interpolation in Matrix to have at the end equidistance points based on X

I want to interpolate a Matrix based on only X values, so I have at the end equidistance points.

For example, If the Matrix is M

M=[ 1	2	1
    3	5	6
    6	11	17
    7	12	19
    11	24	25];

I need function to interpolate M making it to

M_interp=[  1	2	1
            2   3.5 3.5
            3	5	6
            4   7   9.667
            5   9   13.333
            6	11	17
            7	12	19
            8   15  20.5
            9   18  22
            10	21  23.5
            11	24	25];

Answer 1

[Walter Roberson]

format long g
M=[ 1	2	1
    3	5	6
    6	11	17
    7	12	19
    11	24	25];
M_interp = interp1(M(:,1), M, min(M(:,1)):max(M(:,1)))

M_interp = 11×3

1 2 1 2 3.5 3.5 3 5 6 4 7 9.66666666666667 5 9 13.3333333333333 6 11 17 7 12 19 8 15 20.5 9 18 22 10 21 23.5

[Mad Gano]

No, that what I don't need :)

X should be 1,2,3,4,5,6,7...

[Walter Roberson]

format long g
X = 1:11;

M=[ 1	2	1
    3	5	6
    6	11	17
    7	12	19
    11	24	25];

M_interp = interp1(M(:,1), M, X)

M_interp = 11×3

1 2 1 2 3.5 3.5 3 5 6 4 7 9.66666666666667 5 9 13.3333333333333 6 11 17 7 12 19 8 15 20.5 9 18 22 10 21 23.5

[Mad Gano]

Thank you :)