I'm trying to come up with a formula that I can use to represent distance from a central point, and will return a boost value in a range, eg 0..10.
This formula can accept two (or maybe 3) variables:
- importance: this controls the upper limit of the range, eg 0..10, 0..100
- radius: ie any distance within this inner radius should be pretty much as important as any other point within this radius
- dropoff: (optional) how quickly the boost should drop off as distance increases
My basic formula is:
boost = importance / ((radius + distance) ** dropoff)
For instance, an importance
, a dropoff
and a radius
gives me a curve like:
16 : @@@@@@@@@@@@@@@@@@@@@@@@@
32 : @@@@@@@@@@@@@@@@@
64 : @@@@@@@@@@@@
128 : @@@@@@@@
256 : @@@@@@
512 : @@@@
1024 : @@@
2048 : @@
4096 : @
8192 : @
But with a radius
, I get a much smaller range:
16 : @@@
32 : @@@
64 : @@@
128 : @@
256 : @@
512 : @@
1024 : @@
2048 : @
4096 : @
8192 : @
I would like to change the formula to make the upper limit of the range dependent only on importance and not on radius. For the life of me I can't figure out how to do that.
PS: distance can be considered to have an upper limit of, eg, 10,000km if that helps
PPS: As an optional extra, it would be nice to be able to configure the rate of dropoff without affecting the upper limit of the range, but I can live without it
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