Items tagged with sphere

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I want to build interacitv plot ( slider+plot) ( inscribed cylinder in sphere) ?

Thanks

    My profile picture was formerly animation and looked like this: 


  It would be interesting to paint a triangle on a sphere. How can I do that?

Hi all

I would like to plot a quadrilaterial (  spherical quadrilaterial)  on the sphere ( the vertices are known)

How can I do this

 

Many thanks

 

Hello

I have two vectors of angle Theta and Phi  given by

Theta=[ 0, Pi/3, 2*Pi/3, Pi];

Phi=[ 0, Pi/3 , 2*Pi/3 , Pi,4*Pi/3, 5*Pi/3, 2*Pi, 7*Pi/3];

I would like a general procedure how can I put on the unit sphere only the point 

x=cos(Phi).*sin(Theta);
 y=sin(Theta).*sin(Phi);
 z=cos(Theta);

where

(Theta, Phi) in the set {(0,Pi/3),  (0,Pi),  , (0,5*Pi/3),  

(Pi/3,0),   (Pi/3,2*Pi/3),   (Pi/3,4*Pi/3),   (Pi/3,2*Pi), 

(2*Pi/3,Pi/3),   (2*Pi/3,Pi),   (2*Pi/3,5*Pi/3),   (2*Pi/3,7*Pi/3), 

(PI,2*Pi/3),   (Pi,4*Pi/3),   (Pi,2*Pi) }

can we extract these set of point fro the definition of the two vectors Phi and Theta and then make the plot

of course we use 
Many thanks

 

I want to calculate the ratio of the length of day and night for every latitude on earth ?
but i confused on using Maple in a wise way for finding the formula !
this is my demonstration :

shekofte000.mw
 

Equations

 

the grat circle that divides the earth's surface into two dark and bright sides

[sin(t)*cos(tilt), cos(t), sin(t)*sin(tilt)]

[sin(t)*cos(tilt), cos(t), sin(t)*sin(tilt)]

(1.1)

circle of revolving of a point on earth in 24 hours

[sin(t)*cos(Latitude), cos(t)*cos(Latitude), sin(Latitude)]

[sin(t)*cos(Latitude), cos(t)*cos(Latitude), sin(Latitude)]

(1.2)

Visualization of dark and bright side the of earth

 

Explore(plots[display](plots[spacecurve]({[sin(t)*cos(tilt), cos(t), sin(t)*sin(tilt), color = red], [sin(t)*cos(Latitude), cos(t)*cos(Latitude), sin(Latitude), color = blue]}, t = 0 .. 2*Pi, scaling = constrained, thickness = 4, labels = [x, y, Latitudez], labeldirections = [horizontal, horizontal, vertical], axes = frame), plottools[rotate](plottools[hemisphere]([0, 0, 0], 1, capped = false, color = green, grid = [10, 10], style = surface), 0, tilt, 0), plottools[rotate](plottools[hemisphere]([0, 0, 0], 1, capped = false, color = black, grid = [10, 10], style = surface), 0, Pi+tilt, 0)), parameters = [tilt = 0 .. Pi, Latitude = -(1/2)*Pi .. (1/2)*Pi], initialvalues = [tilt = (1/2)*Pi+.409, Latitude = 1.16])

``


 

Download shekofte000.mw

 

Hi.

This is probably not very much maple related question, but to some extend it is.

After failing this question on my exam I have tried to solve it, but it seems like I cant get it right.

Given a sphere z^2+r^2=4 and a cylinder r=1 I was told to set up the volume integral for the element T enclose byt the outer sphere and the inner circle.

I tried to generate a plot but my skills are rather poor in plotting, if I could get the plot right I would be able to set up the volume integral. I have also tried to figure out how to do the surface integral and chose to use a task template as it is a bit more convinient when you find the syntax hard.

I would say I am familiar with the VectorCalculus:-SurfaceInt in cartesian for when i have intersection of two surfaces given in terms of z=

 

but this kind of problem is new to me.

 


 

Surface Integration over a Surface Defined Parametrically

 

Formulate and evaluate the surface integral of f(x, y, z) over a surface defined parametrically.

