Class Triangle

java.lang.Object
org.locationtech.jts.geom.Triangle

public class Triangle extends Object
Represents a planar triangle, and provides methods for calculating various properties of triangles.
Version:
1.7
  • Field Details

    • p0

      public Coordinate p0
      The coordinates of the vertices of the triangle
    • p1

      public Coordinate p1
      The coordinates of the vertices of the triangle
    • p2

      public Coordinate p2
      The coordinates of the vertices of the triangle
  • Constructor Details

    • Triangle

      public Triangle(Coordinate p0, Coordinate p1, Coordinate p2)
      Creates a new triangle with the given vertices.
      Parameters:
      p0 - a vertex
      p1 - a vertex
      p2 - a vertex
  • Method Details

    • isAcute

      public static boolean isAcute(Coordinate a, Coordinate b, Coordinate c)
      Tests whether a triangle is acute. A triangle is acute if all interior angles are acute. This is a strict test - right triangles will return false. A triangle which is not acute is either right or obtuse.

      Note: this implementation is not robust for angles very close to 90 degrees.

      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      true if the triangle is acute
    • isCCW

      public static boolean isCCW(Coordinate a, Coordinate b, Coordinate c)
      Tests whether a triangle is oriented counter-clockwise.
      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      true if the triangle orientation is counter-clockwise
    • intersects

      public static boolean intersects(Coordinate a, Coordinate b, Coordinate c, Coordinate p)
      Tests whether a triangle intersects a point.
      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      p - the point to test
      Returns:
      true if the triangle intersects the point
    • perpendicularBisector

      public static HCoordinate perpendicularBisector(Coordinate a, Coordinate b)
      Computes the line which is the perpendicular bisector of the line segment a-b.
      Parameters:
      a - a point
      b - another point
      Returns:
      the perpendicular bisector, as an HCoordinate
    • circumcentre

      public static Coordinate circumcentre(Coordinate a, Coordinate b, Coordinate c)
      Computes the circumcentre of a triangle. The circumcentre is the centre of the circumcircle, the smallest circle which encloses the triangle. It is also the common intersection point of the perpendicular bisectors of the sides of the triangle, and is the only point which has equal distance to all three vertices of the triangle.

      The circumcentre does not necessarily lie within the triangle. For example, the circumcentre of an obtuse isosceles triangle lies outside the triangle.

      This method uses an algorithm due to J.R.Shewchuk which uses normalization to the origin to improve the accuracy of computation. (See Lecture Notes on Geometric Robustness, Jonathan Richard Shewchuk, 1999).

      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the circumcentre of the triangle
    • circumcentreDD

      public static Coordinate circumcentreDD(Coordinate a, Coordinate b, Coordinate c)
      Computes the circumcentre of a triangle. The circumcentre is the centre of the circumcircle, the smallest circle which encloses the triangle. It is also the common intersection point of the perpendicular bisectors of the sides of the triangle, and is the only point which has equal distance to all three vertices of the triangle.

      The circumcentre does not necessarily lie within the triangle. For example, the circumcentre of an obtuse isosceles triangle lies outside the triangle.

      This method uses DD extended-precision arithmetic to provide more accurate results than circumcentre(Coordinate, Coordinate, Coordinate)

      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the circumcentre of the triangle
    • inCentre

      public static Coordinate inCentre(Coordinate a, Coordinate b, Coordinate c)
      Computes the incentre of a triangle. The inCentre of a triangle is the point which is equidistant from the sides of the triangle. It is also the point at which the bisectors of the triangle's angles meet. It is the centre of the triangle's incircle, which is the unique circle that is tangent to each of the triangle's three sides.

      The incentre always lies within the triangle.

      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the point which is the incentre of the triangle
    • centroid

      public static Coordinate centroid(Coordinate a, Coordinate b, Coordinate c)
      Computes the centroid (centre of mass) of a triangle. This is also the point at which the triangle's three medians intersect (a triangle median is the segment from a vertex of the triangle to the midpoint of the opposite side). The centroid divides each median in a ratio of 2:1.

      The centroid always lies within the triangle.

      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the centroid of the triangle
    • length

      public static double length(Coordinate a, Coordinate b, Coordinate c)
      Compute the length of the perimeter of a triangle
      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the length of the triangle perimeter
    • longestSideLength

      public static double longestSideLength(Coordinate a, Coordinate b, Coordinate c)
      Computes the length of the longest side of a triangle
      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the length of the longest side of the triangle
    • angleBisector

      public static Coordinate angleBisector(Coordinate a, Coordinate b, Coordinate c)
      Computes the point at which the bisector of the angle ABC cuts the segment AC.
      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the angle bisector cut point
    • area

      public static double area(Coordinate a, Coordinate b, Coordinate c)
      Computes the 2D area of a triangle. The area value is always non-negative.
      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the area of the triangle
      See Also:
    • signedArea

      public static double signedArea(Coordinate a, Coordinate b, Coordinate c)
      Computes the signed 2D area of a triangle. The area value is positive if the triangle is oriented CW, and negative if it is oriented CCW.

