Core Concepts¶

Geographical Information Systems (GIS), like any specialized field, has a wealth of jargon and unique concepts. When represented in software, these concepts can sometimes be skewed or expanded from their original forms. We give a thorough definition of many of the core concepts here, while referencing the Geotrellis objects and source files backing them.

This document aims to be informative to new and experienced GIS users alike. If GIS is brand, brand new to you, this document is a useful high level overview.

Glossary¶

The following is a non-exhaustive list of fundamental terms and their definitions that are important to understanding the function of Geotrellis. These definitions will be expanded upon in other sections of this document.

• Vector or Geometry: Structures built up by connecting Points in space; includes Points, Lines, Polygons.
• Extent or Bounding Box: An axis aligned, rectangular region.
• Feature: A Geometry with some associated metadata.
• Cell: A single unit of data in some grid.
• Tile: A grid of numeric cells that represent some data on the Earth.
• Raster: A Tile with an Extent; places data over a specific region of the Earth.
• RDD: “Resilient Distributed Datasets” from Apache Spark. Can be thought of as a distributed Scala Seq.
• Key: Used to index into a grid of tiles.
• Layout Definition or Layout: A structure that relates keys to geographic locations and vice versa.
• Metadata or Layer Metadata: A descriptive structure that defines how to interpret a key-value store as a coherent single raster.
• Layer or Tile Layer: A combined structure of tiles and keys in an RDD with metadata. Represents a very large raster in a distributed computing context.
• Pyramid: A collection of layers, indexed by a zoom level, where each layer represents the same raster data at a different resolution. Essentially a quad tree of raster data where child nodes cover the same area at higher resolution as their parents.
• Catalog: A persistent store for tile layers and/or pyramids, storing both tiles and metadata.

System Organization¶

Core¶

The fundamental components of the Geotrellis system are rasters and vectors. Rasters are 2-dimensional, discrete grids of numerical data, much like matrices. Vectors are 2- (or sometimes 3-) dimensional collections of points that are connected together to form piecewise linear linestrings, polygons, and other compound structures.

Geotrellis is also tied to geographical application domains, and so these fundamental objects can be placed in a geographical context. Specifically, we can ascribe projections to the points in a geometry, and we can apply an extent to raster data to indicate the position and scope of the raster data.

Geotrellis provides a number of operations on these basic data types. One may reproject, resample, crop, merge, combine, and render raster data; vector data may be manipulated in some limited ways, but is mostly used to generate raster data.

The following packages contain the relevant code:

Distributed Processing¶

High resolution imagery on global, national, regional, or even local levels (depending on just how high of a resolution is used) is big. It’s too big to work with effectively on a single machine. Thus, Geotrellis provides the means to use rasters and vectors in a distributed context using Apache Spark.

To distribute data, it is necessary to supply some structure over which we can organize smaller units of raster or vector data. Geotrellis leans on the LayoutDefinition class to provide this structure. The idea is that a region on the globe is specified (along with a projection), and a regular, rectangular grid is overlaid on that region. Each grid cell is given a spatial key, and so it is possible to associate a raster or vector to a given grid cell. (Note that we may also use keys with a temporal component.) This induces a tiled representation of an arbitrarily large layer of data.

Geotrellis provides utilities for coercing data into this gridded representation, for manipulating data within a tiled layer, and for storing processed layers to a variety of backends. Find implementations of these features in this package:

Storage Backends¶

Computations over large data are time consuming, so storage of results is important. Geotrellis mostly relies on distributed key-value stores. Once a layer is built (a set of uniform chunks of raster data keyed to a layout, with some additional metadata), it is possible to write these tiles out to a catalog. These preprocessed layers can then be read back rapidly, and used to support any number of applications.

The necessary componenents for storing and reading layers can be found in the following packages:

Method Extensions¶

Geotrellis utilizes a design pattern called method extensions wherein Scala’s implicits system is used to patch additional functionality onto existing classes. For example, for a raster value r, one may call r.reproject(srcCRS, destCRS), even though the Raster class does not define reproject directly.

Files in the source tree that have names of the form XxxxxMethods.scala define capabilities that should be implemented by an implicit class, usually found in the Implicits.scala file in the same directory. For a MethodExtension[T] subclass implementing the foo() method, an object of type T should be able to have foo() called on it.

Unfortunately, discoverability of valid method extensions is an ongoing problem for Geotrellis as a whole. We are currently seeking better means for documenting these features. In the meantime, perusing the source tree, and using tab-completion in the REPL are workable solutions. Bear in mind, however, that availability of method extensions is contingent on having types that match the T parameter of the desired MethodExtension[T] implementation.

Projections and Coordinate Systems¶

A fundamental component of a GIS system is the ability to specify projections and perform transformations of points between various coordinate systems. Contained in the geotrellis.proj4 package are the means to perform these tasks.

Coordinate Reference Systems¶

As a means of describing geodetic coordinate systems, the geotrellis.proj4.CRS class is provided. CRSs can be constructed by either indicating the EPSG code using the CRS.fromEpsgCode object method, or by the proj4 string using the CRS.fromString object method.

There are also a set of predefined CRS objects provided in geotrellis.proj4. These include the standard WebMercator and LatLng CRSs. Also included is ConusAlbers, giving the Albers equal area projection for the continental United States (EPSG code 5070). Finally, UTM zone CRS objects can be produced using the geotrellis.proj4.util.UTM.getZoneCrs method.

Transformations¶

To move coordinates between coordinate systems, it is necessary to build a geotrellis.proj4.Transform object. These are built simply by supplying the source CRS and the destination CRS. The result is a transformation function with type (Double, Double) => (Double, Double).

Vector Data¶

Data in GIS applications often come in a geometric form. That is, one might encounter data describing, say, population by census region, or road networks. These are termed vector data sources. Geotrellis wraps JTS geometries in a Scala interface and then provides the tools to produce raster data from that vector data, or simply to work directly with the vector data itself. Vector data comes either as raw geometry, or as feature data—that is, geometry with associated data—and can be read from a variety of sources.

Geometries¶

Geometries in Geotrellis are exclusively point sets and piecewise linear representations. A collection of points may be connected by a chain of linear segments into more complex shapes, and then aggregated into collections. All such classes derive from the base geotrellis.vector.Geometry class. The geometry subclasses are as follows:

• geotrellis.vector.Point

Representation of a 2-dimensional point in space.

• geotrellis.vector.Line

More appropriately termed a polyline. A sequence of linear segments formed from a sequence of points, $$[p_1, p_2, ..., p_n]$$, where the $$i^\mathrm{th}$$ line segment is the segment between $$p_i$$ and $$p_{i+1}$$. May be self-intersecting. May be open or closed (the latter meaning that $$p_1 = p_n$$).

