splitCurveSetMesh
Below is a demonstration of the features of the splitCurveSetMesh function
Contents
closeFall;
PLOT SETTINGS
figColor='w'; figColorDef='white'; fontSize=15; faceAlpha1=1; faceAlpha2=0.5; edgeColor=0.25*ones(1,3); edgeWidth=1.5; markerSize1=50;
MESHING BIFURCATION BASED ON INPUT CURVES: from narrowed curve to split curves
Create example curves
t=linspace(0.25*pi,2.25*pi,50); t=t(1:end-1); x=sin(t(:)); y=cos(t(:)); [t,r] = cart2pol(x,y); r=r-0.75*cos(2*t); [x,y] = pol2cart(t,r); z=zeros(size(x)); V1=[x(:) y(:) z(:)]; t=linspace(0,2*pi,25); r2=0.8; x=r2.*sin(t); y=r2.*cos(t); z=0.5*ones(size(x)); V2=[x(:) y(:) z(:)]; V2=V2(1:end-1,:); V2(:,1)=V2(:,1); V2(:,2)=V2(:,2)-1.1; V3=V2; V3(:,1)=V3(:,1); V3(:,2)=V3(:,2)+2.2;
ns=5; V_cell={V1,V2,V3}; patchType='quad'; smoothPar.Method='HC'; smoothPar.n=250; smoothPar.Tolerance=0.001; switch smoothPar.Method case 'HC' smoothPar.Alpa=0.1; %Alpha scale factor to push points back to original smoothPar.Beta=0.5; %Beta case 'LAP' smoothPar.LambdaSmooth=0.25; end splitMethod='nearMid';
Meshing bifurcation
[F,V,curveIndices,faceMarker]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,splitMethod);
% Plotting results hf1=figuremax(figColor,figColorDef); title('Input contours and connected mesh','FontSize',fontSize); xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on; % hpy=patch('Faces',F,'Vertices',V,'EdgeColor','k','FaceColor',0.5.*ones(1,3),'FaceAlpha',faceAlpha1); hpy=patch('Faces',F,'Vertices',V,'EdgeColor','k','FaceColor','flat','CData',faceMarker,'FaceAlpha',faceAlpha1); plotV(V(curveIndices{1},:),'r.-','MarkerSize',25); plotV(V(curveIndices{2},:),'g.-','MarkerSize',25); plotV(V(curveIndices{3},:),'b.-','MarkerSize',25); axis equal; axis tight; view(3); grid on; set(gca,'FontSize',fontSize); drawnow;

MESHING BIFURCATION BASED ON INPUT CURVES: from ellips curve to split curves
Create example curves
t=linspace(0.25*pi,2.25*pi,50); t=t(1:end-1); x=2*sin(t(:)); y=cos(t(:)); z=zeros(size(x)); V1=[x(:) y(:) z(:)]; t=linspace(0,2*pi,25); r2=0.8; x=r2.*sin(t); y=r2.*cos(t); z=0.5*ones(size(x)); V2=[x(:) y(:) z(:)]; V2=V2(1:end-1,:); V2(:,1)=V2(:,1); V2(:,2)=V2(:,2)-1.1; V3=V2; V3(:,1)=V3(:,1); V3(:,2)=V3(:,2)+2.2;
ns=5; V_cell={V1,V2,V3}; patchType='quad'; smoothPar.Method='HC'; smoothPar.n=250; smoothPar.Tolerance=0.001; switch smoothPar.Method case 'HC' smoothPar.Alpa=0.1; %Alpha scale factor to push points back to original smoothPar.Beta=0.5; %Beta case 'LAP' smoothPar.LambdaSmooth=0.25; end splitMethod='nearMid';
Meshing bifurcation
[F_1,V_1,~,~]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,'nearMid'); [F_2,V_2,curveIndices,faceMarker]=splitCurveSetMesh(V_cell,ns,patchType,smoothPar,'ortho');
% Plotting results hf1=figuremax(figColor,figColorDef); subplot(1,2,1); title('nearMid is inappropriate in this case','FontSize',fontSize); xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on; hpy=patch('Faces',F_1,'Vertices',V_1,'EdgeColor','k','FaceColor','flat','CData',faceMarker,'FaceAlpha',faceAlpha1); axis equal; axis tight; view(3); grid on; set(gca,'FontSize',fontSize); drawnow; subplot(1,2,2); title('ortho performs better','FontSize',fontSize); xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize); hold on; hpy=patch('Faces',F_2,'Vertices',V_2,'EdgeColor','k','FaceColor','flat','CData',faceMarker,'FaceAlpha',faceAlpha1); axis equal; axis tight; view(3); grid on; set(gca,'FontSize',fontSize); drawnow;

GIBBON
Kevin M. Moerman (kevinmoerman@hotmail.com)