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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?

In a webinar on July 10, 2013, I solved the related rate problem:

Helium is pumped into a spherical balloon at the constant rate of 25 cu ft per min.
At what rate is the surface area of the balloon increasing at the moment when its radius is 8 ft?

A question in the Q&A at the end of the Webinar asked if it were possible to have an animation illustrate the expanding sphere and the rate of change in the surface area thereof. 

I have a list L. In geom3d, I want to write all tangent of plane of the spherefrom L. But I don't know. I only write one point . I tried 

> restart:

with(geom3d):

L:=[[-5, -5, 8], [-5, -1, 10], [-5, 3, 10], [-5, 7, 8], [-5, 8, -5], [-5, 8, 7], [-5, 10, -1], [-5, 10, 3], [-1, -5, 10], [-1, 7, 10], [-1, 10, -5], [-1, 10, 7...

restart;with(geom3d):

point(M,1,2,1):

plane(P,x+y-3=0,[x,y,z]):

plane(Q,2*x-2*y+z-1=0,[x,y,z]):

line(d,[1+2*t,1-t,t],t):

n:=NormalVector(P):

line(Delta,[M,n],t):

Eq:=Equation(Delta):

intersection(N,d,P):

coordinates(N):

Please write for me a code for the following problem.

Let (S): x^2 + y^2 + z^2 -2*x +2*z + 1 = 0 be a sphere and M(1, 2, -1), N(3, 1, -1) be two points. Find the coordinates of the point K lies on the sphere (S) such that the triangle KHN has minimum area. 

Thank you very much.

Write the equation of the sphere passing through the point B(-1,-1,0) and tangent to the line x = t + 1, y = 2*t + 1, z = -t + 2 at the point A(1, 3, 2) so that its radius obtain minimum value.

This is my code.

> restart:with(geom3d):

point(B,-1,-1,0):

point(A,1,3,2):

a:=[t+1,2*t+3,-t+2]:

line(Delta,a,t):

dsegment(AB,[A,B]):

Problem 1. Write the equation of the sphere passing through three points A(2, 3, -2), B(-2, 3, 4), C(0, -1, 2) and  tangent to the plane (P): x+5*y+z-33=0.

This is my code

> restart:with(geom3d):

point(A,2,3,-2):

point(B,-2,3,4):

point(C,0,-1,2):

plane(P,x+5*y+z-33=0,[x,y,z]):

point(T,x,y,z):

Write the equation of the sphere has its centre at C(1, 2, 3) and cut the  straight line

Delta: x = t+1, y = t-1, z = -t at the points A and B so that the triangle ABC is a equilateral triangle.

This is my code.

Problem. Write the equation of the sphere passing through the three points

A(-1, 2, 1), B(-3, 4, -5), C(1, 2, -3) and its centre 

1) lies in  the plane (P): 2*x + 3*y -z = 0;
2)lies on the sphere (x-3)^2 + (y+1/3)^2 + (z-1)^2=1.
 
This is my code
1) 

restart;with(geom3d):

point(A,-1,2,1):

point(B,3,-4,5):

Let A(1,-2,3), B(-1,0,1) be two points and (P): x+y+z+4=0 be a plane. Write the equation of the sphere has center lies on the line AB, radius of sphere equal to AB/6 and sphere tangent to the plane (P).

This is my code.

> restart:with(geom3d):

point(A,1,-2,3):

point(B,-1,0,1):

line(AB,[A,B],t):

eq:=Equation(AB):

point(M,op(eq)):

Please help me  write a code for the following problem:

Write the equation of the plane which passes through the points A(-1, 3, -6) and B(2, 2, -10) and tangent to the sphere

(x-1)^2 + (y + 1)^2 + (z - 7)^2 = 9.

Thank you very much.

Hello, can you help me? I need to draw a simple model of solar system (9 planets around the sun). I tried to draw planets with

> a[1] := animate(implicitplot3d,

                            [

                    ...

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