• geotrellis.vector.Polygon

A polygonal shape, possibly with holes. Formed from a single closed, simple (non-self-intersecting) polyline exterior, and zero or more closed, simple, mutually non-intersecting interior rings. Proper construction can be verified through the use of the isValid() method.

• geotrellis.vector.MultiPoint

• geotrellis.vector.MultiLine

• geotrellis.vector.MultiPolygon

The three preceding classes aggregate points, lines, and polygons, respectively.

• geotrellis.vector.GeometryCollection

A container class for aggregating dissimilar geometries.

Geometries have a standard interface for typical operations such as finding the convex hull, affine transformation (rotation, scaling, translating, and shearing), determining if one geometry is contained within another, and finding intersections.

The following is a simple example of working with intersections:

import geotrellis.vector._

/** First, let's create a Point. Then, we'll use its intersection method.
* Note: we are also using intersection's alias '&'.
*/
val myPoint = Point(1.0, 1.1) // Create a point
// Intersection method
val selfIntersection = myPoint intersection Point(1.0, 1.1)
// Intersection alias
val nonIntersection = myPoint & Point(200, 300)

Upon execution, the values selfIntersection and nonIntersection are GeometryResult containers, which is a common return type for geometric operations. To extract results from these wrappers, use the as[G <: Geometry] function which either returns Some(G) or None:

val pointIntersection = (Point(1.0, 2.0) & Point(1.0, 2.0)).as[Point]
val pointNonIntersection = (Point(1.0, 2.0) & Point(12.0, 4.0)).as[Point]

assert(pointIntersection == Some(Point(1.0, 2.0)))  // Either some point
assert(pointNonIntersection == None)                // Or nothing at all

When using as[G <: Geometry], be aware that it isn’t necessarily the case that the GeometryResult object may not be convertable to the chosen G. For example, a PointGeometryIntersectionResult.as[Polygon] will always return None.

Alternatively, one may use pattern matching to check intersection results. geotrellis.vector.GeometryResult contains a large ADT which encodes the possible outcomes for different types of outcomes. The result type of a JTS-dependent vector operation can be found somewhere on this tree to the effect that an exhaustive match can be carried out to determine the Geometry (excepting cases of NoResult, for which there is no Geometry).

For example, we note that a Point/Point intersection has the type PointOrNoResult. From this we can deduce that it is either a Point underneath or else nothing:

val p1: Point = Point(0, 0)
val p2: Point = p1
p1 & p2 match {
case PointResult(_) => println("A Point!")
case NoResult => println("Sorry, no result.")
}

yields “A Point!”

There are also implicits in many geotrellis modules which will extend Geometry capabilities. For instance, after importing geotrellis.vector.io._, it becomes possible to call the toGeoJson method on any Geometry:

import geotrellis.vector.io._
assert(Point(1,1).toGeoJson == """{"type":"Point","coordinates":[1.0,1.0]}""")

If you need to move from a geometry to a serialized representation or vice-versa, take a look at the io directory’s contents. This naming convention for input and output is common throughout Geotrellis. So if you’re trying to get spatial representations in or out of your program, spend some time seeing if the problem has already been solved.

Methods which are specific to certain subclasses of Geometry exist too. For example, geotrellis.vector.MultiLine is implicitly extended by geotrellis.vector.op such that this becomes possible:

import geotrellis.vector.op._
val myML = MultiLine.EMPTY
myML.unionGeometries

The following packages extend Geometry capabilities:

Extents¶

Geotrellis makes common use of the Extent class. This class represents an axis-aligned bounding box, where the extreme values are given as Extent(min_x, min_y, max_x, max_y). Note that Extents are not Geometry instances. They can be coerced to a Polygon using the toPolygon method, and they can often be used as arguments to geometric operations such as intersection.

Projected Geometries¶

Note that there is no generally-accepted means to mark the projection of a geometry, so it is incumbent on the user to keep track of and properly coerce geometries into the correct projections. However, the geotrellis.vector.reproject package provides the reproject method extension for performing this task.

Extents, on the other hand, can be wrapped in a ProjectedExtent instance. These are useful for designating the geographical scope of a raster, for example.

Features¶

To associate some arbitrary data with a vector object, often for use in tasks such as rasterization, use the Feature[G <: Geometry, D] container class, or one of its subclasses. For example:

abstract class Feature[D] {
type G <: Geometry
val geom: G ; val data: D
}

case class PointFeature[D](geom: Point, data: D) extends Feature[D] {type G = Point}

Implicit method extensions exist that will allow, for instance, rasterize to be called on a Feature to create a raster where the pixels covered by the geometry are assigned the value of of the feature’s data.

Further Information¶

Please refer to the vector documentation for more detailed information.

Raster Data¶

Tiles and Rasters¶

The geotrellis.raster module provides primitive datatypes to represent two dimensional, gridded numerical data structures, and the methods to manipulate them in a GIS context. These raster objects resemble sequences of numerical sequences like the following (this array of arrays is like a 3x3 tile):

// not real syntax
val myFirstTile = [[1,1,1],[1,2,2],[1,2,3]]
/** It probably looks more like your mental model if we stack them up:
* [[1,1,1],
*  [1,2,2],
*  [1,2,3]]
*/

In the raster module of GeoTrellis, raster data is not represented by simple arrays, but rather as subclasses of Tile. That class is more powerful than a simple array representation, providing many useful operators. Here’s an incomplete list of the types of things on offer:

• Mapping transformations of arbitrary complexity over the constituent cells
• Carrying out operations (side-effects) for each cell
• Querying a specific tile value
• Rescaling, resampling, cropping

Working with Cell Values¶

Tiles contain numerical data. These can be of the form of integers, floats, doubles, and so forth. And even though Scala has generic types, Geotrellis does not implement Tile[V] for performance reasons, since the Java compiler will liberally sprinkle box/unbox commands all through the code to support the genericity, which greatly increase runtime and space usage.

Instead, Geotrellis uses macros to implement a different system of cell types. This preserves speed while maintaining flexibility of data types, with only small compromises in the API. These cell types may also represent no data, that is, a special value can be assigned to represent a missing value. This does require sacrificing a value from the range of possible inputs, but eliminates the problems of boxed types, such as Option. (Note, this means that bit-valued cells cannot have no data values.)

