Pandas ffill() with average of before missing value and after missing value
Your logic is actually what interpolate is doing by default (method='linear'):
df.interpolate()
Output:
val
0 1.0
1 2.0
2 3.0
3 4.0
4 5.0
5 7.0
6 9.0
7 11.0
8 1.0
9 2.0
10 6.0
11 9.0
12 12.0
13 15.0