World Coordinate System

WCS

class WCS(header, images, options)

Create a new coordinate reference system that emulates the WCS (World Coordinate System) used in astronomy.

Arguments:

  • header (object) -- JSON representation of the merged image header.

  • images (Array.<image>) -- Array of image extension metadata.

  • options (object) -- Options.

  • options.nzoom (number) -- Number of zoom levels.

Returns:

WCS -- Instance of a World Coordinate System.

WCS.code

Codename of the WCS coordinate reference system.

static WCS._deltaLng(latLng, latLng0)

Compute the longitude of a point with respect to a reference point.

Arguments:

  • latLng (leaflet.LatLng) -- World coordinates of the point.

  • latLng0 (leaflet.LatLng) -- World coordinates of the reference point.

Returns:

number -- Difference in longitude (in degrees) in the interval -180 to 180 deg.

static WCS.distance(latlng1, latlng2)

Compute the distance between two points on the sphere.

Arguments:

  • latlng1 (leaflet.LatLng) -- World coordinates of the first point.

  • latlng2 (leaflet.LatLng) -- World coordinates of the second point.

Returns:

number -- Spherical distance between the two points in degrees.

static WCS.fovToZoom(map, fov, latlng)
Compute the zoom level that corresponds to a given FoV at the provided

coordinates.

Arguments:

  • map (leaflet.Map) -- Leaflet map.

  • fov (number) -- Field of View in degrees.

  • latlng (leaflet.LatLng) -- World coordinates.

Returns:

number -- Zoom level.

static WCS.getProjection(header, options)

Extract the WCS projection code from a JSON-encoded image header.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (object) -- Projection options.

Returns:

string -- WCS projection code.

static WCS.hmsDMSToLatLng(Coordinate)

Convert an HMSDMS string to world coordinates.

Arguments:

  • Coordinate (string) -- string in HMSDMS.

Returns:

leaflet.LatLng|undefined -- World coordinates, or undefined if the input string could not be translated.

static WCS.latLngToHMSDMS(latlng)
Convert world coordinates to an HMSDMS string

(DMS code from the Leaflet-Coordinates plug-in).

Arguments:

  • latlng (leaflet.LatLng) -- Input world coordinates.

Returns:

string -- Coordinate string in HMSDMS.

static WCS.multiLatLngToIndex(latlng)
Return index of chip closest to the given world coordinates in a

multi-WCS setting.

Arguments:

  • latlng (leaflet.LatLng) -- Input world coordinates.

Returns:

number -- Index of the closest chip (extension).

static WCS.multiLatLngToPoint(latlng, zoom)

Multi-WCS version of the projection to layer coordinates.

Arguments:

  • latlng (leaflet.LatLng) -- Input world coordinates.

  • zoom (number) -- Zoom level.

Returns:

leaflet.Point -- Layer coordinates at the given zoom level.

static WCS.multiPntToIndex(pnt)
Return index of chip closest to the given pixel coordinates in a

multi-WCS setting.

Arguments:

  • pnt (leaflet.Point) -- Input (merged) pixel coordinates.

Returns:

number -- Index of the closest chip (extension).

static WCS.multiPointToLatLng(pnt, zoom)

Multi-WCS version of the de-projection from layer coordinates.

Arguments:

  • pnt (leaflet.Point) -- Input layer coordinates at the given zoom level.

  • zoom (number) -- Zoom level.

Returns:

leaflet.LatLng -- De-projected world coordinates.

static WCS.multiProject(latlng)

Multi-WCS astrometric projection.

Arguments:

  • latlng (leaflet.LatLng) -- Input world coordinates.

Returns:

leaflet.Point -- Projected (merged) pixel coordinates.

static WCS.multiUnproject(pnt)

Multi-WCS version of the astrometric de-projection.

Arguments:

  • pnt (leaflet.Point) -- Input (merged) pixel coordinates.

Returns:

leaflet.LatLng -- De-projected world coordinates.

static WCS.parseCoords(str)

Parse a string of world coordinates.

Arguments:

  • str (string) -- Input string.

Returns:

leaflet.LatLng|undefined -- World coordinates, or undefined if conversion failed.

static WCS.pixelScale(zoom, latlng)

Compute the layer pixel scale at the given world coordinates.

Arguments:

  • zoom (number) -- Zoom level.

