Table of Contents

Class Triangle

Namespace
NetTopologySuite.Geometries
Assembly
NetTopologySuite.dll

Represents a planar triangle, and provides methods for calculating various properties of triangles.

public class Triangle
Inheritance
Triangle
Inherited Members

Constructors

Triangle(Coordinate, Coordinate, Coordinate)

Creates a new triangle with the given vertices.

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

Parameters

p0 Coordinate

A vertex

p1 Coordinate

A vertex

p2 Coordinate

A vertex

Properties

P0

A corner point of the triangle

public Coordinate P0 { get; set; }

Property Value

Coordinate

P1

A corner point of the triangle

public Coordinate P1 { get; set; }

Property Value

Coordinate

P2

A corner point of the triangle

public Coordinate P2 { get; set; }

Property Value

Coordinate

Methods

AngleBisector(Coordinate, Coordinate, Coordinate)

Computes the point at which the bisector of the angle ABC cuts the segment AC.

public static Coordinate AngleBisector(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

Coordinate

The angle bisector cut point

Area()

Computes the 2D area of this triangle. The area value is always non-negative.

public double Area()

Returns

double

The area of this triangle

See Also

Area(Coordinate, Coordinate, Coordinate)

Computes the 2D area of a triangle. The area value is always non-negative.

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

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

double

The area of the triangle

See Also

Area3D()

Computes the 3D area of this triangle. The value computed is always non-negative.

public double Area3D()

Returns

double

The 3D area of this triangle

Area3D(Coordinate, Coordinate, Coordinate)

Computes the 3D area of a triangle. The value computed is always non-negative.

public static double Area3D(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

double

The 3D area of the triangle

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. 
public Coordinate Centroid()

Returns

Coordinate

The centroid of this triangle

Centroid(Coordinate, Coordinate, Coordinate)

Computes the centroid (centre of mass) of a triangle.

public static Coordinate Centroid(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

Coordinate

The centroid of the triangle

Remarks

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.

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). 
public Coordinate Circumcentre()

Returns

Coordinate

The circumcentre of this triangle

Circumcentre(Coordinate, Coordinate, Coordinate)

Computes the circumcentre of a triangle.

public static Coordinate Circumcentre(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

Coordinate

The circumcentre of the triangle

Remarks

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).

CircumcentreDD(Coordinate, Coordinate, Coordinate)

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) 
public static Coordinate CircumcentreDD(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

Coordinate

The circumcentre of the triangle

InCentre()

Computes the InCentre of this triangle

public Coordinate InCentre()

Returns

Coordinate

The point which is the InCentre of the triangle.

Remarks

The InCentre of a triangle is the point which is equidistant from the sides of the triangle. This is also the point at which the bisectors of the 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.

InCentre(Coordinate, Coordinate, Coordinate)

Computes the incentre of a triangle.

public static Coordinate InCentre(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

Coordinate

The point which is the incentre of the triangle

Remarks

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.

InterpolateZ(Coordinate)

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). 
public double InterpolateZ(Coordinate p)

Parameters

p Coordinate

The point to compute the Z-value of

Returns

double

The computed Z-value (elevation) of the point

InterpolateZ(Coordinate, Coordinate, Coordinate, Coordinate)

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). 
public static double InterpolateZ(Coordinate p, Coordinate v0, Coordinate v1, Coordinate v2)

Parameters

p Coordinate

The point to compute the Z-value of

v0 Coordinate

A vertex of a triangle, with a Z ordinate

v1 Coordinate

A vertex of a triangle, with a Z ordinate

v2 Coordinate

A vertex of a triangle, with a Z ordinate

Returns

double

The computed Z-value (elevation) of the point

Intersects(Coordinate, Coordinate, Coordinate, Coordinate)

Tests whether a triangle intersects a point.

public static bool Intersects(Coordinate a, Coordinate b, Coordinate c, Coordinate p)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

p Coordinate

The point to test

Returns

bool

true if the triangle intersects the point

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. 
public bool IsAcute()

Returns

bool

true if this triangle is acute

IsAcute(Coordinate, Coordinate, Coordinate)

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. 
public static bool IsAcute(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

bool

True if the triangle is acute.

IsCCW()

Tests whether this triangle is oriented counter-clockwise.

public bool IsCCW()

Returns

bool

true if the triangle orientation is counter-clockwise

IsCCW(Coordinate, Coordinate, Coordinate)

Tests whether a triangle is oriented counter-clockwise.

public static bool IsCCW(Coordinate a, Coordinate b, Coordinate c)

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

bool

true if the triangle orientation is counter-clockwise

Length()

Computes the length of the perimeter of this triangle.

public double Length()

Returns

double

The length of the perimeter

Length(Coordinate, Coordinate, Coordinate)

Compute the length of the perimeter of a triangle

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

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

double

The length of the perimeter of the triangle

LongestSideLength()

Computes the length of the longest side of this triangle

public double LongestSideLength()

Returns

double

The length of the longest side of this triangle

LongestSideLength(Coordinate, Coordinate, Coordinate)

Computes the length of the longest side of a triangle

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

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

double

The length of the longest side of the triangle

PerpendicularBisector(Coordinate, Coordinate)

Computes the line which is the perpendicular bisector of the

public static HCoordinate PerpendicularBisector(Coordinate a, Coordinate b)

Parameters

a Coordinate

A point

b Coordinate

Another point

Returns

HCoordinate

The perpendicular bisector, as an HCoordinate line segment a-b.

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 Index(Coordinate, Coordinate, Coordinate) for robust orientation calculation. 
public double SignedArea()

Returns

double

The signed 2D area of this triangle

See Also

SignedArea(Coordinate, Coordinate, Coordinate)

Computes the signed 2D area of a triangle.

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

Parameters

a Coordinate

A vertex of the triangle

b Coordinate

A vertex of the triangle

c Coordinate

A vertex of the triangle

Returns

double

The area of the triangle

Remarks

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 Index(Coordinate, Coordinate, Coordinate) for robust orientation calculation.

See Also