Struct Arc2

Namespace

Thunder.UnitsNET.Vectors.Geometry

Assembly

Thunder.UnitsNET.Vectors.Geometry.dll

A directed arc on a circle in 2D space: a curve tracing part of a circle's circumference from a start point to a target point in a specified direction (clockwise or counter-clockwise).

An arc is defined by three things:

1. The Circle it lies on.
2. A StartDirection — the direction from the circle's centre to the start of the arc.
3. An ArcAngle — a signed sweep angle. Positive means counter-clockwise (CCW); negative means clockwise (CW).

From these, all other properties — StartPosition, TargetPosition, ArcLength, and TargetRay — are derived automatically.

Arc2 is a readonly record struct: value-type, immutable, and equality-by-value.

Arc direction follows standard mathematical convention: positive angles are counter-clockwise, negative are clockwise. See ArcDirection for important notes on how arc direction appears in MonoGame's Y-down coordinate system.

public readonly record struct Arc2 : IEquatable<Arc2>

Implements

IEquatable<Arc2>

Inherited Members

ValueType.Equals(object)

ValueType.GetHashCode()

ValueType.ToString()

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Extension Methods

CurveDebugDrawExtensions.DebugDraw(Arc2, SpriteBatch, Texture2D, Transform2, Color, float, int)

CurveDebugDrawExtensions.GetDebugScreenVertices(Arc2, Transform2, int)

GeometryXnaExtensions.GetXnaPolyline(Arc2, int?)

GeometryXnaExtensions.GetXnaPolyline(Arc2, LengthUnit, int?)

GeometryXnaExtensions.GetXnaPolyline(Arc2, LengthUnit, Ratio, int?)

Examples

// Quarter-circle arc: unit circle, starting East, sweeping 90° counter-clockwise to North
var arc = new Arc2(
    new Circle2(LengthPoint2.Origin, new Radius(Length.FromMeters(1))),
    Direction2.East,
    Angle.FromDegrees(90));

Length len  = arc.ArcLength;  // π/2 ≈ 1.5708 m
ArcDirection dir = arc.Direction; // CounterClockwise

// Use PointAt for parametric traversal
var pt = arc.PointAt(Ratio.FromPercent(50)); // Point at 45°

// Use CalculateArcSegments for rendering
IList<LengthSegment2> segments = arc.CalculateArcSegments(8); // 8-segment polyline

Constructors

Arc2(Circle2, Direction2, Angle)

Constructs an Arc2 from a start direction and a signed sweep angle.

public Arc2(Circle2 circle, Direction2 startDirection, Angle arcAngle)

Parameters

circle Circle2

The circle the arc lies on.

startDirection Direction2

The direction from the circle centre to the arc's start point.

arcAngle Angle

The signed sweep angle. Positive = counter-clockwise, negative = clockwise. Automatically normalized to (−360°, 360°].

Examples

var circle = new Circle2(LengthPoint2.FromMeters(0, 0), Radius.FromMeters(1));
var arc = new Arc2(circle, Direction2.East, Angle.FromDegrees(90));
// Starts at (R, 0), sweeps 90° CCW, ends at (0, R)

Arc2(Circle2, LengthPoint2, LengthPoint2, ArcDirection)

Constructs an Arc2 from two positions on the circle and an explicit sweep direction.

The arc sweeps from startPosition to targetPosition in the specified arcDirection. The shorter or longer path is selected based on the direction: CCW always sweeps the CCW way, even if it is the long way around.

public Arc2(Circle2 circle, LengthPoint2 startPosition, LengthPoint2 targetPosition, ArcDirection arcDirection)

Parameters

circle Circle2

The circle the arc lies on.

startPosition LengthPoint2

Start point (must be on the circle's circumference).

targetPosition LengthPoint2

Target point (must be on the circle's circumference).

arcDirection ArcDirection

The sweep direction.

Examples

var circle = new Circle2(LengthPoint2.FromMeters(0, 0), Radius.FromMeters(1));
var start  = LengthPoint2.FromMeters(1, 0);   // East
var target = LengthPoint2.FromMeters(0, 1);   // North
var arc = new Arc2(circle, start, target, ArcDirection.CounterClockwise); // 90° CCW

Arc2(Circle2, LengthPoint2, Angle)

Constructs an Arc2 from a start position on the circle and a signed sweep angle.

public Arc2(Circle2 circle, LengthPoint2 startPosition, Angle arcAngle)

Parameters

circle Circle2

The circle the arc lies on.

startPosition LengthPoint2

A point on the circle's circumference where the arc begins.

arcAngle Angle

The signed sweep angle. Positive = counter-clockwise, negative = clockwise.

