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53 lines
1.9 KiB
53 lines
1.9 KiB
function I = sgPolygonIntegrate(Cellintel,funct,pts,pp,kg)
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% Funct is the x antiderivative of some function defined in the interior
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% of Cellintel. Cellintel contains the boundaries of the region of
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% interest, ordered counterclockwise and expressed as Bezier Curves
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% pts is the number of total quadrature points in each direction, pp is
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% the number of total poles (kg*m+2*m) and kg is the gauss quad pts
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% green's theorem antiderivative
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I=0;
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I2=0;
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for i=1:length(Cellintel)
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cp=Cellintel{i}(1:3:end,:);
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fanti=@(a,b) gauss1D(@(x)funct(x,b),min(min(cp(:))),a,kg);
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mfanti=@(a,b) arrayfun(fanti,a,b);
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for j=1:3:(size(Cellintel{i},1))
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newfunct= @(t) RatGreensFunction(t,Cellintel{i}(j:(j+2),:),mfanti);
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rts=roots(fliplr(BernsteinToMonomial(Cellintel{i}(j+2,:))));
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sgl=repmat(rts,ceil(pp/(size(Cellintel{1},2)-1)),1);
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sgl((length(sgl)+1):(pts),:)=[Inf];
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[fout,sglout ] = transf( @(x)newfunct(x) , sgl , [0,1] );
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% I=I+rfejer(sglout,fout);
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if isempty(rts)
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I=I+gauss1D(newfunct,0,1,pp+pts);
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else
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x = rfejer(sglout);
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if any(x(2,:)<0)
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I=I+gauss1D(newfunct,0,1,pp+pts);
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elseif all(abs(Cellintel{i}(j+2,:)-1)<1e-15)
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I=I+gauss1D(newfunct,0,1,pp+pts);
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else
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I = I + fout(x(1,:))*x(2,:)';
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end
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end
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end
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end
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end
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function I = RatGreensFunction(t,Side,funct)
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xy=dCR_eval(Side,t);
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x=xy(:,1);y=xy(:,2);
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yp = dCR_eval_dt(Side(2:3,:),t);
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I=(funct(x,y).*yp)';
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end
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% a=5; % horizontal radius
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% b=10; % vertical radius
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% x0=Centroid(1); % x0,y0 ellipse centre coordinates
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% y0=Centroid(2);
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% t=-pi:0.01:pi;
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% x=s(4)*cos(t);
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% y=s(1)*sin(t);
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% xy=v*[x;y] +[x0;y0];
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% hh=plot(xy(1,:),xy(2,:),'k','Linewidth',2)
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