flatsphere

A Go library for converting between spherical and planar coordinates.

Prerequisites

• Go: requires Go 1.21 or higher.

Install

go get github.com/owlpinetech/flatsphere

Usage

Projecting/Inverse

Go from latitude/longitude pairs to points on the x/y plane, or the reverse.

mercator := flatsphere.NewMercator() // or some other projection
x, y := mercator.Project(lat, lon)

rlat, rlon := mercator.Inverse(sampleX, sampleY)

Bounds of Projection Plane

Determine the domain of the projection inverse function, to know which valid x/y values can be supplied. Helpful when iterating over the projected space.

mercator := flatsphere.NewMercator()
bounds := mercator.PlanarBounds()
for x := bounds.XMin; x <= bounds.XMax; x += bounds.Width() / xSteps {
    for y := bounds.YMin; y <= bounds.YMax; y += bounds.Height() / ySteps {
        lat, lon := mercator.Inverse(x, y)
    }
}

Reprojecting

Convert planar points in one projection into another projection.

origProj := flatsphere.NewMercator()
newProj := flatsphere.NewLambert()
lat, lon := origProj.Inverse(origX, origY)
newX, newY := newProj.Project(lat, lon)

Oblique Projections

Easily create variants of existing projections with different center points and rotations around the center point.

mercator := flatsphere.NewMercator() // or some other projection
transverseMercator := flatsphere.NewOblique(mercator, 0, math.Pi/2, -math.Pi/2)
x, y := transverseMercator.Project(lat, lon)

Distortion

Determine how representative of reality a projection is at a point on the sphere.

mercator := flatsphere.NewMercator() // or some other projection
areaDistortion, angularDistortion = proj.DistortionAt(lat, lon)

Projections

A list of the predefined projections supported by the package.

Invertability: all projections in this library have a well defined inverse function. However, only some of them reasonably satisfy the invertability property x = f_1(f(x)) due to floating-point error in computations, edge-cases resulting in infinities or NaNs, or ambiguity at some type of critical point (commonly the poles or prime meridian). The table below checks of invertible for all projections which satisfy the x = f_1(f(x)) property for all valid spherical locations except the poles to a reasonably fine degree of precision, referred to here as everywhere floating-point invertible. Oblique transforms of floating-point invertible standard projections do not necessarily share that property.

Efforts are ongoing to improve the coverage of this property to more projections where possible.

Projection	Everywhere Floating-point Invertible
Mercator	✅
Plate carrée	✅
Equirectangular	✅
Lambert cylindrical	✅
Behrmann	✅
Gall orthographic	✅
Hobo-Dyer	✅
Gall stereographic	✅
Miller	✅
Central	✅
Sinusoidal	✅
HEALPix	✅
Mollweide
Homolosine
Eckert IV
Stereographic
Polar
Lambert azimuthal
Gnomonic
Orthographic
Robinson	✅
Natural Earth	✅
Cassini	✅
Aitoff
Hammer
Lagrange	✅

Credits

Inspired by the Map-Projections library made by @jkunimune. Right now this library is essentially a Go-flavored port of his original Java, minus a few things to keep it focused on library use cases.