Items tagged with surface surface Tagged Items Feed

how to use Riemann matrix to output Riemann surface?

and plot this surface?

 

with(algcurves):
f:=y^3+2*x^7-x^3*y;
pm:=periodmatrix(f,x,y);
evalf(pm, 5);
rm:=evalf(periodmatrix(f,x,y,Riemann),10);
M := rm;
A := proc (x, y) options operator, arrow; RiemannTheta([x, y], M, [], 0.1e-1, output = list)[2] end proc;
plot3d(Re(A(x+I*y, 0)), x = 0 .. 1, y = 0 .. 4, grid = [40, 40]);

is this graph Riemann Surface?

if so, how to convert A into polynomials?

How to prove or disprove the flatness of the surface x = (u-v)^2, y =  u^2-3*v^2, z = (1/2)*v*(u-2*v), where u and v are real-valued parameters? Here is my try:

 

plot3d([(u-v)^2, u^2-3*v^2, (1/2)*v*(u-2*v)], u = -1 .. 1, v = -1 .. 1, axes = frame);plot3d([(u-v)^2, u^2-3*v^2, (1/2)*v*(u-2*v)], u = -1 .. 1, v = -1 .. 1, axes = frame)

 

eliminate([x = (u-v)^2, y = u^2-3*v^2, z = (1/2)*v*(u-2*v)], [u, v])

[{u = -2*(-x+2*z+(x^2-8*x*z)^(1/2))/(-2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2), v = (1/2)*(-2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2)}, {-(x^2-8*x*z)^(1/2)*x+y*(x^2-8*x*z)^(1/2)-4*(x^2-8*x*z)^(1/2)*z+x^2-y*x+4*y*z-16*z^2}], [{u = 2*(-x+2*z+(x^2-8*x*z)^(1/2))/(-2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2), v = -(1/2)*(-2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2)}, {-(x^2-8*x*z)^(1/2)*x+y*(x^2-8*x*z)^(1/2)-4*(x^2-8*x*z)^(1/2)*z+x^2-y*x+4*y*z-16*z^2}], [{u = -2*(x-2*z+(x^2-8*x*z)^(1/2))/(2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2), v = -(1/2)*(2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2)}, {(x^2-8*x*z)^(1/2)*x-y*(x^2-8*x*z)^(1/2)+4*(x^2-8*x*z)^(1/2)*z+x^2-y*x+4*y*z-16*z^2}], [{u = 2*(x-2*z+(x^2-8*x*z)^(1/2))/(2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2), v = (1/2)*(2*(x^2-8*x*z)^(1/2)+2*x-8*z)^(1/2)}, {(x^2-8*x*z)^(1/2)*x-y*(x^2-8*x*z)^(1/2)+4*(x^2-8*x*z)^(1/2)*z+x^2-y*x+4*y*z-16*z^2}]

(1)

NULL

I think Gaussian curvature should be used to this end. Dr. Robert J. Lopez is my hope.

Download flat.mw

     Parallel curves on surfaces. The distance between the points of the curves is measured along the curves of intersection of the surface and perpendicular planes.
     (According to tradition, it also does not make sense.)

equidistant_curve_surface_MP.mw

 









 

 

Hello everyone,

I have an issue that I don't know how to solve.
I would like to plot a part of a surface that is enclosed by another surface. I wrote a proc() function with an if statement and when the statement is statisfienied I returned desired function. The roblem is that if statement gets ploted as well..

Here is my proc()

yield := proc (sigma__x, sigma__y, tau__xy, sigma__cx, sigma__cy, f__45, f__cx, f__cy, tau__u, f__tx, f__ty, alpha)

if eval(evalf(f__r(sigma__x, sigma__y, tau__xy, f__tx, f__ty, alpha)) < 0) then

return f__h(sigma__x, sigma__y, tau__xy, sigma__cx, sigma__cy, f__45, f__cx, f__cy, tau__u)

else 9999999

end if

end proc;


Here is my plot request:


Explore(implicitplot3d('yield(sigma__x, sigma__y, tau__xy, sigma__cx, sigma__cy, f__45, f__cx, f__cy, tau__u, f__tx, f__ty, alpha)' = 0, sigma__x = -10 .. 10, sigma__y = -10 .. 10, tau__xy = 0 .. 10, style = surfacecontour, numpoints = 100000, axes = normal), parameters = [f__cx = 0.1e-3 .. 10, f__cy = 0.1e-3 .. 10, f__45 = 0.1e-3 .. 10, sigma__cx = 0.1e-3 .. 10, sigma__cy = 0.1e-3 .. 10, tau__u = 0.1e-3 .. 10, f__tx = 0.1e-3 .. 10, f__ty = 0.1e-3 .. 10, alpha = 0.1e-3 .. 10]

 and this is what i get:

plot

The grainy surface should not be there. If it's not possible to remove it, it would be alright that surface would be smooth. Any ideas?


