Hello Everyone,
From:
How to Fill Surface the Blue Curve ?
Thanks in advance for your time and help.
Regards.
ACCEPTED SOLUTION
Accepted Solutions
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.
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:
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:
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:
@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:
Simply connecting points with equal y coordinates.
You could as well connect the points with equal x coordinates
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.
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.
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:
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, following your hint: ( F6(r , phi) ), the above then:
I really don't know the reason, the above.
Regards.
I don't understand why you are concerned!?
Using the quickplot feature requires you to set the limits in the plot format dialog. If you keep the default values (from -5 to 5) the surface is plotted multiple times and because you used 1/5 in your function definition the surface extends just to the outer blue line.
More reasonable values would be:
Its easier to apply these values in the CreateMesh function which is the reason why I prefer it over the quickplot.
Another reason for using CreateMesh is that you can't use variables in the Plot Format menu and so are limited when making animations like this:
