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Oblique projections, distortion (#1)
* Oblique projection transform * More usage on readme * A couple more azimuthal projections, distortion calculations, big README update
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,135 @@ | ||
| package flatsphere | ||
|
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||
| import ( | ||
| "math" | ||
| ) | ||
|
|
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| type ObliqueProjection struct { | ||
| orig Projection | ||
| poleLat float64 | ||
| poleLon float64 | ||
| poleTheta float64 | ||
|
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| sinPoleLat float64 // cached precompute of sin(poleLat) | ||
| cosPoleLat float64 // cached precompute of cos(poleLat) | ||
| } | ||
|
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| func NewObliqueProjection(original Projection, poleLat float64, poleLon float64, poleTheta float64) ObliqueProjection { | ||
| return ObliqueProjection{ | ||
| orig: original, | ||
| poleLat: poleLat, | ||
| poleLon: poleLon, | ||
| poleTheta: poleTheta, | ||
| sinPoleLat: math.Sin(poleLat), | ||
| cosPoleLat: math.Cos(poleLat), | ||
| } | ||
| } | ||
|
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| func (o ObliqueProjection) Project(latitude float64, longitude float64) (float64, float64) { | ||
| return o.orig.Project(o.TransformFromOblique(latitude, longitude)) | ||
| } | ||
|
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| func (o ObliqueProjection) Inverse(x float64, y float64) (float64, float64) { | ||
| return o.TransformToOblique(o.orig.Inverse(x, y)) | ||
| } | ||
|
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| func (o ObliqueProjection) PlanarBounds() Bounds { | ||
| return o.orig.PlanarBounds() | ||
| } | ||
|
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| // Applies the pole shift and rotation of the Oblique projection transform to the given | ||
| // input latitude and longitude points, so that the returned latitude/longitude are able | ||
| // to be used for the non-transformed 'original' projection. | ||
| func (o ObliqueProjection) TransformFromOblique(latitude float64, longitude float64) (float64, float64) { | ||
| var newLat, newLon float64 | ||
|
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| poleRelCos := math.Cos(o.poleLon - longitude) | ||
|
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| // relative latitude | ||
| if o.poleLat == math.Pi/2 { | ||
| newLat = latitude | ||
| } else { | ||
| preAsin := o.sinPoleLat*math.Sin(latitude) + o.cosPoleLat*math.Cos(latitude)*poleRelCos | ||
| if preAsin > 1 && preAsin < 1+1e-9 { | ||
| preAsin = 1 | ||
| } | ||
| newLat = math.Asin(preAsin) | ||
| } | ||
|
|
||
| // relative longitude | ||
| if o.poleLat == math.Pi/2 { | ||
| newLon = longitude - o.poleLon | ||
| } else if o.poleLat == -math.Pi/2 { | ||
| newLon = o.poleLon - longitude - math.Pi | ||
| } else { | ||
| numer := o.cosPoleLat*math.Sin(latitude) - o.sinPoleLat*math.Cos(latitude)*poleRelCos | ||
| denom := math.Cos(newLat) | ||
| newLon = math.Acos(numer/denom) - math.Pi | ||
|
|
||
| if math.IsNaN(newLon) { | ||
| if (poleRelCos >= 0 && latitude < o.poleLat) || (poleRelCos < 0 && latitude < -o.poleLat) { | ||
| newLon = 0 | ||
| } else { | ||
| newLon = -math.Pi | ||
| } | ||
| } else if math.Sin(longitude-o.poleLon) > 0 { | ||
| newLon = -newLon | ||
| } | ||
| } | ||
|
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| // apply rotate | ||
| newLon = newLon - o.poleTheta | ||
|
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| // constrain and kill roundoff error | ||
| if math.Abs(newLon) > math.Pi { | ||
| newLon = coerceAngle(newLon) | ||
| } | ||
| if newLon >= math.Pi-1e-7 { | ||
| newLon = -math.Pi | ||
| } | ||
|
|
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| return newLat, newLon | ||
| } | ||
|
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| func coerceAngle(angle float64) float64 { | ||
| x := angle + math.Pi | ||
| y := 2 * math.Pi | ||
| floorMod := x - math.Floor(x/y)*y | ||
| return floorMod - math.Pi | ||
| } | ||
|
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| // Given a latitude/longitude in the non-transformed 'original' projection space, applies | ||
| // the pole shift and rotation of the Oblique projection so that the returned latitude/longitude | ||
| // are in the Oblique projection space. | ||
| func (o ObliqueProjection) TransformToOblique(latitude float64, longitude float64) (float64, float64) { | ||
| rotateLon := longitude + o.poleTheta | ||
|
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| preAsin := o.sinPoleLat*math.Sin(latitude) - o.cosPoleLat*math.Cos(latitude)*math.Cos(rotateLon) | ||
| if preAsin > 1 && preAsin < 1+1e-9 { | ||
| preAsin = 1 | ||
| } | ||
| if preAsin < -1 && preAsin > -1-1e-9 { | ||
| preAsin = -1 | ||
| } | ||
| newLat := math.Asin(preAsin) | ||
| var newLon float64 | ||
| inner := math.Sin(latitude)/o.cosPoleLat/math.Cos(newLat) - math.Tan(o.poleLat)*math.Tan(newLat) | ||
| if o.poleLat == -math.Pi/2 { | ||
| newLon = o.poleLon + rotateLon | ||
| } else if math.Abs(inner) > 1 { | ||
| if (rotateLon == 0 && latitude < -o.poleLat) || (rotateLon != 0 && latitude < o.poleLat) { | ||
| newLon = o.poleLon + math.Pi | ||
| } else { | ||
| newLon = o.poleLon | ||
| } | ||
| } else if math.Sin(rotateLon) > 0 { | ||
| newLon = o.poleLon + math.Acos(inner) | ||
| } else { | ||
| newLon = o.poleLon - math.Acos(inner) | ||
| } | ||
|
|
||
| if math.Abs(newLon) > math.Pi { | ||
| newLon = coerceAngle(newLon) | ||
| } | ||
| return newLat, newLon | ||
| } |
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