How to extract data of one solution from multiple solutions?

R0 = 0.917;
h0 = 1;
n = 8;
rk = 1;
k = 1;
d = 32/180*pi;

Lv0 = sqrt(h0.^2+2*R0.^2-2*R0.^2.*cos(d));
Ld0 = sqrt(h0.^2+2*R0.^2-2*R0.^2.*cos(d+2*pi/n));

Lv = @(h,y) sqrt(h.^2+2*R0.^2-2*R0.^2.*cos(d+y));
Ld = @(h,y) sqrt(h.^2+2*R0.^2-2*R0.^2.*cos(d+y+2*pi/n));

Uy = @(h,y) k*(1-Lv0./Lv(h,y)).*sin(y+d)+rk*k*(1-Ld0./Ld(h,y)).*sin(y+d+2*pi/n);

Uyp = fimplicit(Uy,[0 1.2 -80*pi/180 100*pi/180]);

Here is the solutions of an implicit function. How can I extract the x and y data of the upper line only?

Answer 1

[Star Strider]

This can be done using the clusterdata function, followed by accumarray —

R0 = 0.917;
h0 = 1;
n = 8;
rk = 1;
k = 1;
d = 32/180*pi;

Lv0 = sqrt(h0.^2+2*R0.^2-2*R0.^2.*cos(d));
Ld0 = sqrt(h0.^2+2*R0.^2-2*R0.^2.*cos(d+2*pi/n));

Lv = @(h,y) sqrt(h.^2+2*R0.^2-2*R0.^2.*cos(d+y));
Ld = @(h,y) sqrt(h.^2+2*R0.^2-2*R0.^2.*cos(d+y+2*pi/n));

Uy = @(h,y) k*(1-Lv0./Lv(h,y)).*sin(y+d)+rk*k*(1-Ld0./Ld(h,y)).*sin(y+d+2*pi/n);

Uyp = fimplicit(Uy,[0 1.2 -80*pi/180 100*pi/180]);

X = Uyp.XData(:);
Y = Uyp.YData(:);
XY = [X Y];
XY = rmmissing(XY);
X = XY(:,1);
Y = XY(:,2);
cidx = clusterdata(Y(:), 3);
[Ucidx,~,idx] = unique(cidx);

segments = accumarray(idx, (1:numel(idx)).', [], @(x){[X(x) Y(x)]})

segments = 3×1 cell array
    {201×2 double}
    { 25×2 double}
    {131×2 double}

figure
hold on
for k = 1:size(segments,1)
    plot(segments{k}(:,1), segments{k}(:,2), 'LineWidth',3, 'DisplayName',["Line #"+k])
end
hold off
grid
legend('Location','best')

axl = axis;

figure
plot(segments{1}(:,1), segments{1}(:,2), 'LineWidth',3)
grid
title('Upper Line Only')
axis(axl)

The clusterdata function is in the Statistics and Machine Learning Toolbox.

.

[Songlin Yue]

Thanks for your help!

[Star Strider]

As always, my pleasure!