I have two 3d points, A(1,0,0) and B(0,1,0). And I connect these two points as a line AB. How to divide this line into 10 equally segments and get their coordinates?

Hello,

I have two 3d points, A(1,0,0) and B(0,1,0). And I connect these two points as a line AB. How to divide this line into 10 equally segments and get their coordinates?

Many thanks!

Answer 1

[Ameer Hamza]

This is one way

A = [1,0,0];
B = [0,1,0];
n = 10;

X = [A; B];
t = linspace(0, 1, n+1);
points = interp1([0 1], X, t)

Result

>> points
points =
    1.0000         0         0
    0.9000    0.1000         0
    0.8000    0.2000         0
    0.7000    0.3000         0
    0.6000    0.4000         0
    0.5000    0.5000         0
    0.4000    0.6000         0
    0.3000    0.7000         0
    0.2000    0.8000         0
    0.1000    0.9000         0
         0    1.0000         0

[Alan]

Thanks, this is exactly what I want.

Answer 2

[M.Many]

Hi, you can use vectors to solve this problem

AB = [-1 1 0]' %vector AB
discretization = linspace(0,1,10) %10 values
vectors  = AB*discretization %matrix multiplication

This gives the matrix whose columns are the vectors AP, to get the coords of the points P just add the coords of A to the columns of 'vectors'

[Alan]

I am sorry I am not clear the last sentence you mentioned add the coordinates A. Do you mean vectors + A to get the corrdinates of all these equally divided points? thanks

[M.Many]

Yes, you can do this if you add these lines at the end of the code

AB = [-1 1 0]' %vector AB
discretization = linspace(0,1,11) %11 values for 10 segments
vectors  = AB*discretization %matrix multiplication

A = [1,0,0]'
P = A+vectors

The result is

P =

    1.0000    0.9000    0.8000    0.7000    0.6000    0.5000    0.4000    0.3000    0.2000    0.1000         0
         0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    0.7000    0.8000    0.9000    1.0000
         0         0         0         0         0         0         0         0         0         0         0

Where each culumn is the coordinates of corresponding point P

[Alan]

Yes, I got it. This method works well too. Thanks!

Answer 3

[Jan]

A = [1, 0, 0];
B = [0, 1, 0];

ab = B - A;
v  = linspace(0, 1, 10).';

C = A + v .* ab   % >= R2016b, auto-expanding

% For older versions:
C = A + bsxfun(@times, v, ab)

[Alan]

When I input these code, the comment window shows information: Matrix dimentsions must agree.

[Jan]

Which Matlab version are you using? The above code requires >= R2016b.