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