R/transform.R
In jokergoo/spiralize: Visualize Data on Spirals
Defines functions
cartesian_to_xy
flip_theta_back
flip_theta
solve_theta_from_spiral_length
get_theta_from_x
convert_y_to_height
convert_height_to_y
polar_to_x
circular_extend_on_x
radial_extend
spiral_lines_expand
cartesian_to_polar
polar_to_cartesian
xy_to_polar
xy_to_cartesian
Documented in
cartesian_to_polar
cartesian_to_xy
polar_to_cartesian
solve_theta_from_spiral_length
xy_to_cartesian
xy_to_polar
#' Transform between coordinate systems
#'
#' @param x X-locations of the data points.
#' @param y Y-locations of the data points.
#' @param track_index Index of the track.
#'
#' @details
#' There are three coordinate systems: the data coordinate system (xy), the polar coordinate system (polar)
#' and the canvas coordinate system (cartesian). The canvas coordinates correspond to the "native" coordinates of the viewport where the graphics are drawn.
#'
#' Note different settings of `flip` and `reverse` in [`spiral_initialize()`] affect the conversion.
#'
#' `xy_to_cartesian()` converts from the data coordinate system to the canvas coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `xy_to_cartesian()` returns A data frame with two columns: `x` and `y`.
#'
#' @examples
#' x = runif(2)
#' y = runif(2)
#' spiral_initialize(xlim = c(0, 1))
#' spiral_track(ylim = c(0, 1))
#' spiral_points(x, y)
#' xy_to_cartesian(x, y)
#' xy_to_polar(x, y)
xy_to_cartesian = function(x, y, track_index = current_track_index()) {
df_polar = xy_to_polar(x, y, track_index = track_index)
polar_to_cartesian(df_polar$theta, df_polar$r)
}
#' @param flip If it is `FALSE`, it returns theta for the original spiral (before flipping).
#'
#' @details
#' `xy_to_polar()` converts from the data coordinate system to the polar coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `xy_to_polar()` returns a data frame with two columns: `theta` (in radians) and `r` (the radius).
xy_to_polar = function(x, y, track_index = current_track_index(), flip = TRUE) {
if(track_index == 0) {
stop_wrap("No track has been created. Maybe you need to call `spiral_track()` first.")
}
spiral = spiral_env$spiral
if(spiral$scale_by == "angle") {
theta = (x - spiral$xlim[1]) * spiral$theta_range/spiral$xrange + spiral$theta_lim[1]
if(spiral$reverse) {
theta = spiral$theta_lim[2] - (theta - spiral$theta_lim[1])
}
} else if(spiral$scale_by == "curve_length") {
if(spiral$reverse) {
len = (spiral$xlim[2] - x) * spiral$spiral_length_range/spiral$xrange + spiral$spiral_length_lim[1]
} else {
len = (x - spiral$xlim[1]) * spiral$spiral_length_range/spiral$xrange + spiral$spiral_length_lim[1]
}
theta = solve_theta_from_spiral_length(len)
}
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
reverse_y = get_track_data("reverse_y", track_index)
if(reverse_y) {
d = rmax - (y - ymin) * (rmax - rmin)/(ymax - ymin)
} else {
d = (y - ymin) * (rmax - rmin)/(ymax - ymin) + rmin
}
r = spiral$curve(theta) + d
if(flip) theta = flip_theta(theta)
data.frame(theta = theta, r = r)
}
#' @param theta Angles, in radians.
#' @param r Radius.