NULL

 

Surface Integral on a Surface Defined Parametrically

 

 

  Integrand

"f(x,y,z)="

   

 

 

 

   " x(u,v)="

   

 

 

 

"y(u,v)="

   

 

 

 

   " z(u,v)="

   

 

 

 

 

 

`≡`(F(u, v), f(x(u, v), y(u, v), z(u, v)))

`≡`(LinearAlgebra[Norm](N), sqrt((`∂`(y, z)/`∂`(u, v))^2+(`∂`(z, x)/`∂`(u, v))^2+(`∂`(x, y)/`∂`(u, v))^2))

 

 

 

"∫(∫)[S]f ⅆsigma =(∫)[u=a]^(u=b)(∫)[v=g(u)]^(v=h(u))F(u,v)||N|| ⅆv ⅆu"

"="

"b="

"∫(∫)[S]f ⅆsigma=""(∫)[v=a]^(v=b)(∫)[u=G(v)]^(u=H(v))F(u,v)||N|| ⅆu ⅆv"

"="

"a="

 

 

NULLNULL

 

NULL

NULL

 

NULL

                                

 

 

NULL

with(plots):

p1 := plot3d([2*cos(u)*sin(v), 2*sin(u)*sin(v), 2*cos(v)], u = 0 .. 2*Pi, v = 0 .. Pi, color = green, transparency = .55):

p2 := plot3d([cos(u), sin(u), z], u = 0 .. 2*Pi, z = -2 .. 2, color = red, filled = true):

display(p1, p2)

 

p3 := plots:-sphereplot(2, theta = 0 .. 2*Pi, phi = 0 .. Pi, color = green, transparency = .55):

p4 := plots:-cylinderplot(1, theta = 0 .. 2*Pi, z = -2 .. 2, color = red):

plots:-display(p1, p2)

 

``

NULL


 

Download surface_int.mw

   Consider a surface of the unit sphere about the origin, intersecting the volume of the cube [-a..a,-a..a,-a..a] 0<a<1.  What is the best Maple method to plot this surface with a direct mapping, that is without use of implicit plotting over a volume or rejecting grid points?

Dear all,

I would like to find a way to make the reflection of a spherical wave inside a tube (a cylinder). You have herafter an exemple of a sphere increasing inside a tube, but without the reflections...

 

Any idea how to do this?

Thanks a lot for your help.

 

Hi all,

 

I am generating a sphere with increasing radius that interacts at some point with a plan, just like this:

I would like to find a way to make the sphere "wave" (I agree this is not a wave...) reflected by the plan as in a mirror.

How could I do that ?

Thanks a lot for your help.

B

Is there an elegant way to plot in 3d only the portion of the function f(x,y)=sqrt(25-x^2-y^2) for which 9 <= x^2+y^2 <= 16 ? I'm looking for a nice plot that shows it against the whole sphere with radius 5, so that it's clear which part of the sphere is cut out.

@Carl Love 

i guess that it is this.

actually my goal is 

drawing

 tangent vector field on even-dimensional n-spheres

can vector field plot do this too?

if start from draw vector field on a sphere

 

i find that intersectplot under plot, 

is it possible for fieldplot has this

 

such as the graph in wiki

https://en.wikipedia.org/wiki/Hairy_ball_theorem

 

I use Mathematica. This code finds integer points on the sphere

(x-2)^2 + (y-4)^2 + (c-6)^2 =15

and select two of them so that distance of two this points equal to 4.

ClearAll[a, b, r, c];
a = 2;
b = 4;
c = 6;
r = 15; ss =
Subsets[{x, y, z} /.
Solve[{(x \[Minus] a)^2 + (y \[Minus] b)^2 + (z \[Minus] c)^2 ==
r^2, x != a, y != b, z != c, x y z != 0}, {x, y, z},
Integers], {2}];
t = Select[ss, And @@ Unequal @@@ Subsets[Flatten[#], {2}] &];
Length[t]
Select[ss, Apply[EuclideanDistance, #] === 4 &]

 

and this code select four points on the shere so that none of three points make a right triangle

