vector field animation

gistfile1.R

library(data.table)
library(ggplot2)
library(metR)
library(magrittr)
library(gganimate)


# Define la función que genera el campo vector
funcion_campo <- function(x, y, a, b) {
   list(dx = y, 
        dy = a + b*x + x^2 - x*y)
}


###  Un ejemplo
a <- -1
b <- 1

# Genera una grilla equiespaciada
grilla <- as.data.table(expand.grid(x = seq(-4, 4, length.out = 50),
                                   y = seq(-4, 4, length.out = 50)))
grilla[, c("dx", "dy") := funcion_campo(x, y, a, b)]

# Plotea
ggplot(grilla, aes(x, y)) +
   geom_contour(aes(z = dx), breaks = 0, color = "red") +  # Nulclina de dx
   geom_contour(aes(z = dy), breaks = 0, color = "red") +  # Nulclina de dy
   metR::geom_streamline(aes(dx = dx, dy = dy), L = 50, skip = 6, res = 1/2,
                         arrow.angle = 7, arrow.length = 0.6) +  # Trayectorias 
   coord_equal(expand = FALSE, xlim = c(-3, 3), ylim = c(-3, 3)) +
   theme_bw()


# Meto todo eso en una función 
plot_campo <- function(a, b) {
   # Mapita del espacio de parámetros
   inset <- ggplot(data.frame(a = a, b = b), aes(b, a)) +
      geom_vline(xintercept = 0, color = "gray") +
      geom_hline(yintercept = 0, color = "gray") +
      geom_point() +
      ggforce::geom_circle(data = data.frame(x0 = 0, y0 =0, r = 2),
                           aes(x0 = x0, y0 = y0, r = r),
                           inherit.aes = F, size = 0.1, color = "gray20") +
      stat_function(fun = function(x) x^2/4) +
      ylim(c(-4, 4)) + xlim(-4, 4) +
      coord_equal(xlim = c(-4, 4), ylim = c(-4, 4)) +
      theme_void() +
      theme(plot.background = element_rect(color = "black", fill = "white"))
   
   # Campo
   grilla <- as.data.table(expand.grid(x = seq(-4, 4, length.out = 50),
                                       y = seq(-4, 4, length.out = 50)))
   grilla[, c("dx", "dy") := funcion_campo(x, y, a, b)][]
   g <- ggplot(grilla, aes(x, y)) +
      geom_contour(aes(z = dx), breaks = 0, color = "red") +
      geom_contour(aes(z = dy), breaks = 0, color = "red") +
      metR::geom_streamline(aes(dx = dx, dy = dy), L = 50, skip = 6, res = 1/2, 
                            arrow.angle = 7, arrow.length = 0.6) +
      annotation_custom(ggplotGrob(inset), ymin = 1.5, xmin = 1.5) +
      coord_equal(expand = FALSE, xlim = c(-3, 3), ylim = c(-3, 3)) +
      theme_bw()
   print(g)
   return(g)
}

plot_campo(0, -2)

## Ahora la animación 
crear_cuadros <- function(N = 120) {
   # Voy a moverme en el espacio de parámetros en un círculo de radio r
   r <- 2
   thetas <- seq(0, 2*pi, length.out = N+1)
   thetas <- thetas[-1]
   a <- r*sin(thetas)
   b <- r*cos(thetas)
   
   lapply(seq_along(thetas), function(i) {
      plot_campo(a[i], b[i])
   })
} 


gifski::save_gif(crear_cuadros(30), width = 600, height = 600, delay = 30/30, 
                 gif_file = "animation_bad.gif")