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57 lines
2.4 KiB
57 lines
2.4 KiB
1 year ago
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function [Nquads,value] = recurse_quad(CPWmat,bdbx,funct,p,initlvls,lvls,tol)
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%recurse_quad Performs recursive quadtree integration
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% Inputs:
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% CPWmat One bezier object representing one boundary of domain
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% bdbx bdbx a quad which intersects the boundary of the domain
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% funct Function to be integrated f = @(x,y)...
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% p Order of tensor-product Gaussian quad rule to be used
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% lvls Levels of adaptive quadtree subdivision to perform
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%
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% Outputs:
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% Nquads Totol number of quadrature points used
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% value Estimate of value of integral over domain using quadtree
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Nquads = 0;
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value = 0;
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if initlvls>0
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daughtbxs{1} = [bdbx(1) (bdbx(1)+bdbx(2))/2 bdbx(3) (bdbx(3) + bdbx(4))/2];
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daughtbxs{2} = [(bdbx(1)+bdbx(2))/2 bdbx(2) bdbx(3) (bdbx(3) + bdbx(4))/2];
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daughtbxs{3} = [(bdbx(1)+bdbx(2))/2 bdbx(2) (bdbx(3) + bdbx(4))/2 bdbx(4)];
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daughtbxs{4} = [bdbx(1) (bdbx(1)+bdbx(2))/2 (bdbx(3) + bdbx(4))/2 bdbx(4)];
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for i=1:4
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[nqt,vt] = recurse_quad(CPWmat,daughtbxs{i},funct,p,initlvls-1,lvls,tol);
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value = value + vt; Nquads = Nquads + nqt;
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end
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else
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if lvls==0
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quadpts = gauss2Dbdspts(bdbx,p);
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quadpts(:,1:2)=shapIEvalpts(quadpts(:,1:2),CPWmat,
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shapeIEvalpts([x y],funct,CPWmat,1,tol);
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quadpts = gauss2Dbds(Ifun, bdbx, p);
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Nquads = p^2;
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else
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daughtbxs{1} = [bdbx(1) (bdbx(1)+bdbx(2))/2 bdbx(3) (bdbx(3) + bdbx(4))/2];
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daughtbxs{2} = [(bdbx(1)+bdbx(2))/2 bdbx(2) bdbx(3) (bdbx(3) + bdbx(4))/2];
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daughtbxs{3} = [(bdbx(1)+bdbx(2))/2 bdbx(2) (bdbx(3) + bdbx(4))/2 bdbx(4)];
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daughtbxs{4} = [bdbx(1) (bdbx(1)+bdbx(2))/2 (bdbx(3) + bdbx(4))/2 bdbx(4)];
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for i=1:4
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if lvls==3
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bdpts = [daughtbxs{i}(1) daughtbxs{i}(3);
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daughtbxs{i}(1) daughtbxs{i}(4);
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daughtbxs{i}(2) daughtbxs{i}(3);
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daughtbxs{i}(2) daughtbxs{i}(4);];
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% scatter(bdpts(:,1),bdpts(:,2),100,'r.');
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end
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isContID=isContainedBx(daughtbxs{i},CPWmat,1,tol,p);
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if isContID == 0
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value = value + gauss2Dbds(funct,daughtbxs{i},p);
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Nquads = Nquads + p^2;
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elseif isContID == 1
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[nqt,vt] = recurse_quad(CPWmat,daughtbxs{i},funct,p,0,lvls-1,tol);
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value = value + vt; Nquads = Nquads + nqt;
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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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