The **gapfraction** package implements a new barycentric interpolation spike-free canopy height model (CHM) algorithm based on Khosravipour et al. (2013)^{1} and (2016)^{2}, in addition to two new LiDAR metrics of canopy gap fraction (\(P_o\)), several individual tree crown (ITC) detection algorithms, canopy distance and direction metrics, effective leaf area index (\(L_e\)) and apparent clumping index (\(ACI\)) estimation methods. Four mathematical fisheye (hemispherical) lens models are implemented: equi-angular, equi-distant, stereographic, and orthographic. Finally, a new `radial.grid`

function is included for polar plots, while a modified sun path plotting function is also provided. An alphabetical list of functions contained in the **gapfraction** package is provided below.

`chm`

- Simple canopy height model`chm.sf`

- Barycentric interpolation spike-free canopy height model`dd.canopy`

- Euclidean distance and direction to nearest canopy pixel from plot center`dd.crown`

- Euclidean distance and direction to nearest tree crown from plot centers`itc.mw`

- Variable-window individual tree crown detection`itc.mw.h`

- Hierarchical variable-window individual tree crown detection`itc.wat`

- Watershed segmentation individual tree crown detection`itc.wat.h`

- Hierarchical watershed segmentation individual tree crown detection`Le.bl`

- Ground-to-total-return ratio with a spherical leaf angle distribution`Le.n`

- Contact frequency and vertical canopy cover-based effective LAI`radial.grid.hemi`

- Modified radial.grid function supporting hemispherical lens geometries`P.hv`

- Hemipsherical Voronoi canopy gap fraction`P.hv.par`

- Parallel hemispherical Voronoi canopy gap fraction with SOCKS`P.pdn`

- Point-density-normalized canopy gap fraction, effective LAI (Le), and ACI`sun.path`

- Modified solar position plots of Thomas Steiner`vcc.aci`

- Above-height cover index of vertical canopy cover`vcc.bl`

- Beer-Lambert-Law-modified intensity-return ratio of vertical canopy cover`vcc.cv`

- 2-D Cartesian Voronoi vertical canopy cover`vcc.fci`

- First-echo cover index of vertical canopy cover`vcc.fr`

- Canopy-to-first-return ration of vertical canopy cover`vcc.ir`

- Intesity-return ratio of vertical canopy cover`vcc.p`

- Canopy-to-total-pixel ratio of vertical canopy cover`vcc.r`

- Canopy-to-total-return ratio of vertical canopy cover`vcc.sci`

- Solberg’s cover index of vertical canopy cover

Khosravipour et al. (2013) Development of an algorithm to generate a LiDAR pit-free canopy height model. http://www.riegl.com/uploads/tx_pxpriegldownloads/khosravipour_SilviLaser2013.pdf↩

Khosravipour et al. (2016) Generating spike-free digital surface models using LiDAR raw point clouds: A new approach for forestry applications. http://www.sciencedirect.com/science/article/pii/S0303243416300873↩