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A few elliptical/circular projections (#9)
* Aitoff projection * Add an example for Go pkg documentation * Simple distortion calculation tests added * Add Hammer projection and tests * A couple fixes * A couple more fixes for now * Another readme update * Lagrange projection, fixing a few planar bounds that diverge
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,22 @@ | ||
| package flatsphere | ||
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| import "testing" | ||
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| func Test_DistortionNull(t *testing.T) { | ||
| proj := NewMercator() | ||
| eqArea, eqAngular := DistortionAt(proj, 0, 0) | ||
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| if !withinTolerance(eqArea, 0.0, 0.000001) || !withinTolerance(eqAngular, 0.0, 0.000001) { | ||
| t.Errorf("expected 0, 0 distortion at mercator equator, got %f, %f", eqArea, eqAngular) | ||
| } | ||
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| eqArea = AreaDistortionAt(proj, 0, 0) | ||
| if !withinTolerance(eqArea, 0.0, 0.000001) { | ||
| t.Errorf("expected 0 area distortion at mercator equator, got %f", eqArea) | ||
| } | ||
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| eqAngular = AngularDistortionAt(proj, 0, 0) | ||
| if !withinTolerance(eqAngular, 0.0, 0.000001) { | ||
| t.Errorf("expected 0 angular distortion at mercator equator, got %f", eqAngular) | ||
| } | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,28 @@ | ||
| package flatsphere | ||
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| import ( | ||
| "fmt" | ||
| "math" | ||
| ) | ||
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| // Example_Reproject demonstrates taking a position in one projected plane and converting it into the analogous position | ||
| // in a different projection. | ||
| func Example_reproject() { | ||
| // determine the original projection of the data | ||
| original := NewMercator() | ||
| // decide on a new desired projection of the data | ||
| target := NewCassini() | ||
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| // take a point within the PlanarBounds() of the original projection | ||
| ox, oy := math.Pi, math.Pi | ||
| // get a latitude and longitude on the sphere from the original projected point | ||
| lat, lon := original.Inverse(ox, oy) | ||
| // get a projected point in the desired projection | ||
| cx, cy := target.Project(lat, lon) | ||
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| fmt.Printf("original x, y: %f, %f\n", ox, oy) | ||
| fmt.Printf("target x, y: %f, %f\n", cx, cy) | ||
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| // Output: original x, y: 3.141593, 3.141593 | ||
| // target x, y: 0.000000, 1.657170 | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,116 @@ | ||
| package flatsphere | ||
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| import ( | ||
| "math" | ||
| ) | ||
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| // A compromise azimuthal projection stretched into an elliptical shape. | ||
| // https://en.wikipedia.org/wiki/Aitoff_projection | ||
| type Aitoff struct{} | ||
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| func NewAitoff() Aitoff { | ||
| return Aitoff{} | ||
| } | ||
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| func (ai Aitoff) Project(lat float64, lon float64) (float64, float64) { | ||
| a := math.Acos(math.Cos(lat) * math.Cos(lon/2)) | ||
| if a == 0 { | ||
| return 0, 0 | ||
| } | ||
| x := 2 * math.Cos(lat) * math.Sin(lon/2) * a / math.Sin(a) | ||
| y := math.Sin(lat) * a / math.Sin(a) | ||
| return x, y | ||
| } | ||
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| func (ai Aitoff) Inverse(x float64, y float64) (float64, float64) { | ||
| interLat, interLon := NewPolar().Inverse(x/2, y) | ||
| transLat, transLon := NewObliqueAspect(0, 0, 0).TransformToOblique(interLat, interLon) | ||
| return transLat, transLon * 2 | ||
| } | ||
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| func (a Aitoff) PlanarBounds() Bounds { | ||
| return NewEllipseBounds(math.Pi, math.Pi/2) | ||
| } | ||
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| // An elliptical equal-area projection. | ||
| // https://en.wikipedia.org/wiki/Hammer_projection | ||
| type Hammer struct{} | ||
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| func NewHammer() Hammer { | ||
| return Hammer{} | ||
| } | ||
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| func (h Hammer) Project(lat float64, lon float64) (float64, float64) { | ||
| z := math.Sqrt(1 + math.Cos(lat)*math.Cos(lon/2)) | ||
| x := 2 * math.Cos(lat) * math.Sin(lon/2) / z | ||
| y := math.Sin(lat) / z | ||
| return x, y | ||
| } | ||
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| func (h Hammer) Inverse(x float64, y float64) (float64, float64) { | ||
| z := math.Sqrt(1 - x*x/8 - y*y/2) | ||
| shift := 0.0 | ||
| if math.Hypot(x/2, y) > 1 { | ||
| shift = 2 * math.Pi | ||
| if math.Signbit(x) { | ||
| shift = -shift | ||
| } | ||
| } | ||
| preAsin := z * y * math.Sqrt2 | ||
| if preAsin > 1 && preAsin < 1+1e-9 { | ||
| preAsin = 1 | ||
| } | ||
| if preAsin < -1 && preAsin > -1-1e-9 { | ||
| preAsin = -1 | ||
| } | ||
| lat := math.Asin(preAsin) | ||
| lon := 2*math.Atan(math.Sqrt(0.5)*z*x/(2*z*z-1)) + shift | ||
| return lat, lon | ||
| } | ||
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| func (h Hammer) PlanarBounds() Bounds { | ||
| return NewEllipseBounds(2, 1) | ||
| } | ||
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| // A circular conformal projection of the whole earth. | ||
| type Lagrange struct{} | ||
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| func NewLagrange() Lagrange { | ||
| return Lagrange{} | ||
| } | ||
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| func (l Lagrange) Project(lat float64, lon float64) (float64, float64) { | ||
| p := (1 + math.Sin(lat)) / (1 - math.Sin(lat)) | ||
| v := math.Pow(p, 0.25) | ||
| c := (v+1/v)/2 + math.Cos(lon/2) | ||
| if math.IsInf(c, 0) { | ||
| if math.Signbit(lat) { | ||
| return 0, -1 | ||
| } else { | ||
| return 0, 1 | ||
| } | ||
| } | ||
| x := math.Sin(lon/2) / c | ||
| y := (v - 1/v) / (2 * c) | ||
| return x, y | ||
| } | ||
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| func (l Lagrange) Inverse(x float64, y float64) (float64, float64) { | ||
| r2 := x*x + y*y | ||
| th := 2 * y / (1 + r2) | ||
| if th == 1 { | ||
| if math.Signbit(y) { | ||
| return -math.Pi / 2, 0 | ||
| } else { | ||
| return math.Pi / 2, 0 | ||
| } | ||
| } | ||
| t := math.Pow((1+th)/(1-th), 2) | ||
| lat := math.Asin((t - 1) / (t + 1)) | ||
| lon := 2 * math.Atan2(2*x, 1-r2) | ||
| return lat, lon | ||
| } | ||
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| func (l Lagrange) PlanarBounds() Bounds { | ||
| return NewCircleBounds(1) | ||
| } |
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