Crthuky

I want to make 3D animation in Asymptote: the blue small sphere moving along the 3D cyclic curve (that I named "orbit8"). I have heard that curves in Asymptote are parameterized. However, I don't know how to get positions of points along the orbit.

Could you please help me!

My MWE is as follows.

documentclassstandalone
usepackageasymptote
begindocument
beginasy
import three;
currentprojection=obliqueX;
unitsize(1cm);
draw(O--4 * X,Arrow3); 
draw(O--4 * Y,Arrow3); 
draw(-1*Z--4 * Z,Arrow3); 
label("$x$", 4 * X, NW);
label("$y$", 4 * Y, SE);
label("$z$", 4 * Z, E);
real a=.4;
triple U=(-a,-a,1),L=(a,a,1);
path3 orbit8=
(0,1,2)..(0,2,1)..(0,1,0)..U..(1,0,2)..(2,0,1)..(1,0,0)..L..cycle;
draw(orbit8,1bp+black);
dot(L,8bp+.8blue);
dot(U,5bp+.8red);
draw((0,0,2)--(0,0,4),6bp+green,Arrow3()); 
endasy
enddocument

You can use point(orbit8,t) where t is a time. I recommend this great tutorial as well as the asypictureB package by the author of the tutorial. That way you create the output with pdflatex -shell-escape <file>, where file could contain

documentclass[border=3.14mm]standalone
usepackageasypictureB
begindocument
beginasypicturename=asyani
import three;
currentprojection=obliqueX;
unitsize(1cm);
draw(O--4 * X,Arrow3); 
draw(O--4 * Y,Arrow3); 
draw(-1*Z--4 * Z,Arrow3); 
label("$x$", 4 * X, NW);
label("$y$", 4 * Y, SE);
label("$z$", 4 * Z, E);
real a=.4;
triple U=(-a,-a,1),L=(a,a,1);
path3 orbit8=
(0,1,2)..(0,2,1)..(0,1,0)..U..(1,0,2)..(2,0,1)..(1,0,0)..L..cycle;
draw(orbit8,1bp+black);
dot(L,8bp+.8blue);
draw((0,0,2)--(0,0,4),6bp+green,Arrow3()); 
dot(point(orbit8,0.5),5bp+.8red);
endasypicture
enddocument

This is just for fun: creating an actual animation. This snippet creates a series of pdf files that can be converted to an animated gif as explained in this answer. Asymtote has its own facilities to produce animations, but I personally often use these methods (but this may just be me). The most important ingredient here is relpoint, which O.G. pointed out in the comments, so full credit goes to them.

documentclass[border=3.14mm]standalone
usepackagefilecontents
beginfilecontents*orbiter.asf
beginasypicturename=asyani
import three;
currentprojection=obliqueX;
unitsize(1cm);
real mytime = @mytime;
draw(O--4 * X,Arrow3); 
draw(O--4 * Y,Arrow3); 
draw(-1*Z--4 * Z,Arrow3); 
label("$x$", 4 * X, NW);
label("$y$", 4 * Y, SE);
label("$z$", 4 * Z, E);
real a=.4;
triple U=(-a,-a,1),L=(a,a,1);
path3 orbit8=
(0,1,2)..(0,2,1)..(0,1,0)..U..(1,0,2)..(2,0,1)..(1,0,0)..L..cycle;
draw(orbit8,1bp+black);
dot(L,8bp+.8blue);
draw((0,0,2)--(0,0,4),6bp+green,Arrow3()); 
dot(relpoint(orbit8,mytime),5bp+.8red);
endasypicture
endfilecontents*
usepackageasypictureB
standaloneenvasypicture
usepackagepgffor
begindocument
defmyangle45
foreach mytime in 0,0.025,...,0.975

RequireAsyRecompile
inputorbiter.asf

enddocument