  • latlng (leaflet.LatLng) -- World coordinates.

Returns:

number -- Layer pixel scale (in degrees per pixel).

static WCS.rawPixelScale(latlng)

Compute the image pixel scale at the given world coordinates.

Arguments:

  • latlng (leaflet.LatLng) -- World coordinates.

Returns:

number -- Pixel scale (in degrees per pixel).

static WCS.scale(zoom)

Convert zoom level to relative scale.

Arguments:

  • zoom (number) -- Zoom level.

Returns:

number -- Relative scale.

static WCS.transform(pnt, zoom)

Convert pixel (image) coordinates to layer coordinates.

Arguments:

  • pnt (leaflet.Point) -- Pixel coordinates.

  • zoom (number) -- Zoom level.

Returns:

leaflet.Point -- Layer coordinates at the given zoom level.

static WCS.untransform(layerpnt, zoom)

Convert layer coordinates to pixel (image) coordinates.

Arguments:

  • layerpnt (leaflet.Point) -- Layer coordinates.

  • zoom (number) -- Zoom level.

Returns:

leaflet.Point -- Pixel (image) coordinates

static WCS.zoom(scale)

Convert relative scale to zoom level.

Arguments:

  • scale (number) -- Relative scale.

Returns:

number -- Zoom level.

static WCS.zoomToFov(map, zoom, latlng)

Compute the FoV that corresponds to a given zoom level at the provided coordinates.

Arguments:

  • map (leaflet.Map) -- Leaflet map.

  • zoom (number) -- Zoom level.

  • latlng (leaflet.LatLng) -- World coordinates.

Returns:

number -- Field of View in degrees.

wcs(header, images, options)

Instantiate a World Coordinate System.

Arguments:

  • header (object) -- JSON representation of the merged image header.

  • images (Array.<Image>) -- Array of image extensions.

  • options (object) -- Options: see {@link WCS}.

Returns:

WCS -- WCS instance.

Projections

class Projection(header, options)
Base class for the WCS (World Coordinate System) projections used in

astronomy.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options.

Returns:

Projection -- Instance of a projection.

Projection.defaultProjParam

type: projParam

Default WCS projection parameters.

static Projection._cpole()
Set up the celestial pole coordinates of the projection

(delta_p, alpha_p). projection._natpole() should be called first.

Returns:

leaflet.LatLng -- Celestial coordinates of the pole.

static Projection._getCenter(proj)

Compute the pixel coordinates of the geometric image center.

Arguments:

  • proj (Projection) -- Projection for pixel coordinates.

Returns:

leaflet.Point -- Pixel coordinates of the image center.

static Projection._invertCD(cd)

Invert the CD Jacobian matrix of the linear part of the de-projection.

Arguments:

  • cd (Array.<Array.<number>>) -- CD Jacobian matrix.

Returns:

Array.<Array.<number>> -- Matrix inverse.

static Projection._multiToPix(pnt)

Convert sliced (merged) coordinates to pixel coordinates.

Arguments:

  • pnt (leaflet.Point) -- Sliced (merged) coordinates.

Returns:

leaflet.Point -- Pixel coordinates.

static Projection._natpole()

Set up the native pole coordinates of the projection (theta_p, phi_p).

Returns:

leaflet.LatLng -- Latitude and longitude of the pole.

static Projection._paramUpdate(paramSrc)

Update internal projection parameters from external properties. The internal projection parameter object is initialized if it does not exist.

Arguments:

  • paramSrc (projParam) -- Input projection parameters.

static Projection._phiThetaToRADec(latlng)

Convert native coordinates to celestial coordinates.

Arguments:

  • latlng (leaflet.LagLng) -- Native coordinates.

Returns:

leaflet.LatLng -- Celestial coordinates.

static Projection._pixToMulti(pnt)

Convert pixel coordinates to sliced (merged) coordinates.

Arguments:

  • pnt (leaflet.Point) -- Pixel coordinates.

Returns:

leaflet.Point -- Sliced (merged) coordinates.

static Projection._pixToRed(pix)

Convert pixel coordinates to reduced coordinates.

Arguments:

  • pix (leaflet.Point) -- Pixel coordinates.

Returns:

leaflet.Point -- Reduced coordinates.

static Projection._raDecToPhiTheta(latlng)

Convert celestial coordinates to native coordinates.