#'
#' @details
#' `polar_to_cartesian()` converts from the polar coordinate system to the canvas coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `polar_to_cartesian()` returns a data frame with two columns: `x` and `y`.
polar_to_cartesian = function(theta, r) {
x = cos(theta)*r
y = sin(theta)*r
data.frame(x = x, y = y)
}
#' @details
#' `cartesian_to_polar()` converts from the canvas coordinate system to the polar coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `cartesian_to_polar()` returns a data frame with two columns: `theta` (in radians) and `r` (the radius).
cartesian_to_polar = function(x, y) {
theta = atan(y/x)
r = sqrt(x*x + y*y)
data.frame(theta = theta, r = r)
}
# split a spiral line into d seguments
# return in cartesian coordinates
spiral_lines_expand = function(x, y, track_index = current_track_index()) {
df = xy_to_polar(x, y, track_index = track_index)
n = nrow(df)
## here x and y are theta and r
x = df$theta
y = df$r
nx = x[1]
ny = y[1]
min_segment_len = spiral_opt$min_segment_len
for(i in seq_len(n)) {
if(i == 1) {
next
}
if(is.na(x[i]) || is.na(y[i])) {
nx = c(nx, NA)
ny = c(ny, NA)
next
}
if(is.na(x[i-1]) || is.na(y[i-1])) {
next
}
d = min_segment_len/(6*pi)
if(x[i-1] <= 4*pi) {
d = min_segment_len
} else {
d = min_segment_len*(4*pi/x[i-1])
}
if(abs(x[i] - x[i-1]) <= d) {
nc = 2
} else {
nc = ceiling(abs(x[i] - x[i-1])/d)
}
nx = c(nx, seq(x[i-1], x[i], length.out = nc)[-1])
ny = c(ny, seq(y[i-1], y[i], length.out = nc)[-1])
}
polar_to_cartesian(nx, ny)
}
# return in cartesian coordinates
radial_extend = function(x, y, offset, track_index = current_track_index()) {
df = xy_to_polar(x, y, track_index = track_index)
offset_x = convertWidth(offset*cos(df$theta), "native", valueOnly = TRUE)
offset_y = convertHeight(offset*sin(df$theta), "native", valueOnly = TRUE)
df = polar_to_cartesian(df$theta, df$r)
df2 = df
df2$x = df2$x + offset_x
df2$y = df2$y + offset_y
df2
}
# in xy coordinates
circular_extend_on_x = function(x, y, offset, track_index = track_index, coordinate = "polar") {
spiral = spiral_env$spiral
if(is.unit(offset)) {
offset = convertWidth(offset, "native", valueOnly = TRUE)
}
df = xy_to_polar(x, y, track_index = track_index)
if(spiral$scale_by == "curve_length") {
v_offset = convert_y_to_height(y, track_index = track_index)
x_offset = offset/(spiral$spiral_length(spiral$theta_lim[2], v_offset) - spiral$spiral_length(spiral$theta_lim[1], v_offset))*spiral$xrange
df$theta = flip_theta_back(df$theta)
t = solve_theta_from_spiral_length(spiral$spiral_length(df$theta, v_offset) + offset,
c(spiral$spiral_length(-spiral$theta_lim[2], max(v_offset)),
spiral$spiral_length(2*spiral$theta_lim[2], max(v_offset))),
v_offset)
t = flip_theta(t)
if(coordinate == "polar") {
t
} else {
polar_to_x(t)
}
} else {
v_offset = convert_y_to_height(y, track_index = track_index)
df$theta = flip_theta_back(df$theta)
t = solve_theta_from_spiral_length(spiral$spiral_length(df$theta, v_offset) + offset,
c(spiral$spiral_length(-spiral$theta_lim[2], max(v_offset)),
spiral$spiral_length(2*spiral$theta_lim[2], max(v_offset))),
v_offset)
t = flip_theta(t)
if(coordinate == "polar") {
t
} else {
polar_to_x(t)
}
}
}
# given theta in spiral, it returns the corresponding x
polar_to_x = function(theta) {
spiral = spiral_env$spiral
theta = flip_theta_back(theta)
if(spiral$scale_by == "angle") {
x = (theta - spiral$theta_lim[1])/spiral$theta_range*spiral$xrange + spiral$xlim[1]
} else {
x = (spiral$spiral_length(theta) - spiral$spiral_length_lim[1])/spiral$spiral_length_range*spiral$xrange + spiral$xlim[1]
}
if(spiral$reverse) {
x = spiral$xlim[2] - x + spiral$xlim[1]
}
x
}
# given a offset in absolute unit, it returns the offset in xy coordinates
convert_height_to_y = function(offset, track_index = current_track_index()) {
offset = convertWidth(offset, "native", valueOnly = TRUE)
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
offset/(rmax - rmin)*(ymax - ymin)
}
# here `height` is the offset to the base spiral
convert_y_to_height = function(y, track_index = current_track_index()) {
spiral = spiral_env$spiral
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
reverse_y = get_track_data("reverse_y", track_index)
if(reverse_y) {
v_offset = (ymax - y)/(ymax - ymin)*(rmax - rmin)
} else {
v_offset = (y - ymin)/(ymax - ymin)*(rmax - rmin)
}
if(track_index > 1) {
for(i in 1:(track_index - 1)) {
v_offset = v_offset + get_track_data("rmax", i) - get_track_data("rmin", i)
}
}
v_offset
}
get_theta_from_x = function(x, ...) {
xy_to_polar(x, rep(0, length(x)), ...)$theta
}
#' Get theta from given spiral lengths
#'
#' @param len A vector of spiral lengths.