The various cell types are defined as follows:

No NoData Constant NoData User Defined NoData
BitCells BitCellType N/A N/A
ByteCells ByteCellType ByteConstantNoDataCellType ByteUserDefinedNoDataCellType
UbyteCells UByteCellType UByteConstantNoDataCellType UByteUserDefinedNoDataCellType
ShortCells ShortCellType ShortConstantNoDataCellType ShortUserDefinedNoDataCellType
UShortCells UShortCellType UShortConstantNoDataCellType UShortUserDefinedNoDataCellType
IntCells IntCellType IntConstantNoDataCellType IntUserDefinedNoDataCellType
FloatCells FloatCellType FloatConstantNoDataCellType FloatUserDefinedNoDataCellType
DoubleCells DoubleCellType DoubleConstantNoDataCellType DoubleUserDefinedNoDataCellType

The three rightmost columns give the CellTypes that would be used to represent (1) data without a NoData value, (2) data using a default NoData value, and (3) data where the user specifies the value used for the NoData value. User defined NoData CellTypes require a constructor to provide the NoData value.

A caveat: The single most noticeable compromise of this system is that float- and double-valued cell types must be treated differently using functions such as getDouble, setDouble, and mapDouble, provided by the tile classes.

Now, some examples:

/** Here's an array we'll use to construct tiles */
val myData = Array(42, 1, 2, 3)

/** The GeoTrellis-default integer CellType
*   Note that it represents NoData values with the smallest signed
*   integer possible with 32 bits (Int.MinValue or -2147483648).
*/
val defaultCT = IntConstantNoDataCellType
val normalTile = IntArrayTile(myData, 2, 2, defaultCT)

/** A custom, 'user defined' NoData CellType for comparison; we will
*   treat 42 as NoData for this one rather than Int.MinValue
*/
val customCellType = IntUserDefinedNoDataCellType(42)
val customTile = IntArrayTile(myData, 2, 2, customCellType)

/** We should expect that the first (default celltype) tile has the value 42 at (0, 0)
*   This is because 42 is just a regular value (as opposed to NoData)
*   which means that the first value will be delivered without surprise
*/
assert(normalTile.get(0, 0) == 42)
assert(normalTile.getDouble(0, 0) == 42.0)

/** Here, the result is less obvious. Under the hood, GeoTrellis is
*   inspecting the value to be returned at (0, 0) to see if it matches our
*   NoData policy and, if it matches (it does, we defined NoData as
*   42 above), return Int.MinValue (no matter your underlying type, get
*   on a tile will return an Int and getDouble will return a Double).
*
*   The use of Int.MinValue and Double.NaN is a result of those being the
*   GeoTrellis-blessed values for NoData - below, you'll find a chart that
*   lists all such values in the rightmost column
*/
assert(customTile.get(0, 0) == Int.MinValue)
assert(customTile.getDouble(0, 0) == Double.NaN)

One final point is worth making in the context of CellType performance: the Constant types are able to depend upon macros which inline comparisons and conversions. This minor difference can certainly be felt while iterating through millions and millions of cells. If possible, Constant NoData values are to be preferred. For convenience’ sake, we’ve attempted to make the GeoTrellis-blessed NoData values as unobtrusive as possible a priori.

Notes:
• If attempting to convert between CellTypes, see this note on CellType conversions.)

• Lower-precision cell types will translate into smaller tiles. Consider the following:

Bits / Cell 512x512 Raster (mb) Range (inclusive) GeoTrellis NoData Value
BitCells 1 0.032768 [0, 1] N/A
ByteCells 8 0.262144 [-128, 128] -128 (Byte.MinValue)
UbyteCells 8 0.262144 [0, 255] 0
ShortCells 16 0.524288 [-32768, 32767] -32768 (Short.MinValue)
UShortCells 16 0.524288 [0, 65535] 0
IntCells 32 1.048576 [-2147483648, 2147483647] -2147483648 (Int.MinValue)
FloatCells 32 1.048576 [-3.40E38, 3.40E38] Float.NaN
DoubleCells 64 2.097152 [-1.79E308, 1.79E308] Double.NaN

Also note the range and default no data values (ConstantNoDataCellTypes).

• The limits of expected return types (see above table) are used by macros to squeeze as much speed out of the JVM as possible. Check out our macros docs for more on our use of macros like isData and isNoData.

An easy place to begin with building a tile is through one of the following two classes:

abstract class IntArrayTile(
val array: Array[Int],
cols: Int,
rows: Int
) extends MutableArrayTile { ... }

abstract class DoubleArrayTile(
val array: Array[Double],
cols: Int,
rows: Int
) extends MutableArrayTile { ... }

These constructors allow for an Int- or Double-valued tile to be created with specific content. However, the object methods associated with these classes contain most of the useful constructors. Notably, the apply method One may also enjoy using the empty, fill, and ofDim object methods to create new tiles. For these methods,

Tile Inheritance Structure¶

We can consider the inheritance pathway of IntArrayTile to get a feel for the class structure. Note that each listed class is a descendant of the previous class.

• Grid

A Serializable instance giving row and column dimensions.

• CellGrid

Adds cellType to Grid. CellGrid forms the minimum requirement for many algorithms.

• Tile

Provides the basic infrastructure for accessing the content of a tile (get and getDouble).

• ArrayTile

Allows conversion from tiles to arrays.

• MutableArrayTile

Provides the means to change the values in a tile (set and setDouble).

• IntArrayTile

The implementation of MutableArrayTile for discrete data types.

NOTE There is a long-standing bug in the Tile hierarchy where calling mutable on an ArrayTile instance does not create a copy of the original immutable tile, but simply creates a mutable version from the same underlying buffer. Changes to the result of a call to mutable will change the original as well.

Rasters¶

A raster is a general category of data, consisting of values laid out on a regular grid, but in GIS, it carries the double meaning of a tile with location information. The location information is represented by an Extent. This is almost always meant when we use the proper term Raster in the context of Geotrellis code.

The following REPL session constructs a simple Raster:

import geotrellis.raster._
import geotrellis.vector._

scala> IntArrayTile(Array(1,2,3),1,3)

scala> IntArrayTile(Array(1,2,3),3,1)
res1: geotrellis.raster.IntArrayTile = IntArrayTile([S@736a81de,3,1)

scala> IntArrayTile(Array(1,2,3,4,5,6,7,8,9),3,3)
res2: geotrellis.raster.IntArrayTile = IntArrayTile([I@5466441b,3,3)

scala> Extent(0, 0, 1, 1)
res4: geotrellis.vector.Extent = Extent(0.0,0.0,1.0,1.0)

scala> Raster(res2, res4)
res5: geotrellis.raster.Raster = Raster(IntArrayTile([I@7b47ab7,1,3),Extent(0.0,0.0,1.0,1.0))

scala> res0.asciiDraw()
res3: String =
"    1
2
3
"

scala> res2.asciiDraw()
res4: String =
"    1     2     3
4     5     6
7     8     9
"

Tile Hierarchy¶

For the sake of completeness, the following tile hierarchy is presented:

The Tile trait has operations you’d expect for traversing and transforming the contents of the tiles, like:

• map: (Int => Int) => Tile
• foreach: (Int => Unit) => Unit
• combine: Tile => ((Int, Int) => Int) => Tile
• color: ColorMap => Tile

As discussed above, the Tile interface carries information about how big it is and what its underlying Cell Type is:

• cols: Int
• rows: Int
• cellType: CellType

Layouts and Tile Layers¶

The core vector and raster functionality thus far described stands on its own for small scale applications. But, as mentioned, Geotrellis is intended to work with big data in a distributed context. For this, we rely on Apache Spark’s resilient distributed dataset (RDD). RDDs of both raster and vector data are naturally supported by Geotrellis, but some new concepts are required to integrate this abstraction for distributed processing.

