d3-geo-projection

Extended geographic projections for d3-geo. See Command-Line Cartography for an introduction.

Installing

If you use npm, npm install d3-geo-projection. You can also download the latest release on GitHub. For vanilla HTML in modern browsers, import d3-geo-projection from Skypack:

1<script type="module">
2
3import {geoAitoff} from "https://cdn.skypack.dev/d3-geo-projection@4";
4
5const projection = geoAitoff();
6
7</script>

For legacy environments, you can load d3-geo-projection’s UMD bundle from an npm-based CDN such as jsDelivr; a d3 global is exported:

1<script src="https://cdn.jsdelivr.net/npm/d3-array@3"></script>
2<script src="https://cdn.jsdelivr.net/npm/d3-geo@3"></script>
3<script src="https://cdn.jsdelivr.net/npm/d3-geo-projection@4"></script>
4<script>
5
6const projection = d3.geoAitoff();
7
8</script>

API Reference

• Projections
• Interrupted Projections
• Polyhedral Projections
• Quincuncial Projections
• Transformations

Projections

Note: projections tagged [d3-geo] are exported by d3-geo, not d3-geo-projection. These commonly-used projections are also included in the d3 default bundle.

# d3.geoAiry() · Source, Examples
# d3.geoAiryRaw(beta)

Airy’s minimum-error azimuthal projection.

# airy.radius([radius])

Defaults to 90°.

# d3.geoAitoff() · Source, Examples
# d3.geoAitoffRaw

The Aitoff projection.

# d3.geoAlbers() · Source [d3-geo]

Albers’ equal-area conic projection.

# d3.geoArmadillo() · Source, Examples
# d3.geoArmadilloRaw(phi0)

The armadillo projection. The default center assumes the default parallel of 20° and should be changed if a different parallel is used. Note: requires clipping to the sphere.

# armadillo.parallel([parallel])

Defaults to 20°.

# d3.geoAugust() · Source, Examples
# d3.geoAugustRaw

August’s epicycloidal conformal projection.

# d3.geoAzimuthalEqualArea() · Source [d3-geo], Examples
# d3.geoAzimuthalEqualAreaRaw

The Lambert azimuthal equal-area projection.

# d3.geoAzimuthalEquidistant() · Source [d3-geo], Examples
# d3.geoAzimuthalEquidistantRaw

The azimuthal equidistant projection.

# d3.geoBaker() · Source, Examples
# d3.geoBakerRaw

The Baker Dinomic projection.

# d3.geoBerghaus() · Source, Examples
# d3.geoBerghausRaw(lobes)

Berghaus’ star projection. The default center assumes the default lobe number of 5 and should be changed if a different number of lobes is used. Note: requires clipping to the sphere.

# berghaus.lobes([lobes]) · Source

If lobes is specified, sets the number of lobes in the resulting star, and returns this projection. If lobes is not specified, returns the current lobe number, which defaults to 5.

# d3.geoBertin1953() · Source
# d3.geoBertin1953Raw

Jacques Bertin’s 1953 projection.

# d3.geoBoggs() · Source, Examples
# d3.geoBoggsRaw

The Boggs eumorphic projection. More commonly used in interrupted form.

# d3.geoBonne() · Source, Examples
# d3.geoBonneRaw(phi0)

The Bonne pseudoconical equal-area projection. The Werner projection is a limiting form of the Bonne projection with a standard parallel at ±90°. The default center assumes the default parallel of 45° and should be changed if a different parallel is used.

# bonne.parallel([parallel])

Defaults to 45°.

# d3.geoBottomley() · Source, Examples
# d3.geoBottomleyRaw(sinPsi)

The Bottomley projection “draws lines of latitude as concentric circular arcs, with arc lengths equal to their lengths on the globe, and placed symmetrically and equally spaced across the vertical central meridian.”

# bottomley.fraction([fraction])

Defaults to 0.5, corresponding to a sin(ψ) where ψ = π/6.

# d3.geoBromley() · Source, Examples
# d3.geoBromleyRaw

The Bromley projection is a rescaled Mollweide projection.

# d3.geoChamberlin(point0, point1, point2) · Source
# d3.geoChamberlinRaw(p0, p1, p2)

The Chamberlin trimetric projection. This method does not support projection.rotate: the three reference points implicitly determine a fixed rotation.

# d3.geoChamberlinAfrica() · Source

The Chamberlin projection for Africa using points [0°, 22°], [45°, 22°], [22.5°, -22°].

