WebMercatorQuad class

"Web Mercator Quad" tile matrix set.

OGC Two Dimensional Tile Matrix Set: "Level 0 allows representing most of the world (limited to latitudes between approximately ±85 degrees) in a single tile of 256x256 pixels (Mercator projection cannot cover the whole world because mathematically the poles are at infinity). The next level represents most of the world in 2x2 tiles of 256x256 pixels and so on in powers of 2. Mercator projection distorts the pixel size closer to the poles. The pixel sizes provided here are only valid next to the equator."

Using "Web Mercator Quad" involves following coordinates:

  • position: geographic coordinates (longitude, latitude)
  • world: a position projected to the pixel space of the map at level 0
  • pixel: pixel coordinates (x, y) in the pixel space of the map at zoom
  • tile: tile coordinates (x, y) in the tile matrix at zoom

The web mercator projection is often used to project geographic coordinates to metric projected coordinates, with x and y value range of (-20037508.34, 20037508.34). However this tile matrix implementation converts directly between geographic coordinates and world / pixel / tile coordinates.

Coordinate value ranges for the world covered by the tile matrix set (when tile size is 256 pixels):

  • position / longitude: (-180.0°, 180.0°)
  • position / latitude: (-85.051129°, 85.051129°)
  • world / x and y: (0.0, 256.0)
  • pixel at level 0 / x and y: (0, 255)
  • pixel at level 2 / x and y: (0, 1023)
  • tile at level 0 / x and y: (0, 0)
  • tile at level 2 / x and y: (0, 3)

Tile coordinates at level 0 (one tile covering the world between latitudes -85.051129° and 85.051129°):

| 0,0 |

Tile coordinates at level 1 (tile matrix width is 2 and height is 2):

| 0,0 | 1,0 |

| 0,1 | 1,1 |

Tile coordinates at level 2 (tile matrix width is 4 and height is 4):

| 0,0 | 1,0 | 2,0 | 3,0 |

| 0,1 | 1,1 | 2,1 | 3,1 |

| 0,2 | 1,2 | 2,2 | 3,2 |

| 0,3 | 1,3 | 2,3 | 3,3 |

Each tile contains 256 x 256 pixels when the tile size is 256. As for level 2 there are 4 x 4 tiles, then the map canvas size is 1024 x 1024 pixels for that level. If the tile size is 512, then the map canvas size is 2048 x 2048 pixels.

Examples above uses "top-left" origin for world, pixel and tile coordinates. If "bottom-left" origin is used then y coordinates must be flipped, for example zoom level 1:

| 0,1 | 1,1 |

| 0,0 | 1,0 |

More information: https://en.wikipedia.org/wiki/Web_Mercator_projection https://developers.google.com/maps/documentation/javascript/coordinates https://docs.microsoft.com/en-us/bingmaps/articles/bing-maps-tile-system https://docs.opengeospatial.org/is/17-083r2/17-083r2.html

Inheritance
Annotations
  • @immutable

Constructors

WebMercatorQuad.epsg3857({int maxZoom = 22, int tileSize = 256, CanvasOrigin origin = CanvasOrigin.topLeft})
Create "Web Mercator Quad" tile matrix set with tileSize and origin.
const

Properties

converter → ScaledConverter
A map converter between geospatial positions and map coordinates.
no setteroverride
hashCode → int
The hash code for this object.
no setterinherited
maxZoom → int
The maximum (suggested) zoom level for this tile matrix set.
final
origin → CanvasOrigin
The position of the origin in a tile matrix and map pixel "canvas".
final
runtimeType → Type
A representation of the runtime type of the object.
no setterinherited
tileSize → int
The number of pixels for one tile in one axis (normally 256 or 512).
final