Examples

var circle = new Circle2(LengthPoint2.FromMeters(0, 0), Radius.FromMeters(1));
var start = LengthPoint2.FromMeters(1, 0); // East on unit circle
var arc = new Arc2(circle, start, Angle.FromDegrees(-90)); // 90° clockwise to South

Properties

ArcAngle

The signed sweep angle of the arc.

Positive values indicate a counter-clockwise sweep; negative values indicate clockwise. The magnitude equals the angle subtended at the centre. Normalised to (−360°, 360°] via NormalizeToSigned(Angle).

public Angle ArcAngle { get; }

Property Value

Angle

ArcLength

The arc length: the distance along the arc from StartPosition to TargetPosition.

Computed as Radius × |ArcAngle| (in radians). Always non-negative.

public Length ArcLength { get; }

Property Value

Length

Center

The centre position of this arc (the centre of its underlying circle).

Alias for Circle.Center. Provides the standardised Center contract shared by all shape types.

public LengthPoint2 Center { get; }

Property Value

LengthPoint2

Circle

The circle on which this arc lies. The arc's endpoints are on the circumference of this circle.

public Circle2 Circle { get; }

Property Value

Circle2

Direction

Whether the arc sweeps clockwise or counter-clockwise.

Derived from the sign of ArcAngle: positive → CCW, non-positive → CW.

public ArcDirection Direction { get; }

Property Value

ArcDirection

StartDirection

The direction from the circle's centre to the start of the arc.

Multiply by the radius to get StartPosition: StartPosition = Circle.Center + StartDirection * Circle.Radius.

public Direction2 StartDirection { get; }

Property Value

Direction2

StartPosition

The point on the circle's circumference where the arc begins.

public LengthPoint2 StartPosition { get; }

Property Value

LengthPoint2

TargetDirection

The direction from the circle's centre to the end of the arc.

public Direction2 TargetDirection { get; }

Property Value

Direction2

TargetPosition

The point on the circle's circumference where the arc ends.

public LengthPoint2 TargetPosition { get; }

Property Value

LengthPoint2

TargetRay

A LengthRay2 tangent to the arc at the target point, pointing in the direction of travel at that endpoint.

For a CCW arc the tangent at the target is 90° CCW from the target radius direction; for a CW arc it is 90° CW. This ray is useful for chaining arcs and tangent lines together (e.g. Dubins paths in robotics).

public LengthRay2 TargetRay { get; }

Property Value

LengthRay2

Methods

CalculateArcPoints(int)

Calculates a list of points sampled uniformly along the arc.

Returns segmentCount + 1 points: one at each segment boundary, starting at StartPosition (t=0) and ending at TargetPosition (t=1).

public IList<LengthPoint2> CalculateArcPoints(int segmentCount)

Parameters

segmentCount int

The number of segments (minimum 1). The returned list will have segmentCount + 1 points.

Returns

IList<LengthPoint2>

An IList of points sampled uniformly along the arc.

CalculateArcSegments(int?)

Returns a polyline approximation of the arc as a list of LengthSegment2.

When segmentCount is null (the default), the number of segments is automatically chosen as ⌈ArcLength.Meters⌉ — roughly one segment per metre, giving a smooth approximation at typical game-world scales. Pass an explicit count for fine or coarse rendering control.

public IList<LengthSegment2> CalculateArcSegments(int? segmentCount = null)

Parameters

segmentCount int?

The number of line segments in the approximation, or null to use the adaptive default (⌈ArcLength.Meters⌉, minimum 1).

Returns

IList<LengthSegment2>

A list of LengthSegment2 whose endpoints all lie on the arc's circle. An empty list is returned if the arc has zero length.

Examples

var circle = new Circle2(LengthPoint2.FromMeters(0, 0), Radius.FromMeters(1));
var arc = new Arc2(circle, Direction2.East, Angle.FromDegrees(90));

// Automatic resolution (≈ 2 segments for a π/2 ≈ 1.57 m arc on a 1 m radius circle)
var auto = arc.CalculateArcSegments();

// Explicit 8-segment high-quality approximation
var fine = arc.CalculateArcSegments(8);

FromPoints(Circle2, LengthPoint2, LengthPoint2)

Constructs an Arc2 on the given circle passing through two specified points, selecting the shorter of the two possible arcs.

public static Arc2 FromPoints(Circle2 circle, LengthPoint2 startPoint, LengthPoint2 targetPoint)

Parameters

circle Circle2

The circle the arc lies on.

startPoint LengthPoint2

The start point (must be on the circle's circumference).

targetPoint LengthPoint2

The target point (must be on the circle's circumference).

