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14 changes: 7 additions & 7 deletions 02-spatial-data.Rmd
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Expand Up @@ -1058,7 +1058,7 @@ This section explains each type, laying the foundations for Chapter \@ref(reproj
### Geographic coordinate reference systems

\index{CRS!geographic}
Geographic coordinate reference systems identify any location on the earth's surface using two values --- longitude and latitude (Figure \@ref(fig:vector-crs), left panel).
Geographic coordinate reference systems identify any location on the Earth's surface using two values --- longitude and latitude (Figure \@ref(fig:vector-crs), left panel).
*Longitude* is location in the East-West direction in angular distance from the Prime Meridian plane.
*Latitude* is angular distance North or South of the equatorial plane.
Distances in geographic CRSs are therefore not measured in meters.
Expand All @@ -1069,15 +1069,15 @@ Spherical models assume that the Earth is a perfect sphere of a given radius --
Ellipsoidal models are slightly more accurate, and are defined by two parameters: the equatorial radius and the polar radius.
These are suitable because the Earth is compressed: the equatorial radius is around 11.5 km longer than the polar radius [@maling_coordinate_1992].^[
The degree of compression is often referred to as *flattening*, defined in terms of the equatorial radius ($a$) and polar radius ($b$) as follows: $f = (a - b) / a$. The terms *ellipticity* and *compression* can also be used.
Because $f$ is a rather small value, digital ellipsoid models use the 'inverse flattening' ($rf = 1/f$) to define the earth's compression.
Because $f$ is a rather small value, digital ellipsoid models use the 'inverse flattening' ($rf = 1/f$) to define the Earth's compression.
Values of $a$ and $rf$ in various ellipsoidal models can be seen by executing `sf_proj_info(type = "ellps")`.
]

Ellipsoids are part of a wider component of CRSs: the *datum*.
This contains information on what ellipsoid to use and the precise relationship between the coordinates and location on the earth's surface.
This contains information on what ellipsoid to use and the precise relationship between the coordinates and location on the Earth's surface.
There are two types of datum --- geocentric (such as `WGS84`) and local (such as `NAD83`).
You can see examples of these two types of datums in Figure \@ref(fig:datum-fig).
Black lines represent a *geocentric datum*, whose center is located in the earth's center of gravity and is not optimized for a specific location.
Black lines represent a *geocentric datum*, whose center is located in the Earth's center of gravity and is not optimized for a specific location.
In a *local datum*, shown as a purple dashed line, the ellipsoidal surface is shifted to align with the surface at a particular location.
These allow local variations in Earth's surface, for example due to large mountain ranges, to be accounted for in a local CRS.
This can be seen in Figure \@ref(fig:datum-fig), where the local datum is fitted to the area of Philippines, but is misaligned with most of the rest of the planet's surface.
Expand All @@ -1097,16 +1097,16 @@ Projected CRSs are based on Cartesian coordinates on an implicitly flat surface
They have an origin, x and y axes, and a linear unit of measurement such as meters.

This transition cannot be done without adding some deformations.
Therefore, some properties of the earth's surface are distorted in this process, such as area, direction, distance, and shape.
Therefore, some properties of the Earth's surface are distorted in this process, such as area, direction, distance, and shape.
A projected coordinate reference system can preserve only one or two of those properties.
Projections are often named based on a property they preserve: equal-area preserves area, azimuthal preserve direction, equidistant preserve distance, and conformal preserve local shape.

There are three main groups of projection types - conic, cylindrical, and planar (azimuthal).
In a conic projection, the earth's surface is projected onto a cone along a single line of tangency or two lines of tangency.
In a conic projection, the Earth's surface is projected onto a cone along a single line of tangency or two lines of tangency.
Distortions are minimized along the tangency lines and rise with the distance from those lines in this projection.
Therefore, it is the best suited for maps of mid-latitude areas.
A cylindrical projection maps the surface onto a cylinder.
This projection could also be created by touching the earth's surface along a single line of tangency or two lines of tangency.
This projection could also be created by touching the Earth's surface along a single line of tangency or two lines of tangency.
Cylindrical projections are used most often when mapping the entire world.
A planar projection projects data onto a flat surface touching the globe at a point or along a line of tangency.
It is typically used in mapping polar regions.
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4 changes: 2 additions & 2 deletions 04-spatial-operations.Rmd
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Expand Up @@ -619,9 +619,9 @@ As with attribute data, joining adds new columns to the target object (the argum
\index{join!spatial}
\index{spatial!join}

The process is illustrated by the following example: imagine you have ten points randomly distributed across the earth's surface and you ask, for the points that are on land, which countries are they in?
The process is illustrated by the following example: imagine you have ten points randomly distributed across the Earth's surface and you ask, for the points that are on land, which countries are they in?
Implementing this idea in a [reproducible example](https://github.com/geocompx/geocompr/blob/main/code/04-spatial-join.R) will build your geographic data handling skills and show how spatial joins work.
The starting point is to create points that are randomly scattered over the earth's surface.
The starting point is to create points that are randomly scattered over the Earth's surface.

```{r 04-spatial-operations-19}
set.seed(2018) # set seed for reproducibility
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2 changes: 1 addition & 1 deletion geocompr.bib
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Expand Up @@ -1243,7 +1243,7 @@ @book{longley_geocomputation_1998
month = oct,
publisher = {Wiley},
address = {Chichester, Eng. ; New York},
abstract = {Geocomputation A Primer edited by Paul A Longley Sue M Brooks Rachael McDonnell School of Geographical Sciences, University of Bristol, UK and Bill Macmillan School of Geography, University of Oxford, UK This book encompasses all that is new in geocomputation. It is also a primer - that is, a book which sets out the foundations and scope of this important emergent area from the same contemporary perspective. The catalyst to the emergence of geocomputation is the new and creative application of computers to devise and depict digital representations of the earth's surface. The environment for geocomputation is provided by geographical information systems (GIS), yet geocomputation is much more than GIS. Geocomputation is a blend of research-led applications which emphasise process over form, dynamics over statics, and interaction over passive response. This book presents a timely blend of current research and practice, written by the leading figures in the field. It provides insights to a new and rapidly developing area, and identifies the key foundations to future developments. It should be read by all who seek to use geocomputational methods for solving real world problems.},
abstract = {Geocomputation A Primer edited by Paul A Longley Sue M Brooks Rachael McDonnell School of Geographical Sciences, University of Bristol, UK and Bill Macmillan School of Geography, University of Oxford, UK This book encompasses all that is new in geocomputation. It is also a primer - that is, a book which sets out the foundations and scope of this important emergent area from the same contemporary perspective. The catalyst to the emergence of geocomputation is the new and creative application of computers to devise and depict digital representations of the Earth's surface. The environment for geocomputation is provided by geographical information systems (GIS), yet geocomputation is much more than GIS. Geocomputation is a blend of research-led applications which emphasise process over form, dynamics over statics, and interaction over passive response. This book presents a timely blend of current research and practice, written by the leading figures in the field. It provides insights to a new and rapidly developing area, and identifies the key foundations to future developments. It should be read by all who seek to use geocomputational methods for solving real world problems.},
isbn = {978-0-471-98576-1},
langid = {english}
}
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