# d3.geoCollignon() · Source, Examples
# d3.geoCollignonRaw

The Collignon equal-area pseudocylindrical projection. This projection is used in the polar areas of the HEALPix projection.

# d3.geoConicConformal() · Source [d3-geo], Examples
# d3.geoConicConformalRaw

The Lambert conformal conic projection.

# d3.geoConicEqualArea() · Source [d3-geo], Examples
# d3.geoConicEqualAreaRaw

Albers’ conic equal-area projection.

# d3.geoConicEquidistant() · Source [d3-geo], Examples
# d3.geoConicEquidistantRaw

The conic equidistant projection.

# d3.geoCraig() · Source, Examples
# d3.geoCraigRaw(phi)

The Craig retroazimuthal projection. Note: this projection tends to fold over itself if the standard parallel is non-zero; we have not yet implemented the necessary advanced clipping to avoid overlap.

# craig.parallel([parallel])

Defaults to 0°.

# d3.geoCraster() · Source, Examples
# d3.geoCrasterRaw

The Craster parabolic projection; also known as Putniņš P4.

# d3.geoCylindricalEqualArea() · Source, Examples
# d3.geoCylindricalEqualAreaRaw(phi0)

The cylindrical equal-area projection. Depending on the chosen parallel, this projection is also known as the Lambert cylindrical equal-area (0°), Behrmann (30°), Hobo–Dyer (37.5°), Gall–Peters (45°), Balthasart (50°) and Tobler world-in-a-square (~55.654°).

# cylindricalEqualArea.parallel([parallel])

Defaults to approximately 38.58°, fitting the world in a 960×500 rectangle.

# d3.geoCylindricalStereographic() · Source, Examples
# d3.geoCylindricalStereographicRaw(phi0)

The cylindrical stereographic projection. Depending on the chosen parallel, this projection is also known as Braun’s stereographic (0°) and Gall’s stereographic (45°).

# cylindricalStereographic.parallel([parallel])

Defaults to 0°.

# d3.geoEckert1() · Source, Examples
# d3.geoEckert1Raw

The Eckert I projection.

# d3.geoEckert2() · Source, Examples
# d3.geoEckert2Raw

The Eckert II projection.

# d3.geoEckert3() · Source, Examples
# d3.geoEckert3Raw

The Eckert III projection.

# d3.geoEckert4() · Source, Examples
# d3.geoEckert4Raw

The Eckert IV projection.

# d3.geoEckert5() · Source, Examples
# d3.geoEckert5Raw

The Eckert V projection.

# d3.geoEckert6() · Source, Examples
# d3.geoEckert6Raw

The Eckert VI projection.

# d3.geoEisenlohr() · Source, Examples
# d3.geoEisenlohrRaw(lambda, phi)

The Eisenlohr conformal projection.

# d3.geoEquirectangular() · Source [d3-geo], Examples
# d3.geoEquirectangularRaw

The equirectangular (plate carrée) projection. The Cassini projection is the transverse aspect of the equirectangular projection.

# d3.geoFahey() · Source, Examples
# d3.geoFaheyRaw

The Fahey pseudocylindrical projection.

# d3.geoFoucaut() · Source, Examples
# d3.geoFoucautRaw

Foucaut’s stereographic equivalent projection.

# d3.geoFoucautSinusoidal() · Source, Examples
# d3.geoFoucautSinusoidalRaw

Foucaut’s sinusoidal projection, an equal-area average of the sinusoidal and Lambert’s cylindrical projections.

# foucautSinusoidal.alpha([alpha])

Relative weight of the cylindrical projection. Defaults to 0.5.

# d3.geoGilbert([type]) · Source, Examples

Gilbert’s two-world perspective projection. Wraps an instance of the specified projection type; if not specified, defaults to d3.geoOrthographic.

# d3.geoGingery() · Source, Examples
# d3.geoGingeryRaw(rho, lobes)

The U.S.-centric Gingery world projection, as inspired by Cram’s Air Age. Note: requires clipping to the sphere.

# gingery.radius([radius]) · Source

Defaults to 30°.

# gingery.lobes([lobes]) · Source

Defaults to 6.

# d3.geoGinzburg4() · Source, Examples
# d3.geoGinzburg4Raw

The Ginzburg IV projection.

# d3.geoGinzburg5() · Source, Examples
# d3.geoGinzburg5Raw

The Ginzburg V projection.