#' @param interval Interval to search for the solution.
#' @param offset Offset of the spiral. In the general form: ` r = a + r*theta`, offset is the value of `a`.
#'
#' @details
#' The length of the spiral has a complicated form, see [https://downloads.imagej.net/fiji/snapshots/arc_length.pdf](https://downloads.imagej.net/fiji/snapshots/arc_length.pdf).
#' Let's say the form is `l = f(theta)` where `f()` is the complex equation for calculating `l`, `solve_theta_from_spiral_length()` tries to find theta with a known `l`.
#' It uses [`stats::uniroot()`] to search for the solutions.
#'
#' @return The theta value.
#' @export
#' @importFrom stats uniroot
#' @examples
#' spiral_initialize()
#' s = current_spiral()
#' theta = pi*seq(2, 3, length = 10)
#' theta
#' len = s$spiral_length(theta)
#' solve_theta_from_spiral_length(len) # should be very similar as theta
solve_theta_from_spiral_length = function(len, interval = NULL, offset = 0) {
n = length(len)
theta = numeric(n)
spiral = spiral_env$spiral
if(is.null(interval)) {
interval = c(spiral$theta_lim[1] - spiral$theta_range, spiral$theta_lim[2] + spiral$theta_range)
}
offset = offset
if(length(offset) == 1) offset = rep(offset, n)
for(i in seq_len(n)) {
theta[i] = uniroot(function(theta, a) {
spiral$spiral_length(theta, offset[i]) - a
}, interval = interval, a = len[i])$root
}
theta
}
flip_theta = function(theta) {
spiral = spiral_env$spiral
if(spiral$flip == "horizontal") {
theta = pi - theta
} else if(spiral$flip == "vertical") {
theta = 2*pi - theta
} else if(spiral$flip == "both") {
theta = theta - pi
} else {
theta
}
}
flip_theta_back = function(theta) {
spiral = spiral_env$spiral
if(spiral$flip == "horizontal") {
theta = pi - theta
} else if(spiral$flip == "vertical") {
theta = 2*pi - theta
} else if(spiral$flip == "both") {
theta = theta + pi
} else {
theta
}
theta
}
#' @details
#' `cartesian_to_xy()` converts from the canvas coordinate system to the data coordinate system.
#' The data points are assigned to the nearest inner spiral loops (if the point is located inside a certain spiral loop, the distance is zero).
#'
#' @return
#' `cartesian_to_xy()` returns a data frame with two columns: `x` and `y`.
