diff --git a/.Rbuildignore b/.Rbuildignore
index ac70886..6fddd7d 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -10,3 +10,7 @@
 ^data-raw$
 ^\.lintr$
 ^LICENSE\.md$
+^R/lever_rule_ternary\.R$
+^R/mix_exersize\.R$
+^data/.*\.xlsx$
+^data/.*\.csv$
diff --git a/.gitignore b/.gitignore
index 0d7f03b..dd197a9 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,3 +4,12 @@
 .Ruserdata
 docs
 inst/doc
+R/lever_rule_ternary.R
+data/damhus.csv
+data/database-2025_lia.xlsx
+data/mixing_modles_reference_data.xlsx
+data/mixing_modles_test_data.xlsx
+data/REF Salzburg.xlsx
+data/WOD_Salzburg.xlsx
+R/mix_exersize.R
+Rplots.pdf
diff --git a/DESCRIPTION b/DESCRIPTION
index d929137..368f5f7 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -18,14 +18,18 @@ Suggests:
 Imports:
     checkmate,
     dplyr,
+    geometry,
     magrittr,
     purrr,
+    rdist,
     readr,
     rlang,
+    stats,
     tibble,
     tidyselect,
-    units, 
-    rootSolve
+    units,
+    rootSolve,
+    PbIso
 Config/testthat/edition: 3
 Depends: 
     R (>= 3.5)
diff --git a/NAMESPACE b/NAMESPACE
index 96b801a..264ab03 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -14,9 +14,17 @@ export(get_analytical_columns.default)
 export(get_contextual_columns)
 export(get_contextual_columns.default)
 export(pb_iso_age_model)
+export(plot_isocron76)
+export(plot_isocron86)
+export(pointcloud_distribution)
 export(read_archchem)
 export(remove_units)
 export(stacey_kramers_1975)
+importFrom(geometry,convhulln)
+importFrom(geometry,inhulln)
 export(validate)
 importFrom(magrittr,"%>%")
+importFrom(rdist,cdist)
 importFrom(rlang,.data)
+importFrom(stats,aggregate)
+importFrom(stats,as.formula)
diff --git a/R/ASTR-package.R b/R/ASTR-package.R
index a65cf64..9157ef6 100644
--- a/R/ASTR-package.R
+++ b/R/ASTR-package.R
@@ -2,5 +2,10 @@
 "_PACKAGE"
 
 ## usethis namespace: start
+#' @importFrom geometry convhulln
+#' @importFrom geometry inhulln
+#' @importFrom rdist cdist
+#' @importFrom stats aggregate
+#' @importFrom stats as.formula
 ## usethis namespace: end
 NULL
diff --git a/R/isocron.R b/R/isocron.R
new file mode 100644
index 0000000..2a11fec
--- /dev/null
+++ b/R/isocron.R
@@ -0,0 +1,177 @@
+#' @title Isocrong Plot in Base R
+#' @description
+#' Draws a isocron plot for 206Pb/204Pb~207Pb/204Pb and
+#' 206Pb/204Pb~208Pb/204Pb plots on Base R plot using PBIso package
+#'
+#' @param mu1 Mu value of the model curve; Default 10
+#' @param time Vecotr of start, end periods of isocrons, and intervals in million years; Default c(0, 3700, 200)
+#' @param color Vector of line and lable colors for highlights and regular lines; Default c('grey30', 'grey70')
+#' @return
+#' lines and ablines for existing plot
+#' @export
+plot_isocron76 <- function(mu1 = 10,
+                           time = c(0, 3700, 200),
+                           color = c("grey30", "grey70")) {
+  t <- seq(time[1], time[2])
+  sk_model <- PbIso::modelcurve(t = t, Mu1 = mu1)
+  dimensions <- graphics::par("usr")
+  q1 <- dimensions[1] + 0.25 * (dimensions[2] - dimensions[1])
+  diffs <- abs(sk_model$x - q1)
+  closest_index <- which.min(diffs)
+  closest_row <- sk_model[closest_index, ]
+  graphics::text(
+    closest_row$x,
+    closest_row$y,
+    label = "Mu 10",
+    col = color[1],
+    cex = 0.8,
+    pos = 3,
+    srt = 20
+  )
+  graphics::lines(sk_model$x, sk_model$y, col = color[1])
+  time_intervals <- seq(time[1], time[2], by = time[3])
+  q2 <- dimensions[3] + 0.80 * (dimensions[4] - dimensions[3])
+  for (t in time_intervals) {
+    intercept <- PbIso::isochron76yint(t, Mu1 = mu1)
+    slope <- PbIso::isochron76slope(t, Mu1 = mu1)
+    x1 <- (q2 - intercept) / slope
+    graphics::abline(intercept, slope, col = color[2])
+    graphics::text(
+      x1,
