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83 lines
2.2 KiB
83 lines
2.2 KiB
2 years ago
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close all
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Circletemp=load("Circle.mat"); Circle= Circletemp.Circle1;
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exampleCurve=Circle(1:3,:);
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EC{1}=exampleCurve;
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exampleIntegrand=@(x,y) x.^1.*y.^(2);
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antiDerivative=@(x,y) .5*x.^2.*y.^2;
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CPs=exampleCurve(1:2,:)./exampleCurve(3,:);
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xx0=linspace(-1.1,1.1,100);
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yy0=linspace(-1.1,1.1,100);
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[xp0,yp0]=meshgrid(xx0,yy0);
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figure('Position',[10 10 1200 300])
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subplot(1,5,1);
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xpeval=xp0;
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ypeval=yp0;
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xpeval(sqrt(xp0.^2 + yp0.^2)>1)=nan;
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ypeval(sqrt(xp0.^2 + yp0.^2)>1)=nan;
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pcolor(xpeval,ypeval,exampleIntegrand(xpeval,ypeval));
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shading interp
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hold on
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plot_rat_bern_poly(Circle,2,.001,"k.")
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xlim([-1.1 1.1]); ylim([-1.1 1.1]);
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axis square
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axis off
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xmin=min(CPs(1,:))-.1; xmax=max(CPs(1,:))+.1;
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ymin=min(CPs(2,:))-.1; ymax=max(CPs(2,:))+.1;
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xx1=linspace(xmin,xmax,100);
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yy1=linspace(ymin,ymax,100);
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[xp1,yp1]=meshgrid(xx1,yy1);
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xx2=linspace(0,1,5);
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yy2=linspace(0,1,5);
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[xp2,yp2]=meshgrid(xx2,yy2);
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% xp=xp(:); yp=yp(:);
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subplot(1,5,2)
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pcolor(xp1,yp1,exampleIntegrand(xp1,yp1));
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axis square
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shading interp
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hold on
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plot_rat_bern_poly(exampleCurve,2,.001,'k.');
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axis off
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xlim([xmin/1.05 xmax*1.05]);
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ylim([ymin/1.05 ymax*1.05]);
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subplot(1,5,3)
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% quiver(xp2,yp2,zeros(5,5),antiDerivative(xp2,yp2),'k','LineWidth',2,'MaxHeadSize',14)
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quiverc(xp2,yp2,zeros(5,5),antiDerivative(xp2,yp2),1.8)
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set(gca,'Color',[1 1 1]);
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set(gcf,'Color',[0.9400 0.9400 0.9400]);
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hold on
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plot_rat_bern_poly(exampleCurve,2,.001,'k.');
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axis square
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axis off
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axis off
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xlim([xmin/1.3 xmax*1.3]);
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ylim([ymin/1.3 ymax*1.3]);
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subplot(1,5,4)
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quiverc(xp2,yp2,zeros(5,5),antiDerivative(xp2,yp2),1.8)
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set(gca,'Color',[1 1 1]);
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set(gcf,'Color',[0.9400 0.9400 0.9400]);
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axis square
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hold on
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plot_rat_bern_poly(exampleCurve,2,.001,'k.');
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axis off
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xy=[0.9945 0.1050
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0.7071 0.7071
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0.1050 0.9945]
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scatter(xy(:,1),xy(:,2),500,'r.')
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xlim([xmin/1.3 xmax*1.3]);
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ylim([ymin/1.3 ymax*1.3]);
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subplot(1,5,5)
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newx=zeros(3,3);
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for i=1:3
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[xw, w] = GaussLegendreQuad1D(3,0,xy(i,1));
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newx(i,:)=xw;
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end
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pcolor(xp1,yp1,exampleIntegrand(xp1,yp1));
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shading interp
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axis square
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axis off
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hold on
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plot_rat_bern_poly(exampleCurve,2,.001,'k.');
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ss=scatter(newx(:),repmat(xy(:,2),3,1),500,[.5 0 0],'.')
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xlim([xmin/1.05 xmax*1.05]);
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ylim([ymin/1.05 ymax*1.05]);
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