在 Matlab 中绘制球坐标系

Question

我想在Matlab中画一个球坐标系

这是我想要创建的图像类型：

有人可以给我一些提示吗？（到目前为止，我已经绘制了笛卡尔坐标）

这是我自己尝试过的：

hold on
x0=0;
y0=0;
z0=0;

plot3(x0+[0, 1, nan, 0, 0, nan, 0, 0], y0+[0, 0, nan, 0, 1, nan, 0, 0], z0+[0, 0, nan, 0, 0, nan, 0, 1] )       
text([x0+1, x0, x0], [y0, y0+1, y0], [z0, z0, z0+1], ['X';'Y';'Z']);

r=0.5;
[x,y,z] = sphere(100); 
hsurf = surf(x*r, y*r, z*r);
axis equal;

Answer 1

function[]=SphereToCartesian(r,theta,phi)
%% plot cartesian coordinates:
plot3([0 0 0;r 0 0],[0 0 0;0 r 0],[0 0 0;0 0 r],'k');

%% plot the ball
line('xdata',sphcart(r,theta,phi,'x'),'ydata',sphcart(r,theta,phi,'y'),'zdata',sphcart(r,theta,phi,'z'),'marker','.','markersize',5);

%% Plot the arm
line('xdata',[0 sphcart(r,theta,phi,'x')],'ydata',[0 sphcart(r,theta,phi,'y')],'zdata',[0 sphcart(r,theta,phi,'z')],'linestyle','--');

%% Plot the projections
line('xdata',[0 sphcart(r,theta,phi,'x')],'ydata',[0 sphcart(r,theta,phi,'y')],'zdata',[0 0],'linestyle','--');

%% Plot the arcs
thetas=[0:0.1:theta theta];
line('xdata',sphcart(.1*r,thetas,phi,'x'),'ydata', sphcart(.1*r,thetas,phi,'y'),'zdata',sphcart(.1*r,thetas,phi,'z'));

%% Labels
text(sphcart(r,theta,phi,'x'),sphcart(r,theta,phi,'y'),sphcart(r,theta,phi,'z'),'r (x,y,z)')

%% transform
 function[OUT]=sphcart(R,THETA,PHI,COORD)
  if strcmpi(COORD,'x')
   OUT=R.*cos(THETA).*cos(PHI);
  elseif strcmpi(COORD,'y')
   OUT=R.*cos(THETA).*sin(PHI);
  elseif strcmpi(COORD,'z')
   OUT=R.*sin(THETA)
  else
   disp('Wrong coordinate!');
   OUT=nan;
  end
 end
end

您可以使用 axes 和 figure 属性完成其余工作。

Answer 2

由于提供给我的有用答案，我现在制作了一些我很满意的东西。我确实使用了稍微不同的方法来绘制弧线。

hold on 
r =1;
phi = pi/4;
theta = pi/4;

%% plot cartesian coordinates:
x0=0;
y0=0;
z0=0;

plot3(x0+[0, .8, nan, 0, 0, nan, 0, 0], y0+[0, 0, nan, 0, .8, nan, 0, 0], z0+[0, 0, nan, 0, 0, nan, 0, .8],'k' )       
text([x0+.85, x0, x0], [y0, y0+.8, y0], [z0, z0, z0+.85], ['$x$';'$y$';'$z$'],'FontSize',14, 'Interpreter','latex');
%% plot the ball
line('xdata',sphcart(r,theta,phi,'x'),'ydata',sphcart(r,theta,phi,'y'),'zdata',sphcart(r,theta,phi,'z'),'marker','.','markersize',5);

%% Plot the arm
line('xdata',[0 sphcart(r,theta,phi,'x')],'ydata',[0 sphcart(r,theta,phi,'y')],'zdata',[0 sphcart(r,theta,phi,'z')]);

%% Plot the projections
line('xdata',[0 sphcart(r,theta,phi,'x')],'ydata',[0 sphcart(r,theta,phi,'y')],'zdata',[0 0],'linestyle','--');

%% Line from xy plane to point
line('xdata',[sphcart(r,theta,phi,'x') sphcart(r,theta,phi,'x')],'ydata',[sphcart(r,theta,phi,'y') sphcart(r,theta,phi,'y')],'zdata',[0 sphcart(r,theta,phi,'z')],'linestyle','--')

%% label r 
text(.5,.5,.8,'$r$','FontSize',14, 'Interpreter','latex')

%% change view point
az = 100;
el = 45;
view(az,el)

%% get rid of axis labels
set(gca, 'XTick', [], 'YTick', [], 'ZTick', [])
set(gca, 'xcolor', 'w', 'ycolor', 'w','zcolor', 'w') ;
%% arc (xy)
theta = [0: pi/4*0.0001 :pi/4];
phi = linspace(0,0,10001);
r = linspace(0.25,0.25,10001);

[X,Y,Z]=sph2cart(theta,phi,r);

plot3(X,Y,Z,'Color','k');

% label arc
text(.3,0.08,0,'$\theta$','FontSize',14,'Interpreter','latex')

%% arc down from z
phi = [pi/4: pi/4*0.0001 :pi/2];
theta = linspace(pi/4,pi/4,10001);
r = linspace(0.25,0.25,10001);
[X,Y,Z]=sph2cart(theta,phi,r);

plot3(X,Y,Z,'Color','k');

% label arc
text(.1,.08,0.4,'$\phi$','FontSize',14,'Interpreter','latex')

剧情如下：

在 Matlab 中绘制球坐标系

Plotting spherical coordinate system in Matlab

matlab

plot

system

coordinate