+      q2,
+      label = paste("T", t),
+      col = color[2],
+      cex = 0.8,
+      pos = 2,
+      srt = slope
+    )
+
+  }
+  t0_64 <- 9.307
+  t0_74 <- 10.294
+  s <- 0.626208
+  # y = mx + c
+  intercpet <- t0_74 - s * t0_64
+  graphics::abline(intercpet, s, col = color[1])
+  g1 <- (q2 - intercpet) / s
+  graphics::text(
+    g1,
+    q2,
+    label = "Geochron",
+    col = color[1],
+    cex = 0.8,
+    pos = 2,
+    srt = 75
+  )
+}
+
+#' @rdname plot_isocron76
+#' @param kap Kapa Value; Default 4
+#' @export
+plot_isocron86 <- function(mu1 = 10,
+                           kap = 4,
+                           color = c("grey30", "grey70")) {
+  two_stage <- iso_output(mu1 = mu1)
+  ka <- unique(two_stage$kapa)
+  for (k in ka) {
+    df <- two_stage[two_stage$kapa == k, c(5, 7)]
+    df <- df[order(df$X6.4), ]
+    model <- stats::lm(formula = X8.4 ~ X6.4, data = df)
+    slope <- stats::coef(model)[2]
+    intercept <- stats::coef(model)[1]
+    graphics::abline(intercept, slope, col = ifelse(k == kap, color[1], color[2]))
+    if (k == kap) {
+      dimensions <- graphics::par("usr")
+      x1 <- dimensions[1] + 0.25 * (dimensions[2] - dimensions[1])
+      y1 <- (slope * x1) + intercept
+      graphics::text(
+        x1,
+        y1,
+        labels = paste("K", kap),
+        col = color[1],
+        cex = 0.8,
+        pos = 3,
+        srt = 30,
+        adj = c(0.5, 0.5)
+      )
+    }
+  }
+}
+
+# Helper Function
+iso_output <- \(mu1 = 10) {
+  mu_list <- c(6, 9, 10, 12)
+  k_list <- seq(3, 5, by = 0.2)
+  time <- c(seq(0, 3.00E+09, 1.00E+09),
+            3.60E+09,
+            seq(2.00E+08, 8.00E+08, 2.00E+08))
+
+  # Function List
+  ## Set 1 Vatiables
+  ti <- 3.70e+09 # Starting time of Second Stage
+  lambda1 <- 1.55125E-10 # 238U (to 206Pb) decay constant
+  lambda2 <- 9.8485E-10 # 235U (to 207Pb) decay constant
+  lambda3 <- 4.95E-11 # 232Th (to 208Pb) decay constant
+  ## Set 1 Fucntions
+  function_a <- \(t) {
+    exp(lambda1 * ti) - exp(lambda1 * t)
+  }
+  function_b <- \(t) {
+    exp(lambda2 * ti) - exp(lambda2 * t)
+  }
+  function_c <- \(t) {
+    exp(lambda3 * ti) - exp(lambda3 * t)
+  }
+  ## Set 2 Function
+  omega_func <- \(kap, mu) {
+    kap * mu
+  }
+  ## Set 3 Variables
+  a0 <- 11.152 # 206 pb/204pb initial
+  b0 <- 12.998 # 207 pb/204pb initial
+  c0 <- 31.23 # 208 pb/204pb initial
+  ## Set 3 Functions
+  growth_curv64 <- \(t, mu) {
+    a0 + (mu * function_a(t))
+  }
+  growth_curv74 <- \(t, mu) {
+    b0 + (mu / 137.88) * function_b(t)
+  }
+  growth_curv84 <- \(t, kap, mu) {
+    c0 + omega_func(kap, mu) * function_c(t)
+  }
+
+  ##### Output Stage 2 #####
+
+  iso_output <- data.frame(
+    Time = numeric(),
+    mu = numeric(),
+    kapa = numeric(),
+    omega = numeric(),
+    `X6/4` = numeric(),
+    `X7/4` = numeric(),
+    `X8/4` = numeric()
+  )
+
+  for (t in range(time)) {
+    for (m in mu_list) {
+      for (k in k_list) {
+        iso_output <- rbind(
+          iso_output,
+          data.frame(
+            Time = t,
+            mu = m,
+            kapa = k,
+            omega = omega_func(k, m),
+            `X6/4` = growth_curv64(t, m),
+            `X7/4` = growth_curv74(t, m),
+            `X8/4` = growth_curv84(t, k, m)
+          )
+        )
+      }
+    }
+  }
+
+  output <- iso_output[iso_output$mu == mu1, ]
+  return(output)
+}
diff --git a/R/pointcloud_distribution.R b/R/pointcloud_distribution.R
new file mode 100644
index 0000000..001d549
--- /dev/null
+++ b/R/pointcloud_distribution.R
@@ -0,0 +1,88 @@
+#' Comparing Isotope Samples to Reference Data in 3D Space
+#'
+#' This package compares isotope samples to reference data in 3D space
+#' to identify isotopic consistency and the possibility of mixing between sources.
