Source this to load functions needed for visualizing 2x2 matrix transformations.

anime_matrix_transformation.R

if (!requireNamespace("tidyverse")) install.packages('tidyverse')
if (!requireNamespace("gganimate")) install.packages('gganimate')

library(tidyverse)
library(gganimate)

construct_grid <- function(xintercepts = -5:5, yintercepts = -5:5){
  bind_rows(
    crossing(x = xintercepts,
             y = min(yintercepts),
             yend = max(yintercepts)) %>%
      mutate(xend = x),
    crossing(y = yintercepts,
             x = min(xintercepts),
             xend = max(xintercepts)) %>%
      mutate(yend = y)
  ) %>% 
    select(x, y, xend, yend)
}

transform_df_coords <- function(df, ..., m = diag(length(df))){
  
  df_names <- names(df)
  
  df_coords <- df %>% 
    select(...)
  
  df_coords_names <- names(df_coords)
  
  df_matrix <- df_coords %>% 
    as.matrix() %>% 
    t()
  
  df_coords_new <- (m %*% df_matrix) %>% 
    t() %>% 
    as_tibble() %>% 
    set_names(df_coords_names)
  
  df_other <- df %>% 
    select(-one_of(df_coords_names))
  
  bind_cols(df_coords_new, df_other) %>% 
    select(df_names)
}

animate_matrix_transformation <- function(m, return_static = FALSE){
  
  grid_start <- construct_grid() %>% 
    mutate(id = row_number())
  
  grid_trans <- grid_start %>% 
    # need to `transform_df_coords()` twice as each segment is made up of 2 points
    transform_df_coords(x, y, m = m) %>% 
    transform_df_coords(xend, yend, m = m)
  
  grid_all <- bind_rows(
    mutate(grid_start, time = 1),
    mutate(grid_trans, time = 2)
  )
  
  basis_start <- tibble(
    x = c(0, 0),
    y = c(0, 0),
    xend = c(1, 0),
    yend = c(0, 1),
    # `vec` is unnecessary, will just use to differentiate colors
    vec = c("i", "j")
  ) %>% 
    mutate(id = nrow(grid_start) + row_number())
  
  basis_trans <- basis_start %>% 
    transform_df_coords(x, y, m = m) %>% 
    transform_df_coords(xend, yend, m = m)
  
  basis_all <- bind_rows(
    mutate(basis_start, time = 1),
    mutate(basis_trans, time = 2)
  )
  
  x_breaks <- unique(grid_start$x)
  y_breaks <- unique(grid_start$y)
  
  p <- ggplot(aes(x = x, y = y, group = id), data = grid_all)+
    geom_segment(aes(xend = xend, yend = yend))+
    geom_segment(aes(xend = xend, yend = yend, colour = vec), data = basis_all, arrow = arrow(length = unit(0.02, "npc")), size = 1.2)+
    scale_x_continuous(breaks = x_breaks, minor_breaks = NULL)+
    scale_y_continuous(breaks = y_breaks, minor_breaks = NULL)+
    coord_fixed()+
    theme_minimal()+
    theme(axis.text = element_blank(),
          axis.title = element_blank(),
          legend.position = "none")
  
  if(return_static) return(p)
  
  p + gganimate::transition_states(time, wrap = FALSE)
  
}