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Diffstat (limited to 'vendor/github.com/golang/geo/s2/projections.go')
| -rw-r--r-- | vendor/github.com/golang/geo/s2/projections.go | 241 |
1 files changed, 0 insertions, 241 deletions
diff --git a/vendor/github.com/golang/geo/s2/projections.go b/vendor/github.com/golang/geo/s2/projections.go deleted file mode 100644 index f7273609c..000000000 --- a/vendor/github.com/golang/geo/s2/projections.go +++ /dev/null @@ -1,241 +0,0 @@ -// Copyright 2018 Google Inc. All rights reserved. -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -package s2 - -import ( - "math" - - "github.com/golang/geo/r2" - "github.com/golang/geo/s1" -) - -// Projection defines an interface for different ways of mapping between s2 and r2 Points. -// It can also define the coordinate wrapping behavior along each axis. -type Projection interface { - // Project converts a point on the sphere to a projected 2D point. - Project(p Point) r2.Point - - // Unproject converts a projected 2D point to a point on the sphere. - // - // If wrapping is defined for a given axis (see below), then this method - // should accept any real number for the corresponding coordinate. - Unproject(p r2.Point) Point - - // FromLatLng is a convenience function equivalent to Project(LatLngToPoint(ll)), - // but the implementation is more efficient. - FromLatLng(ll LatLng) r2.Point - - // ToLatLng is a convenience function equivalent to LatLngFromPoint(Unproject(p)), - // but the implementation is more efficient. - ToLatLng(p r2.Point) LatLng - - // Interpolate returns the point obtained by interpolating the given - // fraction of the distance along the line from A to B. - // Fractions < 0 or > 1 result in extrapolation instead. - Interpolate(f float64, a, b r2.Point) r2.Point - - // WrapDistance reports the coordinate wrapping distance along each axis. - // If this value is non-zero for a given axis, the coordinates are assumed - // to "wrap" with the given period. For example, if WrapDistance.Y == 360 - // then (x, y) and (x, y + 360) should map to the same Point. - // - // This information is used to ensure that edges takes the shortest path - // between two given points. For example, if coordinates represent - // (latitude, longitude) pairs in degrees and WrapDistance().Y == 360, - // then the edge (5:179, 5:-179) would be interpreted as spanning 2 degrees - // of longitude rather than 358 degrees. - // - // If a given axis does not wrap, its WrapDistance should be set to zero. - WrapDistance() r2.Point - - // WrapDestination that wraps the coordinates of B if necessary in order to - // obtain the shortest edge AB. For example, suppose that A = [170, 20], - // B = [-170, 20], and the projection wraps so that [x, y] == [x + 360, y]. - // Then this function would return [190, 20] for point B (reducing the edge - // length in the "x" direction from 340 to 20). - WrapDestination(a, b r2.Point) r2.Point - - // We do not support implementations of this interface outside this package. - privateInterface() -} - -// PlateCarreeProjection defines the "plate carree" (square plate) projection, -// which converts points on the sphere to (longitude, latitude) pairs. -// Coordinates can be scaled so that they represent radians, degrees, etc, but -// the projection is always centered around (latitude=0, longitude=0). -// -// Note that (x, y) coordinates are backwards compared to the usual (latitude, -// longitude) ordering, in order to match the usual convention for graphs in -// which "x" is horizontal and "y" is vertical. -type PlateCarreeProjection struct { - xWrap float64 - toRadians float64 // Multiplier to convert coordinates to radians. - fromRadians float64 // Multiplier to convert coordinates from radians. -} - -// NewPlateCarreeProjection constructs a plate carree projection where the -// x-coordinates (lng) span [-xScale, xScale] and the y coordinates (lat) -// span [-xScale/2, xScale/2]. For example if xScale==180 then the x -// range is [-180, 180] and the y range is [-90, 90]. -// -// By default coordinates are expressed in radians, i.e. the x range is -// [-Pi, Pi] and the y range is [-Pi/2, Pi/2]. -func NewPlateCarreeProjection(xScale float64) Projection { - return &PlateCarreeProjection{ - xWrap: 2 * xScale, - toRadians: math.Pi / xScale, - fromRadians: xScale / math.Pi, - } -} - -// Project converts a point on the sphere to a projected 2D point. -func (p *PlateCarreeProjection) Project(pt Point) r2.Point { - return p.FromLatLng(LatLngFromPoint(pt)) -} - -// Unproject converts a projected 2D point to a point on the sphere. -func (p *PlateCarreeProjection) Unproject(pt r2.Point) Point { - return PointFromLatLng(p.ToLatLng(pt)) -} - -// FromLatLng returns the LatLng projected into an R2 Point. -func (p *PlateCarreeProjection) FromLatLng(ll LatLng) r2.Point { - return r2.Point{ - X: p.fromRadians * ll.Lng.Radians(), - Y: p.fromRadians * ll.Lat.Radians(), - } -} - -// ToLatLng returns the LatLng projected from the given R2 Point. -func (p *PlateCarreeProjection) ToLatLng(pt r2.Point) LatLng { - return LatLng{ - Lat: s1.Angle(p.toRadians * pt.Y), - Lng: s1.Angle(p.toRadians * math.Remainder(pt.X, p.xWrap)), - } -} - -// Interpolate returns the point obtained by interpolating the given -// fraction of the distance along the line from A to B. -func (p *PlateCarreeProjection) Interpolate(f float64, a, b r2.Point) r2.Point { - return a.Mul(1 - f).Add(b.Mul(f)) -} - -// WrapDistance reports the coordinate wrapping distance along each axis. -func (p *PlateCarreeProjection) WrapDistance() r2.Point { - return r2.Point{p.xWrap, 0} -} - -// WrapDestination wraps the points if needed to get the shortest edge. -func (p *PlateCarreeProjection) WrapDestination(a, b r2.Point) r2.Point { - return wrapDestination(a, b, p.WrapDistance) -} - -func (p *PlateCarreeProjection) privateInterface() {} - -// MercatorProjection defines the spherical Mercator projection. Google Maps -// uses this projection together with WGS84 coordinates, in which case it is -// known as the "Web Mercator" projection (see Wikipedia). This class makes -// no assumptions regarding the coordinate system of its input points, but -// simply applies the spherical Mercator projection to them. -// -// The Mercator projection is finite in width (x) but infinite in height (y). -// "x" corresponds to longitude, and spans a finite range such as [-180, 180] -// (with coordinate wrapping), while "y" is a function of latitude and spans -// an infinite range. (As "y" coordinates get larger, points get closer to -// the north pole but never quite reach it.) The north and south poles have -// infinite "y" values. (Note that this will cause problems if you tessellate -// a Mercator edge where one endpoint is a pole. If you need to do this, clip -// the edge first so that the "y" coordinate is no more than about 5 * maxX.) -type MercatorProjection struct { - xWrap float64 - toRadians float64 // Multiplier to convert coordinates to radians. - fromRadians float64 // Multiplier to convert coordinates from radians. -} - -// NewMercatorProjection constructs a Mercator projection with the given maximum -// longitude axis value corresponding to a range of [-maxLng, maxLng]. -// The horizontal and vertical axes are scaled equally. -func NewMercatorProjection(maxLng float64) Projection { - return &MercatorProjection{ - xWrap: 2 * maxLng, - toRadians: math.Pi / maxLng, - fromRadians: maxLng / math.Pi, - } -} - -// Project converts a point on the sphere to a projected 2D point. -func (p *MercatorProjection) Project(pt Point) r2.Point { - return p.FromLatLng(LatLngFromPoint(pt)) -} - -// Unproject converts a projected 2D point to a point on the sphere. -func (p *MercatorProjection) Unproject(pt r2.Point) Point { - return PointFromLatLng(p.ToLatLng(pt)) -} - -// FromLatLng returns the LatLng projected into an R2 Point. -func (p *MercatorProjection) FromLatLng(ll LatLng) r2.Point { - // This formula is more accurate near zero than the log(tan()) version. - // Note that latitudes of +/- 90 degrees yield "y" values of +/- infinity. - sinPhi := math.Sin(float64(ll.Lat)) - y := 0.5 * math.Log((1+sinPhi)/(1-sinPhi)) - return r2.Point{p.fromRadians * float64(ll.Lng), p.fromRadians * y} -} - -// ToLatLng returns the LatLng projected from the given R2 Point. -func (p *MercatorProjection) ToLatLng(pt r2.Point) LatLng { - // This formula is more accurate near zero than the atan(exp()) version. - x := p.toRadians * math.Remainder(pt.X, p.xWrap) - k := math.Exp(2 * p.toRadians * pt.Y) - var y float64 - if math.IsInf(k, 0) { - y = math.Pi / 2 - } else { - y = math.Asin((k - 1) / (k + 1)) - } - return LatLng{s1.Angle(y), s1.Angle(x)} -} - -// Interpolate returns the point obtained by interpolating the given -// fraction of the distance along the line from A to B. -func (p *MercatorProjection) Interpolate(f float64, a, b r2.Point) r2.Point { - return a.Mul(1 - f).Add(b.Mul(f)) -} - -// WrapDistance reports the coordinate wrapping distance along each axis. -func (p *MercatorProjection) WrapDistance() r2.Point { - return r2.Point{p.xWrap, 0} -} - -// WrapDestination wraps the points if needed to get the shortest edge. -func (p *MercatorProjection) WrapDestination(a, b r2.Point) r2.Point { - return wrapDestination(a, b, p.WrapDistance) -} - -func (p *MercatorProjection) privateInterface() {} - -func wrapDestination(a, b r2.Point, wrapDistance func() r2.Point) r2.Point { - wrap := wrapDistance() - x := b.X - y := b.Y - // The code below ensures that "b" is unmodified unless wrapping is required. - if wrap.X > 0 && math.Abs(x-a.X) > 0.5*wrap.X { - x = a.X + math.Remainder(x-a.X, wrap.X) - } - if wrap.Y > 0 && math.Abs(y-a.Y) > 0.5*wrap.Y { - y = a.Y + math.Remainder(y-a.Y, wrap.Y) - } - return r2.Point{x, y} -} |