################################
#### Cosines to Azimuth/Plunge
#### Eli Amson 10/2017
#### eli.amson1988@gmail.com
#### References: Amson E, Arnold P, Van Heteren AH, Cannoville A, Nyakatura JA. Trabecular architecture in the forelimb epiphyses of extant xenarthrans (Mammalia). Frontiers in Zoology. 
################################

cosap <- function(x,y,z) {

##### A (azimuth, θ) ####

if(z<=0){
  if(y<0){
    A <- 180-atan(x/y)*180/pi #if z = 0, A  is mod 180° 
  } else {
    if(y>0){
      if(x<=0){
        A <- -atan(x/y)*180/pi
      } else {
        A <- 360-atan(x/y)*180/pi
      }
    } else {
      if(z==0){
        if(x<0){
          A <- 270 # same as 90 in this case
        } else {
          A <- 90 # same as 270 in this case
        }
      } else {
        if(x<=0){
          A <-  90
        } else {
          A <-  270
        }
        }
    }
  }   
} else {
  if(-y<0){
    A <- 180-atan(x/y)*180/pi
  } else {
    if(-y>0){
    if(-x<=0){
      A <- -atan(x/y)*180/pi
    } else {
      A <- 360-atan(x/y)*180/pi
    }
    } else{
      if(z==0){
        if(x<0){
          A <-  270 # same as 90 in this case
        } else {
          A <- 90 # same as 270 in this case
        }
    } else {
      if(x<=0){
        A <- 270
      } else {
        A <- 90
      }   
      }
    }  
  }
}  

##### P (plunge, δ) ####

if (z<=0){
  P <- asin(-z)*180/pi
} else{
  P <- -asin(-z)*180/pi
}
  
##### Append results ####
list(A=A,P=P)
  
}