Doing some basic calculus using Reactive Banana

Question

Setup:

I am using Reactive Banana along with OpenGL and I have a gear that I want to spin. I have the following signals:

bTime :: Be         


        

Answer 1

A simple approach is to assume that eDisplay happens at regular time intervals, and consider bAngularVelocity to be a relative rather than absolute measure, whch would give you the really rather short solution below. [Note that this is no good if eDisplay is out of your control, or if it fires visibly irregularly, or varies in regularity because it will cause your gear to rotate at different speeds as the interval of your eDisplay changes. You'd need my other (longer) approach if that's the case.]

eDeltaAngle :: Event t (Double -> Double)
eDeltaAngle = (+) <$> bAngularVelocity <@ eDisplay

i.e. turn the bAngularVelocity into an adder Event that fires when you eDisplay, so then

eAngle :: Event t Double
eAngle = accumE 0.0 eDeltaAngle

and finally

reactimate $ (draw gears) <$> eAngle

Yes, approximating the integral as a sum is appropriate, and here I'm further approximating by making possibly slightly inaccurate assumtions about the step width, but it's clear and should be smooth as long as your eDisplay is more-or-less regular.