The terra package offers and describes the following terrain indices:

x <- terrain(x, v="roughness")
x <- terrain(x, v="TPI")
x <- terrain(x, v="TRI")

I am confused on how this is calculated based on the package description of roughness as "the difference between the maximum and the minimum value of a cell and its 8 surrounding cells" (Hijmans et al. 2023). How does this work for edge and corner cells? I am assuming that the calculation reduces to a cell and its 5 or 3 surrounding cells in these cases?

The ruggedness (TRI) index is described as "the mean of the absolute differences between the value of a cell and the value of its 8 surrounding cells". The following is a graphic illustration of how I envision the calculation of these indices from the description provided.

Does this provide a correct interpretation of these indices?

If this interpretation is incorrect, then I am hoping someone point me in the correct direction (a reference) or explain here. I am interested in coding to calculate a slope of 16° from a DSM and an elevational difference of 1.3 m, but think that a terrain index would give a better indicator of the 1.3 m criterion for this habitat model.

## > 16° slope
habitat_slope_mat <- matrix(nrow = 2, ncol = 3)
habitat_slope_mat[1, ] <- c(0,16,0) # from,to = 0 absent
habitat_slope_mat[2, ] <- c(16,minmax(x)[2],1) # from,to = 1 present

habitat_slope <- classify(x, habitat_slope_mat, include.lowest=TRUE)

I looked at the cited references and was expecting to find the formula for this to help me think of the best way to treat the 1.3 m criterion. I have been unable to locate a written / published description that further explains the method. This paper is listed in the citations for the terrain function description:

Jones, K.H., 1998. A comparison of algorithms used to compute hill (sic) *terrain *as a property of the DEM. Computers & Geosciences 24: 315-323

The correct title for the article (DOI: 10.1016/S0098-3004(98)00032-6) is: "A comparison of algorithms used to compute hill *slope *as a property of the DEM". I cannot locate the formula for roughness in that paper and was interested in reading more on this topic.