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/********************************************************************** * * GEOS - Geometry Engine Open Source * http://geos.osgeo.org * * Copyright (C) 2009-2011 Sandro Santilli * * This is free software; you can redistribute and/or modify it under * the terms of the GNU Lesser General Public Licence as published * by the Free Software Foundation. * See the COPYING file for more information. * ********************************************************************** * * Last port: algorithm/Angle.java r378 (JTS-1.12) * **********************************************************************/ #pragma once #include #include // for constants // Forward declarations namespace geos { namespace geom { class Coordinate; } } namespace geos { namespace algorithm { // geos::algorithm /// Utility functions for working with angles. // /// Unless otherwise noted, methods in this class express angles in radians. /// class GEOS_DLL Angle { public: static constexpr double PI_TIMES_2 = 2.0 * MATH_PI; static constexpr double PI_OVER_2 = MATH_PI / 2.0; static constexpr double PI_OVER_4 = MATH_PI / 4.0; /// Constant representing counterclockwise orientation static const int COUNTERCLOCKWISE = Orientation::COUNTERCLOCKWISE; /// Constant representing clockwise orientation static const int CLOCKWISE = Orientation::CLOCKWISE; /// Constant representing no orientation static const int NONE = Orientation::COLLINEAR; /// Converts from radians to degrees. /// /// @param radians an angle in radians /// @return the angle in degrees /// static double toDegrees(double radians); /// Converts from degrees to radians. /// /// @param angleDegrees an angle in degrees /// @return the angle in radians /// static double toRadians(double angleDegrees); /// \brief /// Returns the angle of the vector from p0 to p1, /// relative to the positive X-axis. /// /// The angle is normalized to be in the range [ -Pi, Pi ]. /// /// @return the normalized angle (in radians) that p0-p1 makes /// with the positive x-axis. /// static double angle(const geom::CoordinateXY& p0, const geom::CoordinateXY& p1); /// \brief /// Returns the angle that the vector from (0,0) to p, /// relative to the positive X-axis. // /// The angle is normalized to be in the range ( -Pi, Pi ]. /// /// @return the normalized angle (in radians) that p makes /// with the positive x-axis. /// static double angle(const geom::CoordinateXY& p); /// Tests whether the angle between p0-p1-p2 is acute. /// /// An angle is acute if it is less than 90 degrees. /// /// Note: this implementation is not precise (deterministic) for /// angles very close to 90 degrees. /// /// @param p0 an endpoint of the angle /// @param p1 the base of the angle /// @param p2 the other endpoint of the angle /// static bool isAcute(const geom::CoordinateXY& p0, const geom::CoordinateXY& p1, const geom::CoordinateXY& p2); /// Tests whether the angle between p0-p1-p2 is obtuse. /// /// An angle is obtuse if it is greater than 90 degrees. /// /// Note: this implementation is not precise (deterministic) for /// angles very close to 90 degrees. /// /// @param p0 an endpoint of the angle /// @param p1 the base of the angle /// @param p2 the other endpoint of the angle /// static bool isObtuse(const geom::CoordinateXY& p0, const geom::CoordinateXY& p1, const geom::CoordinateXY& p2); /// Returns the unoriented smallest angle between two vectors. /// /// The computed angle will be in the range [0, Pi). /// /// @param tip1 the tip of one vector /// @param tail the tail of each vector /// @param tip2 the tip of the other vector /// @return the angle between tail-tip1 and tail-tip2 /// static double angleBetween(const geom::CoordinateXY& tip1, const geom::CoordinateXY& tail, const geom::CoordinateXY& tip2); /// Returns the oriented smallest angle between two vectors. /// /// The computed angle will be in the range (-Pi, Pi]. /// A positive result corresponds to a counterclockwise rotation /// from v1 to v2; /// a negative result corresponds to a clockwise rotation. /// /// @param tip1 the tip of v1 /// @param tail the tail of each vector /// @param tip2 the tip of v2 /// @return the angle between v1 and v2, relative to v1 /// static double angleBetweenOriented(const geom::CoordinateXY& tip1, const geom::CoordinateXY& tail, const geom::CoordinateXY& tip2); /// Computes the interior angle between two segments of a ring. /// /// The ring is assumed to be oriented in a clockwise direction. /// The computed angle will be in the range [0, 2Pi] /// /// @param p0 /// a point of the ring /// @param p1 /// the next point of the ring /// @param p2 /// the next point of the ring /// @return the interior angle based at p1 /// static double interiorAngle(const geom::CoordinateXY& p0, const geom::CoordinateXY& p1, const geom::CoordinateXY& p2); /// \brief /// Returns whether an angle must turn clockwise or counterclockwise /// to overlap another angle. /// /// @param ang1 an angle (in radians) /// @param ang2 an angle (in radians) /// @return whether a1 must turn CLOCKWISE, COUNTERCLOCKWISE or /// NONE to overlap a2. /// static int getTurn(double ang1, double ang2); /// \brief /// Computes the normalized value of an angle, which is the /// equivalent angle in the range ( -Pi, Pi ]. /// /// @param angle the angle to normalize /// @return an equivalent angle in the range (-Pi, Pi] /// static double normalize(double angle); /// \brief /// Computes the normalized positive value of an angle, /// which is the equivalent angle in the range [ 0, 2*Pi ). /// /// E.g.: /// - normalizePositive(0.0) = 0.0 /// - normalizePositive(-PI) = PI /// - normalizePositive(-2PI) = 0.0 /// - normalizePositive(-3PI) = PI /// - normalizePositive(-4PI) = 0 /// - normalizePositive(PI) = PI /// - normalizePositive(2PI) = 0.0 /// - normalizePositive(3PI) = PI /// - normalizePositive(4PI) = 0.0 /// /// @param angle the angle to normalize, in radians /// @return an equivalent positive angle /// static double normalizePositive(double angle); /// Computes the unoriented smallest difference between two angles. /// /// The angles are assumed to be normalized to the range [-Pi, Pi]. /// The result will be in the range [0, Pi]. /// /// @param ang1 the angle of one vector (in [-Pi, Pi] ) /// @param ang2 the angle of the other vector (in range [-Pi, Pi] ) /// @return the angle (in radians) between the two vectors /// (in range [0, Pi] ) /// static double diff(double ang1, double ang2); /// \brief /// Computes both sin and cos of an angle, snapping near-zero values /// to zero. /// /// The angle does not need to be normalized. Unlike std::sin /// and std::cos, this method will snap near-zero values to zero /// for (e.g.) sin(pi) and cos(pi/2). /// /// @param ang the input angle (in radians) /// @param rSin the result of sin(ang) /// @param rCos the result of cos(ang) /// static inline void sinCosSnap(const double ang, double& rSin, double& rCos) { // calculate both; may be optimized with FSINCOS instruction rSin = std::sin(ang); rCos = std::cos(ang); // snap near-zero values if (std::fabs(rSin) < 5e-16) rSin = 0.0; if (std::fabs(rCos) < 5e-16) rCos = 0.0; } }; } // namespace geos::algorithm } // namespace geos