      The signed area value can be used to determine point orientation, but the implementation in this method is susceptible to round-off errors. Use Orientation.index(Coordinate, Coordinate, Coordinate) for robust orientation calculation.

      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the signed 2D area of the triangle
      See Also:
    • area3D

      public static double area3D(Coordinate a, Coordinate b, Coordinate c)
      Computes the 3D area of a triangle. The value computed is always non-negative.
      Parameters:
      a - a vertex of the triangle
      b - a vertex of the triangle
      c - a vertex of the triangle
      Returns:
      the 3D area of the triangle
    • interpolateZ

      public static double interpolateZ(Coordinate p, Coordinate v0, Coordinate v1, Coordinate v2)
      Computes the Z-value (elevation) of an XY point on a three-dimensional plane defined by a triangle whose vertices have Z-values. The defining triangle must not be degenerate (in other words, the triangle must enclose a non-zero area), and must not be parallel to the Z-axis.

      This method can be used to interpolate the Z-value of a point inside a triangle (for example, of a TIN facet with elevations on the vertices).

      Parameters:
      p - the point to compute the Z-value of
      v0 - a vertex of a triangle, with a Z ordinate
      v1 - a vertex of a triangle, with a Z ordinate
      v2 - a vertex of a triangle, with a Z ordinate
      Returns:
      the computed Z-value (elevation) of the point
    • inCentre

      public Coordinate inCentre()
      Computes the incentre of this triangle. The incentre of a triangle is the point which is equidistant from the sides of the triangle. It is also the point at which the bisectors of the triangle's angles meet. It is the centre of the triangle's incircle, which is the unique circle that is tangent to each of the triangle's three sides.
      Returns:
      the point which is the inCentre of this triangle
    • isAcute

      public boolean isAcute()
      Tests whether this triangle is acute. A triangle is acute if all interior angles are acute. This is a strict test - right triangles will return false. A triangle which is not acute is either right or obtuse.

      Note: this implementation is not robust for angles very close to 90 degrees.

      Returns:
      true if this triangle is acute
    • isCCW

      public boolean isCCW()
      Tests whether this triangle is oriented counter-clockwise.
      Returns:
      true if the triangle orientation is counter-clockwise
    • circumcentre

      public Coordinate circumcentre()
      Computes the circumcentre of this triangle. The circumcentre is the centre of the circumcircle, the smallest circle which encloses the triangle. It is also the common intersection point of the perpendicular bisectors of the sides of the triangle, and is the only point which has equal distance to all three vertices of the triangle.

      The circumcentre does not necessarily lie within the triangle.

      This method uses an algorithm due to J.R.Shewchuk which uses normalization to the origin to improve the accuracy of computation. (See Lecture Notes on Geometric Robustness, Jonathan Richard Shewchuk, 1999).

      Returns:
      the circumcentre of this triangle
    • centroid

      public Coordinate centroid()
      Computes the centroid (centre of mass) of this triangle. This is also the point at which the triangle's three medians intersect (a triangle median is the segment from a vertex of the triangle to the midpoint of the opposite side). The centroid divides each median in a ratio of 2:1.

      The centroid always lies within the triangle.

      Returns:
      the centroid of this triangle
    • length

      public double length()
      Computes the length of the perimeter of this triangle.
      Returns:
      the length of the perimeter
    • longestSideLength

      public double longestSideLength()
      Computes the length of the longest side of this triangle
      Returns:
      the length of the longest side of this triangle
    • area

      public double area()
      Computes the 2D area of this triangle. The area value is always non-negative.
      Returns:
      the area of this triangle
      See Also:
    • signedArea

      public double signedArea()
      Computes the signed 2D area of this triangle. The area value is positive if the triangle is oriented CW, and negative if it is oriented CCW.

      The signed area value can be used to determine point orientation, but the implementation in this method is susceptible to round-off errors. Use Orientation.index(Coordinate, Coordinate, Coordinate) for robust orientation calculation.

      Returns:
      the signed 2D area of this triangle
      See Also:
    • area3D

      public double area3D()
      Computes the 3D area of this triangle. The value computed is always non-negative.
      Returns:
      the 3D area of this triangle
    • interpolateZ

      public double interpolateZ(Coordinate p)
      Computes the Z-value (elevation) of an XY point on a three-dimensional plane defined by this triangle (whose vertices must have Z-values). This triangle must not be degenerate (in other words, the triangle must enclose a non-zero area), and must not be parallel to the Z-axis.

      This method can be used to interpolate the Z-value of a point inside this triangle (for example, of a TIN facet with elevations on the vertices).

      Parameters:
      p - the point to compute the Z-value of
      Returns:
      the computed Z-value (elevation) of the point