Determine Quadrant using Circular Package R

Question

Can someone explain to me how one can determine the quadrant that the mean lies in when the Circular stats function is used? Example is below

> mean(df3[[1]])
Circular Data: 
Type = angles 
Units = degrees 
Template = geographics 
Modulo = asis 
Zero = 1.570796 
Rotation = clock 
[1] 152.6511

Usually the quadrant is determined by this mathematically. I am not sure how to apply my mathematical understanding (below) to the Circular function in R

Determining the Quadrant

Sin +, Cos + : the mean angle is computed directly.
Sin +, Cos - : the mean angle = 180 – θr
Sin -, Cos - : the mean angle = 180 + θr
Sin -, Cos + : the mean angle = 360 - θr

Basically the question is this, when do you follow the rules above when you get a number from the Circular package?

It would be helpful if you took the time to create a [reproducible example](http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) with sample input and desired output. — MrFlick, Nov 15 '14 at 22:26

IRTFM · Answer 1 · 2014-11-16T01:08:32.203

I took the example from ?mean.circular and then ran this code. Since that's not a reproducible example, I posted the dput output below the image:

> findInterval( mean(x) , seq(0, 2*pi, by=pi/2) )
[1] 1
> plot(mean(x))

enter image description here

> x <- circular::circular(runif(50, circular(0), pi))
> mean.circular(x)
Circular Data: 
Type = angles 
Units = radians 
Template = none 
Modulo = asis 
Zero = 0 
Rotation = counter 
[1] 1.456398
> x
Circular Data: 
Type = angles 
Units = radians 
Template = none 
Modulo = asis 
Zero = 0 
Rotation = counter 
 [1] 2.327040536 2.785825681 1.308066172 0.465629700 1.591991415
 [6] 2.799895638 0.597101630 1.532398268 2.286539493 2.406796452
[snipped several more lines]
> str(x)
Classes 'circular', 'numeric'  atomic [1:50] 2.327 2.786 1.308 0.466 1.592 ...
  ..- attr(*, "circularp")=List of 6
  .. ..$ type    : chr "angles"
  .. ..$ units   : chr "radians"
  .. ..$ template: chr "none"
  .. ..$ modulo  : chr "asis"
  .. ..$ zero    : num 0
  .. ..$ rotation: chr "counter"

dput output:

> dput(x)
structure(c(2.3270405356074, 2.78582568050163, 1.30806617224081, 
0.46562970044316, 1.59199141527826, 2.79989563818328, 0.5971016303539, 
1.53239826820734, 2.28653949278211, 2.40679645204717, 1.89535428259936, 
2.93137660453899, 0.0177478829505632, 1.42734595196813, 1.87201844464804, 
0.695967970430947, 2.04070832419577, 0.550663977456403, 2.92634734087854, 
0.958306068791458, 2.84969662093696, 2.51629270013684, 2.59782748619366, 
1.02971903657107, 0.561164568631031, 2.23073552882588, 1.22498917136169, 
2.9371640847422, 0.457753977096242, 0.739334808330959, 0.216332478818938, 
0.405318219633614, 1.99178154032455, 0.113127579417766, 0.894931514015444, 
2.35655867340775, 0.246653277344759, 2.70813517178582, 2.18657670803946, 
0.0214119953469805, 0.95793239635793, 2.22692798316346, 0.582003007195641, 
0.611648808005097, 2.67776878946411, 0.00293802811780693, 2.99580227692684, 
0.809807730553898, 0.936388196372667, 0.378983006826294), circularp = structure(list(
    type = "angles", units = "radians", template = "none", modulo = "asis", 
    zero = 0, rotation = "counter"), .Names = c("type", "units", 
"template", "modulo", "zero", "rotation")), class = c("circular", 
"numeric"))

Determine Quadrant using Circular Package R

1 Answers1