Rigidly translating and mirroring 2D coordinates

Hi! I would like to rigidly translate the coordinates of file curve2.txt so that its center of gravity coincides with the center of gravity of file curve1.txt. I tried to use the command "transltform2d" but it gives me an error.

curve1 = importdata("curve1.txt");
x_curve1 = sum(curve1(:,1))/length(curve1(:,1));
y_curve1 = sum(curve1(:,2))/length(curve1(:,2));
G_curve1 = [x_curve1, y_curve1];

curve2 = importdata("curve2.txt");
x_curve2 = sum(curve2(:,1))/length(curve2(:,1));
y_curve2 = sum(curve2(:,2))/length(curve2(:,2));
G_curve2 = [x_curve2, y_curve2];

tx = G_curve2 - G_curve1;
ty = G_curve2 - G_curve1;
tform = transltform2d(tx, ty);

Error using transltform2d
Expected input to be a scalar.

figure
plot(curve1(:,1),curve1(:,2),'k.', 'MarkerSize', 10)
hold on
plot(G_curve1(:,1),G_curve1(:,2),'k.', 'MarkerSize', 15)

plot(curve2(:,1),curve2(:,2),'r.', 'MarkerSize', 10)
plot(G_curve2(:,1),G_curve2(:,2),'r.', 'MarkerSize', 15)
hold off

grid off
axis equal
xlabel('x')
ylabel('y')

And then I should mirror, with respect to the Y axis, curve2.txt with respect to its center of gravity.

Answer 1

[Matt J]

curve1 = importdata("curve1.txt");  curve1(:,3)=[];
curve2 = importdata("curve2.txt");

[ocurve1,ocurve2]=deal(curve1,curve2); %keep a copy of original curves

G=mean(curve1);

curve2=curve2-mean(curve2)+G; %make centroids the same

curve2(:,2)=curve2(:,2) + 2*(G(2)-curve2(:,2)); %reflect across G (y-direction)


tiledlayout(1,2)
nexttile
 plot(ocurve1(:,1), ocurve1(:,2),'k.', 'MarkerSize', 10); hold on
 plot(ocurve2(:,1), ocurve2(:,2),'r.', 'MarkerSize', 10); hold off
 title Original
    grid off
    axis equal
    xlabel('x')
    ylabel('y')

nexttile
 plot(curve1(:,1), curve1(:,2),'k.', 'MarkerSize', 10); hold on
 plot(curve2(:,1), curve2(:,2),'r.', 'MarkerSize', 10); hold off
 title Transformed
    grid off
    axis equal
    xlabel('x')
    ylabel('y')