ClearAll[a, b, r, c];
a = 2;
b = 4;
c = 6;
r = 15;
ss = Subsets[{x, y, z} /.
Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2, x != a, y != b,
z != c, x y z != 0, x > y}, {x, y, z}, Integers], {4}];
nonright =
Pick[ss, (FreeQ[#, \[Pi]/2] &) /@ ({VectorAngle[#2 - #1, #3 - #1],
VectorAngle[#1 - #2, #3 - #2],
VectorAngle[#1 - #3, #2 - #3]} & @@@ ss)];
Select[nonright, (12 == Length[Union @@ #] &)]

 I am looking for a  procedure in Maple.  I have some problems with this sphere. For example:

Choose four points so that 12 coordinates difference and it makes a square.

Can your code improve with sphere?

This post is related to the question. There were  proposed two ways of finding the volume of the cutted part of a sphere in the form of a wedge.  Here the procedure is presented that shows the rest of the sphere. Parameters procedure: R - radius of the sphere, H1 - the distance the first cutting plane to the plane  xOy,  H2 -  the distance the second cutting plane to the plane  zOy. Necessary conditions:  R>0,  H1>=0,  H2>=0,  H1^2+H2^2<R^2 . For clarity, different surfaces are painted in different colors.

restart;

Pic := proc (R::positive, H1::nonnegative, H2::nonnegative)

local A, B, C, E, F;

if R^2 <= H1^2+H2^2 then error "Should be H1^(2)+H2^(2)<R^(2)" end if;

A := plot3d([R*sin(theta)*cos(phi), R*sin(theta)*sin(phi), R*cos(theta)], phi = arctan(sqrt(-H1^2-H2^2+R^2), H2) .. 2*Pi-arctan(sqrt(-H1^2-H2^2+R^2), H2), theta = 0 .. Pi, color = green);

B := plot3d([R*sin(theta)*cos(phi), R*sin(theta)*sin(phi), R*cos(theta)], phi = -arctan(sqrt(-H1^2-H2^2+R^2), H2) .. arctan(sqrt(-H1^2-H2^2+R^2), H2), theta = 0 .. arccos(sqrt(R^2-H2^2-H2^2*tan(phi)^2)/R), color = green);

C := plot3d([R*sin(theta)*cos(phi), R*sin(theta)*sin(phi), R*cos(theta)], phi = -arctan(sqrt(-H1^2-H2^2+R^2), H2) .. arctan(sqrt(-H1^2-H2^2+R^2), H2), theta = arccos(H1/R) .. Pi, color = green);

E := plot3d([r*cos(phi), r*sin(phi), H1], phi = -arccos(H2/sqrt(R^2-H1^2)) .. arccos(H2/sqrt(R^2-H1^2)), r = H2/cos(phi) .. sqrt(R^2-H1^2), color = blue);

F := plot3d([H2, r*cos(phi), r*sin(phi)], phi = arccos(sqrt(-H1^2-H2^2+R^2)/sqrt(R^2-H2^2)) .. Pi-arccos(sqrt(-H1^2-H2^2+R^2)/sqrt(R^2-H2^2)), r = H1/sin(phi) .. sqrt(R^2-H2^2), color = gold);

plots[display](A, B, C, E, F, axes = none, view = [-1.5 .. 1.5, -1.5 .. 1.5, -1.5 .. 1.5], scaling = constrained, lightmodel = light4, orientation = [60, 80]);

end proc:

 

Example of use:

Pic(1,  0.5,  0.3);

                             

 

 

I have drawn a 3d plot of a sphere in maple, but when I try to export this one in an .eps file, only the coordinate system of the plot is shown, but not the colourful plot. The export works if I use jpg and similar file types, but not with .eps, does anybody know if there is a way out of this problem?

I have 3 column vectors:

phi contains the number of radians from the North Pole

theta contains the number of radians from the Greenwich meridian

D contains number data corresponding to the point (phi,theta) on the sphere.

 

How do I plot:

a) a contour plot on the surface of the sphere where each point at (phi, theta) has a corresponding data value D?

b) a plot where the height above the surface at (phi, theta) is some linear function of D such as radius*D*constant?

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