Add mesh generator function

[spsanderson]

#' Generate Mesh Data
#'
#' This function generates a mesh of nodes and edges based on the provided side 
#' length and number of segments.
#' 
#' @author Steven P. Sanderson II, MPH
#' 
#' @description This function creates a square mesh by sampling nodes uniformly 
#' on a square and then connecting these nodes with edges. The nodes are 
#' distributed based on the provided side length and number of segments. Horizontal, 
#' vertical, and diagonal edges are generated to fully connect the mesh. 
#' The function returns a list containing the nodes and edges, along with data 
#' frames and a ggplot object for visualization.
#'
#' @details This function creates a square mesh of nodes and edges, where the 
#' nodes are sampled uniformly on a square. The edges are generated to connect 
#' the nodes horizontally, vertically, and diagonally.
#'
#' @param .side_length A single numeric value representing the side length of 
#' the square.
#' @param .n_seg A positive integer representing the number of segments along 
#' each side of the square.
#' 
#' @examples
#' generate_mesh_data(1, 1)
#' generate_mesh_data(1, 2)
#'
#' @return A list containing:
#' \describe{
#'   \item{nodes}{A matrix with coordinates of the nodes.}
#'   \item{edges}{A list of edges connecting the nodes.}
#'   \item{nodes_df}{A data frame of nodes for ggplot.}
#'   \item{edges_df}{A data frame of edges for ggplot.}
#'   \item{plot}{A ggplot object visualizing the nodes and edges.}
#' }
#' Additionally, the list contains attributes:
#' \describe{
#'   \item{side_length}{The side length used to generate the mesh.}
#'   \item{n_seg}{The number of segments used to generate the mesh.}
#'   \item{nodes_df_dim}{Dimensions of the nodes data frame.}
#'   \item{edges_df_dim}{Dimensions of the edges data frame.}
#' }
#'
#' @name generate_mesh_data
NULL

#' @rdname generate_mesh_data
#' @export
generate_mesh_data <- function(.side_length = 1, .n_seg = 1) {
  side_length <- .side_length
  n_seg <- .n_seg

  # Check if side_length and n_seg are numeric
  if (!is.numeric(side_length) || length(side_length) != 1) {
    abort("side_length must be a single numeric value")
  }

  if (!is.numeric(n_seg) || length(n_seg) != 1 || n_seg <= 0 || floor(n_seg) != n_seg) {
    abort("n_seg must be a positive integer")
  }

  # Check if side_length is positive
  if (side_length <= 0) {
    abort("side_length must be positive")
  }
  # sample nodes uniformly on a square
  x <- matrix(0, nrow = (n_seg + 1) ^ 2, ncol = 2)
  step <- side_length / n_seg
  for (i in 0:n_seg) {
    for (j in 0:n_seg) {
      x[i * (n_seg + 1) + j + 1, ] <- c(-side_length / 2 + i * step, -side_length / 2 + j * step)
    }
  }

  # connect the nodes with edges
  e <- list()
  # horizontal edges
  for (i in 0:(n_seg - 1)) {
    for (j in 0:n_seg) {
      e <- append(e, list(c(i * (n_seg + 1) + j + 1, (i + 1) * (n_seg + 1) + j + 1)))
    }
  }
  # vertical edges
  for (i in 0:n_seg) {
    for (j in 0:(n_seg - 1)) {
      e <- append(e, list(c(i * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 2)))
    }
  }
  # diagonals
  for (i in 0:(n_seg - 1)) {
    for (j in 0:(n_seg - 1)) {
      e <- append(e, list(c(i * (n_seg + 1) + j + 1, (i + 1) * (n_seg + 1) + j + 2)))
      e <- append(e, list(c((i + 1) * (n_seg + 1) + j + 1, i * (n_seg + 1) + j + 2)))
    }
  }

  nodes <- x
  edges <- e
  # Convert nodes to data frame for ggplot
  nodes_df <- as.data.frame(nodes)
  colnames(nodes_df) <- c("x", "y")

  # Create a data frame for edges
  edges_df <- data.frame(
    x = numeric(0),
    y = numeric(0),
    xend = numeric(0),
    yend = numeric(0)
  )

  for (edge in edges) {
    edges_df <- rbind(edges_df, data.frame(
      x = nodes[edge[1], 1],
      y = nodes[edge[1], 2],
      xend = nodes[edge[2], 1],
      yend = nodes[edge[2], 2]
    ))
  }

  # Visualize the nodes and edges
  # Plot the nodes and edges
  p <- ggplot2::ggplot() +
    ggplot2::geom_point(
      data = nodes_df, 
      ggplot2::aes(x = x, y = y), 
      color = "blue", size = 3
    ) +
    ggplot2::geom_segment(
      data = edges_df, 
      ggplot2::aes(x = x, y = y, xend = xend, yend = yend), 
      color = "red"
    ) +
    ggplot2::coord_equal() +
    ggplot2::labs(
      title = "Generated Nodes and Edges", 
      x = "X Coordinate", 
      y = "Y Coordinate"
    ) +
    ggplot2::theme_minimal()

  # Make output
  output <- list(
    nodes = nodes,
    edges = edges,
    nodes_df = nodes_df,
    edges_df = edges_df,
    plot = p
  )

  # Add attributes
  attr(output, "side_length") <- side_length
  attr(output, "n_seg") <- n_seg
  attr(output, "nodes_df_dim") <- dim(nodes_df)
  attr(output, "edges_df_dim") <- dim(edges_df)

  # Final return
  return(output)
}