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on 28 Nov 2023
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function drawframe(f)
% Rotation
rx=f/48*pi;
% Shorteners
q=@triangulation;
j=@polyshape;
K='KeepCollinearPoints';
% Transforms
persistent WX EX
if f==1
%% WORD SHAPE
% Basic idea - draw a word using a text object in a wide
% figure, screen-cap it, then contourit.
f=figure('Color','w','Vis','of','Pos',[ 100 100 3000 300 ]);
ax=axes(f,'Vis','off');
t=text(ax,15,15,'MATLAB','Units','pixel',...
'FontSize',30,'FontWeight','bold','FontUnits','Pix',...
'VerticalA','baseline');
F=getframe(ax,t.Extent);
close(f)
V=contourc(double(flipud(F.cdata(:,:,1))),[50 50])';
% Convert contour matrix into polyshape verts
idx=1;
while idx<size(V,1)
n=V(idx,2);
V(idx,:)=nan;
idx=idx+1+n;
end
% Center and scale to unit height
V=(V-min(V))/max(V,[],'all');
% Convert to polyshape so we get a clean triangulation
W1=j(V(2:end,:),K,true);
W1=XP(W1.polybuffer(.006));
%% Create the WordSphere
% Constants
R1=1.3; % radius of inner/outer part of sphere.
R2=1.5;
SP=.8; % Span of the word
T=q(W1);
% Aspects of the triangulation.
V=T.Points; % Get improved V
F=T.ConnectivityList;
E=T.freeBoundary;
% Constants for this shape when computing connecting edges
R=1:size(E,1); % All the boundary edges.
L2=size(V,1); % Layer 2 starts here.
% New triangulation faces
NF=[F; F+L2; % top and bottom
E(R,[2 1 2])+[0 0 L2]; % edges connecting top/bottom
E(R,[1 1 2])+[0 L2 L2];
];
x=max(V);
T=V(:,1)/x(1)*SP; % Stretch around part of theta
zV=(V(:,2)-x(2)/2);
P=zV*.2/R1/max(zV);
%% Cheap Earth (do this before patches due to newplot)
axes(CreateFcn='earthmap');
EX=hgtransform;
set(findobj('type','surface'),'parent',EX);
%% Word Sphere (or 2 half spheres)
WX=hgtransform;
for o=[0 1]
V2=[cospi(T+o).*cospi(P),sinpi(T+o).*cospi(P),sinpi(P)];
WT=q(NF,[V2.*[R1 R1 1]
V2.*[R2 R2 1]]);
patch(WX,'Vertices',WT.Points,'Faces',WT.ConnectivityList,...
'FaceC','#0076a8','FaceA',1,'FaceL','n',...
'FaceVertexCData',[T;T],...
'EdgeC','n');
patch(WX,'Vertices',WT.Points,'Faces',WT.featureEdges(pi/4.5),...
'FaceVertexCData',[],'FaceC','none','EdgeC','#fff00f','LineW',1);
end
clim(clim);
% Prettify
set(gcf,'Color','k');
daspect([1 1 1]);
view([220 5])
axis([-1.5 1.5 -1.5 1.5 -1.1 1.1],'off')
camzoom(1.7)
end
WX.Matrix=makehgtform('zrotate',-rx+pi/3);
EX.Matrix=makehgtform('zrotate',rx*2);
%% HELPER FCNS
% The below fcns add verticies into a polyshape so that the resolution along
% long edges is high enough so we can bend those edges around the sphere.
function ps=XP(psIn)
% Make all long straight edges in the polyshape be made of many short
% segments.
% Get the regions
r=regions(psIn);
% New polyshape should keep all the extra pts we'll be adding.
ps=j();
% Loop over all the regions
for i=1:numel(r)
[x,y]=boundary(r(i),1); % Exclude all the holes in this region
ps=union(ps,XE(x,y),K,true);
end
% Get the holes in those regions
h=holes(psIn);
% Loop over all the holes
for i=1:numel(h)
[x,y]=boundary(h(i),1);
ps=subtract(ps,XE(x,y),K,true);
end
end
function ps=XE(x,y)
% Expand the edges for one polyregion
if x(end)==x(1) && y(end)==y(1)
inp=[x y];
else
inp=[x(end) y(end)% This is a loop, re-add the end
x y];
end
P=[];
for i=2:size(inp,1)
d=norm(inp(i-1,:)-inp(i,:));% distance between adjacent pts
n=max(2,floor(150*d));% n pts to increase it to
if n==2
P=[P%#ok
inp(i-1,:)];
else
%disp expand
xe=linspace(inp(i-1,1),inp(i,1),n)'; % interp
ye=linspace(inp(i-1,2),inp(i,2),n)';
% Add all but last pt to avoid dups
P=[P;%#ok
xe(1:end-1) ye(1:end-1)];
end
end
ps=j(P,K,true);
end
end
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