# d3.geoGinzburg6() · Source, Examples
# d3.geoGinzburg6Raw

The Ginzburg VI projection.

# d3.geoGinzburg8() · Source, Examples
# d3.geoGinzburg8Raw

The Ginzburg VIII projection.

# d3.geoGinzburg9() · Source, Examples
# d3.geoGinzburg9Raw

The Ginzburg IX projection.

# d3.geoGnomonic() · Source [d3-geo], Examples
# d3.geoGnomonicRaw

The gnomonic projection.

# d3.geoGringorten() · Source, Examples
# d3.geoGringortenRaw

The Gringorten square equal-area projection, rearranged to give each hemisphere an entire square.

# d3.geoGuyou() · Source, Examples
# d3.geoGuyouRaw

The Guyou hemisphere-in-a-square projection. Peirce is credited with its quincuncial form.

# d3.geoHammer() · Source, Examples
# d3.geoHammerRaw(A, B)

The Hammer projection. Depending the chosen coefficient and aspect, also known as Eckert–Greifendorff, quartic authalic, and Briesemeister.

# hammer.coefficient([coefficient]) · Source

Defaults to 2.

# d3.geoHammerRetroazimuthal() · Source, Examples
# d3.geoHammerRetroazimuthalRaw(phi0)

The Hammer retroazimuthal projection. Note: requires clipping to the sphere.

# hammerRetroazimuthal.parallel([parallel])

Defaults to 45°.

# d3.geoHealpix() · Source, Examples
# d3.geoHealpixRaw(lobes)

The HEALPix projection: a Hierarchical Equal Area isoLatitude Pixelisation of a 2-sphere. In this implementation, the parameter K is fixed at 3. Note: requires clipping to the sphere.

# healpix.lobes([lobes])

If lobes is specified, sets the number of lobes (the parameter H in the literature) and returns this projection. If lobes is not specified, returns the current lobe number, which defaults to 4.

# d3.geoHill() · Source, Examples
# d3.geoHillRaw(K)

Hill eucyclic projection is pseudoconic and equal-area.

# hill.ratio([ratio])

Defaults to 1. With a ratio of 0, this projection becomes the Maurer No. 73. As it approaches ∞, the projection converges to the Eckert IV.

# d3.geoHomolosine() · Source, Examples
# d3.geoHomolosineRaw

The pseudocylindrical, equal-area Goode homolosine projection is normally presented in interrupted form.

# d3.geoHufnagel() · Source, Examples
# d3.geoHufnagelRaw

A customizable family of pseudocylindrical equal-area projections by Herbert Hufnagel.

# hufnagel.a([a])

# hufnagel.b([b])

# hufnagel.psiMax([psiMax])

# hufnagel.ratio([ratio])

# d3.geoHyperelliptical() · Source, Examples
# d3.geoHyperellipticalRaw

Waldo R. Tobler’s hyperelliptical is a family of equal-area pseudocylindrical projections. Parameters include k, the exponent of the superellipse (or Lamé curve) that defines the shape of the meridians (default k = 2.5); alpha, which governs the weight of the cylindrical projection that is averaged with the superellipse (default alpha = 0); and gamma, that shapes the aspect ratio (default: gamma = 1.183136).

# d3.geoKavrayskiy7() · Source, Examples
# d3.geoKavrayskiy7Raw

The Kavrayskiy VII pseudocylindrical projection.

# d3.geoLagrange() · Source, Examples
# d3.geoLagrangeRaw(n)

The Lagrange conformal projection.

# lagrange.spacing([spacing])

Defaults to 0.5.

# d3.geoLarrivee() · Source, Examples
# d3.geoLarriveeRaw

The Larrivée projection.

# d3.geoLaskowski() · Source, Examples
# d3.geoLaskowskiRaw

The Laskowski tri-optimal projection simultaneously minimizes distance, angular, and areal distortion.

# d3.geoLittrow() · Source, Examples
# d3.geoLittrowRaw

The Littrow projection is the only conformal retroazimuthal map projection. Typically clipped to the geographic extent [[-90°, -60°], [90°, 60°]].

# d3.geoLoximuthal() · Source, Examples
# d3.geoLoximuthalRaw(phi0)

The loximuthal projection is “characterized by the fact that loxodromes (rhumb lines) from one chosen central point (the intersection of the central meridian and central latitude) are shown as straight lines, correct in azimuth from the center, and are ‘true to scale’… It is neither an equal-area projection nor conformal.”