For most applications, the data of interest must be keyed to a layout to give the content of an RDD—which is usually a collection of key-value pairs (i.e., RDD[(K, V)])—a consistent interpretation as a cohesive raster. In such an RDD, the key type, K, is one of TemporalKey, SpatialKey, or SpaceTimeKey. The latter two key types obviously contain spatial data (declared in context bounds as [K: SpatialComponent], where values of such a type K can have their spatial component extracted using the getComponent[SpatialKey] extension method), which is used to identify a region in space.

The geotrellis.spark.tiling.LayoutDefinition class is used to describe how SpatialKeys map to regions in space. The LayoutDefinition is a GridExtent subclass defined with an Extent and CellSize. The Extent is subdivided into a grid of uniform, rectangular regions. The size and number of the sub-regions is determined using the CellSize of the LayoutDefinition, and then the pixel dimensions of the constituent tiles. The sub-regions are then assigned a SpatialKey with the (0, 0) position corresponding to the upper-left corner of the extent; the x coordinate increases toward the right, and the y coordinate increases moving down (into lower latitude values, say).

Thus far, we’ve described how an RDD[(K, V)] plus a LayoutDefinition can be used to represent a large, distributed raster (when [K: SpatialComponent]). To solidify this notion, Geotrellis has a notion of a Tile Layer, which is defined as RDD[(K, V)] with Metadata[M]. The M type is usually represented by a TileLayerMetadata[K] object. These metadata, provide a LayoutDefinition plus a CRS, CellType, and bounds for the keys found in the RDD.

Note: The easiest means to represent a tile layer is with a ContextRDD object.

Note: Geotrellis offers many method extensions that operate on tile layers, but it is occasionally necessary to explicitly declare the types of V, K, and M to access those methods.

The following figure summarizes the structure of a tile layer and its constituent parts:

In this diagram:

• CustomTile, CustomMetadata, and CustomKey don’t exist, they represent types that you could write yourself for your application.
• The K seen in several places is the same K.
• The type RDD[(K, V)] with Metadata[M] is a Scala Anonymous Type. In this case, it means RDD from Apache Spark with extra methods injected from the Metadata trait. This type is sometimes aliased in GeoTrellis as ContextRDD.
• RDD[(K, V)] resembles a Scala Seq[(K, V)], but also has further Map-like methods injected by Spark when it takes this shape. See Spark’s PairRDDFunctions Scaladocs for those methods. Note: Unlike Map, the Ks here are not guaranteed to be unique.

TileLayerRDD¶

Geotrellis defines a type alias for a common variant of a tile layer, RDD[(K, V)] with Metadata[M], as follows:

This type represents a grid (or cube!) of Tiles on the earth, arranged according to some K. Features of this grid are:

• Grid location (0, 0) is the top-leftmost Tile.
• The Tiles exist in some CRS. In TileLayerMetadata, this is kept track of with an actual CRS field.
• In applications, K is mostly SpatialKey or SpaceTimeKey.

Keys and Key Indexes¶

Keys¶

As mentioned in the Tile Layers section, grids (or cubes) of Tiles on the earth are organized by keys. This key, often refered to generically as K, is typically a SpatialKey or a SpaceTimeKey:

case class SpatialKey(col: Int, row: Int)

case class SpaceTimeKey(col: Int, row: Int, instant: Long)

It is also possible to define custom key types.

Reminder: Given a layout over some Extent, SpatialKey(0, 0) would index the top-leftmost Tile in the grid covering that extent.

When doing Layer IO, certain optimizations can be performed if we know that Tiles stored near each other in a filesystem or database (like Accumulo or HBase) are also spatially-close in the grid they’re from. To make such a guarantee, we use a KeyIndex.

Key Indexes¶

A KeyIndex is a GeoTrellis trait that represents Space Filling Curves. They are a means by which to translate multi-dimensional indices into a single-dimensional one, while maintaining spatial locality. In GeoTrellis, we use these chiefly when writing Tile Layers to one of our Tile Layer Backends.

Although KeyIndex is often used in its generic trait form, we supply three underlying implementations.

Z-Curve¶

The Z-Curve is the simplest KeyIndex to use (and implement). It can be used with both SpatialKey and SpaceTimeKey.

val b0: KeyBounds[SpatialKey] = ... /* from TileLayerRDD.metadata.bounds */
val b1: KeyBounds[SpaceTimeKey] = ...

val i0: KeyIndex[SpatialKey] = ZCurveKeyIndexMethod.createIndex(b0)
val i1: KeyIndex[SpaceTimeKey] = ZCurveKeyIndexMethod.byDay().createIndex(b1)

val k: SpatialKey = ...
val oneD: Long = i0.toIndex(k) /* A SpatialKey's 2D coords mapped to 1D */
Hilbert¶

Another well-known curve, available for both SpatialKey and SpaceTimeKey.

val b: KeyBounds[SpatialKey] = ...

val index: KeyIndex[SpatialKey] = HilbertKeyIndexMethod.createIndex(b)
Index Resolution Changes Index Order¶

Changing the resolution (in bits) of the index causes a rotation and/or reflection of the points with respect to curve-order. Take, for example the following code (which is actually derived from the testing codebase):

HilbertSpaceTimeKeyIndex(SpaceTimeKey(0,0,y2k), SpaceTimeKey(2,2,y2k.plusMillis(1)),2,1)

The last two arguments are the index resolutions. If that were changed to:

HilbertSpaceTimeKeyIndex(SpaceTimeKey(0,0,y2k), SpaceTimeKey(2,2,y2k.plusMillis(1)),3,1)

The index-order of the points would be different. The reasons behind this are ultimately technical, though you can imagine how a naive implementation of an index for, say, a 10x10 matrix (in terms of 100 numbers) would need to be reworked if you were to change the number of cells (100 would no longer be enough for an 11x11 matrix and the pattern for indexing you chose may no longer make sense). Obviously, this is complex and beyond the scope of GeoTrellis’ concerns, which is why we lean on Google’s uzaygezen library.