Arguments:

  • latlng (leaflet.LagLng) -- Celestial coordinates.

Returns:

leaflet.LatLng -- Native coordinates.

static Projection._readWCS(header)

Update internal projection parameters from an image header.

Arguments:

  • header (object) -- JSON representation of the image header.

static Projection._redToPix(red)

Convert reduced coordinates to pixel coordinates.

Arguments:

  • red (leaflet.Point) -- Reduced coordinates.

Returns:

leaflet.Point -- Pixel coordinates.

static Projection._shiftWCS(projparam)

Correct projection parameters for data slicing.

Arguments:

  • projparam (projParam) -- Projection parameters.

static Projection.project(latlng)

Project world coordinates to pixel (image) coordinates.

Arguments:

  • latlng (leaflet.LatLng) -- World coordinates.

Returns:

leaflet.Point -- Pixel (image) coordinates.

static Projection.unproject(pnt)

De-project pixel (image) coordinates to world coordinates.

Arguments:

  • pnt (leaflet.Point) -- Pixel coordinates.

Returns:

leaflet.LatLng -- World coordinates.

class Conical(header, options)

Base class for conic WCS (World Coordinate System) projections.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Projection}.

Returns:

Conical -- Instance of a conic projection.

static Conical._phiRToRed(phiR)

Convert conic (phi,R) coordinates to reduced coordinates.

Arguments:

  • phiR (leaflet.LatLng) -- (phi,R) conic coordinates in degrees.

Returns:

leaflet.Point -- Reduced coordinates.

static Conical._redToPhiR(red)

Convert reduced coordinates to conic (phi,R) coordinates.

Arguments:

  • red (leaflet.Point) -- Reduced coordinates.

Returns:

leaflet.LatLng -- (phi,R) conic coordinates in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=19}

class Cylindrical(header, options)

Base class for cylindrical WCS (World Coordinate System) projections.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Projection}.

Returns:

Cylindrical -- Instance of a cylindrical projection.

static Cylindrical._projInit()

Initialize a cylindrical projection.

static Cylindrical._rToTheta(r)

Convert cylindrical R coordinate to native theta angle.

Arguments:

  • r (number) -- R cylindrical coordinate in degrees.

Returns:

number -- Native theta angle in degrees.

static Cylindrical._thetaToR(theta)

Convert native theta angle to cylindrical R.

Arguments:

  • theta (number) -- Native theta angle in degrees.

Returns:

number -- R cylindrical coordinate in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=15}

class Zenithal(header, options)

Base class for zenithal WCS (World Coordinate System) projections.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Projection}.

Returns:

Zenithal -- Instance of a zenithal projection.

static Zenithal._phiRToRed(phiR)

Convert zenithal (phi,R) coordinates to reduced coordinates.

Arguments:

  • phiR (leaflet.LatLng) -- (phi,R) zenithal coordinates in degrees.

Returns:

leaflet.Point -- Reduced coordinates.

static Zenithal._projInit()

Initialize a Zenithal projection.

static Zenithal._redToPhiR(red)

Convert reduced coordinates to zenithal (phi,R) coordinates.

Arguments:

  • red (leaflet.Point) -- Reduced coordinates.

Returns:

leaflet.LatLng -- (phi,R) zenithal coordinates in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=9}

Built-in

class PIX(header, options)

Pixel (identity) projection.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Projection}.

Returns:

PIX -- Instance of a PIX projection.

static PIX._projInit()

Initialize a pixel (identity) projection.

static PIX.project(latlng)
Project "world" pixel coordinates to (image) pixel coordinates

(identity).

Arguments:

  • latlng (leaflet.LatLng) -- "World" pixel coordinates.

Returns:

leaflet.Point -- Pixel (image) coordinates.

static PIX.unproject(pnt)
De-project (image) pixel coordinates to "world" pixel coordinates

(identity).

Arguments:

  • pnt (leaflet.Point) -- Pixel (image) coordinates.

Returns:

leaflet.LatLng -- "World" pixel coordinates.

class CAR(header, options)

Cylindrical Plate carrée projection.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Cylindrical}.

Returns:

CAR -- Instance of a CAR projection.

static CAR._phiRToRed(phiR)

Convert CAR (phi,R) coordinates to reduced coordinates.

Arguments:

  • phiR (leaflet.LatLng) -- (phi,R) CAR coordinates in degrees.