#' @rdname coordinate
#' @export
#' @examples
#'
#' x = runif(100, -4, 4)
#' y = runif(100, -4, 4)
#' spiral_initialize(xlim = c(0, 1))
#' spiral_track(ylim = c(0, 1))
#' df = cartesian_to_xy(x, y)
#' # directly draw in the viewport
#' grid.points(x, y, default.units = "native")
#' # check whether the converted xy are correct (should overlap to the previous points)
#' spiral_points(df$x, df$y, pch = 16, gp = gpar(col = 2))
cartesian_to_xy = function(x, y, track_index = current_track_index()) {
if(length(x) > 1) {
n = length(x)
df = data.frame(x = numeric(n), y = numeric(n))
for(i in seq_len(n)) {
df2 = cartesian_to_xy(x[i], y[i], track_index)
df[i, 1] = df2[1, 1]
df[i, 2] = df2[1, 2]
}
return(df)
}
s = spiral_env$spiral
r0 = sqrt(x^2 + y^2)
if(r0 == 0) {
theta = mean(s$theta_lim)
} else {
# make sure alpha is between [0, 2pi)
alpha = atan(y/x)
if(y >= 0 & x < 0) {
alpha = alpha + pi
} else if(y < 0 & x < 0) {
alpha = alpha + pi
} else if(x >= 0 & y < 0) {
alpha = alpha + 2*pi
}
while(alpha < s$theta_lim[1]) {
alpha = alpha + 2*pi
}
if(alpha > s$theta_lim[2]) {
stop_wrap("The radial line the connects data point and the origin should intersect the spiral.")
}
t2 = seq(alpha, s$theta_lim[2], by = 2*pi)
all_r = s$curve(t2)
if(all_r[length(all_r)] <= r0) {
theta = t2[length(t2)]
} else if(all_r[1] >= r0) {
theta = t2[1]
} else {
ind = which(all_r <= r0)
theta = t2[ ind[length(ind)] ]
}
}
x2 = polar_to_x(theta)
d0 = r0 - s$curve(theta)
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
reverse_y = get_track_data("reverse_y", track_index)
if(reverse_y) {
y2 = ymax - (d0 - rmin)/(rmax - rmin)*(ymax - ymin)
} else {
y2 = (d0 - rmin)/(rmax - rmin)*(ymax - ymin) + ymin
}
data.frame(x = x2, y = y2)
}
jokergoo/spiralize documentation built on June 16, 2024, 4:35 a.m.
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Defines functions cartesian_to_xy flip_theta_back flip_theta solve_theta_from_spiral_length get_theta_from_x convert_y_to_height convert_height_to_y polar_to_x circular_extend_on_x radial_extend spiral_lines_expand cartesian_to_polar polar_to_cartesian xy_to_polar xy_to_cartesian
Documented in cartesian_to_polar cartesian_to_xy polar_to_cartesian solve_theta_from_spiral_length xy_to_cartesian xy_to_polar
#' Transform between coordinate systems
#'
#' @param x X-locations of the data points.
#' @param y Y-locations of the data points.
#' @param track_index Index of the track.
#'
#' @details
#' There are three coordinate systems: the data coordinate system (xy), the polar coordinate system (polar)
#' and the canvas coordinate system (cartesian). The canvas coordinates correspond to the "native" coordinates of the viewport where the graphics are drawn.
#'
#' Note different settings of `flip` and `reverse` in [`spiral_initialize()`] affect the conversion.
#'
#' `xy_to_cartesian()` converts from the data coordinate system to the canvas coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `xy_to_cartesian()` returns A data frame with two columns: `x` and `y`.
#'
#' @examples
#' x = runif(2)
#' y = runif(2)
#' spiral_initialize(xlim = c(0, 1))
#' spiral_track(ylim = c(0, 1))
#' spiral_points(x, y)
#' xy_to_cartesian(x, y)
#' xy_to_polar(x, y)
xy_to_cartesian = function(x, y, track_index = current_track_index()) {
df_polar = xy_to_polar(x, y, track_index = track_index)
polar_to_cartesian(df_polar$theta, df_polar$r)
}
#' @param flip If it is `FALSE`, it returns theta for the original spiral (before flipping).
#'
#' @details
#' `xy_to_polar()` converts from the data coordinate system to the polar coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `xy_to_polar()` returns a data frame with two columns: `theta` (in radians) and `r` (the radius).
xy_to_polar = function(x, y, track_index = current_track_index(), flip = TRUE) {
if(track_index == 0) {
stop_wrap("No track has been created. Maybe you need to call `spiral_track()` first.")
