Code covered by the BSD License

### Highlights fromChebfun

from Chebfun by Chebfun Team
Numerical computation with functions instead of numbers.

chebsnake(nodes,alpha)
function chebsnake(nodes,alpha)
%CHEBSNAKE   Chebfun snake game.
%   CHEBSNAKE() Feed the snake with more and more interpolation nodes, but
%   avoid that it hits the boundary or itself! Use the arrow keys to
%   control the snake. Any other key will quit the game.
%
%   CHEBSNAKE(NODES) allows one to change the interpolation type. The
%   default type 'cheby' is polynomial interpolation in Chebyshev points.
%   Other types are polynomial interpolation in equispaced points ('equi')
%   and Floater-Hormann rational interpolation in equispaced points ('fh').
%   The blue dots on the snake indicate the interpolated function values.
%
%   CHEBSNAKE(NODES,ALPHA) allows to change the initial game speed by a
%   factor ALPHA > 0, ALPHA > 1 increases the game speed, ALPHA < 1
%   decreases it (default = 1).
%
%   To prevent you from neglecting your actual work, the game speed
%   increases with the total number of achieved points...

% Copyright 2011 by The University of Oxford and The Chebfun Developers.
% See http://www.maths.ox.ac.uk/chebfun/ for Chebfun information.

% get some constants right
if nargin < 2, alpha = 1; end
if nargin > 0 && strcmp(nodes,'equi'), nodes = 0;
elseif nargin > 0 && strcmp(nodes,'fh'), nodes = 2;  else nodes = 1; end
LW = 'LineWidth'; lw = 2;
res = 0.15; len = 5; dom = domain(-1,1); d = 1;
food = @() res*(round((1.8*rand-.9)/res)+1i*round((1.8*rand-.9)/res));
pause on

% keyboard interaction
figure('KeyPressFcn',@keypress);
function keypress(~,evnt)
dold = d;
switch evnt.Key
case 'leftarrow', d = -1;
case 'rightarrow', d = 1;
case 'downarrow', d = -1i;
case 'uparrow', d = 1i;
otherwise, d = 0; % quit
end;
if d == -dold; d = dold; end
end

alpha0 = alpha;                     % set base level for alpha
fails = 0;                          % fail counter (no food eaten)
failmax = 5;                        % number of consecutive fails before quit
while ~(d==0), % until quit
d = 1;
clf;
s = linspace(res*(1-len),0,len) + 1i*eps;
hs1 = plot(s(1:end-1),'b-',LW,lw); hold on
hs2 = plot(s(1:end-1),'bo',LW,lw);
f = food();
hf = plot(real(f),imag(f),'md','MarkerSize',10,'MarkerFaceColor','m');
ht = plot(8,0);                     % dummy handle
title('Control the snake with arrow keys. Quit with any other key.');
axis([-1,1,-1,1]); shg; pause(0.3);
pts = 0;                            % points counter
alpha = alpha0;                     % reset alpha (speed)
t = 1;                              % convex factor for nodes
tic;
while ~(d==0),                      % until game over or quit
t = t + .2*alpha;
if t > 1,
t = 0; dr = res*d;
s = [ s(2:end),s(end)+dr ];
if length(s) < len+pts, s = [ s(2),s ]; end
end
y = (1-t)*s(1:end-1)+t*s(2:end);
if nodes==1,
c = chebfun(y);
elseif nodes==2,
fhd = min(ceil(0.4*sqrt(length(y))),4);
c = bary(linspace(-1,1,5*length(y)),y,linspace(-1,1,...
length(y)),weights(length(y)-1,fhd));
elseif nodes==0
c = polyfit(linspace(-1,1,length(y)),y,length(y)-1,dom);
end
for k = 1:numel(hs1)
if isnan(hs1(k)), continue, end
delete(hs1(k));
end
hs1 = plot(c,'b-',LW,lw);
delete(hs2);
hs2 = plot(y,'bo',LW,lw);
shg; pause(max(0.01,0.03-toc)/alpha); tic;

% check if the snake hits itself or the boundary
if max(abs([real(y(end)),imag(y(end))])) > 1 || ...
min(abs(y(end)-y(1:end-1))) < res/2,
ht = plot(.8*scribble('game over'),'r',LW,lw);
shg; pause(1);
if pts == 0, fails = fails + 1; end
if fails > failmax, d = 0; end
break
end
if abs(y(end)-f) < res/2, % snake eats food ?
pts = pts + 1; alpha = alpha * 1.003; fails = 0;
title(['Points : ' num2str(pts)]);
f = food();
set(hf,'XData',real(f),'YData',imag(f));
end
end
for k = 1:numel(ht)
if isnan(ht(k)), continue, end
delete(ht(k));
end
end;
plot(.8*scribble('goodbye'),'r',LW,lw);
shg; pause(1); close(gcf);

function w = weights(n,fhd) % weights for Floater-Hormann interpolation
w = zeros(1,n+1);
for l = 0:n
ji = max(l-fhd,0);
jf = min(l,n-fhd);
sumcoeff = zeros(jf-ji+1,1);
for i=ji:jf
sumcoeff(i-ji+1) = nchoosek(fhd,l-i);
end
w(l+1) = (-1)^(l-fhd)*sum(sumcoeff);
end
end

end % chebsnake()