org.apache.commons.math3.geometry.euclidean.twod

## Class Line

- java.lang.Object
- - org.apache.commons.math3.geometry.euclidean.twod.Line

- All Implemented Interfaces:
    Embedding<Euclidean2D,Euclidean1D>, Hyperplane<Euclidean2D>

      public class Line
      extends Object
      implements Hyperplane<Euclidean2D>, Embedding<Euclidean2D,Euclidean1D>

  This class represents an oriented line in the 2D plane.

  An oriented line can be defined either by prolongating a line segment between two points past these points, or by one point and an angular direction (in trigonometric orientation).

  Since it is oriented the two half planes at its two sides are unambiguously identified as a left half plane and a right half plane. This can be used to identify the interior and the exterior in a simple way by local properties only when part of a line is used to define part of a polygon boundary.

  A line can also be used to completely define a reference frame in the plane. It is sufficient to select one specific point in the line (the orthogonal projection of the original reference frame on the line) and to use the unit vector in the line direction and the orthogonal vector oriented from left half plane to right half plane. We define two coordinates by the process, the abscissa along the line, and the offset across the line. All points of the plane are uniquely identified by these two coordinates. The line is the set of points at zero offset, the left half plane is the set of points with negative offsets and the right half plane is the set of points with positive offsets.

  Since:
    3.0

- - ### Constructor Summary

    Constructors
    Constructor and Description
    `Line(Line line)` Copy constructor.
    `Line(Vector2D p, double angle)` Deprecated. as of 3.3, replaced with `Line(Vector2D, double, double)`
    `Line(Vector2D p, double angle, double tolerance)` Build a line from a point and an angle.
    `Line(Vector2D p1, Vector2D p2)` Deprecated. as of 3.3, replaced with `Line(Vector2D, Vector2D, double)`
    `Line(Vector2D p1, Vector2D p2, double tolerance)` Build a line from two points.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `boolean` | `contains(Vector2D p)` Check if the line contains a point.
    `Line` | `copySelf()` Copy the instance.
    `double` | `distance(Vector2D p)` Compute the distance between the instance and a point.
    `double` | `getAngle()` Get the angle of the line.
    `double` | `getOffset(Line line)` Get the offset (oriented distance) of a parallel line.
    `double` | `getOffset(Point<Euclidean2D> point)` Get the offset (oriented distance) of a point.
    `double` | `getOffset(Vector<Euclidean2D> vector)` Get the offset (oriented distance) of a vector.
    `double` | `getOriginOffset()` Get the offset of the origin.
    `Vector2D` | `getPointAt(Vector1D abscissa, double offset)` Get one point from the plane.
    `Line` | `getReverse()` Get the reverse of the instance.
    `double` | `getTolerance()` Get the tolerance below which points are considered to belong to the hyperplane.
    `static Transform<Euclidean2D,Euclidean1D>` | `getTransform(AffineTransform transform)` Deprecated. as of 3.6, replaced with `getTransform(double, double, double, double, double, double)`
    `static Transform<Euclidean2D,Euclidean1D>` | `getTransform(double cXX, double cYX, double cXY, double cYY, double cX1, double cY1)` Get a `Transform` embedding an affine transform.
    `Vector2D` | `intersection(Line other)` Get the intersection point of the instance and another line.
    `boolean` | `isParallelTo(Line line)` Check the instance is parallel to another line.
    `Point<Euclidean2D>` | `project(Point<Euclidean2D> point)` Project a point to the hyperplane.
    `void` | `reset(Vector2D p, double alpha)` Reset the instance as if built from a line and an angle.
    `void` | `reset(Vector2D p1, Vector2D p2)` Reset the instance as if built from two points.
    `void` | `revertSelf()` Revert the instance.
    `boolean` | `sameOrientationAs(Hyperplane<Euclidean2D> other)` Check if the instance has the same orientation as another hyperplane.
    `void` | `setAngle(double angle)` Set the angle of the line.
    `void` | `setOriginOffset(double offset)` Set the offset of the origin.
    `Vector2D` | `toSpace(Point<Euclidean1D> point)` Transform a sub-space point into a space point.
    `Vector2D` | `toSpace(Vector<Euclidean1D> vector)` Transform a sub-space point into a space point.
    `Vector1D` | `toSubSpace(Point<Euclidean2D> point)` Transform a space point into a sub-space point.
    `Vector1D` | `toSubSpace(Vector<Euclidean2D> vector)` Transform a space point into a sub-space point.
    `void` | `translateToPoint(Vector2D p)` Translate the line to force it passing by a point.
    `SubLine` | `wholeHyperplane()` Build a sub-hyperplane covering the whole hyperplane.
    `PolygonsSet` | `wholeSpace()` Build a region covering the whole space.

