diff options
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, 241 insertions, 0 deletions
diff --git a/vendor/github.com/golang/geo/s2/projections.go b/vendor/github.com/golang/geo/s2/projections.go new file mode 100644 index 000000000..f7273609c --- /dev/null +++ b/vendor/github.com/golang/geo/s2/projections.go @@ -0,0 +1,241 @@ +// 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} +} |