I want to produce an animation of a graph with Asymptote. To achieve this the function needs a parameter d;
real f(real x, real y) {
return (x^2 + y^2 + d * x);
}
guide[][] thegraphs = contour(f, a=(-2,-2), b=(2,2), new real[] {0});
How we can send a parameter using the contour?
Yes, in Asymptote there are so-called anonymous functions (see here, page 290) can be created with the keyword new, so that function definition in your example could be simplified without using programming tricks (you are difficult ^^ your trick is quite comfortable!).
size(5cm);
import graph;
import contour;
typedef real function(real, real);
function f(real d) {
return new real(real x, real y) {
return x^2 + y^2 -1+ dx^2y^2;
};
}
pen[] c={red, blue,purple,orange}; c.cyclic=true; // for different Edwards curves
for(int d=100; d > 0; d -= 10) {
guide[][] thegraphs = contour(f(d), a=(-2,-2), b=(2,2), new real[] {0},nx=200,operator..);
// nx=200 >>> for larger sample (default nx=100,ny=nx)
// operator.. >>> smoother join
draw(thegraphs[0],c[d]);
}
shipout(bbox(5mm,invisible));
I hope you can adapt this to your animation. By the way, I am very impressive with recently-discovered Edwards curves and their application in cryptography.
Asymptote is rich in mathematical flavor!
Update Animation version
// x.asy >>> x.pdf >>> making GIF ưith ImageMagick command in the command line window
// magick -density 200 x.pdf -alpha remove x.gif
unitsize(2cm);
import contour;
import animate;
typedef real function(real, real);
function f(real d) {
return new real(real x, real y) {
return x^2 + y^2 -1+ dx^2y^2;
};
}
real a=1.25;
draw(box((a,a),(-a,-a)),invisible);
draw((a,0)--(-a,0)^^(0,a)--(0,-a),gray);
animation A;
for(real d=360; d > -1; d -= 5) {
save();
guide[][] Edwards = contour(f(d), a=(-1,-1), b=(1,1), new real[] {0},nx=200,operator..);
draw(Edwards[0],blue);
label("$d = $ "+string(d),(-a+.2, -a+.2),align=E);
A.add();
restore();
}
erase();
A.movie();
label(format("d = %4.1f",i),(-1.25, -1.25),align=E);
– kelalaka
Feb 10 '21 at 17:48
draw(box((2,2),(-2,-2)),invisible); to make bounding box fixed, so the animation will be fine!
– Black Mild
Feb 10 '21 at 17:51
typedef real function(real, real); function f(real d) { return new real(real x, real y) { return x^2 + y^2 -1+ dx^2y^2; }; }
pen[] c={red, blue,purple,orange}; c.cyclic=true; // for different Edwards curves
draw(box((-1.5,1.5),(1.5,-1.75)),gray);
for(int d=10; d > 0; d -= 10) { guide[][] thegraphs = contour(f(d), a=(-2,-2), b=(2,2), new real[] {0}); draw(thegraphs[0],c[d]); label(format("d = ",d),(0, -1.25),align=(0,0)); }
shipout(bbox(5mm,invisible)); `
– Black Mild Feb 10 '21 at 18:01string( floor(i * 10 )/10). Does the posted image is produced exactly with this code? I've smaller and nonsmooth drawings.
– kelalaka
Feb 10 '21 at 19:24
magick -density 200 Edwards.pdf -alpha remove Edwards.gif for gif
– Black Mild
Feb 10 '21 at 19:56
convert command. One more issue to reproduce the same result; I compile with asy x.as and that produce gif for animations by default. Forcing output the pdf is a mess. Am I missing something?
– kelalaka
Feb 11 '21 at 18:24
I've solved my issue with programming tricks as;
real g(real x, real y, real d) {
return (x^2 + y^2 + d * x);
}
animation A=animation(global=false);
for(int i=300; i != 1; i -= 1) {
erase();
real f(real x, real y) {
return g(x, y, i);
}
guide[][] thegraphs = contour(f, a=(-2,-2), b=(2,2), new real[] {0});
draw(thegraphs[0]);
A.add(BBox(1cm, nullpen));
}
erase();
A.movie(delay=240);
Here is the animation for Edwards curves;
