Quote:
Originally Posted by G-Sun
I had the same request many years ago,
and I still could like to use such lines.
But then I went down the rabbit-hole and got a deeper understanding of a DAW and it's tempo-line at a mathematical and technical level.
The tempo-line is the fundament that everything in your project is locked into. Using straight line is complicated enough -using curves is a can of worms.
Just put in as many points as you like to get what you want.
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Not true, as I mentioned, all continuous curves can be approximated as lines... If it it can be done with lines it can be done with continuous curves.
The mathematics proves this and hence you didn't dig deep enough. In fact, reaper already approximates the continuous curves as splines because that is all a digital computer can do(everything is discrete in nature since the computer is a device that is discreatized... e.g., digit audio).
For example, suppose we wanted the exponential curve between two points.
f(t) = a*exp(b*t)
between points 0 and 1, where a and b are appropriately chosen.
then f(0 + k*dt) = a*exp(b*dt)
is really just a set of N points which are then connected by lines to interpolate.
This is all reaper does behind the scenes(even if it uses the continuous formula) for it's curves in other areas...
For example, if N = 2, then
f(0) = a and f(1) = a*exp(b)
where a and b are chosen to to map between the two tempo points. It's just a line though. So a spline of degree 1 for f(t) above is just single straight line.
Reaper has no problems with lines, right?
So, having an order 2 just splits the midpoint and adds two lines... which again, reaper can do lines.
Since, we can do this by hand with lines and draw any curve, or use a script to draw them(which I already have done but it is tedious), your conclusions are wrong and I suggest you go back and figure out where your logic went wrong.
Again, if it can do it with lines then it can do it with any curve that can be approximated by splines and everyone familiar with calculus knows this is all continuous functions.
What you have to get through your *thick* skull(not an attack, but get upset if you must) is that:
1. Reaper allows one to use lines to draw any curve.
2. Any "curve" can be draw with lines.
3. Any existing problem with "curves" will also exist with lines.
It is simply false to state what you have. You may believe what you say is true but it is fundamentally false(and it can be proven).
For example, Could you not write a script that simply draws the curves for you(what reaper does for envelopes) as splines(lines?) With significant degree of accuracy?(N is large))
If so, then that means reaper can do it too.
One can claim that curves have problems, but they have no more problems than lines have because any curve is a spline and a spline is lines... it's basic logic.
Again, I'm not asking for some infinite precision processor...
The fact is, if one can do it with lines then they can do it with curves to all practical accuracy required... to pretend otherwise is being ignorant. (It's ignorance because it perpetuates a falsity which is wrong. I know that no one likes to be wrong but it's ok to put your emotions aside for the truth.)
(Again, I'm not attacking you, just trying to correct your misconception so you benefit from increased awareness(hopefully you care enough about it to not get emotional)).
All you have to do is this:
1. Convince yourself that any curve that is continuous can be approximated by lines to any degree of accuracy is a fact. If you don't believe this then we can prove you are wrong quite easily and so it will solve that problem, so assume it is true for now if you disagree.
2. Reaper handles lines(splines) without issue(or with issue, it doesn't matter because if it has issues with lines then it will have them independently of the curves and so the curves have nothing to do with that problem).
Hence curves have no problem being implemented. Again, there is ample proof in many directions to show that reaper is fully capable of implementing this. Saying it can't on belief is not good enough, you must prove it can't handle it for some reason.. I've already proven that there is no logical reason why it can't do it and it has all the tech to do it... the question is if the will is there to do it.