}
spiral = spiral_env$spiral
if(spiral$scale_by == "angle") {
theta = (x - spiral$xlim[1]) * spiral$theta_range/spiral$xrange + spiral$theta_lim[1]
if(spiral$reverse) {
theta = spiral$theta_lim[2] - (theta - spiral$theta_lim[1])
}
} else if(spiral$scale_by == "curve_length") {
if(spiral$reverse) {
len = (spiral$xlim[2] - x) * spiral$spiral_length_range/spiral$xrange + spiral$spiral_length_lim[1]
} else {
len = (x - spiral$xlim[1]) * spiral$spiral_length_range/spiral$xrange + spiral$spiral_length_lim[1]
}
theta = solve_theta_from_spiral_length(len)
}
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
reverse_y = get_track_data("reverse_y", track_index)
if(reverse_y) {
d = rmax - (y - ymin) * (rmax - rmin)/(ymax - ymin)
} else {
d = (y - ymin) * (rmax - rmin)/(ymax - ymin) + rmin
}
r = spiral$curve(theta) + d
if(flip) theta = flip_theta(theta)
data.frame(theta = theta, r = r)
}
#' @param theta Angles, in radians.
#' @param r Radius.
#'
#' @details
#' `polar_to_cartesian()` converts from the polar coordinate system to the canvas coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `polar_to_cartesian()` returns a data frame with two columns: `x` and `y`.
polar_to_cartesian = function(theta, r) {
x = cos(theta)*r
y = sin(theta)*r
data.frame(x = x, y = y)
}
#' @details
#' `cartesian_to_polar()` converts from the canvas coordinate system to the polar coordinate system.
#'
#' @export
#' @rdname coordinate
#' @return
#' `cartesian_to_polar()` returns a data frame with two columns: `theta` (in radians) and `r` (the radius).
cartesian_to_polar = function(x, y) {
theta = atan(y/x)
r = sqrt(x*x + y*y)
data.frame(theta = theta, r = r)
}
# split a spiral line into d seguments
# return in cartesian coordinates
spiral_lines_expand = function(x, y, track_index = current_track_index()) {
df = xy_to_polar(x, y, track_index = track_index)
n = nrow(df)
## here x and y are theta and r
x = df$theta
y = df$r
nx = x[1]
ny = y[1]
min_segment_len = spiral_opt$min_segment_len
for(i in seq_len(n)) {
if(i == 1) {
next
}
if(is.na(x[i]) || is.na(y[i])) {
nx = c(nx, NA)
ny = c(ny, NA)
next
}
if(is.na(x[i-1]) || is.na(y[i-1])) {
next
}
d = min_segment_len/(6*pi)
if(x[i-1] <= 4*pi) {
d = min_segment_len
} else {
d = min_segment_len*(4*pi/x[i-1])
}
if(abs(x[i] - x[i-1]) <= d) {
nc = 2
} else {
nc = ceiling(abs(x[i] - x[i-1])/d)
}
nx = c(nx, seq(x[i-1], x[i], length.out = nc)[-1])
ny = c(ny, seq(y[i-1], y[i], length.out = nc)[-1])
}
polar_to_cartesian(nx, ny)
}
# return in cartesian coordinates
radial_extend = function(x, y, offset, track_index = current_track_index()) {
df = xy_to_polar(x, y, track_index = track_index)
offset_x = convertWidth(offset*cos(df$theta), "native", valueOnly = TRUE)
offset_y = convertHeight(offset*sin(df$theta), "native", valueOnly = TRUE)
df = polar_to_cartesian(df$theta, df$r)
df2 = df
df2$x = df2$x + offset_x
df2$y = df2$y + offset_y
df2
}
# in xy coordinates
circular_extend_on_x = function(x, y, offset, track_index = track_index, coordinate = "polar") {
spiral = spiral_env$spiral
if(is.unit(offset)) {
offset = convertWidth(offset, "native", valueOnly = TRUE)