Beware the 62-bit Limit¶

Currently, the spatial and temporal resolution required to index the points, expressed in bits, must sum to 62 bits or fewer.

For example, the following code appears in HilbertSpaceTimeKeyIndex.scala:

@transient
lazy val chc = {
val dimensionSpec =
new MultiDimensionalSpec(
List(
xResolution,
yResolution,
temporalResolution
).map(new java.lang.Integer(_))
)
}

where xResolution, yResolution and temporalResolution are numbers of bits required to express possible locations in each of those dimensions. If those three integers sum to more than 62 bits, an error will be thrown at runtime.

Row Major¶

Row Major is only available for SpatialKey, but provides the fastest toIndex lookup of the three curves. It doesn’t however, give good locality guarantees, so should only be used when locality isn’t as important to your application.

val b: KeyBounds[SpatialKey] = ...

val index: KeyIndex[SpatialKey] = RowMajorKeyIndexMethod.createIndex(b)

Pyramids¶

In practice, many map applications have an interactive component. Interaction often takes the form of scrolling around the map to a desired location and “zooming in”. This usage pattern implies a need for levels of detail. That is, if we start with a layer with a cell size of 10 meters on a side, say, then viewing the whole continental US would require a raster in the neighborhood of 400,000 x 250,000 pixels, and most of that information would never be seen.

The common solution for this problem is to build a level of detail pyramid, that is, we generate from the base layer a series of less resolute layers, with larger cell size, but a smaller number of pixels. Each layer of the pyramid is called a zoom level.

It is typical for web maps to employ power of two zoom levels, which is to say that the map should double its cell size (halve its resolution) at each successive zoom level. In terms of tile layers, this means that we will end up grouping each layer’s tiles into 2x2 clusters, and merge these chunks into a single tile in the successive layer. In short, we are creating a quad tree where each interior node has an associated tile formed from the resampled and merged tiles of its children.

Note: In a Geotrellis pyramid, each level of the pyramid is a layer with its associated metadata.

To build a pyramid, Geotrellis provides the geotrellis.spark.pyramid.Pyramid class. Consult that documentation for usage.

Zoom Levels and Layout Schemes¶

The generation of a pyramid is the generation of a quadtree, but that is not entirely sufficient, because it is necessary to “contextualize” a tree level. In some cases, the layer on which the pyramid is based has a well-defined LayoutDefinition that is significant to the application. In those cases, we simply build the pyramid. In other cases, we need to generate LayoutDefinitions that conform to the application’s demand. This is the job of a geotrellis.spark.tiling.LayoutScheme.

A LayoutScheme sets the definition of a zoom level. Given an extent and a cell size, the LayoutScheme will provide an integer zoom level and the layout definition for that canonical zoom level (the levelFor() method). Above and beyond that, a LayoutScheme allows for the navigation between adjacent zoom levels with the zoomIn() and zoomOut() methods.

There are two primary modes of setting zoom levels, which can be thought of as local and global. A local method is akin to starting with a LayoutDefinition and assigning an arbitrary zoom number to it. The leaf nodes of the pyramid’s quad tree are rooted at this level, and subsequent zoom levels (lower resolution levels) are generated through power of two reductions. Use the geotrellis.spark.tiling.LocalLayoutScheme class for this purpose.

Note: The user must specify the numerical value of the initial zoom level when using a LocalLayoutScheme.

Global layout schemes, on the other hand, have a predefined structure. These schemes start with a global extent, which each CRS defines. A tile resolution is set, which defines the cell size at zoom level 0—that is, global layout schemes are defined by having one tile which covers the world extent completely at zoom 0. That cell size is then halved at the next highest (more resolute) zoom level. For historical reasons, global schemes are called geotrellis.spark.tiling.ZoomedLayoutSchemes

Note: the global layout scheme defined here establishes a zoom and spatial key layout that is used by many prevalent web map tile serving standards such as TMS.

Catalogs & Tile Layer IO¶

There is a significant amount of embodied effort in any given layer or pyramid, thus it is a common use case to want to persist these layers to some storage back end. A set of saved layers under a common location with some metadata store is called a catalog in Geotrellis parlance. There can be multiple different pyramids in a catalog, and the metadata can be extended for a particular use case. This section explains the components of a catalog and how to perform IO between an application and a catalog.

Layer IO requires a Tile Layer Backend. Each backend has an AttributeStore, a LayerReader, and a LayerWriter.

An example using the file system backend:

import geotrellis.spark._
import geotrellis.spark.io._
import geotrellis.spark.io.file._

val catalogPath: String = ...  /* Some location on your computer */

val store: AttributeStore = FileAttributeStore(catalogPath)

val writer = FileLayerWriter(store)

Writing an entire layer:

/* Zoom level 13 */
val layerId = LayerId("myLayer", 13)

/* Produced from an ingest, etc. */
val rdd: TileLayerRDD[SpatialKey] = ...

/* Order your Tiles according to the Z-Curve Space Filling Curve */

/* Returns Unit */
writer.write(layerId, rdd, index)

/* .read has many overloads, but this is the simplest */

Querying a layer (a “filtered” read):

/* Some area on the earth to constrain your query to */
val extent: Extent = ...

/* There are more types that can go into where */
val filteredLayer: TileLayerRDD[SpatialKey] =

Catalog Organization¶

Our Landsat Tutorial produces a simple single-pyramid catalog on the filesystem at data/catalog/ which we can use here as a reference. Running tree -L 2 gives us a view of the directory layout:

.
├── attributes
└── landsat
├── 0
├── 1
├── 10
├── 11
├── 12
├── 13
├── 2
├── 3
├── 4
├── 5
├── 6
├── 7
├── 8
└── 9

16 directories, 14 files

The children of landsat/ are directories, but we used -L 2 to hide their contents. They actually contain thousands of Tile files, which are explained below.

