Vector Data Models for Geographic Information

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# Vector Data Models for Geographic Information

.class-info[

**Session 5**

.light[HES597: Introduction to Spatial Data in R<br>
Boise State University Human-Environment Systems<br>
Fall 2021]

]

---

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# Plan for today

What do we mean by vector data?

Types of vector data

Creating vector data in `R`

Operations on vector data

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# Defining the vector data model

## __Vector data__ provide a way to represent real-world features in a GIS

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* Useful for locations with discrete, well-defined boundaries

* Very precise (not necessarily accurate)

* Not the same as the `vector` data class

]

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<figure>
  <img src="img/03/landscape_geometry.jpeg" alt="ZZZ" title="ZZZ" width="100%">
  <figcaption>Image Source: QGIS User's manual </figcaption>
</figure>

---
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# Vector as a data model

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* __Vertices__ (i.e., discrete x-y locations) define the shape of the vector

* The organization of those vertices define the _shape_ of the vector

* General types: points, lines, polygons
]

.pull-right[
<figure>
  <img src="img/03/points-lines-polygons-vector-data-types.png" alt="ZZZ" title="ZZZ" width="100%">
  <figcaption>Image Source: Colin Williams (NEON)</figcaption>
</figure>
]

---

# Representing vector data in R

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* `sf` hierarchy reflects increasing complexity of geometry
  * `st_point`, `st_linestring`, `st_polygon` for single features
  * `st_multi*` for multiple features of the same type
  * `st_geometrycollection` for multiple feature types
  * `st_as_sfc` creates the geometry list column for many `sf` operations
]
.pull-right[
<figure>
  <img src="img/03/sf-classes.png" alt="ZZZ" title="ZZZ" width="100%">
  <figcaption>Simple feature types suppored in R (from Lovelace et al. 2020)</figcaption>
</figure>
]
---
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# Representing vector data in R

* `sp` is more general, reflects increasing complexity of attributes: 
  * Points, SpatialPoints, SpatialPointsDataframe
  * Lines, SpatialLines, SpatialLiinesDataframe
  * Polygon, SpatialPolygons, SpatialPolygonsDataframe
  
---
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# Points

## `Spatial*` objects

```r
library(sp)
library(raster) #loaded to improve printing of Spatil objects
proj <- CRS('+proj=longlat +datum=WGS84')
long <- c(-116.7, -120.4, -116.7, -113.5, -115.5, -120.8, -119.5, -113.7, -113.7, -110.7)
lat <- c(45.3, 42.6, 38.9, 42.1, 35.7, 38.9, 36.2, 39, 41.6, 36.9)
pts <- SpatialPoints(cbind(long, lat), proj4string = proj)
pts
```

```
## class       : SpatialPoints 
## features    : 10 
## extent      : -120.8, -110.7, 35.7, 45.3  (xmin, xmax, ymin, ymax)
## crs         : +proj=longlat +datum=WGS84 +no_defs
```
---

# Points

## `sf` objects

```r
library(sf)
pts <- st_multipoint(cbind(long, lat))
str(pts)
```

```
##  'XY' num [1:10, 1:2] -117 -120 -117 -114 -116 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:2] "long" "lat"
```

```r
pts2 <- pts %>% st_sfc(., crs = st_crs(proj))
str(pts2)
```

```
## sfc_MULTIPOINT of length 1; first list element:  'XY' num [1:10, 1:2] -117 -120 -117 -114 -116 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : NULL
##   ..$ : chr [1:2] "long" "lat"
```
---
# Lines

## `Spatial*` objects
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```r
lon <- c(-116.8, -114.2, -112.9, -111.9, -114.2, -115.4, -117.7)
lat <- c(41.3, 42.9, 42.4, 39.8, 37.6, 38.3, 37.6)
lonlat <- cbind(lon, lat)
line1 <- Line(lonlat[1:3,])
line2 <- Line(lonlat[4:7,])
linelst <- Lines(list(line1), ID="a")
linelst2 <- Lines(list(line2), ID="b")
slines <-  SpatialLines(list(linelst, linelst2), proj4string = proj)
```
]

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```r
plot(slines, col="blue")
```

<img src="03-slides_files/figure-html/splineplot-1.png" width="216" style="display: block; margin: auto;" />
]
---
# Lines

## `sf` objects
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```r
lon <- c(-116.8, -114.2, -112.9, -111.9, -114.2, -115.4, -117.7)
lat <- c(41.3, 42.9, 42.4, 39.8, 37.6, 38.3, 37.6)
lonlat <- cbind(lon, lat)
pts <- st_multipoint(lonlat)

sfline <- st_multilinestring(list(pts[1:3,], pts[4:7,]))
```
]

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```r
plot(sfline, col="green")
```

<img src="03-slides_files/figure-html/sglineplot-1.png" width="216" style="display: block; margin: auto;" />
]

---
# Polygons

## `Spatial*` objects

.pull-left[

```r
lon <- c(-116.8, -114.2, -112.9, -111.9, -114.2, -115.4, -117.7)
lat <- c(41.3, 42.9, 42.4, 39.8, 37.6, 38.3, 37.6)
lonlat <- cbind(lon, lat)
poly <- Polygon(lonlat, hole=FALSE)
polylst <- Polygons(list(poly), 's1')
spP <- SpatialPolygons(list(polylst))
```
]

