#########################################################################################################
###############Adapted circular functions not included in R packages - Pail et al. 2020 (Herpetozoa)
#########################################################################################################

axis.circularLL =function (at = NULL, labels = NULL, units = NULL, template = NULL, 
                           modulo = NULL, zero = NULL, rotation = NULL, tick = TRUE, 
                           lty, lwd, cex, col, font, tcl = 0.025, tcl.text = 0.125, 
                           digits = 2) 
{
  if (missing(cex)) 
    cex <- par("cex.axis")
  if (missing(col)) 
    col <- par("col.axis")
  if (missing(font)) 
    font <- par("font.axis")
  if (missing(lty)) 
    lty <- par("lty")
  if (missing(lwd)) 
    lwd <- par("lwd")
  if (is.null(at)) {
    if (is.null(template) | template == "none" | template == 
        "geographics") {
      at <- circular(c(0, pi/2, pi, 3/2 * pi), rotation = rotation, 
                     zero = zero)
    }
    else if (template == "clock24") {
      at <- circular(seq(0, 23), units = "hours", rotation = rotation, 
                     zero = zero)
      units <- "hours"
    }
    else if (template == "clock12") {
      at <- circular(seq(0, 11), units = "hours", rotation = rotation, 
                     zero = zero)
      units <- "hours"
    }
  }
  at <- na.omit(at)
  atcircularp <- attr(as.circular(at), "circularp")
  type <- atcircularp$type
  if (is.null(modulo)) 
    modulo <- atcircularp$modulo
  if (is.null(units)) 
    units <- atcircularp$units
  if (is.null(template)) 
    template <- atcircularp$template
  if (template == "geographics" | template == "clock24") {
    zero <- pi/2
    rotation <- "clock"
  }
  else if (template == "clock12") {
    zero <- pi/2
    rotation <- "clock"
  }
  else {
    if (is.null(zero)) 
      zero <- atcircularp$zero
    if (is.null(rotation)) 
      rotation <- atcircularp$rotation
  }
  atasis <- at
  attr(atasis, "circularp") <- attr(atasis, "class") <- NULL
  attext <- atasis/pi
  if (modulo == "2pi") {
    if (units == "radians") {
      atasis <- atasis%%(2 * pi)
    }
    else if (units == "degrees") {
      atasis <- atasis%%(360)
    }
    else if (units == "hours") {
      atasis <- atasis%%(24)
    }
    attext <- attext%%2
  }
  else if (modulo == "pi") {
    if (units == "radians") {
      atasis <- atasis%%pi
    }
    else if (units == "degrees") {
      atasis <- atasis%%180
    }
    else if (units == "hours") {
      atasis <- atasis%%12
    }
    attext <- attext%%1
  }
  attext <- round(attext, digits = digits)
  if (template == "clock12") 
    at <- 2 * at
  at <- conversion.circular(at, units = "radians", modulo = "2pi", 
                            zero = 0, rotation = "counter")
  attr(at, "circularp") <- attr(at, "class") <- NULL
  if (is.null(labels)) {
    if (length(atasis) == 4 && all(atasis == c(0, pi/2, 
                                               pi, 3/2 * pi))) {
      if (template == "geographics") {
        labels <- c("N", "E", "S", "W")
      }
      else {
        if (units == "radians") {
          labels <- c("0", expression(frac(pi, 2)), 
                      expression(pi), expression(frac(3 * pi, 
                                                      2)))
        }
        else if (units == "degrees") {
          labels <- c("0", "90", "180", "270")
        }
      }
    }
    else if (length(atasis) == 12 && all(atasis == 0:11) && 
             template == "clock12") {
      labels <- c("0/12", "1", "2", "3", "4", "5", "6", 
                  "7", "8", "9", "10", "11")
    }
    else if (length(atasis) == 24 && all(atasis == 0:23) && 
             template == "clock24") {
      labels <- c("0/24", "1", "2", "3", "4", "5", "6", 
                  "7", "8", "9", "10", "11", "12", "13", "14", 
                  "15", "16", "17", "18", "19", "20", "21", "22", 
                  "23")
    }
    else if (units == "radians") {
      labels <- as.character(round(atasis, digits = digits))
    }
    else if (units == "degrees") {
      labels <- as.character(round(atasis, digits = digits))
    }
    else if (units == "hours") {
      labels <- as.character(round(atasis, digits = digits))
    }
  }
  if (!is.null(labels) && length(at) != length(labels)) 
    stop("'at' and 'labels' must have the same length")
  AxisCircularRadLL(at, units, labels, attext, tick, tcl, tcl.text, 
                    cex, col, lty, lwd)
}

AxisCircularRadLL = function (at, units, labels, attext, tick, tcl, tcl.text, cex, 
                              col, lty, lwd) 
{
  r <- 1 + tcl * c(-1/2, 1/2)
  r.l <- 1 - tcl.text
  z <- cos(at)
  y <- sin(at)
  for (i in 1:length(at)) {
    if (tick) {
      lines.default(z[i] * r, y[i] * r, col = col, lty = lty, 
                    lwd = lwd)
    }
    if (is.null(labels)) {
      labeltext <- substitute(at * pi, list(at = attext[i]))
    }
    else {
      labeltext <- labels[i]
    }
    text.default(z[i] * r.l, y[i] * r.l, labeltext, cex = cex, 
                 col = col)
  }
  
}

Reducing_to_modulo_deg = function (x) {ifelse((x>(360)),(x-360),(x))}
  
Reducing_to_modulo_rad = function (x) {x=deg(x); x=ifelse((x>(360)),(x-360),(x));rad(x)}

DoublingAnglesDeg = function (x) { x=x*2;Reducing_to_modulo_deg(x)}

DoublingAnglesRad = function (x) {x=deg(x); x=x*2;x=Reducing_to_modulo_deg(x);rad(x)}

plot_bootstrap_CI_doubled_inRad_outDeg =function (x) 
{bootci <- mle.vonmises.bootstrap.ci(x, alpha = 0.05, reps = 10000, control.circular = list())
ci2_5 <-(bootci[["mu.ci"]][["2.5%"]])/2;ci2_5 <-ifelse(((ci2_5+2*pi)>(2*pi)),(ci2_5),(ci2_5+2*pi))
ci97_5 <-(bootci[["mu.ci"]][["97.5%"]])/2;ci97_5 <-ifelse(((ci97_5+2*pi)>(2*pi)),(ci97_5),(ci97_5+2*pi))

arrows.circular(x=ci2_5,y=1,lwd=1,lty=2, rotation = "clock",zero = rad(90),code = 0) 
arrows.circular(x=ci97_5,y=1,lwd=1,lty=2, rotation = "clock",zero = rad(90),code = 0) 
arrows.circular(x=(ci2_5-pi),y=1,lwd=1,lty=2, rotation = "clock",zero = rad(90),code = 0) 
arrows.circular(x=(ci97_5-pi),y=1,lwd=1,lty=2, rotation = "clock",zero = rad(90),code = 0)
}
  
plot_bootstrap_CI_inRad_outDeg =function (x) 
{bootci <- mle.vonmises.bootstrap.ci(x, alpha = 0.05,reps = 10000, control.circular = list())
  ci2_5 <-(bootci[["mu.ci"]][["2.5%"]])
  ci97_5 <-(bootci[["mu.ci"]][["97.5%"]])
  
  arrows.circular(x=ci2_5,y=1,lwd=1,lty=2, rotation = "clock",zero = rad(90),code = 0) 
  arrows.circular(x=ci97_5,y=1,lwd=1,lty=2, rotation = "clock",zero = rad(90),code = 0) 
}