The metadata JSON files contain familiar information:

$jshon < lansat__.__6__.__metadata.json [ { "name": "landsat", "zoom": 6 }, { "header": { "format": "file", "keyClass": "geotrellis.spark.SpatialKey", "valueClass": "geotrellis.raster.MultibandTile", "path": "landsat/6" }, "metadata": { "extent": { "xmin": 15454940.911194608, "ymin": 4146935.160646211, "xmax": 15762790.223459147, "ymax": 4454355.929947533 }, "layoutDefinition": { ... } }, ... // more here "keyIndex": { "type": "zorder", "properties": { "keyBounds": { "minKey": { "col": 56, "row": 24 }, "maxKey": { "col": 57, "row": 25 } } } }, ... // more here } ] Of note is the header block, which tells GeoTrellis where to look for and how to interpret the stored Tiles, and the keyIndex block which is critical for reading/writing specific ranges of tiles. For more information, see our section on Key Indexes. As we have multiple storage backends, header can look different. Here’s an example for a Layer ingested to S3: ... // more here "header": { "format": "s3", "key": "catalog/nlcd-tms-epsg3857/6", "keyClass": "geotrellis.spark.SpatialKey", "valueClass": "geotrellis.raster.Tile", "bucket": "azavea-datahub" }, ... // more here Tiles¶ From above, the numbered directories under landsat/ contain serialized Tile files.$ ls
attributes/  landsat/
$cd landsat/6/$ ls
1984  1985  1986  1987
\$ du -sh *
12K     1984
8.0K    1985
44K     1986
16K     1987

Note

These Tile files are not images, but can be rendered by GeoTrellis into PNGs.

Notice that the four Tile files here have different sizes. Why might that be, if Tiles are all Rasters of the same dimension? The answer is that a Tile file can contain multiple tiles. Specifically, it is a serialized Array[(K, V)] of which Array[(SpatialKey, Tile)] is a common case. When or why multiple Tiles might be grouped into a single file like this is the result of the Space Filling Curve algorithm applied during ingest.

Separate Stores for Attributes and Tiles¶

The real story here is that layer attributes and the Tiles themselves don’t need to be stored via the same backend. Indeed, when instantiating a Layer IO class like S3LayerReader, we notice that its AttributeStore parameter is type-agnostic:

So it’s entirely possible to store your metadata with one service and your tiles with another. Due to the header block in each Layer’s metadata, GeoTrellis will know how to fetch the Tiles, no matter how they’re stored. This arrangement could be more performant/convenient for you, depending on your architecture.

Map Algebra¶

Map Algebra is the name given by Dana Tomlin to a method of manipulating and transforming raster data. There are many references on map algebra, including Tomlin’s book, so we will only give a brief introduction here. GeoTrellis follows Tomlin’s vision of map algebra operations, although there are many operations that fall outside of the realm of Map Algebra that it also supports.

Map Algebra operations fall into 3 general categories:

Local Operations¶

Local operations are ones that only take into account the information of on cell at a time. In the animation above, we can see that the blue and the yellow cell are combined, as they are corresponding cells in the two tiles. It wouldn’t matter if the tiles were bigger or smaller - the only information necessary for that step in the local operation is the cell values that correspond to each other. A local operation happens for each cell value, so if the whole bottom tile was blue and the upper tile were yellow, then the resulting tile of the local operation would be green.

Focal Operations¶

Focal operations take into account a cell, and a neighborhood around that cell. A neighborhood can be defined as a square of a specific size, or include masks so that you can have things like circular or wedge-shaped neighborhoods. In the above animation, the neighborhood is a 5x5 square around the focal cell. The focal operation in the animation is a focalSum. The focal value is 0, and all of the other cells in the focal neighborhood; therefore the cell value of the result tile would be 8 at the cell corresponding to the focal cell of the input tile. This focal operation scans through each cell of the raster. You can imagine that along the border, the focal neighborhood goes outside of the bounds of the tile; in this case the neighborhood only considers the values that are covered by the neighborhood. GeoTrellis also supports the idea of an analysis area, which is the GridBounds that the focal operation carries over, in order to support composing tiles with border tiles in order to support distributed focal operation processing.

Zonal Operations¶

Zonal operations are ones that operate on two tiles: an input tile, and a zone tile. The values of the zone tile determine what zone each of the corresponding cells in the input tile belong to. For example, if you are doing a zonalStatistics operation, and the zonal tile has a distribution of zone 1, zone 2, and zone 3 values, we will get back the statistics such as mean, median and mode for all cells in the input tile that correspond to each of those zone values.

Using Map Algebra Operations¶

Map Algebra operations are defined as implicit methods on Tile or Traversable[Tile], which are imported with import geotrellis.raster._.

import geotrellis.raster._

val tile1: Tile = ???
val tile2: Tile = ???

// If tile1 and tile2 are the same dimensions, we can combine
// them using local operations

// There are operators for some local operations.
// This is equivalent to the localAdd call above

tile1 + tile2

// There is a local operation called "reclassify" in literature,
// which transforms each value of the function.
// We actually have a map method defined on Tile,
// which serves this purpose.

tile1.map { z => z + 1 } // Map over integer values.

tile2.mapDouble { z => z + 1.1 } // Map over double values.

tile1.dualMap({ z => z + 1 })({ z => z + 1.1 }) // Call either the integer value or double version, depending on cellType.

// You can also combine values in a generic way with the combine funciton.
// This is another local operation that is actually defined on Tile directly.

tile1.combine(tile2) { (z1, z2) => z1 + z2 }

The following packages are where Map Algebra operations are defined in GeoTrellis:

• geotrellis.raster.mapalgebra.local defines operations which act on a cell without regard to its spatial relations. Need to double every cell on a tile? This is the module you’ll want to explore.
• geotrellis.raster.mapalgebra.focal defines operations which focus on two-dimensional windows (internally referred to as neighborhoods) of a raster’s values to determine their outputs.
• geotrellis.raster.mapalgebra.zonal defines operations which apply over a zones as defined by corresponding cell values in the zones raster.

Conway’s Game of Life can be seen as a focal operation in that each cell’s value depends on neighboring cell values. Though focal operations will tend to look at a local region of this or that cell, they should not be confused with the operations which live in geotrellis.raster.local - those operations describe transformations over tiles which, for any step of the calculation, need only know the input value of the specific cell for which it is calculating an output (e.g. incrementing each cell’s value by 1).

Vector Tiles¶

Invented by Mapbox, VectorTiles are a combination of the ideas of finite-sized tiles and vector geometries. Mapbox maintains the official implementation spec for VectorTile codecs. The specification is free and open source.

VectorTiles are advantageous over raster tiles in that:

• They are typically smaller to store
• They can be easily transformed (rotated, etc.) in real time
• They allow for continuous (as opposed to step-wise) zoom in Slippy Maps.

Raw VectorTile data is stored in the protobuf format. Any codec implementing the spec must decode and encode data according to this .proto schema.

GeoTrellis provides the geotrellis-vectortile module, a high-performance implementation of Version 2.1 of the VectorTile spec. It features:

• Decoding of Version 2 VectorTiles from Protobuf byte data into useful Geotrellis types.
• Lazy decoding of Geometries. Only parse what you need!
• Read/write VectorTile layers to/from any of our backends.

As of 2016 November, ingests of raw vector data into VectorTile sets aren’t yet possible.