+#'
+#' @param wod Working data, with 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb
+#' @param samples Heading of a column with Samples names from working data. Default "samples".
+#' @param ref Reference data with 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb
+#' @param groupby Heading of a column with reference group names from reference data. Default "group".
+#'
+#' @returns
+#' A \code{list} of three elements:
+#'
+#' \item{hull_inclusion}{\code{logical}. A Boolean value indicating the **inclusion**
+#' of the working data (sample points) within the convex **hull** of the reference data.}
+#' \item{centroids}{\code{data.frame}. The coordinates of the **centroids**
+#' (mean values) for each defined reference group.}
+#' \item{distances}{\code{matrix}. A distance **matrix** where rows represent the working data samples
+#' and columns represent the reference **centroids**, containing the distance of each sample from each centroid.}
+#'
+#' @export
+#'
+#' @examples
+#' # Creaete Synthetic Data
+#' iso <- c("206Pb/204Pb","207Pb/204Pb","208Pb/204Pb")
+#' ## Create Synthetic Reference data
+#' groups <- LETTERS[1:4]
+#' rand_iso <- \(){c(runif(1, 18.3, 19), runif(1, 15.5, 15.9), runif(1, 37.5, 39))}
+#' list_df <- lapply(groups, \(x){
+#'   ls <- sapply(rand_iso(),  \(g){stats::rnorm(20, g, stats::runif(1, 0.05, 0.1))})
+#'   colnames(ls) <- iso
+#'   ls <- as.data.frame(ls)
+#'   ls$groups <- x
+#'   ls
+#' })
+#' ref <- as.data.frame(do.call(rbind, list_df))
+#' ## Create working data
+#' wod <- as.data.frame(sapply(rand_iso(),  \(g){rnorm(20, g, 0.1)}))
+#' colnames(wod) <- iso
+#' wod$samples <- letters[1:20]
+#' rm(list_df, iso, groups, rand_iso)
+#' # Run Pointcloud_distribution
+#' pointcloud_distribution(ref, "sample", ref, "groups")
+pointcloud_distribution <- function(wod,
+                                    samples = "samples",
+                                    ref,
+                                    groupby = "groups") {
+  # Get iso names from Wod
+  wod_names <- grep("204", names(wod), value = TRUE)
+  # Get iso names for Ref
+  ref_names <- grep("204", names(ref), value = TRUE)
+
+  # Get working data list
+  wod_points <- wod[wod_names]
+  # Get Ref data list
+  ref <- ref[, c(groupby, ref_names)]
+  # Finds hull for the ref Data
+  ref_hull <- geometry::convhulln(ref[ref_names])
+  # Checks if working points are within the hull
+  hull_inout <- geometry::inhulln(ref_hull, as.matrix(wod_points))
+  # Identifes unique group names
+  groups <- unique(ref[[groupby]])
+  # Finds out if the points are within the hull of each indificual group
+  group_inout <- sapply(groups, \(i) {
+    t <- geometry::convhulln(ref[ref[[groupby]] == i, ref_names])
+    geometry::inhulln(t, as.matrix(wod_points))
+  })
+  # Combines total and individual in and out logic
+  hull_inclustion <- cbind(hull_inout, group_inout)
+  # Renames rows of hull_inclustions
+  rownames(hull_inclustion) <- wod[[samples]]
+  # Calculate centroides
+  formula_srt <- paste0(".~`", groupby, "`")
+  ref_centroids <- aggregate(as.formula(formula_srt), ref, mean)
+  # Calculate distance of each point from centroides
+  distances <- rdist::cdist(wod[wod_names], ref_centroids[grep("204", names(ref_centroids))]) # Correct this.
