Function with constant derivative

Question

We have a column matrix $P_i$ defined as follows $P_i= {\begin{pmatrix} a_i \\ b_i \\ c_i \end{pmatrix}}_{3\times 1}\tag 1 $.

Given Data

1. All $a_i,b_i,c_i$ are constants
2. It is given that $i$ can only take four values such that $i=0,1,2,3$. Means we are considering $P_0,P_1,P_2,P_3$ only.$P_i$s must be unique
3. s is not matrix(mentioned below). $s\in[0,3]$. Means is a parameter which can take values from $0$ to $3$

Question

Can we make a function ${Q(s)}_{3\times1}=f(s,P_1,P_2,P_3,P_4),\tag 2$

such that $\frac{\mathrm{d} Q(s) }{\mathrm{d} s} $ is a constant column matrix and satisfying the following condition

1. $Q(0)=P_0 ,Q(1)=P_1 ,Q(2)=P_2 ,Q(3)=P_3 ,$

NB:: There are no other constraints on $Q(s)$ . All constraints are already mentioned in question and data section above. Thanks for reading this question