Is there an elegant way to plot a surface with three given parameters, such as
x=(5+w\cos v)\cos u, y=(5+w\cos v)\sin u, z=w\sin v

with u,v between 0 and 2Pi and w between 0 and 3?

Hi,

 

I am having trouble in plotting the following surface (it is a quite complicated expression, but should be fine).

OwnSurface := [-Re(arctan(exp(I*Pi*(1/4))*(u^2+v^2)^(1/2)))-(1/2)*ln((1+(u^2+v^2)^2)^(1/2)), -arctan(1/((2*(u^2+v^2))^(1/2)-1))+7*Pi*(1/4), (1/8)*ln(u^2+v^2-(2*(u^2+v^2))^(1/2)+1)-(1/8)*ln(u^2+v^2+(2*(u^2+v^2))^(1/2)+1)-(1/4)*arctan(1/((2*(u^2+v^2))^(1/2)+1))+(1/4)*arctan(1/((2*(u^2+v^2))^(1/2)-1))];

plot3d(OwnSurface, u = -.4 .. .4, v = -.4 .. .4, labels = [x1, x2, x3]);

The only thing maple does is plotting a box with a diagonal line. How can I fix this?

 

Is there an elegant way to plot the region between the surfaces z=-y^2 and z=x^2, only on the domain of the XY-plane bounded by the triangle with vertices (0,0), (1,0) and (1,1)?

Hi all,

I have a 3D graph and when I right click on the surface, under style, I can see the option of contour. When I click on that I can see some contour associated with the surface. I want maple to show the values for each contour when I observe it from the top . I want to copy and paste some surfaces in a same figure and campare the contours.

 

Thank you

 

 

 

Hey guys,

 

I want to fit experimental data and I was wondering if there is a special PolynomialFit function for a surface.

My data consist of a X,Y, Matrix of densities and I want to have a function describing the surface of the values. On matlab the following code will do so:

[x, y, z] = prepareSurfaceData(temps, concs, densities);
ft = fittype('poly33');
fitresult = fit([x, y], z, ft);

Maybe that gives you a better view of what I want.

Best regards

Why maple is not plotting the whole surface in the domain specified?

Thanks for the help.

I would like to plot a 2D contour plot in the botton of a 3D plot of a spacial curve. I don't know how to do that in maple, but I found something similar done in Matlab for a 2Dcontour plot in the botton of a 3D surface.

Can someone help me?


Thanks,

Fernando 

How can I add fixed point to the surface in 3 dimensions ?

Hi All,

I would like to create a 3D plot or surface plot and got stuck here and need your help.

I have a text file cretaed from C++ program. This file contains data in 8 columns. The first columns are X and Y values and rest of the columns are my calculated values based on X and Y. How can I visualize column numbers 3 to 8 based on X and Y values? Here is a sample:

0.00 0.00 0.378629 0.043703 0.259182 0.221199 0.181269 0.139292
1.00 0.50 0.151368 0.037717 0.451188 0.393469 0.329680 0.259182
2.00 1.00 0.034938 0.045672 0.593430 0.527633 0.451188 0.362372
3.00 1.50 0.003482 0.061922 0.698806 0.632121 0.550671 0.451188
4.00 2.00 0.000134 0.083040 0.776870 0.713495 0.632121 0.527633
5.00 2.50 0.000002 0.106675 0.834701 0.776870 0.698806 0.593430

 

Thanks.

Hello,

I´ve got 2-dimensional array (100x100) of values, which I'd like to plot as 3d graph, where x,y axis would be coords in the array and z-axis would be the value there.

Values are formed by procedure, not by function, so I can't use standard 3d plot, that plots a 3d surface. I think the best is to use the pointplot3d function, but you have to assign each point separately. 

I tried to create a list of pointplot3d plots, one for each row of the array, and then display these plots all in one, but I just received GLException error.

Do you have any ideas?

   Hi there,

   How can we pl0t the volume or surface of revolution of cardioid r=1-cos(\theta) about  polar axis or the vertical axis in maple14.

 Any help will be appreciated.

M.R.Yegan

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