How can I connect the upper endpoint of the red curve to the red dot while keeping the curvature nearly the same?

How can I connect the upper endpoint of the red curve to the red dot while keeping the curvature nearly the same?

clear all
format long
warning off
figure
set(0,'DefaultAxesFontSize',20);
load('BT_Hom(2).mat')
[~,idx] = max(x(326,:));
plot(x(326,1:idx-20),x(325,1:idx-20),'r', 'LineWidth',2); 
hold on
axis([0.14 .18 .15 .18]);
scatter(0.174701,0.177614,  'o', 'MarkerFaceColor', 'r');
xlabel('$a\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$b\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')

Answer 1

[Star Strider]

Here are options using pchip, makima and spline —

clear all
format long
warning off
figure
set(0,'DefaultAxesFontSize',20);
load('BT_Hom(2).mat')
[~,idx] = max(x(326,:));
plot(x(326,1:idx-20),x(325,1:idx-20),'r', 'LineWidth',2); 
hold on
axis([0.14 .18 .15 .18]);
scatter(0.174701,0.177614,  'o', 'MarkerFaceColor', 'r');

% line_end = [x(326,idx-20),x(325,idx-20)];
line_end = [x(326,idx-21:idx-20);x(325,idx-21:idx-20)];
scatter_point = [0.174701,0.17761];
connecting_line(1,:) = linspace(line_end(1), scatter_point(1), 150);
connecting_line(2,:) = pchip([line_end(1,:) scatter_point(1)], [line_end(2,:) scatter_point(2)], connecting_line(1,:));
plot(connecting_line(1,:), connecting_line(2,:),'r', 'LineWidth',2);
title('Using ‘pchip’')

xlabel('$a\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$b\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')

figure
set(0,'DefaultAxesFontSize',20);
load('BT_Hom(2).mat')
[~,idx] = max(x(326,:));
plot(x(326,1:idx-20),x(325,1:idx-20),'r', 'LineWidth',2); 
hold on
axis([0.14 .18 .15 .18]);
scatter(0.174701,0.177614,  'o', 'MarkerFaceColor', 'r');

% line_end = [x(326,idx-20),x(325,idx-20)];
line_end = [x(326,idx-21:idx-20);x(325,idx-21:idx-20)];
scatter_point = [0.174701,0.17761];
connecting_line(1,:) = linspace(line_end(1), scatter_point(1), 150);
connecting_line(2,:) = makima([line_end(1,:) scatter_point(1)], [line_end(2,:) scatter_point(2)], connecting_line(1,:));
plot(connecting_line(1,:), connecting_line(2,:),'r', 'LineWidth',2);
title('Using ‘makima’')

xlabel('$a\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$b\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')

figure
set(0,'DefaultAxesFontSize',20);
load('BT_Hom(2).mat')
[~,idx] = max(x(326,:));
plot(x(326,1:idx-20),x(325,1:idx-20),'r', 'LineWidth',2); 
hold on
axis([0.14 .18 .15 .18]);
scatter(0.174701,0.177614,  'o', 'MarkerFaceColor', 'r');

% line_end = [x(326,idx-20),x(325,idx-20)];
line_end = [x(326,idx-21:idx-20);x(325,idx-21:idx-20)];
scatter_point = [0.174701,0.17761];
connecting_line(1,:) = linspace(line_end(1), scatter_point(1), 150);
connecting_line(2,:) = spline([line_end(1,:) scatter_point(1)], [line_end(2,:) scatter_point(2)], connecting_line(1,:));
plot(connecting_line(1,:), connecting_line(2,:),'r', 'LineWidth',2);
title('Using ‘spline’')

xlabel('$a\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$b\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')

This uses the last two points of the red line so that the interpolation functions can use that slope information as well. That is straightforward to expand if necessary. The original (and now commented-out) vales for ‘line_end’ used only the last point.

Zoom in on these to see which works best for you.

.

[Atom]

Thank you very much.

[Star Strider]

As always, my pleasure!

Answer 2

[Image Analyst]

Try using plot after you use scatter to draw a line from the last point on the curve to the marker you placed with scatter():

figure
set(0,'DefaultAxesFontSize',20);
load('BT_Hom(2).mat')

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[~,idx] = max(x(326,:));
plot(x(326,1:idx-20), x(325,1:idx-20), 'r', 'LineWidth',2); 
hold on
axis([0.14 .18 .15 .18]);
scatter(0.174701,0.177614,  'o', 'MarkerFaceColor', 'r');
xTip = [x(326,1:idx-20), 0.174701];
yTip = [x(325,1:idx-20), 0.177614];
plot(xTip, yTip, 'r-', 'LineWidth', 2);
grid on;
xlabel('$a\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')
ylabel('$b\rightarrow$','FontSize',20,'interpreter','latex','FontWeight','normal','Color','k')

There will be a slight change in curvature. It it's really objectionable, you can use the scatter point and the last two points of the curve and fit a cubic to it and interpolate a bunch of points in between. Not sure it would look much different though than the straight line.

[Atom]

Thank you. I tried using the straight line approach, but the curvature isn't very smooth. If the gap of curve and point is increased a bit more, it will look bad. Could you please help me with the code of the other method you mentioned?

[Image Analyst]

As you can see, Star used some more sophisticated methods and the plot looks virtually the same. Are they still not good enough? Is so, why not? What is the purpose of the plot? Who is the consumer/viewer of these plots and will they be annoyed if it's not smoother?

But realize that as the final point gets much further away, the connecting curve will have to look more and more like a line. I mean if the point was out at 0.4 or 0.5, what would you expect the connecting curve to look like? It can't be very curvy!

[Atom]

Yes I understand. Thank yo very much. It will work for me.