Class Angle


  • public class Angle
    extends java.lang.Object
    Utility functions for working with angles. Unless otherwise noted, methods in this class express angles in radians.
    • Field Summary

      Fields 
      Modifier and Type Field Description
      static int CLOCKWISE
      Constant representing clockwise orientation
      static int COUNTERCLOCKWISE
      Constant representing counterclockwise orientation
      static int NONE
      Constant representing no orientation
      static double PI_OVER_2
      The value of Pi/2
      static double PI_OVER_4
      The value of Pi/4
      static double PI_TIMES_2
      The value of 2*Pi
    • Method Summary

      All Methods Static Methods Concrete Methods 
      Modifier and Type Method Description
      static double angle​(Coordinate p)
      Returns the angle of the vector from (0,0) to p, relative to the positive X-axis.
      static double angle​(Coordinate p0, Coordinate p1)
      Returns the angle of the vector from p0 to p1, relative to the positive X-axis.
      static double angleBetween​(Coordinate tip1, Coordinate tail, Coordinate tip2)
      Returns the unoriented smallest angle between two vectors.
      static double angleBetweenOriented​(Coordinate tip1, Coordinate tail, Coordinate tip2)
      Returns the oriented smallest angle between two vectors.
      static double bisector​(Coordinate tip1, Coordinate tail, Coordinate tip2)
      Computes the angle of the unoriented bisector of the smallest angle between two vectors.
      static double diff​(double ang1, double ang2)
      Computes the unoriented smallest difference between two angles.
      static int getTurn​(double ang1, double ang2)
      Returns whether an angle must turn clockwise or counterclockwise to overlap another angle.
      static double interiorAngle​(Coordinate p0, Coordinate p1, Coordinate p2)
      Computes the interior angle between two segments of a ring.
      static boolean isAcute​(Coordinate p0, Coordinate p1, Coordinate p2)
      Tests whether the angle between p0-p1-p2 is acute.
      static boolean isObtuse​(Coordinate p0, Coordinate p1, Coordinate p2)
      Tests whether the angle between p0-p1-p2 is obtuse.
      static double normalize​(double angle)
      Computes the normalized value of an angle, which is the equivalent angle in the range ( -Pi, Pi ].
      static double normalizePositive​(double angle)
      Computes the normalized positive value of an angle, which is the equivalent angle in the range [ 0, 2*Pi ).
      static Coordinate project​(Coordinate p, double angle, double dist)
      Projects a point by a given angle and distance.
      static double toDegrees​(double radians)
      Converts from radians to degrees.
      static double toRadians​(double angleDegrees)
      Converts from degrees to radians.
      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
    • Field Detail

      • COUNTERCLOCKWISE

        public static final int COUNTERCLOCKWISE
        Constant representing counterclockwise orientation
        See Also:
        Constant Field Values
      • CLOCKWISE

        public static final int CLOCKWISE
        Constant representing clockwise orientation
        See Also:
        Constant Field Values
      • NONE

        public static final int NONE
        Constant representing no orientation
        See Also:
        Constant Field Values
    • Method Detail

      • toDegrees

        public static double toDegrees​(double radians)
        Converts from radians to degrees.
        Parameters:
        radians - an angle in radians
        Returns:
        the angle in degrees
      • toRadians

        public static double toRadians​(double angleDegrees)
        Converts from degrees to radians.
        Parameters:
        angleDegrees - an angle in degrees
        Returns:
        the angle in radians
      • angle

        public static double angle​(Coordinate p0,
                                   Coordinate p1)
        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 ].
        Parameters:
        p0 - the initial point of the vector
        p1 - the terminal point of the vector
        Returns:
        the normalized angle (in radians) that p0-p1 makes with the positive x-axis.
      • angle

        public static double angle​(Coordinate p)
        Returns the angle of the vector from (0,0) to p, relative to the positive X-axis. The angle is normalized to be in the range ( -Pi, Pi ].
        Parameters:
        p - the terminal point of the vector
        Returns:
        the normalized angle (in radians) that p makes with the positive x-axis.
      • isAcute

        public static boolean isAcute​(Coordinate p0,
                                      Coordinate p1,
                                      Coordinate p2)
        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.

        Parameters:
        p0 - an endpoint of the angle
        p1 - the base of the angle
        p2 - the other endpoint of the angle
        Returns:
        true if the angle is acute
      • isObtuse

        public static boolean isObtuse​(Coordinate p0,
                                       Coordinate p1,
                                       Coordinate 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.

        Parameters:
        p0 - an endpoint of the angle
        p1 - the base of the angle
        p2 - the other endpoint of the angle
        Returns:
        true if the angle is obtuse
      • angleBetween

        public static double angleBetween​(Coordinate tip1,
                                          Coordinate tail,
                                          Coordinate tip2)
        Returns the unoriented smallest angle between two vectors. The computed angle will be in the range [0, Pi).
        Parameters:
        tip1 - the tip of one vector
        tail - the tail of each vector
        tip2 - the tip of the other vector
        Returns:
        the angle between tail-tip1 and tail-tip2
      • angleBetweenOriented

        public static double angleBetweenOriented​(Coordinate tip1,
                                                  Coordinate tail,
                                                  Coordinate 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 (CCW) rotation from v1 to v2; a negative result corresponds to a clockwise (CW) rotation; a zero result corresponds to no rotation.
        Parameters:
        tip1 - the tip of v1
        tail - the tail of each vector
        tip2 - the tip of v2
        Returns:
        the angle between v1 and v2, relative to v1
      • bisector

        public static double bisector​(Coordinate tip1,
                                      Coordinate tail,
                                      Coordinate tip2)
        Computes the angle of the unoriented bisector of the smallest angle between two vectors. The computed angle will be in the range (-Pi, Pi].
        Parameters:
        tip1 - the tip of v1
        tail - the tail of each vector
        tip2 - the tip of v2
        Returns:
        the angle of the bisector between v1 and v2
      • interiorAngle

        public static double interiorAngle​(Coordinate p0,
                                           Coordinate p1,
                                           Coordinate p2)
        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]
        Parameters:
        p0 - a point of the ring
        p1 - the next point of the ring
        p2 - the next point of the ring
        Returns:
        the interior angle based at p1
      • getTurn

        public static int getTurn​(double ang1,
                                  double ang2)
        Returns whether an angle must turn clockwise or counterclockwise to overlap another angle.
        Parameters:
        ang1 - an angle (in radians)
        ang2 - an angle (in radians)
        Returns:
        whether a1 must turn CLOCKWISE, COUNTERCLOCKWISE or NONE to overlap a2.
      • normalize

        public static double normalize​(double angle)
        Computes the normalized value of an angle, which is the equivalent angle in the range ( -Pi, Pi ].
        Parameters:
        angle - the angle to normalize
        Returns:
        an equivalent angle in the range (-Pi, Pi]
      • normalizePositive

        public static double normalizePositive​(double angle)
        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
        Parameters:
        angle - the angle to normalize, in radians
        Returns:
        an equivalent positive angle
      • diff

        public static double diff​(double ang1,
                                  double ang2)
        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].
        Parameters:
        ang1 - the angle of one vector (in [-Pi, Pi] )
        ang2 - the angle of the other vector (in range [-Pi, Pi] )
        Returns:
        the angle (in radians) between the two vectors (in range [0, Pi] )
      • project

        public static Coordinate project​(Coordinate p,
                                         double angle,
                                         double dist)
        Projects a point by a given angle and distance.
        Parameters:
        p - the point to project
        angle - the angle at which to project
        dist - the distance to project
        Returns:
        the projected point