I want to draw the intersection line (curve line) of two functions x^2+y^2+z^2=4 (Zmin= 0) and x^2+y^2=2y in the same coordinate system as follows.

I have read pst-3dplot and pst-solides3d but I can only draw the following.

MWE

documentclass[12pt,pstricks,border=15pt]{standalone}



usepackage{pst-3dplot,pst-solides3d}

begin{document}

begin{pspicture}(-5,-5)(5,5)

pstThreeDCoor



psImplicitSurface[XMinMax=-2.0 2.0 0.15,YMinMax=-2.0 2.0 0.15,ZMinMax= 0 2.25 0.15,algebraic,ImplFunction=x^2+y^2+z^2-4]%

end{pspicture}



end{document}

Question

How to plot two surfaces and the intersection curve?

What about:

documentclass{article}

usepackage{pst-solides3d}



begin{document}

begin{pspicture}(-4,-2)(6,6)

psset{viewpoint=30 40 40 rtp2xyz,lightsrc=viewpoint}

psset{solidmemory,opacity=0.75}

axesIIID(0,0,0)(3,3,3)

psSolid[%

object=cylindrecreux,

r=1,

h=2,

ngrid=36 36,

fillcolor=red,

incolor=orange,

action=none,

name=A1](0,1,0)%

psSolid[%

object=calottesphere,

r=2,

ngrid=36 36,

action=none,

name=B1]

psSolid[object=fusion,

base=A1 B1,

action=draw**]

composeSolid

% Equation of "Window of Viviani"

defFunction[algebraic]{g}(t)%

{sin(t)}%

{cos(t)+1}%

{2*sin(1/2*t)}

psSolid[%

object=courbe,

range=0 6.28,

fillcolor=yellow,

linewidth=0,

function=g,

name=C1,

opacity=0.9,

r=0.0125]

end{pspicture}

end{document}

A quick TikZ version for comparison.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz,tikz-3dplot}

begin{document}

tdplotsetmaincoords{70}{120}

begin{tikzpicture}[tdplot_main_coords,scale=3,declare function={

myz(x)=sqrt((1-sin(x))/2);

mytheta(x)=atan(cot(tdplotmaintheta)/(cos(tdplotmainphi)*cos(x)

-sin(tdplotmainphi)*sin(x)));}]

draw[-latex] (-2,0,0)  -- (2,0,0) node[pos=1.05]{$x$};

draw[-latex] (0,0,0) coordinate(O)  -- (0,2,0) node[pos=1.1]{$y$};

draw[-latex] (0,0,0)  -- (0,0,2) node[pos=1.1]{$z$};

begin{scope}

 clip plot[variable=x,domain=tdplotmainphi-180:90,smooth] 

 ({cos(x)},{sin(x)},0)--

  plot[variable=x,domain=90:450,smooth,samples=101] 

({0.5*cos(x)},{0.5+0.5*sin(x)},{myz(x)})--

 plot[variable=x,domain=90:tdplotmainphi,smooth] ({cos(x)},{sin(x)},0) -- ++ (0,0,2) --

 ({cos(tdplotmainphi-180)},{sin(tdplotmainphi-180)},2) -- cycle; 

 draw[ball color=gray,opacity=0.3,tdplot_screen_coords] (O) circle (1);

end{scope}

draw[top color=gray,bottom color=gray!30,middle color=gray!20,shading angle=90,

fill opacity=0.3]  plot[variable=x,domain=90:450,smooth,samples=101] 

({0.5*cos(x)},{0.5+0.5*sin(x)},{myz(x)});

shade[top color=gray!50,bottom color=gray!50!black,middle color=gray,shading angle=90,

fill opacity=0.3]  plot[variable=x,domain=90:-64,smooth,samples=101] 

({0.5*cos(x)},{0.5+0.5*sin(x)},{myz(x)})

--plot[variable=x,domain=-64:90,smooth,samples=101] 

({0.5*cos(x)},{0.5+0.5*sin(x)},0);

draw[dashed] plot[variable=x,domain=90:-64,smooth,samples=101] 

({0.5*cos(x)},{0.5+0.5*sin(x)},0) --

({0.5*cos(-64)},{0.5+0.5*sin(-64)},{myz(-64)});

end{tikzpicture}

end{document}

documentclass{article}

usepackage{pst-solides3d}



begin{document}



begin{pspicture}[solidmemory](-4,-2)(6,6)

psset{viewpoint=30 10 20 rtp2xyz,lightsrc=viewpoint}

psSolid[object=plan,

  definition=normalpoint,args={0 0 0 [0 0 1]},

  base=-2.5 2.5 -2.5 2.5,

  planmarks,name=plane]

psset{plan=plane}

psProjection[object=cercle,args=0 1 1,range=0 360,

  linecolor=red,linestyle=dashed]

axesIIID(0,0,0)(3,3,3)

psSolid[

  object=calottesphere,r=2,ngrid=16 18,opacity=0.4,

  linewidth=0.01pt,fillcolor=blue!60,theta=90,phi=0]

end{pspicture}



end{document}

documentclass{article}

usepackage{pst-solides3d}

usepackage[a4paper,showframe]{geometry}



begin{document}

begin{center}

begin{pspicture}[solidmemory](-5,-2)(6,6)

psset{viewpoint=30 80 25 rtp2xyz,lightsrc=viewpoint}

psSolid[object=plan,

    definition=normalpoint,args={0 0 0 [0 0 1]},

    base=-2.5 2.5 -2.5 2.5,

    planmarks,name=plane]

    psset{plan=plane}

psProjection[object=cercle,args=0 1 1,range=0 360,

    linecolor=red,linestyle=dashed]

axesIIID(0,0,0)(3,3,3)

psSolid[object=calottesphere,r=2,ngrid=64 72,action=none,

    linewidth=0.01pt,fillcolor=blue!60,theta=90,phi=0,name=sp]

psSolid[object=cylindrecreux,h=2.5,r=1,fillcolor=white,action=none,

    ngrid=30 72,incolor=green!50,name=py](0,1,0)

psSolid[object=fusion,base=sp py,opacity=0.8,grid,action=draw**]

defFunction[algebraic]{g}(t){sin(t)}{cos(t)+1}{2*sin(1/2*t)}

psset{object=courbe,fillcolor=red,linecolor=red,

    linewidth=0.1,function=g,r=0,action=draw**}

psSolid[range=0 1.9]psSolid[range=2.6 3.9]psSolid[range=5 TwoPi]

end{pspicture}

end{center}



end{document}

and printed on A4:

Hemisphere as a parameterized surface:

documentclass{article}

usepackage{pst-solides3d}



begin{document}

begin{pspicture}(-4,-2)(6,6)

psset{viewpoint=30 40 40 rtp2xyz,lightsrc=viewpoint}

axesIIID(0,0,0)(3,3,3)

defFunction[algebraic]{hemisphere}(u,v)

{2*cos(u)*sin(v)}{2*sin(u)*sin(v)}{2*cos(v)}

psSolid[object=surfaceparametree,

base=0 2 pi mul 0 pi 2 div,

fillcolor=red,

opacity=0.7,

function=hemisphere,

linewidth=0.5pslinewidth,

ngrid=36 36]%

end{pspicture}

end{document}