How to draw a paraboloid?

Question

The official image:

This is a Asymptote code:

\documentclass[border=5pt,varwidth]{standalone}
\usepackage{asymptote}

\begin{document}

\begin{asy} 
import graph3;
import palette;
currentprojection=orthographic(3,1,1.5);
currentlight=(1,0.5,1);
settings.render=4;
defaultpen(fontsize(6pt));
real r=2;
unitsize(1cm);
size(10cm,0);
draw(-1.7*r*X--1.7*r*X,red,Arrow3);
draw(-1.5*r*Y--1.5*r*Y,cyan,Arrow3);
draw(O--2.7*r*Z,blue,Arrow3);
label("$x$", 1.7*r*X, dir(-140));
label("$y$", 1.5*r*Y, dir(-20));
label("$z$", 2.7*r*Z, dir(90));
triple S=(0,0,2*r);
path3 c=circle(O,r,Z);
draw(c,heavyblue+opacity(.5));
///////
triple f(pair M) {real x = (M.x)*cos(M.y);real y = (M.x)*sin(M.y);return (x,y,x^2+y^2);}
surface s=surface(f,(0,0),(r,r*pi), Spline);
//////
pen[] pens=mean(palette(s.map(zpart), Gradient(red,yellow,brown)));
draw(s,heavygreen+opacity(0.3),meshpen=black+thin());
real x(real t) {return cos(t);}
real y(real t) {return sqrt(r)*sin(t);}
real z(real t) {return 1+sqrt(r)*sin(t)*sin(t);}
path3 g=graph(x,y,z,0,2*pi,operator ..);
draw(g,brown);
transform3 tv=shift(S);
path3 cv=tv*c;
draw(cv,heavyblue);
shipout(bbox(1mm));
\end{asy}

\end{document}

This is my code:

\documentclass[border=10pt,pstricks]{standalone}
\usepackage{pst-solides3d,pst-3dplot,}

\begin{document}
\psset{unit=.65,viewpoint=40 30 22 rtp2xyz,lightsrc=viewpoint}
\begin{pspicture}(-5,-4)(6,10)

 \axesIIID[linewidth=.5pt](0,0,0)(3,3,6.5)
\defFunction[algebraic]{funkce}(t){sin(t)}{cos(t)}{0}%
\psSolid[object=courbe,linewidth=.4pt,r=0,range=0 2 Pi mul,linecolor=blue,function=funkce]
\defFunction[algebraic]{projection}(t){cos(t)}{1.41*sin(t)}{1+sin(t)*sin(t)*1.41}
\psSolid[plotpoints=1000,object=courbe,linewidth=.3pt,r=0,range=0 2 Pi mul,linecolor=green!80!black,function=projection]
\psSurface[ngrid=.25 .25,incolor=yellow,linewidth=0.5\pslinewidth,algebraic](-2,-1)(2,1){ x^2+2*y^2 }
\end{pspicture}
\end{document}

I don't know how to covert this to PSTricks:

///////
triple f(pair M) {real x = (M.x)*cos(M.y);real y = (M.x)*sin(M.y);return (x,y,x^2+y^2);}
surface s=surface(f,(0,0),(r,r*pi), Spline);
//////

And I see plotstyle=curve or plotpoints=... make no sence in the second \psSolid.

Can anyone help me?

My compliments for your effort. – Sebastiano Sep 12 '19 at 21:51 — Sebastiano, Sep 12 '19 at 21:51

user187802 · Accepted Answer · 2019-09-11T06:08:11.887

4

\documentclass[border=10pt,pstricks]{standalone}
\usepackage{pst-solides3d}

\begin{document}
\psset{unit=.65,viewpoint=40 30 22 rtp2xyz,lightsrc=viewpoint}
\begin{pspicture}(-5,-4)(6,10)
\defFunction[algebraic]{funkce}(t){sin(t)}{cos(t)}{0}%
\psSolid[object=courbe,linewidth=1pt,r=0,range=0 2 Pi mul,linecolor=blue,function=funkce]
\psSurface*[ngrid=.5 .5,incolor=yellow,linewidth=0.5\pslinewidth](-2,-1)(2,1){
         x dup mul y dup mul add dup 4 gt { pop 4 } if}
\defFunction[algebraic]{projection}(t){cos(t)}{1.41*sin(t)}{1+sin(t)*sin(t)*1.41}
\psSolid[object=courbe,linewidth=1pt,r=0,range=0 2 Pi 
mul,linecolor=red!80!black,function=projection]
\axesIIID[linewidth=.5pt](0,0,3.5)(3,3,6.5)
\end{pspicture}
\end{document}

edited Sep 11 '19 at 06:08

answered Sep 10 '19 at 19:12

user187802

16,850

1

the number of points is declared by the variable resolution. – user187802 Sep 11 '19 at 07:11
Oh, can you explain clearly about x dup mul y dup mul add dup 4 gt { pop 4 } if ? I don't understand how gt, { pop 4 }, if executed ! ... – Sep 11 '19 at 09:28
1

it tests if the z value is greater than 4. If yes, it deletes (pop) the current value and replaces it by 4. You can choose any other value. The purpose is to get a solid which ends at the same z height. – user187802 Sep 11 '19 at 09:41
Can the PSTricks be loaded on https://www.overleaf.com/? I tried but it is wrong. – Sep 11 '19 at 17:24
I never used overleaf – user187802 Sep 11 '19 at 18:33
Have any problems that TikZ can but PSTricks can't ? And opposite .... (neutral opinion) – Sep 12 '19 at 10:51
I do not understand what you mean ... – user187802 Sep 12 '19 at 13:25
You can see your answer no .... in https://tex.stackexchange.com/questions/60778/fundamental-differences-pstricks-tikz-pgf-and-others#comment129166_60809 . Until now, that is true ? – Sep 12 '19 at 14:04
Waiting for ..... :-) – Sep 13 '19 at 15:52
1

waiting for what?? – user187802 Sep 13 '19 at 18:26

How to draw a paraboloid?

1 Answers1