Returns

Arc2

An arc with the shorter angular span connecting the two points.

FromPoints(LengthPoint2, LengthPoint2, LengthPoint2)

Constructs an Arc2 from three points: a start, a through-point, and an end. The arc passes through all three points in order, and the sweep direction is inferred automatically from the winding of start → through → end.

If the signed area of the triangle formed by the three points is positive, the winding is counter-clockwise (CCW); if negative, it is clockwise (CW). This eliminates the need to compute a cross-product manually at the call site.

public static Arc2 FromPoints(LengthPoint2 start, LengthPoint2 through, LengthPoint2 end)

Parameters

start LengthPoint2

The point where the arc begins.

through LengthPoint2

A point the arc passes through between start and end.

end LengthPoint2

The point where the arc ends.

Returns

Arc2

An Arc2 from start to end passing through through.

Examples

var p1 = LengthPoint2.FromMeters(1, 0);
var p2 = LengthPoint2.FromMeters(0, 1);
var p3 = LengthPoint2.FromMeters(-1, 0);
var arc = Arc2.FromPoints(p1, p2, p3);
// arc.Direction == ArcDirection.CounterClockwise
// arc.PointAt(0.5) ≈ (0, 1)

Exceptions

ArgumentException

Thrown when the three points are collinear (no unique circle passes through them).

GetClosestPoint(LengthPoint2)

Returns the point on the arc (or its endpoints) that is closest to position.

If the projection of position onto the circle's circumference falls within the arc's angular span, the closest point is that projection. Otherwise the closest arc endpoint (start or target) is returned.

public LengthPoint2 GetClosestPoint(LengthPoint2 position)

Parameters

position LengthPoint2

The query point in world space.

Returns

LengthPoint2

The closest point on or at the ends of the arc.

Examples

var circle = new Circle2(LengthPoint2.FromMeters(0, 0), Radius.FromMeters(1));
var arc = new Arc2(circle, Direction2.East, Angle.FromDegrees(90));
LengthPoint2 closest = arc.GetClosestPoint(LengthPoint2.FromMeters(0.7, 0.7));
// Returns approximately (0.707, 0.707) — the 45° point on the circle

MoveCenterTo(LengthPoint2)

Returns a new Arc2 with its centre moved to newCenter, preserving all other properties.

public Arc2 MoveCenterTo(LengthPoint2 newCenter)

Parameters

newCenter LengthPoint2

The new centre position.

Returns

Arc2

A translated Arc2 centred at newCenter.

Examples

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

PointAt(double)

Returns the point on the arc at the specified normalized parameter t.

t = 0 returns StartPosition; t = 1 returns TargetPosition.

public LengthPoint2 PointAt(double t)

Parameters

t double

Normalized parameter in [0, 1].

Returns

LengthPoint2

The point on the arc at that parameter.

PointAt(Ratio)

Returns the point on the arc at the specified normalized parameter t.

t = 0 returns StartPosition; t = 1 returns TargetPosition. The point is computed by rotating from StartDirection by ArcAngle * t.

public LengthPoint2 PointAt(Ratio t)

Parameters

t Ratio

Normalized parameter as a UnitsNet.Ratio (0–1).

Returns

LengthPoint2

The point on the arc at that parameter.

TangentAt(double)

Returns the forward direction (tangent) of the arc at the specified parameter t.

public Direction2 TangentAt(double t)

Parameters

t double

Normalized parameter in [0, 1].

Returns

Direction2

The unit tangent direction at that point on the arc.

TangentAt(Ratio)

Returns the forward direction (tangent) of the arc at the specified parameter t.

The tangent is perpendicular to the radius at that point, signed by the arc direction: positive (CCW) means 90° counterclockwise from the radius; negative (CW) means 90° clockwise.

public Direction2 TangentAt(Ratio t)

Parameters

t Ratio

Normalized parameter as a UnitsNet.Ratio (0–1).

Returns

Direction2

The unit tangent direction at that point on the arc.

Operators

operator +(Arc2, LengthVector2)

Returns a new Arc2 translated by right. The arc angle and radius are preserved; the circle's centre moves.

public static Arc2 operator +(Arc2 left, LengthVector2 right)

Parameters

left Arc2

The arc to translate.

right LengthVector2

The displacement vector.

Returns

Arc2

A new Arc2 with the circle centre moved by right.