右转弯

这是使用复数的另一种方法.您可以通过乘以在复平面中"向右"旋转矢量-1i.下面的代码使第一次遍历进入正X(Re() - al轴)并且每次后续遍历将旋转到"右"

imVecs <- lengths*c(0-1i)^(0:3)
imVecs
# [1]  9+0i  0-5i -9+0i  0+9i  8+0i  0-5i -8+0i  0+7i  8+0i  0-1i -5+0i  0+3i  4+0i  0-7i -4+0i  0+2i
#[17]  3+0i  0-7i -5+0i  0+8i

cumsum(imVecs)
# [1] 9+0i 9-5i 0-5i 0+4i 8+4i 8-1i 0-1i 0+6i 8+6i 8+5i 3+5i 3+8i 7+8i 7+1i 3+1i 3+3i 6+3i 6-4i 1-4i
#[20] 1+4i
plot(cumsum(imVecs))
lines(cumsum(imVecs))

这是使用复平面旋转向右旋转45度的方法:

> sqrt(-1i)
[1] 0.7071068-0.7071068i
> imVecs <- lengths*sqrt(0-1i)^(0:7)
Warning message:
In lengths * sqrt(0 - (0+1i))^(0:7) :
  longer object length is not a multiple of shorter object length
> plot(cumsum(imVecs))
> lines(cumsum(imVecs))

情节:

(正如@DWin所建议的)这是一个使用复数的解决方案,它可以灵活地应用于任何类型turn,而不仅仅是90度(-pi/2弧度)的直角.一切都是矢量化的:

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

该turn变量应该被视为一个输入lens.现在所有转弯都是-pi/2弧度,但你可以将它们中的每一个设置为你想要的任何一个.所有其他变量都是输出.

现在玩得开心吧:

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))

(我在这里复制图表的尝试:http://en.wikipedia.org/wiki/Turtle_graphics)

我也让你尝试这些:

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))

随意添加你的!

这不是一个漂亮的情节,但我已经将它包括在内,以表明这种"矢量化"坐标计算产生了正确的结果,不应该太难以适应您的需求:

xx <- c(1,0,-1,0)
yy <- c(0,-1,0,1)

coords <- suppressWarnings(cbind(x = cumsum(c(0,xx*dat$lens)), 
                                 y = cumsum(c(0,yy*dat$lens))))
plot(coords, type="l", xlim=c(-10,10), ylim=c(-10,10))