Thursday, January 7, 2016

Notation for Direction and Distance plots on Cartesian plane

I will be considering these two formulas which are good for modelling a situation when you know the angle you want the plot to go in with respect to the x axis from a point and how far in that direction for each of n discrete steps...
With the meaning that X(n), Y(n) is the nth point in a series...

And to show with an example first let L(i) = i and theta(i) = i*2*pi/5
Interestingly Maple knew the closed form, but it's not necessary for a limited number of points, it does make it easy to plug in any value of n and find the point without knowing any of the previous points though...

And we can make a list over n=1, 2, 3,4,5
And we can let the initial point be [0,0] to get:
An then plotting the above, both with natural number n and continuous n:

In general L(i) can be any discrete function of length of lines for the plot and theta(i) can be any function for the angle the lines make with the x axis...

**Next is to see what happens when L(i) is a constant with a delta->0 length and theta(i) gets more continuous