plotting a spherical segment

Hi, I need to plot a spherical segment (blue region of the sphere in the attached picture).

Do you have any suggestions?

Gilles

Answer 1

[KSSV]

clc; clear all ;
[X,Y,Z] = sphere(200) ;
surf(X,Y,Z) ;

r = 1; b = 0.9 ; h = 1 ;
%%Get radius 
R = sqrt(X.^2+Y.^2) ;
X1 = X ; Y1 = Y ; Z1 = Z ;
X1(Z<r/2) = NaN ; Y1(Z<r/2) = NaN ; Z1(Z<r/2) = NaN ; 
X1(Z>b) = NaN ; Y1(Z>b) = NaN ; Z1(Z>b) = NaN ; 

surf(X1,Y1,Z1) ;
axis equal 
% shading interp ;

Answer 2

[isku]

My code:

>> clear; syms t x y z real;

r = 1

a = .4*r % 40 pct. of r

b = .6*r % 60 pct. of r

eq = x^2+y^2+z^2 == r^2 % equation of a sphere with center at the origin

% define high by projecting on xz-plane by setting y=0. And then x=0 e,g. the high on z-axe

za = solve( subs( eq, [x^2, y^2,r^2], [0,0, (r^2-a^2)] ), z ) % by Pythagoras, see figure under

za = za(2) % only positive value, upper half of the sphere.

% Similarly

zb = solve( subs( eq, [x^2, y^2,r^2], [0,0, (r^2-b^2)] ), z ) % by Pythagoras

zb = zb(2) % only positive value

h = za - zb

% plotting

>> clear x;

x(t) = sin(t) *r ; % -1<x<1

[X,Y,Z] = sphere;

s = mesh(X,Y,Z, 'edgecolor', 'k', 'FaceAlpha',0.3) ;

hold on

yApos = sqrt( r^2 -x^2-za^2)

yAneg = -yApos

zA(t) = 0*t + za;

fplot3( x, yApos, zA, [-pi, pi], 'red', 'LineWidth', 2 ),

fplot3( x, yAneg, zA, [-pi, pi], 'red', 'LineWidth', 2 )

yBpos = sqrt( r^2 -x^2-zb^2)

yBneg = -yBpos

zB(t) = 0*t+ zb

fplot3( x, yBpos, zB, [-pi, pi], 'red', 'LineWidth', 2 )

fplot3( x, yBneg, zB, [-pi, pi], 'red', 'LineWidth', 2 )

xlabel('x'), ylabel('y'), zlabel('z'), axis equal , grid on

axis( [-1,1, -1,1, -1,1] *r )

campos( [5,5,5])

Using Pythagoras to define the hight at given a and b.

The high on z-axe at b:

zb^2 = r^2 - b^2 % b= 0.6*r