - just a couple of numbers in nested matrix SS will be of any value without showing where they may stem from. What exactly are you trying to achieve with this?

What you sell as surface by connecting/meshing some precalculated points of your curve may be an approximation of another one of the infinite number of solutions 😉

 

For future question please be (much) more specific as to what exactly you are REALLY looking for. It could save some of us empty miles...

 

BTW, it looks to me like you could achieve the very same surface you show much simpler that way:

Werner_E_0-1742874816800.png

Simply connecting points with equal y coordinates.

You could as well connect the points with equal x coordinates

Werner_E_1-1742875207806.png

The difference lies in the parameterisation.
The animation allows the second parameter u to vary. The colours are, as is unfortunately usual with AVIs generated by Mathcad, suboptimal.

ani.gif

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