A particle trapped inside a torus

on 13 Oct 2021

% Signed Distance Function (SDF) of Torus

e=@(x)((x(:,1).^2+x(:,2).^2).^.5-1).^.5+x(:,3).^2-1;

E=8e2;

x=[0,2,0];

v=x-4;

s=E;

% bouncing particle simulation

for j=0:(E*3)

p=x(end,:);

d=e(p);

% if hits boundary, compute reflected velocity

if d>=-1/E

% compute gradient of SDF

n=(e(repmat(p,[3,1])+eye(3)/E).'-d)*E;

n=n/norm(n);

v=v-2*n*v.'*n;

end

% update vectors: timestep = 1/10

x=[x;p+v/10];

s=[s;rand*E];

end

% plotting magic ;)

scatter(x(:,1),x(:,2),s,s,'.');

colormap(turbo);

axis equal off;