+  # Rename distance table rows and columns
+  rownames(distances) <- wod[[samples]]
+  colnames(distances) <- ref_centroids[[groupby]]
+  # Creat an output list.
+  output <- list(
+    "hull_inclustion" = hull_inclustion,
+    "centroids" = ref_centroids,
+    "distances" = distances
+  )
+  # Returns Output.
+  return(output)
+}
diff --git a/man/plot_isocron76.Rd b/man/plot_isocron76.Rd
new file mode 100644
index 0000000..10843e9
--- /dev/null
+++ b/man/plot_isocron76.Rd
@@ -0,0 +1,27 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/isocron.R
+\name{plot_isocron76}
+\alias{plot_isocron76}
+\alias{plot_isocron86}
+\title{Isocrong Plot in Base R}
+\usage{
+plot_isocron76(mu1 = 10, time = c(0, 3700, 200), color = c("grey30", "grey70"))
+
+plot_isocron86(mu1 = 10, kap = 4, color = c("grey30", "grey70"))
+}
+\arguments{
+\item{mu1}{Mu value of the model curve; Default 10}
+
+\item{time}{Vecotr of start, end periods of isocrons, and intervals in million years; Default c(0, 3700, 200)}
+
+\item{color}{Vector of line and lable colors for highlights and regular lines; Default c('grey30', 'grey70')}
+
+\item{kap}{Kapa Value; Default 4}
+}
+\value{
+lines and ablines for existing plot
+}
+\description{
+Draws a isocron plot for 206Pb/204Pb~207Pb/204Pb and
+206Pb/204Pb~208Pb/204Pb plots on Base R plot using PBIso package
+}
diff --git a/man/pointcloud_distribution.Rd b/man/pointcloud_distribution.Rd
new file mode 100644
index 0000000..bde264e
--- /dev/null
+++ b/man/pointcloud_distribution.Rd
@@ -0,0 +1,53 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/pointcloud_distribution.R
+\name{pointcloud_distribution}
+\alias{pointcloud_distribution}
+\title{Comparing Isotope Samples to Reference Data in 3D Space}
+\usage{
+pointcloud_distribution(wod, samples = "samples", ref, groupby = "groups")
+}
+\arguments{
+\item{wod}{Working data, with 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb}
+
+\item{samples}{Heading of a column with Samples names from working data. Default "samples".}
+
+\item{ref}{Reference data with 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb}
+
+\item{groupby}{Heading of a column with reference group names from reference data. Default "group".}
+}
+\value{
+A \code{list} of three elements:
+
+\item{hull_inclusion}{\code{logical}. A Boolean value indicating the \strong{inclusion}
+of the working data (sample points) within the convex \strong{hull} of the reference data.}
+\item{centroids}{\code{data.frame}. The coordinates of the \strong{centroids}
+(mean values) for each defined reference group.}
+\item{distances}{\code{matrix}. A distance \strong{matrix} where rows represent the working data samples
+and columns represent the reference \strong{centroids}, containing the distance of each sample from each centroid.}
+}
+\description{
+This package compares isotope samples to reference data in 3D space
+to identify isotopic consistency and the possibility of mixing between sources.
+}
+\examples{
+# Creaete Synthetic Data
+iso <- c("206Pb/204Pb","207Pb/204Pb","208Pb/204Pb")
+## Create Synthetic Reference data
+groups <- LETTERS[1:4]
+rand_iso <- \(){c(runif(1, 18.3, 19), runif(1, 15.5, 15.9), runif(1, 37.5, 39))}
+list_df <- lapply(groups, \(x){
+  ls <- sapply(rand_iso(),  \(g){stats::rnorm(20, g, stats::runif(1, 0.05, 0.1))})
+  colnames(ls) <- iso
+  ls <- as.data.frame(ls)
+  ls$groups <- x
+  ls
+})
+ref <- as.data.frame(do.call(rbind, list_df))
+## Create working data
+wod <- as.data.frame(sapply(rand_iso(),  \(g){rnorm(20, g, 0.1)}))
+colnames(wod) <- iso
+wod$samples <- letters[1:20]
+rm(list_df, iso, groups, rand_iso)
+# Run Pointcloud_distribution
+pointcloud_distribution(ref, "sample", ref, "groups")
+}