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Constructor Detail

    - #### Line

          public Line(Vector2D p1,
              Vector2D p2,
              double tolerance)

      Build a line from two points.

      The line is oriented from p1 to p2

      Parameters:
        `p1` - first point
        `p2` - second point
        `tolerance` - tolerance below which points are considered identical
      Since:
        3.3

    - #### Line

          public Line(Vector2D p,
              double angle,
              double tolerance)

      Build a line from a point and an angle.
      Parameters:
        `p` - point belonging to the line
        `angle` - angle of the line with respect to abscissa axis
        `tolerance` - tolerance below which points are considered identical
      Since:
        3.3

    - #### Line

          @Deprecated
          public Line(Vector2D p1,
                         Vector2D p2)

      Deprecated. as of 3.3, replaced with `Line(Vector2D, Vector2D, double)`
      Build a line from two points.

      The line is oriented from p1 to p2

      Parameters:
        `p1` - first point
        `p2` - second point

    - #### Line

          @Deprecated
          public Line(Vector2D p,
                         double angle)

      Deprecated. as of 3.3, replaced with `Line(Vector2D, double, double)`
      Build a line from a point and an angle.
      Parameters:
        `p` - point belonging to the line
        `angle` - angle of the line with respect to abscissa axis

    - #### Line

          public Line(Line line)

      Copy constructor.

      The created instance is completely independent from the original instance, it is a deep copy.

      Parameters:
        `line` - line to copy

  - ### Method Detail

    - #### copySelf

          public Line copySelf()

      Copy the instance.

      The instance created is completely independant of the original one. A deep copy is used, none of the underlying objects are shared (except for immutable objects).

      Specified by:
        `copySelf` in interface `Hyperplane<Euclidean2D>`
      Returns:
        a new hyperplane, copy of the instance

    - #### reset

          public void reset(Vector2D p1,
                   Vector2D p2)

      Reset the instance as if built from two points.

      The line is oriented from p1 to p2

      Parameters:
        `p1` - first point
        `p2` - second point

    - #### reset

          public void reset(Vector2D p,
                   double alpha)

      Reset the instance as if built from a line and an angle.
      Parameters:
        `p` - point belonging to the line
        `alpha` - angle of the line with respect to abscissa axis

    - #### revertSelf

          public void revertSelf()

      Revert the instance.

    - #### getReverse

          public Line getReverse()

      Get the reverse of the instance.

      Get a line with reversed orientation with respect to the instance.

      As long as neither the instance nor its reverse are modified (i.e. as long as none of the `reset(Vector2D, Vector2D)`, `reset(Vector2D, double)`, `revertSelf()`, `setAngle(double)` or `setOriginOffset(double)` methods are called), then the line and its reverse remain linked together so that `line.getReverse().getReverse() == line`. When one of the line is modified, the link is deleted as both instance becomes independent.

