com.vividsolutions.jts.geom

Class Triangle


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

    • Field Detail

      • 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 Detail

      • 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 Detail

      • isAcute

        public static boolean isAcute(Coordinate a,
                              Coordinate b,
                              Coordinate c)
        Tests whether a triangle is acute. A triangle is acute iff 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

      • 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 isoceles 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 vertx of the triangle
        b - a vertx of the triangle
        c - a vertx 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 vertx of the triangle
        b - a vertx of the triangle
        c - a vertx 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

      • 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

      • area3D

        public static double area3D(Coordinate a,
                            Coordinate b,
                            Coordinate c)
        Computes the 3D area of a triangle. The value computed is alway 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 iff 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

      • 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

      • 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()

      • area3D

        public double area3D()
        Computes the 3D area of this triangle. The value computed is alway 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