Methods

mapBounds() → GeoBox
Returns a bounding box with min and max positions for the whole map.
inherited
mapHeight(int zoom) → int
The number of pixels ("map height") at zoom in the Y axis.
override
mapSize(int zoom) → int
The number of pixels at zoom (level of detail) in one axis.
mapWidth(int zoom) → int
The number of pixels ("map width") at zoom in the X axis.
override
matrixHeight(int zoom) → int
The number of tiles ("matrix height") at zoom in the Y axis.
override
matrixSize(int zoom) → int
The number of tiles at zoom (level of detail) in one axis.
matrixWidth(int zoom) → int
The number of tiles ("matrix width") at zoom in the X axis.
override
noSuchMethod(Invocation invocation) → dynamic
Invoked when a nonexistent method or property is accessed.
inherited
pixelArcResolution(int zoom) → double
The arc resolution (longitudal) of a pixel in degrees at zoom.
inherited
pixelGroundResolution(int zoom) → double
The pixel ground resolution in meters at zoom.
override
pixelGroundResolutionAt({required double latitude, required int zoom}) → double
The pixel ground resolution in meters at given latitude and zoom.
pixelToPosition(Scalable2i pixel) → Geographic
Transforms pixel coordinates to a position.
inherited
pixelToTile(Scalable2i pixel) → Scalable2i
Returns a tile covering a region in pixel coordinates.
inherited
pixelToWorld(Scalable2i pixel) → Projected
Transforms pixel coordinates to world coordinates.
inherited
positionToPixel(covariant Position position, {int zoom = 0}) → Scalable2i
Transforms position to pixel coordinates at zoom.
inherited
positionToTile(covariant Position position, {int zoom = 0}) → Scalable2i
Returns a tile at zoom covering a region in position.
inherited
positionToWorld(covariant Position position) → Projected
Transforms position to world coordinates.
inherited
quadKeyToTile(String quadKey) → Scalable2i
Returns a tile identified by quadKey (as specified by Microsoft).
scaleDenominator(int zoom, {double screenPPI = screenPPIbyOGC}) → double
The map scale denominator at zoom and screenPPI.
override
scaleDenominatorAt({required double latitude, required int zoom, double screenPPI = screenPPIbyOGC}) → double
The map scale denominator at given latitude, zoom and screenPPI.
tileArcResolution(int zoom) → double
The arc resolution (longitudal) of a tile in degrees at zoom.
inherited
tileGroundResolution(int zoom) → double
The tile ground resolution in meters at zoom.
override
tileToBounds(Scalable2i tile) → GeoBox
Returns a bounding box with min and max positions for tile.
inherited
tileToPixel(Scalable2i tile, {Aligned align = Aligned.center, bool requireInside = false}) → Scalable2i
Transforms a fractional point defined by align inside tile to pixel coordinates.
inherited
tileToPosition(Scalable2i tile, {Aligned align = Aligned.center}) → Geographic
Transforms a fractional point defined by align inside tile to a position.
inherited
tileToQuadKey(Scalable2i tile) → String
Returns the quad key (as specified by Microsoft) for tile.
tileToWorld(Scalable2i tile, {Aligned align = Aligned.center}) → Projected
Transforms a fractional point defined by align inside tile to world coordinates.
inherited
toString() → String
A string representation of this object.
inherited
worldToPixel(Projected world, {int zoom = 0}) → Scalable2i
Transforms world coordinates to pixel coordinates at zoom.
inherited
worldToPosition(Projected world) → Geographic
Transforms world coordinates to a position.
inherited
worldToTile(Projected world, {int zoom = 0}) → Scalable2i
Returns a tile at zoom covering a region in world coordinates.
inherited
zoomFromPixelGroundResolution(double resolution) → double
The zoom from pixel ground resolution in meters.
override
zoomFromPixelGroundResolutionAt({required double latitude, required double resolution}) → double
The zoom from pixel ground resolution in meters at given latitude.
zoomFromScaleDenominator(double denominator, {double screenPPI = screenPPIbyOGC}) → double
The zoom from map scale denominator at given screenPPI.
override
zoomFromScaleDenominatorAt({required double latitude, required double denominator, double screenPPI = screenPPIbyOGC}) → double
The zoom from map scale denominator at given latitude and screenPPI.

Operators

operator ==(Object other) → bool
The equality operator.
inherited