# loximuthal.parallel([parallel])

Defaults to 40°.

# d3.geoMercator() · Source [d3-geo], Examples
# d3.geoMercatorRaw

The spherical Mercator projection.

# d3.geoMiller() · Source, Examples
# d3.geoMillerRaw

The Miller cylindrical projection is a modified Mercator projection.

# d3.geoModifiedStereographic(coefficients, rotate) · Source
# d3.geoModifiedStereographicRaw(coefficients)

The family of modified stereographic projections. The default clip angle for these projections is 90°. These projections do not support projection.rotate: a fixed rotation is applied that is specific to the given coefficients.

# d3.geoModifiedStereographicAlaska() · Source

A modified stereographic projection for Alaska.

# d3.geoModifiedStereographicGs48() · Source

A modified stereographic projection for the conterminous United States.

# d3.geoModifiedStereographicGs50() · Source

A modified stereographic projection for the United States including Alaska and Hawaii. Typically clipped to the geographic extent [[-180°, 15°], [-50°, 75°]].

# d3.geoModifiedStereographicMiller() · Source, Examples

A modified stereographic projection for Europe and Africa. Typically clipped to the geographic extent [[-40°, -40°], [80°, 80°]].

# d3.geoModifiedStereographicLee() · Source, Examples

A modified stereographic projection for the Pacific ocean.

# d3.geoMollweide() · Source, Examples
# d3.geoMollweideRaw

The equal-area, pseudocylindrical Mollweide projection. The oblique aspect is known as the Atlantis projection. Goode’s interrupted Mollweide is also widely known.

# d3.geoMtFlatPolarParabolic() · Source, Examples
# d3.geoMtFlatPolarParabolicRaw

The McBryde–Thomas flat-polar parabolic pseudocylindrical equal-area projection.

# d3.geoMtFlatPolarQuartic() · Source, Examples
# d3.geoMtFlatPolarQuarticRaw

The McBryde–Thomas flat-polar quartic pseudocylindrical equal-area projection.

# d3.geoMtFlatPolarSinusoidal() · Source, Examples
# d3.geoMtFlatPolarSinusoidalRaw

The McBryde–Thomas flat-polar sinusoidal equal-area projection.

# d3.geoNaturalEarth1() · Source [d3-geo], Examples
# d3.geoNaturalEarth1Raw

The Natural Earth projection.

# d3.geoNaturalEarth2() · Source, Examples
# d3.geoNaturalEarth2Raw

The Natural Earth II projection. Compared to Natural Earth, it is slightly taller and rounder.

# d3.geoNellHammer() · Source, Examples
# d3.geoNellHammerRaw

The Nell–Hammer projection.

# d3.geoNicolosi() · Source, Examples
# d3.geoNicolosiRaw

The Nicolosi globular projection.

# d3.geoOrthographic() · Source [d3-geo], Examples
# d3.geoOrthographicRaw

The orthographic projection.

# d3.geoPatterson() · Source, Examples
# d3.geoPattersonRaw

The Patterson cylindrical projection.

# d3.geoPolyconic() · Source, Examples
# d3.geoPolyconicRaw

The American polyconic projection.

# d3.geoRectangularPolyconic() · Source, Examples
# d3.geoRectangularPolyconicRaw(phi0)

The rectangular (War Office) polyconic projection.

# rectangularPolyconic.parallel([parallel])

Defaults to 0°.

# d3.geoRobinson() · Source, Examples
# d3.geoRobinsonRaw

The Robinson projection.

# d3.geoSatellite() · Source, Examples
# d3.geoSatelliteRaw(P, omega)

The satellite (tilted perspective) projection.

# satellite.tilt([tilt])

Defaults to 0°.

# satellite.distance([distance])

Distance from the center of the sphere to the point of view, as a proportion of the sphere’s radius; defaults to 2.0. The recommended maximum clip angle for a given distance is acos(1 / distance) converted to degrees. If tilt is also applied, then more conservative clipping may be necessary. For exact clipping, the in-development geographic projection pipeline is needed; see the satellite explorer.

# d3.geoSinusoidal() · Source, Examples
# d3.geoSinusoidalRaw

The sinusoidal projection.

# d3.geoSinuMollweide() · Source, Examples
# d3.geoSinuMollweideRaw

Allen K. Philbrick’s Sinu-Mollweide projection. See also the interrupted form.

