README.md

In mannfred/curvr: Calculate Total Curvature From Landmarked Specimens

Installation

You can install the development version of curvr by:

# install.packages("devtools")
devtools::install_github("mannfred/curvr")

Citation

If you find this package useful, please cite:

@article{boehm_2022,
  title={Plant-pollinator specialization: Origin and measurement of curvature},
  author={Boehm, Mannfred M.A. and Jankowski, J.E. and Cronk, Q.C.B.},
  year={2022},
  journal={The American Naturalist},
  volume={199},
  number={2},
  pages={206--222}
}

Click here for a .pdf of the paper, where we outline the motivation for this package, define "curvature", and offer a case study with Epimedium nectar spurs.

Example

This photograph of Centropogon granulosus and Buff-tailed Sicklebill was taken by Julian Heavyside in the southeastern Andes of Peru:

A common practice in ecology is to measure and compare traits. For example, in a comparative study, we might ask "how curved is the bill of this hummingbird?". One way to measure bill curvature is to add landmarks along the dorsal side of the bill using geomorph. Given these landmark data, curvr can find the best-fit spline, and then calculate total curvature from said spline.

library(curvr)
library(geomorph)

# landmark the .jpg in this R package's directory
geomorph::digitize2d(filelist="man/figures/Figure_A2.jpg", nlandmarks=10, tpsfile="sicklebill.tps", verbose=F)

Typically, one would need to be more methodical with landmarking. E.g. we have not told digitize2d() what the scale is (although curvature is scale invariant, it's still good practice).

curvr fits a spline to these 10 landmarks (in red) and calculates the curvature of the spline.

# import the .tps file for curve-fitting
tps <- readland.tps(file="man/figures/sicklebill.tps")

# preview structure of the landmark file
tps
, , 1

          [,1]     [,2]
 [1,] 211.9709 230.2057
 [2,] 191.8694 233.5560
 [3,] 176.5540 230.6843
 [4,] 164.1103 225.4197
 [5,] 150.2307 216.8048
 [6,] 141.1372 208.1899
 [7,] 134.4368 198.6178
 [8,] 127.2577 186.1740
 [9,] 122.4716 170.3800
[10,] 121.0358 145.0139

plot(tps[,,1])
lines(smooth.spline(tps[,,1]), lwd=2, col='red')

# calculate curvature (curvr gives radians)
ktot <- curvr::curvature_spline(tps[,,1], x_range=range(tps[,,1]))$Ktot

# convert to degrees
ktot * (180/pi)
# 57.7 degrees

mannfred/curvr documentation built on June 13, 2025, 6:22 a.m.