Make right hand turns

plot, r, rotational-matrices

Solution

(As suggested by @DWin) Here is a solution using complex numbers, which is flexible to any kind of `turn`, not just 90 degrees (-pi/2 radians) right angles. Everything is vectorized:

set.seed(11)
dat <- data.frame(id = LETTERS[1:6], lens = sample(2:9, 6),
                                     turn = -pi/2)

dat <- within(dat, { facing   <- pi/2 + cumsum(turn)
                     move     <- lens * exp(1i * facing)
                     position <- cumsum(move)
                     x2       <- Re(position)
                     y2       <- Im(position)
                     x1       <- c(0, head(x2, -1))
                     y1       <- c(0, head(y2, -1))
                   })

dat[c("id", "lens", "x1", "y1", "x2", "y2")]
#   id lens x1 y1 x2 y2
# 1  A    4  0  0  4  0
# 2  B    2  4  0  4 -2
# 3  C    5  4 -2 -1 -2
# 4  D    8 -1 -2 -1  6
# 5  E    6 -1  6  5  6
# 6  F    9  5  6  5 -3

The `turn` variable should really be considered as an input together with `lens`. Right now all turns are `-pi/2` radians but you can set each one of them to whatever you want. All other variables are outputs.

Now having a little fun with it:

trace.path <- function(lens, turn) {
  facing   <- pi/2 + cumsum(turn)
  move     <- lens * exp(1i * facing)
  position <- cumsum(move)
  x        <- c(0, Re(position))
  y        <- c(0, Im(position))

  plot.new()
  plot.window(range(x), range(y))
  lines(x, y)
}

trace.path(lens = seq(0, 1,  length.out = 200),
           turn = rep(pi/2 * (-1 + 1/200), 200))

(My attempt at replicating the graph here: http://en.wikipedia.org/wiki/Turtle_graphics)

I also let you try these:

trace.path(lens = seq(1, 10, length.out = 1000),
           turn = rep(2 * pi / 10, 1000))

trace.path(lens = seq(0, 1,  length.out = 500),
           turn = seq(0, pi, length.out = 500))

trace.path(lens = seq(0, 1,  length.out = 600) * c(1, -1),
           turn = seq(0, 8*pi, length.out = 600) * seq(-1, 1, length.out = 200))

Feel free to add yours!

Problem

I have a problem where I have a bunch of lengths and want to start at the origin (pretend I'm facing to the positive end of the y axis), I make a right and move positively along the x axis for the distance of length_i. At this time I make another right turn, walk the distance of length_i and repeat n times. I can do this but I think there's a more efficient way to do it and I lack a math background: ``` ## Fake Data set.seed(11) dat <- data.frame(id = LETTERS[1:6], lens=sample(2:9, 6), x1=NA, y1=NA, x2=NA, y2=NA) ## id lens x1 y1 x2 y2 ## 1 A 4 NA NA NA NA ## 2 B 2 NA NA NA NA ## 3 C 5 NA NA NA NA ## 4 D 8 NA NA NA NA ## 5 E 6 NA NA NA NA ## 6 F 9 NA NA NA NA ## Add a cycle of 4 column dat[, "cycle"] <- rep(1:4, ceiling(nrow(dat)/4))[1:nrow(dat)] ##For loop to use the information from cycle column for(i in 1:nrow(dat)) { ## set x1, y1 if (i == 1) { dat[1, c("x1", "y1")] <- 0 } else { dat[i, c("x1", "y1")] <- dat[(i - 1), c("x2", "y2")] } col1 <- ifelse(dat[i, "cycle"] %% 2 == 0, "x1", "y1") col2 <- ifelse(dat[i, "cycle"] %% 2 == 0, "x2", "y2") dat[i, col2] <- dat[i, col1] col3 <- ifelse(dat[i, "cycle"] %% 2 != 0, "x2", "y2") col4 <- ifelse(dat[i, "cycle"] %% 2 != 0, "x1", "y1") mag <- ifelse(dat[i, "cycle"] %in% c(1, 4), 1, -1) dat[i, col3] <- dat[i, col4] + (dat[i, "lens"] * mag) } ``` This gives the desired result: ``` > dat id lens x1 y1 x2 y2 cycle 1 A 4 0 0 4 0 1 2 B 2 4 0 4 -2 2 3 C 5 4 -2 -1 -2 3 4 D 8 -1 -2 -1 6 4 5 E 6 -1 6 5 6 1 6 F 9 5 6 5 -3 2 ``` Here it is as a plot: ``` library(ggplot2); library(grid) ggplot(dat, aes(x = x1, y = y1, xend = x2, yend = y2)) + geom_segment(aes(color=id), size=3, arrow = arrow(length = unit(0.5, "cm"))) + ylim(c(-10, 10)) + xlim(c(-10, 10)) ``` This seems slow and clunky. I'm guessing there's a better way to do this than the items I do in the `for` loop. What's a more efficient way to keep making programatic rights?

Original source