Hello everyone, how to divide a piece of data into upper and lower parts along the y-axis with C point and D point as the boundary?

[Wesley]

Points C and D have been calculated.

load data1.mat

x = data1(:, 1);

y = data1(:, 2);

%Calculate points C and D

[a,I]=min(x);

C=[a,y(I)];

[b,J]=max(x);

D=[b,y(J)];

hold on

Answer 1

[Star Strider]

Try this:

D = load('data1.mat');
data1 = D.data1;
x = data1(:, 1);
y = data1(:, 2);

[C,ixmin] = min(x);
[D,ixmax] = max(x);
B = [x(ixmin) 1; x(ixmax) 1] \ [y(ixmin); y(ixmax)];
[xsort,sortidx] = sort(x);
fitline = [xsort ones(size(xsort))] * B;
topidx = y(sortidx) >= fitline;

figure
plot(x(sortidx(topidx)), y(sortidx(topidx)), '.r')
hold on
plot(x(sortidx(~topidx)), y(sortidx(~topidx)), '.g')
plot(xsort, fitline, '-b')
plot(C,y(ixmin), 'bo', 'MarkerFaceColor','b')
plot(D,y(ixmax), 'bo', 'MarkerFaceColor','b')
hold off
xlabel('X')
ylabel('Y')
legend('Above Line', 'Below Line', 'Line', 'Location','SE')
text(C,y(ixmin), 'C  ', 'HorizontalAlignment','right', 'VerticalAlignment','middle')
text(D,y(ixmax), '  D', 'HorizontalAlignment','left', 'VerticalAlignment','middle')

producing:

.

[Wesley]

I wonder if I can save the separated points as a file.

[Wesley]

[Image Analyst]

Sure

xAbove = x(sortidx(topidx));
yAbove = y(sortidx(topidx));
save('dataA.mat', 'xAbove', 'yAbove');
xBelow = x(sortidx(~topidx));
yBelow = y(sortidx(~topidx));
save('dataB.mat', 'xBelow', 'yBelow');

[Wesley]

Thank you very much for your answers, I will adjust it with my own code.

[Star Strider]

Wesley — As always, my pleasure!

Image Analyst — Thank you!

[Wesley]

I'm very sorry, I still have a question. How to save the points of arc C-A-D and arc C-B-D.

[Star Strider]

Success!

This took several hours to solve, and I wasn’t initially confident of the outcome.

This code works on this data set, however I seriously doubt that it is sufficiently robust to work on even similar data sets.

The Code —

D = load('data1.mat');
data1 = D.data1;
x = data1(:, 1);
y = data1(:, 2);

[data1_sorted,sortidx] = sortrows(data1,2);
xsort = data1_sorted(:,1);
ysort = data1_sorted(:,2);

[C,ixmin] = min(xsort);
[D,ixmax] = max(xsort);

ymin_idx = find(ysort == min(ysort));                                                                                       % Minimum ‘y’ (Defines Approximate Minima Of Both Parts)
x_ymin = xsort(ymin_idx);                                                                                                   % Corresponding ‘x’ Values
x_yminidx = find(ismember(xsort, x_ymin));                                                                                  % Indices Of Both Parts Corresponding To Minimum ‘x’ Values
[maxymin,maxyminidx] = max(ysort(x_yminidx));                                                                               % Maximum O?f Corresponding ‘y’ Values (Defines Upper Part ‘y’ Values)
searchidxrange = x_yminidx(maxyminidx)+(-70:70);                                                                            % Search Range For Minimum Upper Part ‘y’ Values
[min_uprcurv,minucidx] = min(ysort(searchidxrange));                                                                        % Minimum Upper Part ‘y’ Value & Index
min_uprcurvidx = searchidxrange(minucidx);                                                                                  % Index Of Search Range Corresponding To Minimum
idx4curv = ((xsort >= C) & (xsort <= D)) & (ysort >= ysort(min_uprcurvidx));                                                % Indices Of Upper Part Values
curlimidx = find(ysort == ysort(min_uprcurvidx));                                                                           % ‘y’ Values Corresponding To Minimum Of Upper Curve Indices
idxleft = (xsort >= C) & (xsort <= xsort(curlimidx(1))) & (ysort < ysort(ixmin)) & (ysort > ysort(min_uprcurvidx));         % ‘Tail’ Part Of Left Side To Be Excluded
idxright = (xsort <= D) & (xsort >= xsort(curlimidx(end))) & (ysort < ysort(ixmax)) & (ysort > ysort(min_uprcurvidx));      % ‘Tail’ Part Of Left Side To Be Excluded
idx4curv = idx4curv & ~(idxleft | idxright);                                                                                % Upper Part Indices
idx4curvf = find(idx4curv);                                                                                                 % Corresponding Numeric Indices
UpperPart = [xsort(idx4curv) ysort(idx4curv)];                                                                              % Upper Part ‘x’ & ‘y’ Values
LowerPart = [xsort(~idx4curv) ysort(~idx4curv)];                                                                            % Lower Part ‘x’ & ‘y’ Values

figure
scatter(UpperPart(:,1), UpperPart(:,2), '.r')
hold on
scatter(LowerPart(:,1), LowerPart(:,2), '.g')
plot(C,ysort(ixmin), 'bo', 'MarkerFaceColor','b')
plot(D,ysort(ixmax), 'bo', 'MarkerFaceColor','b')
hold off
axis('equal')
text(C,ysort(ixmin), 'C  ', 'HorizontalAlignment','right', 'VerticalAlignment','middle')
text(D,ysort(ixmax), '  D', 'HorizontalAlignment','left', 'VerticalAlignment','middle')
legend('Upper Part', 'Lower Part', 'Location','SE')

The Plot —

.

[Wesley]

You did a great job, wonderful！Give you a thumbs up.

[Star Strider]

As always, my pleasure!

This was likely the most challenging anallysis I’ve done here on Answers!

Answer 2

[KSSV]

Option 1: You should get the indices of C, D in the given points of curve. Read about knnsearch, this will give indices of points in curve which are close/ same as C and D. Once you know these indices, you can get the upper and lower curve depending on whether the points are in clockwise direction or anti clockwise direction.

Option 2: This is simple, you know C, D; as they lie on x-axes/ parallel to x-axes, these points should have same y. So:

idx1 = P(:,2)>=C(2) ;   % C(2), D(2) both will be same
dataA = P(idx1,:) ; 
dataB = P(~idx1,:) ;

[Wesley]

Thank you very much for your answers.