XY = [1 1; 2 1; 3 1; 5 1; 9 1];
Q = [7 1];
XYQ = sortrows([XY;Q])
For coordinates along a non-linear line, you can compute the distance between Q (1xn) and each point in XY (mxn). Q is inserted between the two points in XY that are the shortest distance to Q if and only if the two points are next to each other. If the two closest points are not next to each other then placement of Q cannot be determined and an error will be thrown by the assert command.
XY = [1 1; 2 1; 3 1; 5 1; 9 1];
Q = [7 1];
dist = pdist2(Q,XY);
[~, min2idx] = mink(dist,2);
assert(diff(min2idx)==1, 'Placement cannot be determined.')
XYQ = [XY(1:min2idx(1),:); Q; XY(min2idx(2):end,:)]
Demo using non-linear coordinates
x = 0:.5:pi;
XY = [x',sin(x)'];
Q = XY(5,:)
XY(5,:) = []
dist = pdist2(Q,XY);
[~, min2idx] = mink(dist,2);
assert(diff(min2idx)==1, 'Placement cannot be determined.')
XYQ = [XY(1:min2idx(1),:); Q; XY(min2idx(2):end,:)]
plot(XYQ(:,1), XYQ(:,2), 'bo-')
hold on; grid on
plot(Q(1),Q(2),'r*')
The first method, using sortrows, works for all of these examples but would fail in some non-linear lines such as circles.