}
df = xy_to_polar(x, y, track_index = track_index)
if(spiral$scale_by == "curve_length") {
v_offset = convert_y_to_height(y, track_index = track_index)
x_offset = offset/(spiral$spiral_length(spiral$theta_lim[2], v_offset) - spiral$spiral_length(spiral$theta_lim[1], v_offset))*spiral$xrange
df$theta = flip_theta_back(df$theta)
t = solve_theta_from_spiral_length(spiral$spiral_length(df$theta, v_offset) + offset,
c(spiral$spiral_length(-spiral$theta_lim[2], max(v_offset)),
spiral$spiral_length(2*spiral$theta_lim[2], max(v_offset))),
v_offset)
t = flip_theta(t)
if(coordinate == "polar") {
t
} else {
polar_to_x(t)
}
} else {
v_offset = convert_y_to_height(y, track_index = track_index)
df$theta = flip_theta_back(df$theta)
t = solve_theta_from_spiral_length(spiral$spiral_length(df$theta, v_offset) + offset,
c(spiral$spiral_length(-spiral$theta_lim[2], max(v_offset)),
spiral$spiral_length(2*spiral$theta_lim[2], max(v_offset))),
v_offset)
t = flip_theta(t)
if(coordinate == "polar") {
t
} else {
polar_to_x(t)
}
}
}
# given theta in spiral, it returns the corresponding x
polar_to_x = function(theta) {
spiral = spiral_env$spiral
theta = flip_theta_back(theta)
if(spiral$scale_by == "angle") {
x = (theta - spiral$theta_lim[1])/spiral$theta_range*spiral$xrange + spiral$xlim[1]
} else {
x = (spiral$spiral_length(theta) - spiral$spiral_length_lim[1])/spiral$spiral_length_range*spiral$xrange + spiral$xlim[1]
}
if(spiral$reverse) {
x = spiral$xlim[2] - x + spiral$xlim[1]
}
x
}
# given a offset in absolute unit, it returns the offset in xy coordinates
convert_height_to_y = function(offset, track_index = current_track_index()) {
offset = convertWidth(offset, "native", valueOnly = TRUE)
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
offset/(rmax - rmin)*(ymax - ymin)
}
# here `height` is the offset to the base spiral
convert_y_to_height = function(y, track_index = current_track_index()) {
spiral = spiral_env$spiral
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
reverse_y = get_track_data("reverse_y", track_index)
if(reverse_y) {
v_offset = (ymax - y)/(ymax - ymin)*(rmax - rmin)
} else {
v_offset = (y - ymin)/(ymax - ymin)*(rmax - rmin)
}
if(track_index > 1) {
for(i in 1:(track_index - 1)) {
v_offset = v_offset + get_track_data("rmax", i) - get_track_data("rmin", i)
}
}
v_offset
}
get_theta_from_x = function(x, ...) {
xy_to_polar(x, rep(0, length(x)), ...)$theta
}
#' Get theta from given spiral lengths
#'
#' @param len A vector of spiral lengths.
#' @param interval Interval to search for the solution.
#' @param offset Offset of the spiral. In the general form: ` r = a + r*theta`, offset is the value of `a`.
#'
#' @details
#' The length of the spiral has a complicated form, see [https://downloads.imagej.net/fiji/snapshots/arc_length.pdf](https://downloads.imagej.net/fiji/snapshots/arc_length.pdf).
#' Let's say the form is `l = f(theta)` where `f()` is the complex equation for calculating `l`, `solve_theta_from_spiral_length()` tries to find theta with a known `l`.
#' It uses [`stats::uniroot()`] to search for the solutions.
#'
#' @return The theta value.