Small Example¶

import geotrellis.spark.SpatialKey
import geotrellis.spark.tiling.LayoutDefinition
import geotrellis.vector.Extent
import geotrellis.vectortile.VectorTile
import geotrellis.vectortile.protobuf._

val bytes: Array[Byte] = ...  // from some .mvt file
val key: SpatialKey = ...  // preknown
val layout: LayoutDefinition = ...  // preknown
val tileExtent: Extent = layout.mapTransform(key)

/* Decode Protobuf bytes. */
val tile: VectorTile = ProtobufTile.fromBytes(bytes, tileExtent)

/* Encode a VectorTile back into bytes. */
val encodedBytes: Array[Byte] = tile match {
case t: ProtobufTile => t.toBytes
case _ => ???  // Handle other backends or throw errors.
}

See our VectorTile Scaladocs for detailed usage information.

Implementation Assumptions¶

This particular implementation of the VectorTile spec makes the following assumptions:

• Geometries are implicitly encoded in ‘’some’’ Coordinate Reference system. That is, there is no such thing as a “projectionless” VectorTile. When decoding a VectorTile, we must provide a Geotrellis [[Extent]] that represents the Tile’s area on a map. With this, the grid coordinates stored in the VectorTile’s Geometry are shifted from their original [0,4096] range to actual world coordinates in the Extent’s CRS.
• The id field in VectorTile Features doesn’t matter.
• UNKNOWN geometries are safe to ignore.
• If a VectorTile geometry list marked as POINT has only one pair of coordinates, it will be decoded as a Geotrellis Point. If it has more than one pair, it will be decoded as a MultiPoint. Likewise for the LINESTRING and POLYGON types. A complaint has been made about the spec regarding this, and future versions may include a difference between single and multi geometries.

GeoTiffs¶

GeoTiffs are a type of Tiff image file that contain image data pertaining to satellite, aerial, and elevation data among other types of geospatial information. The additional pieces of metadata that are needed to store and display this information is what sets GeoTiffs apart from normal Tiffs. For instance, the positions of geographic features on the screen and how they are projected are two such pieces of data that can be found within a GeoTiff, but is absent from a normal Tiff file.

GeoTiff File Format¶

Because GeoTiffs are Tiffs with extended features, they both have the same file structure. There exist three components that can be found in all Tiff files: the header, the image file directory, and the actual image data. Within these files, the directories and image data can be found at any point within the file; regardless of how the images are presented when the file is opened and viewed. The header is the only section which has a constant location, and that is at the begining of the file.

As stated earlier, the header is found at the beginning of every Tiff file, including GeoTiffs. All Tiff files have the exact same header size of 8 bytes. The first two bytes of the header are used to determine the ByteOrder of the file, also known as “Endianness”. After these two, comes the next two bytes which are used to determine the file’s magic number. .tif, .txt, .shp, and all other file types have a unique identifier number that tells the program kind of file it was given. For Tiff files, the magic number is 42. Due to how the other components can be situated anywhere within the file, the last 4 bytes of the header provide the offset value that points to the first file directory. Without this offset, it would be impossible to read a Tiff file.

Image File Directory¶

For every image found in a Tiff file there exists a corresponding image file directory for that picture. Each property listed in the directory is referred to as a Tag. Tags contain information on, but not limited to, the image size, compression types, and the type of color plan. Since we’re working with Geotiffs, geo-spatial information is also documented within the Tags. These directories can vary in size, as users can create their own tags and each image in the file does not need to have exact same tags.

Other than image attributes, the file directory holds two offset values that play a role in reading the file. One points to where the actual image itself is located, and the other shows where the the next file directory can be found.

Image Data¶

A Tiff file can store any number of images within a single file, including none at all. In the case of GeoTiffs, the images themselves are almost always stored as bitmap data. It is important to understand that there are two ways in which the actual image data is formatted within the file. The two methods are: Striped and Tiled.

Striped¶

Striped storage breaks the image into segments of long, vertical bands that stretch the entire width of the picture. Contained within them are columns of bitmapped image data. If your GeoTiff file was created before the realse of Tiff 6.0, then this is the data storage method in which it most likely uses.

If an image has strip storage, then its corresponding file directory contains the tags: RowsPerStrip, StripOffsets, and StripByteCount. All three of these are needed to read that given segment. The first one is the number of rows that are contained within the strips. Every strip within an image must have the same number of rows within it except for the last one in certain instances. StripOffsets is an array of offsets that shows where each strip starts within the file. The last tag, ByteSegmentCount, is also an array of values that contains the size of each strip in terms of Bytes.

Tiled¶

Tiff 6.0 introduced a new way to arrange and store data within a Tiff, tiled storage. These rectangular segments have both a height and a width that must be divisible by 16. There are instances where the tiled grid does not fit the image exactly. When this occurs, padding is added around the image so as to meet the requirement of each tile having dimensions of a factor of 16.

As with stips, tiles have specific tags that are needed in order to process each segment. These new tags are: TileWidth, TileLength, TileOffsets, and TileByteCounts. TileWidth is the number of columns and TileLength is the number of rows that are found within the specified tile. As with striped, TileOffsets and TileByteCounts are arrays that contain the begining offset and the byte count of each tile in the image, respectively.

Layout: Columns and Rows¶

At a high level, there exist two ways to refer to a location within GeoTiffs. One is to use Map coordinates which are X and Y values. X’s are oriented along the horizontal axis and run from west to east while Y’s are on the vertical axis and run from south to north. Thus the further east you are, the larger your X value; and the more north you are the larger your Y value.

The other method is to use the grid coordinate system. This technique of measurement uses Cols and Rows to describe the relative location of things. Cols run east to west whereas Rows run north to south. This then means that Cols increase as you go east to west, and rows increase as you go north to south.

Each (X, Y) pair corresponds to some real location on the planet. Cols and rows, on the other hand, are ways of specifying location within the image rather than by reference to any actual location. For more on coordinate systems supported by GeoTiffs, check out the relevant parts of the spec.

Big Tiffs¶

In order to qualify as a BigTiff, your file needs to be at least 4gb in size or larger. At this size, the methods used to store and find data are different. The accommodation that is made is to change the size of the various offsets and byte counts of each segment. For a normal Tiff, this size is 32-bits, but BigTiffs have these sizes at 64-bit. GeoTrellis transparently supports BigTiffs, so so you shouldn’t need to worry about size.