Returns:

leaflet.Point -- Reduced coordinates.

static CAR._redToPhiR(red)

Convert reduced coordinates to CAR (phi,R) coordinates.

Arguments:

  • red (leaflet.Point) -- Reduced coordinates.

Returns:

leaflet.LatLng -- (phi,R) CAR coordinates in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=16}

class CEA(header, options)

Cylindrical Equal-Area projection.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Cylindrical}.

Returns:

CEA -- Instance of a CEA projection.

static CEA._phiRToRed(phiR)

Convert CEA (phi,R) coordinates to reduced coordinates.

Arguments:

  • phiR (leaflet.LatLng) -- (phi,R) CEA coordinates in degrees.

Returns:

leaflet.Point -- Reduced coordinates.

static CEA._redToPhiR(red)

Convert reduced coordinates to CEA (phi,R) coordinates.

Arguments:

  • red (leaflet.Point) -- Reduced coordinates.

Returns:

leaflet.LatLng -- (phi,R) CEA coordinates in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=15}

class COE(header, options)

Conic Equal-Area projection.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Conical}.

Returns:

COE -- Instance of a COE projection.

static COE._projInit()

Initialize a COE projection.

static COE._rToTheta(r)

Convert conic equal-area R coordinate to native theta angle.

Arguments:

  • r (number) -- R conic equal-area coordinate in degrees.

Returns:

number -- Native theta angle in degrees.

static COE._thetaToR(theta)

Convert native theta angle to conic equal-area R.

Arguments:

  • theta (number) -- Native theta angle in degrees.

Returns:

number -- R conic equal-area coordinate in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=20}

class TAN(header, options)

Gnomonic (tangential) projection.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Zenithal}.

Returns:

TAN -- Instance of a TAN projection.

static TAN._rToTheta(r)

Convert tangential R coordinate to native theta angle.

Arguments:

  • r (number) -- R tangential coordinate in degrees.

Returns:

number -- Native theta angle in degrees.

static TAN._thetaToR(theta)

Convert native theta angle to tangential R.

Arguments:

  • theta (number) -- Native theta angle in degrees.

Returns:

number -- R tangential coordinate in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=12}

class TPV(header, options)

Distorted gnomonic (tangential) projection.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Zenithal}.

Returns:

TPV -- Instance of a TPV projection.

static TPV._dRedToRed(dred)

Convert distorted reduced coordinates to reduced coordinates using a TPV polynomial.

Arguments:

  • dred (leaflet.Point) -- Distorted reduced coordinates.

Returns:

leaflet.Point -- Reduced coordinates.

static TPV._pixToRed(pix)

Convert pixel coordinates to reduced coordinates, taking into account distortions.

Arguments:

  • pix (leaflet.Point) -- Pixel coordinates.

Returns:

leaflet.Point -- Reduced coordinates.

static TPV._redToDRed(red)

Convert reduced coordinates to distorted reduced coordinates using second order approximation to the inverted TPV polynomial.

Arguments:

  • red (leaflet.Point) -- Reduced coordinates.

Returns:

leaflet.Point -- Distorted reduced coordinates.

static TPV._redToPix(red)

Convert reduced coordinates to pixel coordinates, taking into account geometric distortions.

Arguments:

  • red (leaflet.Point) -- Reduced coordinates.

Returns:

leaflet.Point -- Pixel coordinates.

See also

  • {@link https://fits.gsfc.nasa.gov/registry/tpvwcs/tpv.html}

class ZEA(header, options)

Zenithal Equal-Area projection.

Arguments:

  • header (object) -- JSON representation of the image header.

  • options (projParam) -- Projection options: see {@link Zenithal}.

Returns:

ZEA -- Instance of a ZEA projection.

static ZEA._rToTheta(r)

Convert zenithal equal-area R coordinate to native theta angle.

Arguments:

  • r (number) -- R zenithal equal-area coordinate in degrees.

Returns:

number -- Native theta angle in degrees.

static ZEA._thetaToR(theta)

Convert native theta angle to zenithal equal-area R.

Arguments:

  • theta (number) -- Native theta angle in degrees.

Returns:

number -- R zenithal equal-area coordinate in degrees.

See also

  • {@link https://www.atnf.csiro.au/people/mcalabre/WCS/ccs.pdf#page=14}