Class Triangle

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

Inheritance

object

Triangle

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Namespace: NetTopologySuite.Geometries

Assembly: NetTopologySuite.dll

Syntax

public class Triangle

Constructors

Triangle(Coordinate, Coordinate, Coordinate)

Creates a new triangle with the given vertices.

Declaration

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

Parameters

Type	Name	Description
Coordinate	p0	A vertex
Coordinate	p1	A vertex
Coordinate	p2	A vertex

Properties

P0

A corner point of the triangle

Declaration

public Coordinate P0 { get; set; }

Property Value

Type	Description
Coordinate

P1

A corner point of the triangle

Declaration

public Coordinate P1 { get; set; }

Property Value

Type	Description
Coordinate

P2

A corner point of the triangle

Declaration

public Coordinate P2 { get; set; }

Property Value

Type	Description
Coordinate

Methods

AngleBisector(Coordinate, Coordinate, Coordinate)

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

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
Coordinate	The angle bisector cut point

Area()

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

Declaration

public double Area()

Returns

Type	Description
double	The area of this triangle

See Also

SignedArea()

Area(Coordinate, Coordinate, Coordinate)

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

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
double	The area of the triangle

See Also

SignedArea(Coordinate, Coordinate, Coordinate)

Area3D()

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

Declaration

public double Area3D()

Returns

Type	Description
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.

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
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.

Declaration

public Coordinate Centroid()

Returns

Type	Description
Coordinate	The centroid of this triangle

Centroid(Coordinate, Coordinate, Coordinate)

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

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
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 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).

Declaration

public Coordinate Circumcentre()

Returns

Type	Description
Coordinate	The circumcentre of this triangle

Circumcentre(Coordinate, Coordinate, Coordinate)

Computes the circumcentre of a triangle.

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
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)

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
Coordinate	The circumcentre of the triangle

Circumradius()

Computes the radius of the circumcircle of a triangle.

Declaration

public double Circumradius()

Returns

Type	Description
double	The triangle circumradius

Circumradius(Coordinate, Coordinate, Coordinate)

Computes the radius of the circumcircle of a triangle.

Formula is as per

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
double	The circumradius of the triangle

InCentre()

Computes the InCentre of this triangle

Declaration

public Coordinate InCentre()

Returns

Type	Description
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.

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
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).

Declaration

public double InterpolateZ(Coordinate p)

Parameters

Type	Name	Description
Coordinate	p	The point to compute the Z-value of

Returns

Type	Description
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).

Declaration

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

Parameters

Type	Name	Description
Coordinate	p	The point to compute the Z-value of
Coordinate	v0	A vertex of a triangle, with a Z ordinate
Coordinate	v1	A vertex of a triangle, with a Z ordinate
Coordinate	v2	A vertex of a triangle, with a Z ordinate

Returns

Type	Description
double	The computed Z-value (elevation) of the point

Intersects(Coordinate, Coordinate, Coordinate, Coordinate)

Tests whether a triangle intersects a point.

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle
Coordinate	p	The point to test

Returns

Type	Description
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.

Declaration

public bool IsAcute()

Returns

Type	Description
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.

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
bool	True if the triangle is acute.

IsCCW()

Tests whether this triangle is oriented counter-clockwise.

Declaration

public bool IsCCW()

Returns

Type	Description
bool	true if the triangle orientation is counter-clockwise

IsCCW(Coordinate, Coordinate, Coordinate)

Tests whether a triangle is oriented counter-clockwise.

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
bool	true if the triangle orientation is counter-clockwise

Length()

Computes the length of the perimeter of this triangle.

Declaration

public double Length()

Returns

Type	Description
double	The length of the perimeter

Length(Coordinate, Coordinate, Coordinate)

Compute the length of the perimeter of a triangle

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
double	The length of the perimeter of the triangle

LongestSideLength()

Computes the length of the longest side of this triangle

Declaration

public double LongestSideLength()

Returns

Type	Description
double	The length of the longest side of this triangle

LongestSideLength(Coordinate, Coordinate, Coordinate)

Computes the length of the longest side of a triangle

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
double	The length of the longest side of the triangle

PerpendicularBisector(Coordinate, Coordinate)

Computes the line which is the perpendicular bisector of the

Declaration

public static HCoordinate PerpendicularBisector(Coordinate a, Coordinate b)

Parameters

Type	Name	Description
Coordinate	a	A point
Coordinate	b	Another point

Returns

Type	Description
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.

Declaration

public double SignedArea()

Returns

Type	Description
double	The signed 2D area of this triangle

See Also

Index(Coordinate, Coordinate, Coordinate)

SignedArea(Coordinate, Coordinate, Coordinate)

Computes the signed 2D area of a triangle.

Declaration

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

Parameters

Type	Name	Description
Coordinate	a	A vertex of the triangle
Coordinate	b	A vertex of the triangle
Coordinate	c	A vertex of the triangle

Returns

Type	Description
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

Area(Coordinate, Coordinate, Coordinate)

Index(Coordinate, Coordinate, Coordinate)