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