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49 lines
1.7 KiB
49 lines
1.7 KiB
function [xquad,yquad,wquad] = SPECTRAL_quads(Cellintel,pts,kg)
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% Calculates quadrature points for the region defined by Cellintel using
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% the "SPECTRAL" method from the paper "spectral mesh-free quadrature for
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% planar regions bounded by rational parametric curves."
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% Input:
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% Cellintel Oriented boundaries of the region
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% pts Number of intermediate quadrature points to use
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% kg Number of antiderivative quadrature points to use
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%
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% Output:
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% [xquad, yquad] Quadrature points locations
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% wquad Quadrature weights
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xquad=zeros(0,1); yquad=zeros(0,1); wquad=zeros(0,1);
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for i=1:length(Cellintel)
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cp=Cellintel{i}(1:3:end,:);
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for j=1:3:(size(Cellintel{i},1))
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[xg, wg ]=GaussLegendreQuad1D(pts,0,1);
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x=[xg';wg];
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[xc,yc,yp]= RatGreensFunctionQuad(x(1,:),Cellintel{i}(j:(j+2),:));
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clear xq; clear wq; clear yq;
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for ii=1:length(xc)
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[xxq,wwq]=GaussLegendreQuad1D(kg,min(min(cp(:))),xc(ii));
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xq(ii,:)=xxq;
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wq(ii,:)=wwq.*yp(ii).*x(2,ii);
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end
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yq=repmat(yc,1,kg);
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xquad=[xquad; xq(:)];
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yquad=[yquad; yq(:)];
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wquad=[wquad; wq(:)];
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end
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end
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end
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function [x,y,yp] = RatGreensFunctionQuad(t,Side)
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% Finds x(t),y(t), and y'(t) on a Bezier Curve defined in Side
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% Input:
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% t Parameter values at which evaluation should occur
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% Side Rational Bezier Curve
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%
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% Output:
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% [x,y,yp] x,y, and dy/ds values for "Side" at t-values
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for i=1:length(t)
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xy=dCR_eval(Side,t(i));
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x(i,:)=xy(:,1)';y(i,:)=xy(:,2)';
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yp(i,:) = dCR_eval_dt(Side(2:3,:),t(i));
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end
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end
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