_05-ex.Rmd

```{r 05-ex-e0, message=FALSE}
library(sf)
library(terra)
library(dplyr)
library(spData)
library(spDataLarge)
```

E1. Generate and plot simplified versions of the `nz` dataset.
Experiment with different values of `keep` (ranging from 0.5 to 0.00005) for `ms_simplify()` and `dTolerance` (from 100 to 100,000) `st_simplify()`.

- At what value does the form of the result start to break down for each method, making New Zealand unrecognizable?
- Advanced: What is different about the geometry type of the results from `st_simplify()` compared with the geometry type of `ms_simplify()`? What problems does this create and how can this be resolved?

```{r 05-ex-e1}
plot(rmapshaper::ms_simplify(st_geometry(nz), keep = 0.5))
plot(rmapshaper::ms_simplify(st_geometry(nz), keep = 0.05))
# Starts to breakdown here at 0.5% of the points:
plot(rmapshaper::ms_simplify(st_geometry(nz), keep = 0.005))
# At this point no further simplification changes the result
plot(rmapshaper::ms_simplify(st_geometry(nz), keep = 0.0005))
plot(rmapshaper::ms_simplify(st_geometry(nz), keep = 0.00005))
plot(st_simplify(st_geometry(nz), dTolerance = 100))
plot(st_simplify(st_geometry(nz), dTolerance = 1000))
# Starts to breakdown at 10 km:
plot(st_simplify(st_geometry(nz), dTolerance = 10000))
plot(st_simplify(st_geometry(nz), dTolerance = 100000))
plot(st_simplify(st_geometry(nz), dTolerance = 100000, preserveTopology = TRUE))

# Problem: st_simplify returns POLYGON and MULTIPOLYGON results, affecting plotting
# Cast into a single geometry type to resolve this
nz_simple_poly = st_simplify(st_geometry(nz), dTolerance = 10000) |> 
  st_sfc() |> 
  st_cast("POLYGON")
nz_simple_multipoly = st_simplify(st_geometry(nz), dTolerance = 10000) |> 
  st_sfc() |> 
  st_cast("MULTIPOLYGON")
plot(nz_simple_poly)
length(nz_simple_poly)
nrow(nz)
```

E2. In the first exercise in Chapter Spatial Data Operations it was established that Canterbury region had 70 of the 101 highest points in New Zealand. 
Using `st_buffer()`, how many points in `nz_height` are within 100 km of Canterbury?

```{r 05-ex-e2}
canterbury = nz[nz$Name == "Canterbury", ]
cant_buff = st_buffer(canterbury, 100000)
nz_height_near_cant = nz_height[cant_buff, ]
nrow(nz_height_near_cant) # 75 - 5 more
```

E3. Find the geographic centroid of New Zealand. 
How far is it from the geographic centroid of Canterbury?

```{r 05-ex-e3}
cant_cent = st_centroid(canterbury)
nz_centre = st_centroid(st_union(nz))
st_distance(cant_cent, nz_centre) # 234 km
```

E4. Most world maps have a north-up orientation.
A world map with a south-up orientation could be created by a reflection (one of the affine transformations not mentioned in this chapter) of the `world` object's geometry.
Write code to do so.
Hint: you can to use the `rotation()` function from this chapter for this transformation.
Bonus: create an upside-down map of your country.
 
```{r 05-ex-e4}
rotation = function(a){
  r = a * pi / 180 #degrees to radians
  matrix(c(cos(r), sin(r), -sin(r), cos(r)), nrow = 2, ncol = 2)
} 

world_sfc = st_geometry(world)
world_sfc_mirror = world_sfc * rotation(180)
plot(world_sfc)
plot(world_sfc_mirror)

us_states_sfc = st_geometry(us_states)
us_states_sfc_mirror = us_states_sfc * rotation(180)
plot(us_states_sfc)
plot(us_states_sfc_mirror)
```

E5. Run the code in Section [5.2.6](https://r.geocompx.org/geometry-operations.html#subsetting-and-clipping). With reference to the objects created in that section, subset the point in `p` that is contained within `x` *and* `y`.

- Using base subsetting operators.
- Using an intermediary object created with `st_intersection()`\index{vector!intersection}.

```{r 05-ex-e5a, echo=FALSE}
b = st_sfc(st_point(c(0, 1)), st_point(c(1, 1))) # create 2 points
b = st_buffer(b, dist = 1) # convert points to circles
x = b[1]
y = b[2]
bb = st_bbox(st_union(x, y))
box = st_as_sfc(bb)
set.seed(2017)
p = st_sample(x = box, size = 10)
```

```{r 05-ex-e5}
p_in_y = p[y]
p_in_xy = p_in_y[x]
x_and_y = st_intersection(x, y)
p[x_and_y]
```

E6. Calculate the length of the boundary lines of US states in meters.
Which state has the longest border and which has the shortest?
Hint: The `st_length` function computes the length of a `LINESTRING` or `MULTILINESTRING` geometry.

```{r 05-ex-e6}
us_states9311 = st_transform(us_states, "EPSG:9311")
us_states_bor = st_cast(us_states9311, "MULTILINESTRING")
us_states_bor$borders = st_length(us_states_bor)
arrange(us_states_bor, borders)
arrange(us_states_bor, -borders)
```

E7. Read the srtm.tif file into R (`srtm = rast(system.file("raster/srtm.tif", package = "spDataLarge"))`).
This raster has a resolution of 0.00083 * 0.00083 degrees. 
Change its resolution to 0.01 * 0.01 degrees using all of the methods available in the **terra** package.
Visualize the results.
Can you notice any differences between the results of these resampling methods?

```{r 05-ex-e7}
srtm = rast(system.file("raster/srtm.tif", package = "spDataLarge"))
rast_template = rast(ext(srtm), res = 0.01)
srtm_resampl1 = resample(srtm, y = rast_template, method = "bilinear")
srtm_resampl2 = resample(srtm, y = rast_template, method = "near")
srtm_resampl3 = resample(srtm, y = rast_template, method = "cubic")
srtm_resampl4 = resample(srtm, y = rast_template, method = "cubicspline")
srtm_resampl5 = resample(srtm, y = rast_template, method = "lanczos")

srtm_resampl_all = c(srtm_resampl1, srtm_resampl2, srtm_resampl3,
                     srtm_resampl4, srtm_resampl5)
plot(srtm_resampl_all)

# differences
plot(srtm_resampl_all - srtm_resampl1, range = c(-300, 300))
plot(srtm_resampl_all - srtm_resampl2, range = c(-300, 300))
plot(srtm_resampl_all - srtm_resampl3, range = c(-300, 300))
plot(srtm_resampl_all - srtm_resampl4, range = c(-300, 300))
plot(srtm_resampl_all - srtm_resampl5, range = c(-300, 300))
```