Get theta from given spiral lengths

solve_theta_from_spiral_length(len, interval = NULL, offset = 0)

Arguments

len: A vector of spiral lengths.
interval: Interval to search for the solution.
offset: Offset of the spiral. In the general form: r = a + r*theta, offset is the value of a.

Value

The theta value.

Details

The length of the spiral has a complicated form, see 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.

Examples

spiral_initialize()

s = current_spiral()
theta = pi*seq(2, 3, length = 10)
theta
#>  [1] 6.283185 6.632251 6.981317 7.330383 7.679449 8.028515 8.377580 8.726646
#>  [9] 9.075712 9.424778
len = s$spiral_length(theta)
solve_theta_from_spiral_length(len) # should be very similar as theta
#>  [1] 6.283185 6.632251 6.981317 7.330383 7.679445 8.028513 8.377580 8.726646
#>  [9] 9.075712 9.424782