.pull-right[
<img src="03-slides_files/figure-html/sppolyplot-1.png" width="216" style="display: block; margin: auto;" />
]

---
# Polygons

## `sf` objects

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```r
outer = matrix(c(0,0,10,0,10,10,0,10,0,0),ncol=2, byrow=TRUE)
hole1 = matrix(c(1,1,1,2,2,2,2,1,1,1),ncol=2, byrow=TRUE)
hole2 = matrix(c(5,5,5,6,6,6,6,5,5,5),ncol=2, byrow=TRUE)
pts = list(outer, hole1, hole2)
pl1 = st_polygon(pts)
```
]

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```r
plot(pl1)
```

<img src="03-slides_files/figure-html/sfpolyplot-1.png" width="216" style="display: block; margin: auto;" />
]

---
# Common problems with vector data
 
 * Vectors and scale
 
 * Slivers and overlaps 
 
 * Undershoots and overshoots
 
 * Self-intersections and rings
 
 
 ### _It can be very difficult to deal with topological errors in `R`_

---
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# Common operations on vector data

> Moving forward we will rely primarily on the `sf` package for vector manipulation. I'll demonstrate a few common operations on vector data here. We'll explore more during the sections on database operations. If you need to `Spatial*` objects for particular functions (e.g., anything in `raster`), you can use `as(your.object, "Spatial")`. Both packages provide access to many of the 'spatial' backbones of `R` (like `geos` and `gdal`), they just differ in how the "verbs" are specified. For `sf` operations the `st_` prefix is typical. For `rgeos` operations, the `g` prefix is common.

---

# Convert a data frame to `sf` object

* Useful for situations where point locations given as columns in spreadsheet
* Requires that you the projection used when the data were collected 
* Using the `meuse` dataset (use `?sp::meuse` to learn more about it)

```r
data(meuse)
head(meuse, n=3)
```

```
##        x      y cadmium copper lead zinc  elev       dist   om ffreq soil lime
## 1 181072 333611    11.7     85  299 1022 7.909 0.00135803 13.6     1    1    1
## 2 181025 333558     8.6     81  277 1141 6.983 0.01222430 14.0     1    1    1
## 3 181165 333537     6.5     68  199  640 7.800 0.10302900 13.0     1    1    1
##   landuse dist.m
## 1      Ah     50
## 2      Ah     30
## 3      Ah    150
```

---

# Convert a data frame to `sf` object
 
 * Using the `x` and `y` columns in the data
 
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```r
meuse_sf = st_as_sf(meuse, coords = c("x", "y"), crs = 28992, agr = "constant")
meuse_sf[1:3,]
```

```
## Simple feature collection with 3 features and 12 fields
## Attribute-geometry relationship: 12 constant, 0 aggregate, 0 identity
## Geometry type: POINT
## Dimension:     XY
## Bounding box:  xmin: 181025 ymin: 333537 xmax: 181165 ymax: 333611
## Projected CRS: Amersfoort / RD New
##   cadmium copper lead zinc  elev       dist   om ffreq soil lime landuse dist.m
## 1    11.7     85  299 1022 7.909 0.00135803 13.6     1    1    1      Ah     50
## 2     8.6     81  277 1141 6.983 0.01222430 14.0     1    1    1      Ah     30
## 3     6.5     68  199  640 7.800 0.10302900 13.0     1    1    1      Ah    150
##                geometry
## 1 POINT (181072 333611)
## 2 POINT (181025 333558)
## 3 POINT (181165 333537)
```
]

.pull-right[
<img src="03-slides_files/figure-html/meuseplot-1.png" width="504" style="display: block; margin: auto;" />
]

---
# Buffer vectors

* When we want our analysis to extend beyond the 'edges' of our study area

* When we are trying to develop samples

* Distance is in units of the CRS 
+proj=sterea +lat_0=52.1561605555556 +lon_0=5.38763888888889 +k=0.9999079 +x_0=155000 +y_0=463000 +ellps=bessel +units=m +no_defs

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```r
meuse.buf <- st_buffer(meuse_sf, dist = 500)
```
]

.pull-right[

```r
plot(st_geometry(meuse.buf))  
```

<img src="03-slides_files/figure-html/plotmbuf-1.png" width="216" style="display: block; margin: auto;" />
]
---

# Estimate area, distance, (or length)

```r
st_area(meuse.buf)[1:5]
```

```
## Units: [m^2]
## [1] 785039.3 785039.3 785039.3 785039.3 785039.3
```

---
# Estimate area, distance, (or length)

```r
st_distance(meuse_sf)[1:5, 1:5]
```

```
## Units: [m]
##           [,1]      [,2]     [,3]     [,4]     [,5]
## [1,]   0.00000  70.83784 118.8486 259.2393 366.3141
## [2,]  70.83784   0.00000 141.5662 282.8516 362.6403
## [3,] 118.84864 141.56624   0.0000 143.1712 251.0239
## [4,] 259.23927 282.85155 143.1712   0.0000 154.2628
## [5,] 366.31407 362.64032 251.0239 154.2628   0.0000
```

```r
st_distance(meuse.buf)[1:5,1:5]
```

```
## Units: [m]
##      [,1] [,2] [,3] [,4] [,5]
## [1,]    0    0    0    0    0
## [2,]    0    0    0    0    0
## [3,]    0    0    0    0    0
## [4,]    0    0    0    0    0
## [5,]    0    0    0    0    0
```