Accelerating circular movements in motrack. Example of custom step_function and variable speed.

motrack_planets.R

library(tidyverse)
library(motrack)

f1 <- function(time, moment) {
  # base speed = 3, acceleration (increasing by) 1 deg/s^2
  3 + time
}

position <- tibble(object = 1:4, x = c(-7, 5, 7, -5), y = c(5, 7, -5, -7))
position <- position %>% mutate(rx = c(-5, 5, 5, -5), ry = c(5, 5, -5, -5))
position <- position %>% mutate(rot = c("cw", "cw", "ccw", "ccw"))
position <- position %>% mutate(speed = c(f1))
plot_position(position) + geom_point(aes(x = rx, y = ry))

step_planet <- function(moment, time_next, settings) {
  time_now <- moment$time[1]
  timestep <- time_next - time_now
  # calculate angles
  # 0 = 3 o'clock, pi/2 = 12 o'clock, pi = 9 o'clock, 3*pi/2 = 6 o'clock
  # initial angle relative to orbit center
  a <- atan2(moment$y - moment$ry, moment$x - moment$rx)
  # radius
  r <- sqrt((moment$y - moment$ry)^2 + (moment$x - moment$rx)^2)
  # current speed
  s <- cur_speed(moment, time_now)
  # cat(s) # uncomment to see the actual speeds
  # angle change corresponding to arc length, speed and radius
  d_a <- s * timestep / r
  # new angle realtive to orbit center
  new_a <- if_else(moment$rot == "cw", a - d_a, a + d_a)
  # we don't use `extrapolate_moment` because we want to avoid linear segments
  moment_next <- moment %>%
    dplyr::mutate(
      x = .data$rx + cos(new_a) * r,
      y = .data$ry + sin(new_a) * r,
      time = time_next
    )
  moment_next
}

sett_move <-
  new_settings(
    xlim = c(-9, 9), ylim = c(-9, 9),
    bounce_off_square = F,
    bounce_off_circle = T, circle_bounce_jitter = pi / 6
  )

timescale <- seq(0, 8, by = 0.1)
trajectory_p <-
  make_random_trajectory(
    position, timescale, sett_move,
    step_planet
  )

plot_trajectory(trajectory_p)

animation::ani.options(ffmpeg = "/opt/homebrew/bin/ffmpeg") # update to your path

render_trajectory_video("trajectory_p.mp4", trajectory_p,
  new_settings(show_labels = T),
  targets = 1:4
)