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114 lines
5.1 KiB
C++
114 lines
5.1 KiB
C++
// Copyright 2008, Google Inc. All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are met:
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//
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// 1. Redistributions of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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// 2. Redistributions in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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// 3. Neither the name of Google Inc. nor the names of its contributors may be
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// used to endorse or promote products derived from this software without
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// specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED
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// WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
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// EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
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// OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
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// WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
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// ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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// This file contains the declarations of some mathematical functions useful
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// when working with KML or, more generally, geometry on a Great Circle.
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//
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// Many of the formulae here were cribbed from the excellent Aviation
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// Formulary: http://williams.best.vwh.net/avform.htm
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//
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// NOTE: with the exception of the functions explicitly for converting between
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// units, all functions here accept and return coordinates and angles in
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// decimal degrees, and distances in meters.
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#ifndef KML_BASE_MATH_UTIL_H__
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#define KML_BASE_MATH_UTIL_H__
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#include <math.h>
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// At least one variant of MSVC does not define M_PI.
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#ifndef M_PI
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#define M_PI 3.14159265358979323846
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#endif
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#include <utility>
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#include "kml/base/vec3.h"
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namespace kmlbase {
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// Returns the initial azimuth (the angle measured clockwise from true north)
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// at a point from that point to a second point. For example, the azimuth
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// from 0,0 to 1,0 is 0 degrees. From 0,0 to 0,1 is 90 degrees (due east).
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// The range of the result is (-180, 180].
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//
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// This is directly useful as the value of <heading> in KML's AbstractView.
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//
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// Note that this is the _initial_ azimuth; it changes as one follows the
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// great circle path from point 1 to point2.
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double AzimuthBetweenPoints(double lat_from, double lng_from,
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double lat_to, double lng_to);
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// Returns the angle from the horizontal plane between alt1 and alt2.
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// For example, the returned angle from (37.00, -121.98, 600) to a point
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// about 1778 meters west, 400 meters below at (37.00, -122.00, 200) is
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// -12.7 degrees.
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//
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// To use this as the value of KML's <tilt>, add 90 degrees (since in KML a
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// tilt of 0 is vertical.
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//
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// TODO: this is a naive implementation accurate only over short distances.
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// It does not yet account for surface curvature.
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double ElevationBetweenPoints(double lat_from, double lng_from, double alt_from,
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double lat_to, double lng_to, double alt_to);
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// Returns the great circle distance in meters between two points on the
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// Earth's surface. The antemeridian is not considered here.
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double DistanceBetweenPoints(double lat_from, double lng_from,
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double lat_to, double lng_to);
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// Returns the great circle distance in meters between two 3d points. The
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// antemeridian is not considered here.
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double DistanceBetweenPoints3d(
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double lat_from, double lng_from, double alt_from,
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double lat_to, double lng_to, double alt_to);
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// Given a vector describing a line at an angle from the horizontal plane,
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// where the vector starts at a point on the surface of the Earth,
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// returns the absolute distance between the ground point and the point
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// directly under the end point.
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double GroundDistanceFromRangeAndElevation(double range, double elevation);
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// Given a vector describing a line at an angle from the horizontal plane,
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// where the vector starts at a point on the surface of the Earth,
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// returns the absolute height between the end point and the surface
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// point directly under it.
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double HeightFromRangeAndElevation(double range, double elevation);
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// Returns a Vec3 containing the latitude and longitude of a point at a
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// distance (meters) out on the radial (degrees) from a center point lat, lng.
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// The radial is measured clockwise from north. The antemeridian is not
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// considered here.
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Vec3 LatLngOnRadialFromPoint(double lat, double lng,
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double distance, double radial);
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// These functions are mostly internal, used in converting between degrees and
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// radians.
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double DegToRad(double degrees);
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double RadToDeg(double radians);
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double MetersToRadians(double meters);
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double RadiansToMeters(double radians);
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} // end namespace kmlbase
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#endif // KML_BASE_MATH_UTIL_H__
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