Struct Transform2

Namespace

Thunder.UnitsNET.Vectors.Geometry

Assembly

Thunder.UnitsNET.Vectors.Geometry.dll

A 2D spatial transform composed of a position (Position), an orientation (Rotation), and a uniform scale (Scale).

Transform2 converts between local space (relative to the transform's origin) and world space. The order of operations when going local → world is: scale, then rotate, then translate.

public readonly record struct Transform2 : IEquatable<Transform2>

Implements

IEquatable<Transform2>

Inherited Members

ValueType.Equals(object)

ValueType.GetHashCode()

ValueType.ToString()

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Extension Methods

PrimitiveDebugDrawExtensions.DebugDraw(Transform2, SpriteBatch, Texture2D, Transform2, Color?, Color?, float, float)

PrimitiveDebugDrawExtensions.GetDebugScreenAxes(Transform2, Transform2, float)

Transform2XnaExtensions.ToXnaMatrix(Transform2)

Transform2XnaExtensions.ToXnaMatrix(Transform2, LengthUnit)

Transform2XnaExtensions.ToXnaMatrix(Transform2, LengthUnit, Ratio)

Examples

// Translate 5 m right, rotate 90° CCW, scale by 2
var t = new Transform2(LengthPoint2.FromMeters(5, 0), Direction2.FromDegrees(90), Ratio.FromDecimalFractions(2.0));
var world = t.Apply(LengthPoint2.FromMeters(1, 0)); // (5, 2)

Remarks

Math overview:

• Apply(p) (local → world): w = Position + Scale × R(Rotation) × p
• ApplyInverse(w) (world → local): l = (1/Scale) × R(-Rotation) × (w - Position)
• Compose(child): applies child in the parent's local space, equivalent to evaluating parent.Apply(child.Apply(p)) for any point p.

Constructors

Transform2(LengthPoint2, Direction2, Ratio)

Initialises a Transform2 with the given position, rotation, and scale.

public Transform2(LengthPoint2 position, Direction2 rotation, Ratio scale)

Parameters

position LengthPoint2

The world-space position.

rotation Direction2

The orientation.

scale Ratio

The uniform scale factor.

Properties

Identity

The identity transform: no translation, no rotation, scale = 1. Identity.Apply(p) == p for any point p.

public static Transform2 Identity { get; }

Property Value

Transform2

Position

The world-space position of the transform's origin.

public LengthPoint2 Position { get; init; }

Property Value

LengthPoint2

Rotation

The orientation of the transform, applied after scale.

public Direction2 Rotation { get; init; }

Property Value

Direction2

Scale

The uniform scale factor. 1.0 = no scaling.

public Ratio Scale { get; init; }

Property Value

Ratio

Methods

Apply(LengthPoint2)

Transforms a point from local space to world space.

Order: scale → rotate → translate.

public LengthPoint2 Apply(LengthPoint2 localPoint)

Parameters

localPoint LengthPoint2

A point in this transform's local coordinate space.

Returns

LengthPoint2

The equivalent world-space position.

Examples

var t = new Transform2(LengthPoint2.FromMeters(1, 0), Direction2.FromDegrees(90), Ratio.FromDecimalFractions(2.0));
var world = t.Apply(LengthPoint2.FromMeters(1, 0)); // (1, 2)

ApplyInverse(LengthPoint2)

Transforms a point from world space back to local space (the inverse of Apply(LengthPoint2)).

Order: un-translate → un-rotate → un-scale.

public LengthPoint2 ApplyInverse(LengthPoint2 worldPoint)

Parameters

worldPoint LengthPoint2

A point in world coordinate space.

Returns

LengthPoint2

The equivalent local-space position.

Examples

var t = new Transform2(LengthPoint2.FromMeters(1, 0), Direction2.FromDegrees(90), Ratio.FromDecimalFractions(2.0));
var local = t.ApplyInverse(t.Apply(LengthPoint2.FromMeters(1, 0))); // back to (1, 0)

Compose(Transform2)

Composes this transform with child, returning a single combined transform that is equivalent to applying child first, then this one.

result.Apply(p) == this.Apply(child.Apply(p)) for any point p.

public Transform2 Compose(Transform2 child)

Parameters

child Transform2

The inner (child) transform to apply first.

Returns

Transform2

A single Transform2 equivalent to parent(child(p)).

Examples

var parent = new Transform2(LengthPoint2.FromMeters(2, 0), Direction2.Zero, Ratio.FromDecimalFractions(1.0));
var child  = new Transform2(LengthPoint2.FromMeters(1, 0), Direction2.Zero, Ratio.FromDecimalFractions(1.0));
var combined = parent.Compose(child); // translate by (3, 0) total

Inverse()

Returns the inverse of this transform — applying the inverse undoes this transform.

this.Inverse().Apply(this.Apply(p)) ≈ p for any point p.

public Transform2 Inverse()

Returns

Transform2

The inverse Transform2.

Examples

var t = new Transform2(LengthPoint2.FromMeters(3, 1), Direction2.FromDegrees(30), Ratio.FromDecimalFractions(1.5));
var inv = t.Inverse();
var p = LengthPoint2.FromMeters(5, 2);
// inv.Apply(t.Apply(p)) ≈ p

Lerp(Transform2, Transform2, double)

Linearly interpolates between two transforms.

Position is lerped component-wise; rotation is lerped along the shortest arc (via Lerp(Direction2, Direction2, double)); scale is lerped linearly.

public static Transform2 Lerp(Transform2 a, Transform2 b, double t)

Parameters

a Transform2

The start transform.

b Transform2

The end transform.

t double

Interpolation factor, typically in [0, 1].

Returns

Transform2

A Transform2 interpolated between a and b.

Examples

var a = new Transform2(LengthPoint2.Origin, Direction2.Zero, Ratio.FromDecimalFractions(1.0));
var b = new Transform2(LengthPoint2.FromMeters(10, 0), Direction2.North, Ratio.FromDecimalFractions(2.0));
var mid = Transform2.Lerp(a, b, 0.5); // (5, 0), 45°, 1.5×