H-curve — sfc_h • sfcurve

H-curve

Usage

sfc_h(h, iteration = 1, connect = c("h", "v"), random = FALSE)

expand_h(h1, h2 = h1, h3 = h1, h4 = h1, connect = "hhhh")

Arguments

h: The seed of the H-curve. The value should be one of H0, H1 or H2.
iteration: Number of iterations.
connect: How the four subunits are connected to form the H-curve on the next level. See Details.
random: Whether to generate subunits randomly on each iteration.
h1: The first subunit on the bottom left.
h2: The second subunit on the top left.
h3: The third subunit on the top right.
h4: The fourth subunit on the bottom right.

Value

A two-column matrix of coordinates of points on the curve.

Details

An H-curve on level k is composed with four subunits on level k-1. If we number the four subunits in the following order:

2  3
1  4

where subunit 1 connects to subunit 2, subunit 2 connects to subunit 3, et al., and e.g. subunit 1 connects to subunit 2 via its toprigth corner. Since H-curve can be thought of as a closed curve, to, e.g. let subunit 1 to connect to subunit 2, its topright corner needs to be opened. There are two segments on subunit 1 that can be removed/opened: the horizontal segment and the vertical segment on the topright corner in subunit 1.

In this way, in sfc_h(), the argument connect only accepts a single value of "h" or "v" where the types of segments for all the four subunits are the same, i.e. whether all the horizontal corner segments are opened or whether all the vertical corner segments are opened. In expand_h(), the argument connect can be set to a string with four letters or a vector of length four where the type of segments of the four subunits can be set separately.

In the random mode, each subunit is generated randomly, the type of the open segment is choosen randomly, also each subunit has a probability of 0.5 to rotate by 90 degrees.

Examples

draw_multiple_curves(
    sfc_h(H0, iteration = 2),
    sfc_h(H2, iteration = 2),
    closed = TRUE, nrow =1
)

draw_multiple_curves(
    sfc_h(H1, iteration = 3, random = TRUE),
    sfc_h(H1, iteration = 3, random = TRUE),
    closed = TRUE, nrow = 1
)

draw_multiple_curves(
    expand_h(H0, connect = "hvvh"),
    expand_h(H1, connect = "vvhh"),
    closed = TRUE, nrow = 1
)


# set the four subunits separately
h1 = expand_h(H0, connect = "hhhh")
h2 = expand_h(H0, connect = "vvvv")
h3 = expand_h(H0, connect = "hvhv")
h4 = expand_h(H0, connect = "hvvh")
expand_h(h1, h2, h3, h4, connect = "vhvh") |> 
    plot_segments(closed = TRUE)


fun = function(h, iteration) {
    for(i in 1:iteration) h = expand_h(h, connect = "vhvh")
    h
}
fun(H0, 4) |> plot_segments(closed = TRUE)