org.locationtech.jts.geom

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 Summary

Fields

Modifier and Type	Field and Description
Coordinate	p0 The coordinates of the vertices of the triangle
Coordinate	p1 The coordinates of the vertices of the triangle
Coordinate	p2 The coordinates of the vertices of the triangle

Constructor Summary

Constructors

Constructor and Description
Triangle(Coordinate p0, Coordinate p1, Coordinate p2) Creates a new triangle with the given vertices.

Method Summary

Modifier and Type	Method and Description
static Coordinate	angleBisector(Coordinate a, Coordinate b, Coordinate c) Computes the point at which the bisector of the angle ABC cuts the segment AC.
double	area() Computes the 2D area of this triangle.
static double	area(Coordinate a, Coordinate b, Coordinate c) Computes the 2D area of a triangle.
double	area3D() Computes the 3D area of this triangle.
static double	area3D(Coordinate a, Coordinate b, Coordinate c) Computes the 3D area of a triangle.
Coordinate	centroid() Computes the centroid (centre of mass) of this triangle.
static Coordinate	centroid(Coordinate a, Coordinate b, Coordinate c) Computes the centroid (centre of mass) of a triangle.
Coordinate	circumcentre() Computes the circumcentre of this triangle.
static Coordinate	circumcentre(Coordinate a, Coordinate b, Coordinate c) Computes the circumcentre of a triangle.
static Coordinate	circumcentreDD(Coordinate a, Coordinate b, Coordinate c) Computes the circumcentre of a triangle.
double	circumradius() Computes the radius of the circumcircle of a triangle.
static double	circumradius(Coordinate a, Coordinate b, Coordinate c) Computes the radius of the circumcircle of a triangle.
Coordinate	inCentre() Computes the incentre of this triangle.
static Coordinate	inCentre(Coordinate a, Coordinate b, Coordinate c) Computes the incentre of a triangle.
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).
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.
static boolean	intersects(Coordinate a, Coordinate b, Coordinate c, Coordinate p) Tests whether a triangle intersects a point.
boolean	isAcute() Tests whether this triangle is acute.
static boolean	isAcute(Coordinate a, Coordinate b, Coordinate c) Tests whether a triangle is acute.
boolean	isCCW() Tests whether this triangle is oriented counter-clockwise.
static boolean	isCCW(Coordinate a, Coordinate b, Coordinate c) Tests whether a triangle is oriented counter-clockwise.
double	length() Computes the length of the perimeter of this triangle.
static double	length(Coordinate a, Coordinate b, Coordinate c) Compute the length of the perimeter of a triangle
double	longestSideLength() Computes the length of the longest side of this triangle
static double	longestSideLength(Coordinate a, Coordinate b, Coordinate c) Computes the length of the longest side of a triangle
static HCoordinate	perpendicularBisector(Coordinate a, Coordinate b) Computes the line which is the perpendicular bisector of the line segment a-b.
double	signedArea() Computes the signed 2D area of this triangle.
static double	signedArea(Coordinate a, Coordinate b, Coordinate c) Computes the signed 2D area of a triangle.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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 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

circumradius

public static double circumradius(Coordinate a,
                                  Coordinate b,
                                  Coordinate c)

Computes the radius of the circumcircle of a triangle.

Formula is as per https://math.stackexchange.com/a/3610959

Parameters:

a - a vertex of the triangle

b - a vertex of the triangle

c - a vertex of the triangle

Returns:

the circumradius of the triangle

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(Coordinate, Coordinate, Coordinate)

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:

Orientation.index(Coordinate, Coordinate, Coordinate)

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 passes through all the triangle vertices. 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

circumradius

public double circumradius()

Computes the radius of the circumcircle of a triangle.

Returns:

the triangle circumradius

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()

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:

Orientation.index(Coordinate, Coordinate, Coordinate)

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