Cloud Optimized GeoTiffs¶

Just as the GeoTiff is a subset of Tiff meant to convey information not only about image values but also the spatial extent of that imagery, Cloud Optimized GeoTiffs (COGs for short) are a nascent subset of GeoTiff meant to increase their expressiveness, ease of use, and portability through further standardization. We call these GeoTiffs “cloud optimized” because the features they add allow for remote access to GeoTiff that, with the help of HTTP GET range requests, access the parts of a tiff you’re interested without consuming large portions of the image which are irrelevant to your computation.

COGs are thus capable of serving as a self-describing backing for raster layers. The only cost associated with the use of COGs over GeoTrellis’ Avro-based layers is the extra effort related to metadata retrieval and munging (metadata for each individual GeoTiff will need to be collected as opposed to the monolithic metadata of Avro layers, which is read and handled once for the entire layer).

The COG specification (which is not a 100% complete as of the writing of this documentation) defines required tags and means of access (a server accepting GET range requests). These required features are necessary to even support remotely reading subsets of the overall image data from some remote Tiff.

COG requirements: - Tiled storage of image data - Overviews at different levels of resolution - Infrastructure capable of handling GET Range requests

// Constructing a COG from a non-COG tiff
val nonCog = SinglebandGeoTiff(path = file:///path/to/my/tiff.tif)
val almostCog = nonCog.withStorageMethod(Tiled)

// most likely either NearestNeighbor or BilinearInterpolation; depends on context
val resampleMethod: ResampleMethod = ???
val fullCog = almostCog.withOverviews(resampleMethod)

> A note on sidecar files > The spec seems to indicate that overviews be part of the GeoTiff itself to > count as a COG. In practice, things are messier than that. Content providers > aren’t always going to want to rewrite their tiffs to stuff generated > overviews into them. The practical upshot of this is that separate overview > files should be supported (GDAL will actually inspect some canonical relative > paths within the directory of the Tiff being read).

// Constructing a COG with sidecar overviews
val mainTile = SinglebandGeoTiff(path = file:///path/to/my/file.tif)
val overview1 = SinglebandGeoTiff(path = file:///path/to/my/file.tif.ovr1)
val overview2 = SinglebandGeoTiff(path = file:///path/to/my/file.tif.ovr2)
val tileWithOverview = mainTile.withOverviews(List(overview1, overview2))

Structured vs Unstructured COGs¶

Historically, Geotrellis layers have been backed by specially encoded Avro layers which are were designed to maximize the performance of distributed reading and querying. With the advent of the COG and the development of tooling to support this subset of the GeoTiff spec, however, the advantages of depending upon a bespoke raster format are less obvious than they once were. Avro support is likely to continue, but support for applications backed by COGs are a priority for continued GeoTrellis development.

To this end, GeoTrellis is introducing the notion of a ‘structured’ COG layer. Structured COG layers are actually a collection of COGs tiled out in a consistent manner and described through common (GeoTrellis-specific) metadata which is designed to enhance query performance for larger layers by allowing GeoTrellis programs to infer information about underlying, individual COG files without having to read multiple of them.

Structured COG metadata: - cellType: Underlying Tiff celltype (width of cell representation and NoData strategy) - zoomRangeInfos: A map from some range of supported zoom levels to a collection of key extents - layoutScheme: The scheme by which individual COG tiles are cut for this layer - extent: The overall extent of all underlying COGs - crs: The projection of all underlying COGs

// We'll need to get a layer from somewhere
// The native resolution for this layer (assumes standard TMS zoom levels)
val baseZoom = 8

// With that, we should be able to construct a 'structured' COG layer
val structured: CogLayer[K, V] = CogLayer.fromLayerRDD(layer, baseZoom)

Typeclasses¶

Typeclasses are a common feature of Functional Programming. As stated in the FAQ, typeclasses group data types by what they can do, as opposed to by what they are. If traditional OO inheritance arranges classes in a tree hierarchy, typeclasses arrange them in a graph.

Typeclasses are realized in Scala through a combination of traits and implicit class wrappings. A typeclass constraint is visible in a class/method signature like this:

class Foo[A: Order](a: A) { ... }

Meaning that Foo can accept any A, so long as it is “orderable”. In reality, this in syntactic sugar for the following:

class Foo[A](a: A)(implicit ev: Order[A]) { ... }

Here’s a real-world example from GeoTrellis code:

protected def _write[
K: AvroRecordCodec: JsonFormat: ClassTag,
V: AvroRecordCodec: ClassTag,
M: JsonFormat: GetComponent[?, Bounds[K]]
](layerId: LayerId, rdd: RDD[(K, V)] with Metadata[M], keyIndex: KeyIndex[K]): Unit = { ... }

A few things to notice:

• Multiple constraints can be given to a single type variable: K: Foo: Bar: Baz
• ? refers to M, helping the compiler with type inference. Unfortunately M: GetComponent[M, Bounds[K]] is not syntactically possible

Below is a description of the most-used typeclasses used in GeoTrellis. All are written by us, unless otherwise stated.

ClassTag¶

Built-in from scala.reflect. This allows classes to maintain some type information at runtime, which in GeoTrellis is important for serialization. You will never need to use this directly, but may have to annotate your methods with it (the compiler will let you know).

JsonFormat¶

From the spray library. This constraint says that its type can be converted to and from JSON, like this:

def toJsonAndBack[A: JsonFormat](a: A): A = {
val json: Value = a.toJson

json.convertTo[A]
}

AvroRecordCodec¶

Any type that can be serialized by Apache Avro. While references to AvroRecordCodec appear frequently through GeoTrellis code, you will never need to use its methods. They are used internally by our Tile Layer Backends and Spark.

Boundable¶

Always used on K, Boundable means your key type has a finite bound.

trait Boundable[K] extends Serializable {
def minBound(p1: K, p2: K): K

def maxBound(p1: K, p2: K): K
...  // etc
}

Component¶

Component is a bare-bones Lens. A Lens is a pair of functions that allow one to generically get and set values in a data structure. They are particularly useful for nested data structures. Component looks like this:

trait Component[T, C] extends GetComponent[T, C] with SetComponent[T, C]

Which reads as “if I have a T, I can read a C out of it” and “if I have a T, I can write some C back into it”. The lenses we provide are as follows:

• SpatialComponent[T] - read a SpatialKey out of a some T (usually SpatialKey or SpaceTimeKey)
• TemporalComponent[T] - read a TemporalKey of some T (usually SpaceTimeKey)

Cats¶

There is a wide variety of standard typeclasses employed by the functional programming community. Rather than implement them ourselves, we have elected to depend on the Cats project to provide this extra functionality. We intend to provide as much compatibility with Cats as is reasonable without sacrificing readability for users who are not functional programming mavens. Initially, we rely on Functors, Semigroups, and Monoids, but there is some use of the IO monad in limited parts of the code base. Please see the documentation for Cats for more information.