      Returns:
        a new line, with orientation opposite to the instance orientation

    - #### toSubSpace

          public Vector1D toSubSpace(Vector<Euclidean2D> vector)

      Transform a space point into a sub-space point.
      Parameters:
        `vector` - n-dimension point of the space
      Returns:
        (n-1)-dimension point of the sub-space corresponding to the specified space point

    - #### toSpace

          public Vector2D toSpace(Vector<Euclidean1D> vector)

      Transform a sub-space point into a space point.
      Parameters:
        `vector` - (n-1)-dimension point of the sub-space
      Returns:
        n-dimension point of the space corresponding to the specified sub-space point

    - #### toSubSpace

          public Vector1D toSubSpace(Point<Euclidean2D> point)

      Transform a space point into a sub-space point.
      Specified by:
        `toSubSpace` in interface `Embedding<Euclidean2D,Euclidean1D>`
      Parameters:
        `point` - n-dimension point of the space
      Returns:
        (n-1)-dimension point of the sub-space corresponding to the specified space point
      See Also:
        `Embedding.toSpace(org.apache.commons.math3.geometry.Point<T>)`

    - #### toSpace

          public Vector2D toSpace(Point<Euclidean1D> point)

      Transform a sub-space point into a space point.
      Specified by:
        `toSpace` in interface `Embedding<Euclidean2D,Euclidean1D>`
      Parameters:
        `point` - (n-1)-dimension point of the sub-space
      Returns:
        n-dimension point of the space corresponding to the specified sub-space point
      See Also:
        `Embedding.toSubSpace(org.apache.commons.math3.geometry.Point<S>)`

    - #### intersection

          public Vector2D intersection(Line other)

      Get the intersection point of the instance and another line.
      Parameters:
        `other` - other line
      Returns:
        intersection point of the instance and the other line or null if there are no intersection points

    - #### project

          public Point<Euclidean2D> project(Point<Euclidean2D> point)

      Project a point to the hyperplane.
      Specified by:
        `project` in interface `Hyperplane<Euclidean2D>`
      Parameters:
        `point` - point to project
      Returns:
        projected point
      Since:
        3.3

    - #### getTolerance

          public double getTolerance()

      Get the tolerance below which points are considered to belong to the hyperplane.
      Specified by:
        `getTolerance` in interface `Hyperplane<Euclidean2D>`
      Returns:
        tolerance below which points are considered to belong to the hyperplane
      Since:
        3.3

    - #### wholeHyperplane

          public SubLine wholeHyperplane()

      Build a sub-hyperplane covering the whole hyperplane.
      Specified by:
        `wholeHyperplane` in interface `Hyperplane<Euclidean2D>`
      Returns:
        a sub-hyperplane covering the whole hyperplane

    - #### wholeSpace

          public PolygonsSet wholeSpace()

      Build a region covering the whole space.
      Specified by:
        `wholeSpace` in interface `Hyperplane<Euclidean2D>`
      Returns:
        a region containing the instance (really a `PolygonsSet` instance)

    - #### getOffset

          public double getOffset(Line line)

      Get the offset (oriented distance) of a parallel line.

      This method should be called only for parallel lines otherwise the result is not meaningful.

      The offset is 0 if both lines are the same, it is positive if the line is on the right side of the instance and negative if it is on the left side, according to its natural orientation.

      Parameters:
        `line` - line to check
      Returns:
        offset of the line

    - #### getOffset

          public double getOffset(Vector<Euclidean2D> vector)

      Get the offset (oriented distance) of a vector.
      Parameters:
        `vector` - vector to check
      Returns:
        offset of the vector

    - #### getOffset

          public double getOffset(Point<Euclidean2D> point)

      Get the offset (oriented distance) of a point.

      The offset is 0 if the point is on the underlying hyperplane, it is positive if the point is on one particular side of the hyperplane, and it is negative if the point is on the other side, according to the hyperplane natural orientation.

      Specified by:
        `getOffset` in interface `Hyperplane<Euclidean2D>`
      Parameters:
        `point` - point to check
      Returns:
        offset of the point

    - #### sameOrientationAs

          public boolean sameOrientationAs(Hyperplane<Euclidean2D> other)

      Check if the instance has the same orientation as another hyperplane.

