How can we graph the sawtooth function #x - floor(x)#?
1 Answer
It's possible to impersonate it with...
...or better if you add some cubed terms.
Explanation:
Without the hashes, that's:
((abs(sin(x * pi/2))-abs(cos(x * pi/2))) * (tan(x * pi/2)/abs(tan(x * pi/2)))+1)/2
Here's how it looks...
graph{((abs(sin(xpi/2))-abs(cos(xpi/2)))(tan(xpi/2)/abs(tan(x*pi/2)))+1)/2 [-4.98, 5.02, -2, 3]}
Not entirely convincing, but probably close enough.
For better linearity, add some cubed terms...
3/5(abs(sin(x * pi/2))-abs(cos(x * pi/2))-abs(sin(x * pi/2)^3)/6+abs(cos(x * pi/2)^3)/6) * tan(x * pi/2)/abs(tan(x * pi/2))+1/2
graph{3/5(abs(sin(xpi/2))-abs(cos(xpi/2))-abs(sin(xpi/2)^3)/6+abs(cos(xpi/2)^3)/6)tan(xpi/2)/abs(tan(x*pi/2))+1/2 [-2.48, 2.52, -0.75, 1.75]}