Struct Triangle2

Namespace

Thunder.UnitsNET.Vectors.Geometry

Assembly

Thunder.UnitsNET.Vectors.Geometry.dll

A triangle in 2D space defined by three vertices A, B, and C.

Triangle2 is a readonly record struct: value-type, immutable, and comparable by value. All geometric properties (area, perimeter, centroid, sides) are computed from the three vertices.

Triangles are the fundamental building block of 2D geometry. You can use them to test point containment, compute signed areas, or approximate curved shapes as polygon fans. The vertex order determines orientation: counter-clockwise (CCW) is the positive convention, matching standard mathematical coordinates where Y increases upward.

public readonly record struct Triangle2 : IEquatable<Triangle2>

Implements

IEquatable<Triangle2>

Inherited Members

ValueType.Equals(object)

ValueType.GetHashCode()

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Extension Methods

GeometryXnaExtensions.GetXnaVertices(Triangle2)

GeometryXnaExtensions.GetXnaVertices(Triangle2, LengthUnit)

GeometryXnaExtensions.GetXnaVertices(Triangle2, LengthUnit, Ratio)

PolygonDebugDrawExtensions.DebugDraw(Triangle2, SpriteBatch, Texture2D, Transform2, Color, float)

PolygonDebugDrawExtensions.GetDebugScreenVertices(Triangle2, Transform2)

Examples

var tri = new Triangle2(
    LengthPoint2.FromMeters(0, 0),
    LengthPoint2.FromMeters(6, 0),
    LengthPoint2.FromMeters(3, 6));

var center = tri.Center;   // centroid at (3, 2)
var area   = tri.Area;     // 18 m²
tri.Contains(LengthPoint2.FromMeters(3, 2)); // => true

Constructors

Triangle2(LengthPoint2, LengthPoint2, LengthPoint2)

A triangle in 2D space defined by three vertices A, B, and C.

Triangle2 is a readonly record struct: value-type, immutable, and comparable by value. All geometric properties (area, perimeter, centroid, sides) are computed from the three vertices.

Triangles are the fundamental building block of 2D geometry. You can use them to test point containment, compute signed areas, or approximate curved shapes as polygon fans. The vertex order determines orientation: counter-clockwise (CCW) is the positive convention, matching standard mathematical coordinates where Y increases upward.

public Triangle2(LengthPoint2 A, LengthPoint2 B, LengthPoint2 C)

Parameters

A LengthPoint2

B LengthPoint2

C LengthPoint2

Examples

var tri = new Triangle2(
    LengthPoint2.FromMeters(0, 0),
    LengthPoint2.FromMeters(6, 0),
    LengthPoint2.FromMeters(3, 6));

var center = tri.Center;   // centroid at (3, 2)
var area   = tri.Area;     // 18 m²
tri.Contains(LengthPoint2.FromMeters(3, 2)); // => true

Properties

A

public LengthPoint2 A { get; init; }

Property Value

LengthPoint2

AB

The side from vertex A to vertex B.

public LengthSegment2 AB { get; }

Property Value

LengthSegment2

Area

The area of the triangle, computed as half the absolute value of the cross product of vectors AB and AC.

Formula: Area = ½ × |AB × AC|

This formula works for any triangle regardless of orientation. If the vertices are counter-clockwise (CCW), the cross product is positive; clockwise gives a negative cross product. The absolute value handles both cases.

public Area Area { get; }

Property Value

Area

Examples

var t = new Triangle2(
    LengthPoint2.FromMeters(0, 0),
    LengthPoint2.FromMeters(6, 0),
    LengthPoint2.FromMeters(3, 6));
t.Area.SquareMeters; // => 18.0

B

public LengthPoint2 B { get; init; }

Property Value

LengthPoint2

BC

The side from vertex B to vertex C.

public LengthSegment2 BC { get; }

Property Value

LengthSegment2

C

public LengthPoint2 C { get; init; }

Property Value

LengthPoint2

CA

The side from vertex C to vertex A.

public LengthSegment2 CA { get; }

Property Value

LengthSegment2

Center

The centroid (geometric centre) of the triangle: the arithmetic mean of the three vertices.

The centroid is the point where all three medians of a triangle intersect. It is always located inside the triangle (one-third of the way from each side to the opposite vertex).

public LengthPoint2 Center { get; }

Property Value

LengthPoint2

Examples

var t = new Triangle2(
    LengthPoint2.FromMeters(0, 0),
    LengthPoint2.FromMeters(6, 0),
    LengthPoint2.FromMeters(3, 6));
var center = t.Center; // centroid (3, 2)

IsDegenerate

Returns true if the three vertices are collinear (area is zero). A degenerate triangle has no interior and represents a line segment, not a surface.

public bool IsDegenerate { get; }

Property Value

bool

Perimeter

The perimeter of the triangle (sum of all three side lengths).

public Length Perimeter { get; }

Property Value

Length

Methods

Contains(LengthPoint2)

Returns true if point lies inside or on the boundary of this triangle.