      This method is expected to be called on parallel hyperplanes. The method should not re-check for parallelism, only for orientation, typically by testing something like the sign of the dot-products of normals.

      Specified by:
        `sameOrientationAs` in interface `Hyperplane<Euclidean2D>`
      Parameters:
        `other` - other hyperplane to check against the instance
      Returns:
        true if the instance and the other hyperplane have the same orientation

    - #### getPointAt

          public Vector2D getPointAt(Vector1D abscissa,
                            double offset)

      Get one point from the plane.
      Parameters:
        `abscissa` - desired abscissa for the point
        `offset` - desired offset for the point
      Returns:
        one point in the plane, with given abscissa and offset relative to the line

    - #### contains

          public boolean contains(Vector2D p)

      Check if the line contains a point.
      Parameters:
        `p` - point to check
      Returns:
        true if p belongs to the line

    - #### distance

          public double distance(Vector2D p)

      Compute the distance between the instance and a point.

      This is a shortcut for invoking FastMath.abs(getOffset(p)), and provides consistency with what is in the org.apache.commons.math3.geometry.euclidean.threed.Line class.

      Parameters:
        `p` - to check
      Returns:
        distance between the instance and the point
      Since:
        3.1

    - #### isParallelTo

          public boolean isParallelTo(Line line)

      Check the instance is parallel to another line.
      Parameters:
        `line` - other line to check
      Returns:
        true if the instance is parallel to the other line (they can have either the same or opposite orientations)

    - #### translateToPoint

          public void translateToPoint(Vector2D p)

      Translate the line to force it passing by a point.
      Parameters:
        `p` - point by which the line should pass

    - #### getAngle

          public double getAngle()

      Get the angle of the line.
      Returns:
        the angle of the line with respect to the abscissa axis

    - #### setAngle

          public void setAngle(double angle)

      Set the angle of the line.
      Parameters:
        `angle` - new angle of the line with respect to the abscissa axis

    - #### getOriginOffset

          public double getOriginOffset()

      Get the offset of the origin.
      Returns:
        the offset of the origin

    - #### setOriginOffset

          public void setOriginOffset(double offset)

      Set the offset of the origin.
      Parameters:
        `offset` - offset of the origin

    - #### getTransform

          @Deprecated
          public static Transform<Euclidean2D,Euclidean1D> getTransform(AffineTransform transform)
                                                                 throws MathIllegalArgumentException

      Deprecated. as of 3.6, replaced with `getTransform(double, double, double, double, double, double)`
      Get a `Transform` embedding an affine transform.
      Parameters:
        `transform` - affine transform to embed (must be inversible otherwise the `apply(Hyperplane)` method would work only for some lines, and fail for other ones)
      Returns:
        a new transform that can be applied to either `Vector2D`, `Line` or `SubHyperplane` instances
      Throws:
        `MathIllegalArgumentException` - if the transform is non invertible

    - #### getTransform

          public static Transform<Euclidean2D,Euclidean1D> getTransform(double cXX,
                                                        double cYX,
                                                        double cXY,
                                                        double cYY,
                                                        double cX1,
                                                        double cY1)
                                                                 throws MathIllegalArgumentException

      Get a `Transform` embedding an affine transform.
      Parameters:
        `cXX` - transform factor between input abscissa and output abscissa
        `cYX` - transform factor between input abscissa and output ordinate
        `cXY` - transform factor between input ordinate and output abscissa
        `cYY` - transform factor between input ordinate and output ordinate
        `cX1` - transform addendum for output abscissa
        `cY1` - transform addendum for output ordinate
      Returns:
        a new transform that can be applied to either `Vector2D`, `Line` or `SubHyperplane` instances
      Throws:
        `MathIllegalArgumentException` - if the transform is non invertible
      Since:
        3.6

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