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  • Pi to 10080 decimal places (polar pi patch)

on 14 Nov 2023
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drawframe(1);
Write your drawframe function below
Originally appeared in the MATLAB Community blog
function drawframe(f)
persistent x y d pitxt
nDecimalPlaces = 10080;
if f==1 || isempty(x)
digits(nDecimalPlaces+2);
piStr = char(vpa(pi));
pDigits = piStr(3:end-1)-'0';
% Assign each digit an angular coordinate based on its value 0:9
theta = ((0:36:324)+linspace(0,36,nDecimalPlaces+1)')*pi/180;
ang = theta(sub2ind(size(theta),1:nDecimalPlaces,pDigits+1));
% Compute the length of each line segment; used to set color
[x,y] = pol2cart(ang,1);
[~,~,d] = uniquetol(hypot(diff(x),diff(y)));
d = [d;d(end)];
% Plot line segements using the edge property of a Patch object
% Plot segments using patch so we can control transparency within one
% graphics object.
set(gcf, 'Color','k');
axes(Position = [0 0 1 1]);
pitxt = plotpitxt(text());
hold on
axis equal padded off
% Labels
gap = 3; % gap between segments in degrees
startpt = ((0:36:324) + gap/2)*pi/180; % starting point of each segment, radians
segAng = (0:0.02:1)'.*((36-gap)*pi/180) + startpt; % angular coordinates for segments
radius = 1.08;
[segx,segy] = pol2cart(segAng,radius);
plot(segx,segy,'-w',LineWidth=1,Color=[.8 .8 .8])
% add bounds labels
midAng = ((0:36:324)+18) * pi/180;
tradius = radius + .08;
[tx,ty] = pol2cart(midAng,tradius);
text(tx, ty, string(0:9), ...,
FontUnits='normalized',...
FontSize=0.05, ...
Color=[.8 .8 .8], ...
HorizontalAlignment='center',...
VerticalAlignment='middle');
end
nFrames = 48;
frameIdx = [1,find(mod(1:nDecimalPlaces,nDecimalPlaces/nFrames)==0)];
plotalpha = @(parent,x,y,color,alpha) patch(parent,'XData',[x(:);nan],'YData',[y(:);nan],'EdgeColor',color,'EdgeAlpha',alpha);
cmap = jet(10);
for i = frameIdx(f) : frameIdx(f+1)
if i==nDecimalPlaces
continue
end
plotalpha(gca,x(i:i+1),y(i:i+1),cmap(d(i),:),0.1)
end
pitxt = plotpitxt(pitxt); % faster than uistack
function pitxt = plotpitxt(h)
h.delete
pitxt = text(0,0.05,'\pi', ...
HorizontalAlignment='Center', ...
FontUnits='normalized', ...
FontSize = 0.2, ...
Color = 'k');
end
end
Animation
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