#' @export
#' @importFrom stats uniroot
#' @examples
#' spiral_initialize()
#' s = current_spiral()
#' theta = pi*seq(2, 3, length = 10)
#' theta
#' len = s$spiral_length(theta)
#' solve_theta_from_spiral_length(len) # should be very similar as theta
solve_theta_from_spiral_length = function(len, interval = NULL, offset = 0) {
n = length(len)
theta = numeric(n)
spiral = spiral_env$spiral
if(is.null(interval)) {
interval = c(spiral$theta_lim[1] - spiral$theta_range, spiral$theta_lim[2] + spiral$theta_range)
}
offset = offset
if(length(offset) == 1) offset = rep(offset, n)
for(i in seq_len(n)) {
theta[i] = uniroot(function(theta, a) {
spiral$spiral_length(theta, offset[i]) - a
}, interval = interval, a = len[i])$root
}
theta
}
flip_theta = function(theta) {
spiral = spiral_env$spiral
if(spiral$flip == "horizontal") {
theta = pi - theta
} else if(spiral$flip == "vertical") {
theta = 2*pi - theta
} else if(spiral$flip == "both") {
theta = theta - pi
} else {
theta
}
}
flip_theta_back = function(theta) {
spiral = spiral_env$spiral
if(spiral$flip == "horizontal") {
theta = pi - theta
} else if(spiral$flip == "vertical") {
theta = 2*pi - theta
} else if(spiral$flip == "both") {
theta = theta + pi
} else {
theta
}
theta
}
#' @details
#' `cartesian_to_xy()` converts from the canvas coordinate system to the data coordinate system.
#' The data points are assigned to the nearest inner spiral loops (if the point is located inside a certain spiral loop, the distance is zero).
#'
#' @return
#' `cartesian_to_xy()` returns a data frame with two columns: `x` and `y`.
#' @rdname coordinate
#' @export
#' @examples
#'
#' x = runif(100, -4, 4)
#' y = runif(100, -4, 4)
#' spiral_initialize(xlim = c(0, 1))
#' spiral_track(ylim = c(0, 1))
#' df = cartesian_to_xy(x, y)
#' # directly draw in the viewport
#' grid.points(x, y, default.units = "native")
#' # check whether the converted xy are correct (should overlap to the previous points)
#' spiral_points(df$x, df$y, pch = 16, gp = gpar(col = 2))
cartesian_to_xy = function(x, y, track_index = current_track_index()) {
if(length(x) > 1) {
n = length(x)
df = data.frame(x = numeric(n), y = numeric(n))
for(i in seq_len(n)) {
df2 = cartesian_to_xy(x[i], y[i], track_index)
df[i, 1] = df2[1, 1]
df[i, 2] = df2[1, 2]
}
return(df)
}
s = spiral_env$spiral
r0 = sqrt(x^2 + y^2)
if(r0 == 0) {
theta = mean(s$theta_lim)
} else {
# make sure alpha is between [0, 2pi)
alpha = atan(y/x)
if(y >= 0 & x < 0) {
alpha = alpha + pi
} else if(y < 0 & x < 0) {
alpha = alpha + pi
} else if(x >= 0 & y < 0) {
alpha = alpha + 2*pi
}
while(alpha < s$theta_lim[1]) {
alpha = alpha + 2*pi
}
if(alpha > s$theta_lim[2]) {
stop_wrap("The radial line the connects data point and the origin should intersect the spiral.")
}
t2 = seq(alpha, s$theta_lim[2], by = 2*pi)
all_r = s$curve(t2)
if(all_r[length(all_r)] <= r0) {
theta = t2[length(t2)]
} else if(all_r[1] >= r0) {
theta = t2[1]
} else {
ind = which(all_r <= r0)
theta = t2[ ind[length(ind)] ]
}
}
x2 = polar_to_x(theta)
d0 = r0 - s$curve(theta)
ymin = get_track_data("ymin", track_index)
ymax = get_track_data("ymax", track_index)
rmin = get_track_data("rmin", track_index)
rmax = get_track_data("rmax", track_index)
reverse_y = get_track_data("reverse_y", track_index)
if(reverse_y) {
y2 = ymax - (d0 - rmin)/(rmax - rmin)*(ymax - ymin)
} else {
y2 = (d0 - rmin)/(rmax - rmin)*(ymax - ymin) + ymin
}
data.frame(x = x2, y = y2)
}
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