/**********************************************************************
*
* GEOS - Geometry Engine Open Source
* http://geos.osgeo.org
*
* Copyright (C) 2009-2011 Sandro Santilli <strk@kbt.io>
*
* 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 <geos/export.h>
#include <geos/algorithm/Orientation.h> // 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 <code>p1</code>
///
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