If we consider a portion of the number line, say on the interval $[0,100]$, and split that into regions e.g. split at $80$ to create $2$ regions.
Now I want to subdivide the two regions. The region $[0,80]$ has $m$ partitions and the region $[80,100]$ has $n$ partitions. If $m = 2$ and $n = 10$ (for example), and the subpartitioning was done by splitting the region up equally, when we go from the first region to the second, the partition size is very different. What I want to do is blend the divisions between regions.
Suggestions on how I can do this (bearing in mind I'm not that good at maths) welcome!
EDIT: Sorry for being unclear. Picture should help. In this pic there's 2 regions divided into 2 and 4 (I couldn't easily draw 10 divisions!). The upper part shows equidistant splitting which is ignorant of what's happening in a neighbouring region. The lower part of the picture is roughly what I want. A key requirement is the nodes in the interval $[80,100]$ go from having larger spacing to smaller spacing the further they get away from the interval $[0,80]$. If there was 10 nodes within $[80,100]$, they'd be mainly bunched up towards 100 and the gaps between the nodes would get progressively smaller. The larger spacing is because of the large division size in the neighbouring interval.
The number line could be split up into any number of regions, and the number of divisions on each region is not chosen by me, but imposed on me. One region would affect adjacent regions only.