com.revolsys.jts.geom

Class Triangle

java.lang.Object

com.revolsys.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
Point	p0 The coordinates of the vertices of the triangle
Point	p1 The coordinates of the vertices of the triangle
Point	p2 The coordinates of the vertices of the triangle

Constructor Summary

Constructors

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

Method Summary

Methods

Modifier and Type	Method and Description
static Point	angleBisector(Point a, Point b, Point 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(Point a, Point b, Point c) Computes the 2D area of a triangle.
double	area3D() Computes the 3D area of this triangle.
static double	area3D(Point a, Point b, Point c) Computes the 3D area of a triangle.
Point	centroid() Computes the centroid (centre of mass) of this triangle.
static Point	centroid(Point a, Point b, Point c) Computes the centroid (centre of mass) of a triangle.
Point	circumcentre() Computes the circumcentre of this triangle.
static Point	circumcentre(Point a, Point b, Point c) Computes the circumcentre of a triangle.
Point	inCentre() Computes the incentre of this triangle.
static Point	inCentre(Point a, Point b, Point c) Computes the incentre of a triangle.
double	interpolateZ(Point 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(Point p, Point v0, Point v1, Point v2) Computes the Z-value (elevation) of an XY point on a three-dimensional plane defined by a triangle whose vertices have Z-values.
boolean	isAcute() Tests whether this triangle is acute.
static boolean	isAcute(Point a, Point b, Point c) Tests whether a triangle is acute.
double	longestSideLength() Computes the length of the longest side of this triangle
static double	longestSideLength(Point a, Point b, Point c) Computes the length of the longest side of a triangle
static HCoordinate	perpendicularBisector(Point a, Point 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(Point a, Point b, Point c) Computes the signed 2D area of a triangle.

Methods inherited from class java.lang.Object

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

Field Detail

p0

public Point p0

The coordinates of the vertices of the triangle

p1

public Point p1

The coordinates of the vertices of the triangle

p2

public Point p2

The coordinates of the vertices of the triangle

Constructor Detail

Triangle

public Triangle(Point p0,
        Point p1,
        Point p2)

Creates a new triangle with the given vertices.

Parameters:

p0 - a vertex

p1 - a vertex

p2 - a vertex

Method Detail

angleBisector

public static Point angleBisector(Point a,
                  Point b,
                  Point 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(Point a,
          Point b,
          Point 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)

area3D

public static double area3D(Point a,
            Point b,
            Point 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

centroid

public static Point centroid(Point a,
             Point b,
             Point 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

circumcentre

public static Point circumcentre(Point a,
                 Point b,
                 Point 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 Point inCentre(Point a,
             Point b,
             Point 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

interpolateZ

public static double interpolateZ(Point p,
                  Point v0,
                  Point v1,
                  Point 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

isAcute

public static boolean isAcute(Point a,
              Point b,
              Point 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

longestSideLength

public static double longestSideLength(Point a,
                       Point b,
                       Point 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

perpendicularBisector

public static HCoordinate perpendicularBisector(Point a,
                                Point 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

signedArea

public static double signedArea(Point a,
                Point b,
                Point 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 CGAlgorithms#orientationIndex(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:

CGAlgorithms#orientationIndex(Coordinate, Coordinate, Coordinate)

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

centroid

public Point 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

circumcentre

public Point 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

inCentre

public Point 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

interpolateZ

public double interpolateZ(Point 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

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

longestSideLength

public double longestSideLength()

Computes the length of the longest side of this triangle

Returns:

the length of the longest side of this triangle

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 CGAlgorithms#orientationIndex(Coordinate, Coordinate, Coordinate) for robust orientation calculation.

Returns:

the signed 2D area of this triangle

See Also:

CGAlgorithms#orientationIndex(Coordinate, Coordinate, Coordinate)