# d3.geoStereographic() · Source [d3-geo], Examples
# d3.geoStereographicRaw

The stereographic projection.

# d3.geoTimes() · Source, Examples
# d3.geoTimesRaw

John Muir’s Times projection.

# d3.geoTransverseMercator() · Source [d3-geo], Examples
# d3.geoTransverseMercatorRaw

The transverse spherical Mercator projection.

# d3.geoTwoPointAzimuthal(point0, point1) · Source
# d3.geoTwoPointAzimuthalRaw(d)

The two-point azimuthal projection “shows correct azimuths (but not distances) from either of two points to any other point. [It can] be used to locate a ship at sea, given the exact location of two radio transmitters and the direction of the ship to the transmitters.” This projection does not support projection.rotate, as the rotation is fixed by the two given points.

# d3.geoTwoPointAzimuthalUsa() · Source

The two-point azimuthal projection with points [-158°, 21.5°] and [-77°, 39°], approximately representing Honolulu, HI and Washington, D.C.

# d3.geoTwoPointEquidistant(point0, point1) · Source
# d3.geoTwoPointEquidistantRaw(z0)

The two-point equidistant projection. This projection does not support projection.rotate, as the rotation is fixed by the two given points. Note: to show the whole Earth, this projection requires clipping to spherical polygons (example).

# d3.geoTwoPointEquidistantUsa() · Source

The two-point equidistant projection with points [-158°, 21.5°] and [-77°, 39°], approximately representing Honolulu, HI and Washington, D.C.

# d3.geoVanDerGrinten() · Source, Examples
# d3.geoVanDerGrintenRaw

The Van der Grinten projection.

# d3.geoVanDerGrinten2() · Source, Examples
# d3.geoVanDerGrinten2Raw

The Van der Grinten II projection.

# d3.geoVanDerGrinten3() · Source, Examples
# d3.geoVanDerGrinten3Raw

The Van der Grinten III projection.

# d3.geoVanDerGrinten4() · Source, Examples
# d3.geoVanDerGrinten4Raw

The Van der Grinten IV projection.

# d3.geoWagner() · Source, Examples
# d3.geoWagnerRaw

The Wagner projection is customizable: default values produce the Wagner VIII projection.

# wagner.poleline([poleline])

Defaults to 65°.

# wagner.parallels([parallels])

Defaults to 60°.

# wagner.inflation([inflation])

Defaults to 20.

# wagner.ratio([ratio])

Defaults to 200.

# d3.geoWagner4() · Source, Examples
# d3.geoWagner4Raw

The Wagner IV projection, also known as Putniṇš P2´.

# d3.geoWagner6() · Source, Examples
# d3.geoWagner6Raw

The Wagner VI projection.

# d3.geoWagner7() · Source, Examples

The Wagner VII projection.

# d3.geoWiechel() · Source, Examples
# d3.geoWiechelRaw

The Wiechel projection.

# d3.geoWinkel3() · Source, Examples
# d3.geoWinkel3Raw

The Winkel tripel projection.

Interrupted Projections

# d3.geoInterrupt(project, lobes) · Source, Examples

Defines a new interrupted projection for the specified raw projection function project and the specified array of lobes. The array lobes contains two elements representing the hemilobes for the northern hemisphere and the southern hemisphere, respectively. Each hemilobe is an array of triangles, with each triangle represented as three points (in degrees): the start, midpoint, and end. For example, the lobes in Goode’s interrupted homolosine projection are defined as:

1[
2  [
3    [[-180,   0], [-100,  90], [ -40,   0]],
4    [[ -40,   0], [  30,  90], [ 180,   0]]
5  ],
6  [
7    [[-180,   0], [-160, -90], [-100,   0]],
8    [[-100,   0], [ -60, -90], [ -20,   0]],
9    [[ -20,   0], [  20, -90], [  80,   0]],
10    [[  80,   0], [ 140, -90], [ 180,   0]]
11  ]
12]

Note: interrupted projections typically require clipping to the sphere.

# interrupted.lobes([lobes]) · Source

If lobes is specified, sets the new array of hemilobes and returns this projection; see d3.geoInterrupt for details on the format of the hemilobes array. If lobes is not specified, returns the current array of hemilobes.

# d3.geoInterruptedHomolosine() · Source, Examples

Goode’s interrupted homolosine projection. Its ocean-centric aspect is also well-known.