---
title: "Algorithms Extended"
author: "Robin Lovelace, Jakub Nowosad, Jannes Muenchow"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Algorithms Extended}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

This vignette provides some further detail on the chapter Scripts, algorithms and functions (see https://geocompr.robinlovelace.net/algorithms.html ) of [the Geocomputation with R book](https://geocompr.github.io/).

It starts with the same input data:

```{r}
x_coords = c(10, 0, 0, 12, 20, 10)
y_coords = c(0, 0, 10, 20, 15, 0)
poly_mat = cbind(x_coords, y_coords)
Origin = poly_mat[1, ] # create a point representing the origin
T1 = rbind(Origin, poly_mat[2:3, ], Origin) # create 'triangle matrix'
C1 = (T1[1, , drop = FALSE] + T1[2, , drop = FALSE] + T1[3, , drop = FALSE]) / 3 # find centroid
```

```{r}
t_area = function(x) {
  abs(
    x[1, 1] * (x[2, 2] - x[3, 2]) +
    x[2, 1] * (x[3, 2] - x[1, 2]) +
    x[3, 1] * (x[1, 2] - x[2, 2])
  ) / 2
}
```

The function `t_area` generalizes the solution by taking any object `x`, assumed to have the same dimensions as the triangle represented in `T1`.
We can verify it works on the triangle matrix `T1` as follows:

```{r}
t_area(T1)
```

Likewise we can create a function that finds the triangle's centroid:

```{r}
t_centroid = function(x) {
  (x[1, ] + x[2, ] + x[3, ]) / 3
}
t_centroid(T1)
```

The next stage is to create the second triangle and calculate its area and centroid.
This is done in the code chunk below, which binds the 3^rd^ and 4^th^ coordinates onto the 1^st^, and uses the same functions we created above to calculate its area and width:

```{r}
T2 = rbind(Origin, poly_mat[3:4, ], Origin)
A2 = t_area(T2)
C2 = t_centroid(T2)
```

From this point it is not a big leap to see how to create the 3^rd^ and final triangle that constitutes the polygon represented by `poly_mat`.

Note: it would also be possible to create the polygons with the **decido** package (code not run):

```{r, eval=FALSE}
ind = decido::earcut(poly_mat)
decido::plot_ears(poly_mat, idx = ind)
i = seq(1, length(ind), by = 3)
i_list = purrr::map(i, ~c(.:(.+2), .))
T_all = purrr::map(i_list, ~poly_mat[ind[.], ])
```