Question on how to position points on a line

I've the following to divide a line to equal segments ref

xy1            = [141.64 399.53];
xy2            = [213.32 250.96];
t              = linspace(0,1,11)';
xy             = (1-t)*xy1 + t*xy2;
plot(xy(:,1),xy(:,2),'b-o') 

Output:
xy =

  141.6400  399.5300
  148.8080  384.6730
  155.9760  369.8160
  163.1440  354.9590
  170.3120  340.1020
  177.4800  325.2450
  184.6480  310.3880
  191.8160  295.5310
  198.9840  280.6740
  206.1520  265.8170
  213.3200  250.9600

I'd like to do the following for positioning new points along the line between points xy1 and xy2.

                    xy             del   

  141.6400  399.5300                0
  148.8080  384.6730                1
  155.9760  369.8160                2                   
  163.1440  354.9590                0                
  170.3120  340.1020                0
  177.4800  325.2450                1
  184.6480  310.3880                0
  191.8160  295.5310                0
  198.9840  280.6740                0
  206.1520  265.8170                1.5
  213.3200  250.9600                0

when shift is 0 , no point has to be added in the neighborhood of the corresponding (x,y).

For any nonzero value, 2 points (one to right and one to left) have to be added.

For example if xy = (10,0)

del=2 would mean 2 points (8,0) and (12,0) have to be generated in the code for adding the new points on line between points xy1 and xy2.

del=1 would mean 2 points (9,0) and (11,0) have to be generated in the code for adding the new points on line between points xy1 and xy2.

Any suggestions on how to do this will be of great help!

Answer 1

[Toder]

Assuming del is a column vector of the same size as t and is the desired change in x, try this

xy1            = [141.64 399.53];
xy2            = [213.32 250.96];
t              = linspace(0,1,11)';
% new stuff
del = [0 1 2 0 0 1 0 0 0 1.5 0]';
m = (xy1(2)-xy2(2))/(xy1(1)-xy2(1));
xOld = (1-t)*xy1(1) + t*xy2(1);
ind = del~=0;
x = unique(sort([xOld; xOld(ind)+del(ind); xOld(ind)-del(ind)]));
y = m*(x-xy1(1))+xy1(2);
plot(x,y,'b-o')

If del is the desired distance (2 norm) between the original point and one of the new points, try this

xy1 = [141.64 399.53];
xy2 = [213.32 250.96];
t = linspace(0,1,11)';
xyOld = (1-t)*xy1 + t*xy2;
del = [0 1 2 0 0 1 0 0 0 1.5 0]';
m = (xy1(2)-xy2(2))/(xy1(1)-xy2(1));
theta = atan(m);
ind = del~=0;
xy = unique( [xyOld; ...
    xyOld(ind,:) + [del(ind)*cos(theta),del(ind)*sin(theta)]; ...
    xyOld(ind,:) - [del(ind)*cos(theta),del(ind)*sin(theta)] ], 'rows' );
plot(xy(:,1),xy(:,2),'b-o') 

[Deepa Maheshvare]

Thanks a lot. Can we remove the old points (xy1 and xy2) in x,y? I'd like to plot only the new stuff.

[Deepa Maheshvare]

x = unique(sort([xOld(ind)+del(ind); xOld(ind)-del(ind)]));

helped.

[Toder]

Glad to help. You can do this to remove the endpoints:

x = x(2:end-1);
y = y(2:end-1);

[Deepa Maheshvare]

I'm facing a problem

xy1            = [141.64 399.53];
xy2            = [213.32 250.96];
t              = linspace(0,1,9)';
% new stuff
del = [0 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0]';
m = (xy1(2)-xy2(2))/(xy1(1)-xy2(1));
xOld = (1-t)*xy1(1) + t*xy2(1);
ind = del~=0;
x = unique(sort([xOld; xOld(ind)+del(ind); xOld(ind)-del(ind)]));
%x = unique(sort([xOld(ind)+del(ind); xOld(ind)-del(ind)]));

y = m*(x-xy1(1))+xy1(2);
plot(x,y,'b-o')

When del=0.8 , I expect sqrt((xl-xr)^2 + (yl-yr)^2) to be 1.6 . But it's 2.3. I'm not sure what's going on.

Here, (xl = xleft,yl =yleft ) (x,y) (xr=xright, yr = yright). Could you please look into this?

[Deepa Maheshvare]

I see a problem in this line

unique(sort([xOld; xOld(ind)+del(ind); xOld(ind)-del(ind)]));

I think it's not correct to do this xold + del and xold - del. This would work if the slope of a line is zero.

[Toder]

I've edited my answer.