Algorithm — sign-of-cross (same-side test): point P is inside triangle ABC if and only if it is on the same side of each directed edge as the opposite vertex. Equivalently, all three cross products (AB × AP), (BC × BP), and (CA × CP) must have the same sign (all non-negative or all non-positive).

Points on edges or at vertices satisfy at least one cross product equal to zero, which passes the test when all non-zero values share the same sign.

public bool Contains(LengthPoint2 point)

Parameters

point LengthPoint2

The world-space point to test.

Returns

bool

true if the point is inside or on the triangle.

Examples

var t = new Triangle2(
    LengthPoint2.FromMeters(0, 0),
    LengthPoint2.FromMeters(6, 0),
    LengthPoint2.FromMeters(3, 6));
t.Contains(LengthPoint2.FromMeters(3, 2));  // => true
t.Contains(LengthPoint2.FromMeters(0, 5));  // => false
t.Contains(LengthPoint2.FromMeters(3, 0));  // => true

DistanceTo(LengthPoint2)

Returns the distance from this shape to point. Returns UnitsNet.Length.Zero if the point is inside or on the boundary.

public Length DistanceTo(LengthPoint2 point)

Parameters

point LengthPoint2

The point to measure distance to.

Returns

Length

The shortest distance from the shape's boundary to point, or UnitsNet.Length.Zero if the point is contained.

Examples

Length d = shape.DistanceTo(LengthPoint2.FromMeters(10, 0));

GetBoundingRectangle()

Returns the smallest axis-aligned bounding rectangle that completely contains this triangle.

public Rectangle2 GetBoundingRectangle()

Returns

Rectangle2

An axis-aligned Rectangle2 bounding all three vertices.

Examples

var t = new Triangle2(
    LengthPoint2.FromMeters(1, 1),
    LengthPoint2.FromMeters(5, 1),
    LengthPoint2.FromMeters(3, 4));
var bounds = t.GetBoundingRectangle();
// bounds.Center = (3, 2.5), bounds.Dimensions = (4, 3)

GetClosestPoint(LengthPoint2)

Returns the point on the triangle's boundary (or interior) nearest to point. If the point is inside the triangle it is returned unchanged. Otherwise the closest point on any of the three edges is returned.

public LengthPoint2 GetClosestPoint(LengthPoint2 point)

Parameters

point LengthPoint2

The world-space query point.

Returns

LengthPoint2

The nearest point on or inside the triangle.

Examples

var tri = new Triangle2(
    LengthPoint2.FromMeters(0, 0),
    LengthPoint2.FromMeters(6, 0),
    LengthPoint2.FromMeters(3, 6));
LengthPoint2 p = tri.GetClosestPoint(LengthPoint2.FromMeters(3, -2)); // (3, 0)

MoveCenterTo(LengthPoint2)

Returns a new Triangle2 with its centre moved to newCenter, preserving all other properties.

public Triangle2 MoveCenterTo(LengthPoint2 newCenter)

Parameters

newCenter LengthPoint2

The new centre position.

Returns

Triangle2

A translated Triangle2 centred at newCenter.

Examples

var moved = shape.MoveCenterTo(LengthPoint2.FromMeters(5, 0));

ToString()

Returns the fully qualified type name of this instance.

public override string ToString()

Returns

string

The fully qualified type name.

TryGetManifold(Polygon2, out CollisionManifold)

Tests whether this triangle overlaps other and, if so, returns the collision manifold describing the penetration.

public bool TryGetManifold(Polygon2 other, out CollisionManifold manifold)

Parameters

other Polygon2

The polygon to test against.

manifold CollisionManifold

When this method returns true, contains the collision data.

Returns

bool

true if the shapes penetrate (overlap strictly greater than zero).

Exceptions

InvalidOperationException

Thrown when other is not convex. Use IsConvex to check before calling.

TryGetManifold(Triangle2, out CollisionManifold)

Tests whether this triangle overlaps other and, if so, returns the collision manifold describing the penetration.

public bool TryGetManifold(Triangle2 other, out CollisionManifold manifold)

Parameters

other Triangle2

The other triangle to test against.

manifold CollisionManifold

When this method returns true, contains the collision data: penetration depth, contact normal (pointing from other toward this triangle), and the contact point. Otherwise the default value.

Returns

bool

true if the triangles penetrate (overlap strictly greater than zero); false if they are separated or only touching.

Operators

operator +(Triangle2, LengthVector2)

Translates all three vertices by the given displacement vector.

public static Triangle2 operator +(Triangle2 triangle, LengthVector2 displacement)

Parameters

triangle Triangle2

The triangle to translate.

displacement LengthVector2

The displacement to add to each vertex.

Returns

Triangle2

A new Triangle2 with all vertices shifted.

operator +(LengthVector2, Triangle2)

Translates all vertices (commutative overload).

public static Triangle2 operator +(LengthVector2 displacement, Triangle2 triangle)

Parameters

displacement LengthVector2

The displacement to add.

triangle Triangle2

The triangle to translate.

Returns

Triangle2

A new Triangle2 with all vertices shifted.