Entity3D: позиция, поворот и масштаб родителя

using System;
using Reckfell;

public partial class TransformRig3D : Entity3D
{
    public Entity3D Pivot { get; private set; } = null!;
    public MeshInstance3D Marker { get; private set; } = null!;
    public Plane GroundPlane => new(Vector3.Up, 0);
    public Vector3 ProjectedPoint => GroundPlane.Project(Marker.GlobalPosition);

    private static MeshInstance3D Box(Vector3 size, Color color, Vector3 position)
    {
        return new MeshInstance3D
        {
            Mesh = new BoxMesh { Size = size }, Position = position,
            MaterialOverride = new StandardMaterial3D
            {
                AlbedoColor = color, ShadingMode = BaseMaterial3D.ShadingModeEnum.Unshaded
            }
        };
    }

    public override void _Ready()
    {
        AddChild(new WorldEnvironment { Environment = new Reckfell.Environment
        {
            BackgroundMode = Reckfell.Environment.BGMode.Color,
            BackgroundColor = new Color(0.035f, 0.04f, 0.05f)
        }});
        AddChild(Box(new Vector3(8, 0.05f, 6), new Color(0.10f, 0.11f, 0.13f), new Vector3(0, -0.025f, 0)));
        Pivot = new Entity3D
        {
            Position = new Vector3(1, 0, 0), Rotation = new Vector3(0, Mathf.Pi / 4, 0),
            Scale = new Vector3(1.5f, 1, 0.6f)
        };
        AddChild(Pivot);
        Pivot.AddChild(Box(new Vector3(1.6f, 0.045f, 0.045f), new Color(0.25f, 0.46f, 1), new Vector3(0.8f, 0, 0)));
        Pivot.AddChild(Box(new Vector3(0.045f, 1.5f, 0.045f), Colors.White, new Vector3(0, 0.75f, 0)));
        Pivot.AddChild(Box(new Vector3(0.045f, 0.045f, 1.5f), new Color(0.45f, 0.48f, 0.55f), new Vector3(0, 0, 0.75f)));
        Marker = Box(new Vector3(0.2f, 0.2f, 0.2f), new Color(0.25f, 0.46f, 1), new Vector3(1, 1, 0));
        Pivot.AddChild(Marker);
        AddChild(Box(new Vector3(0.25f, 0.035f, 0.25f), Colors.White, ProjectedPoint + Vector3.Up * 0.025f));
        var camera = new Camera3D { Position = new Vector3(5, 4.5f, 7), Current = true, Fov = 48 };
        AddChild(camera); camera.LookAt(new Vector3(0.7f, 0.4f, 0), Vector3.Up);
        var canvas = new CanvasLayer(); AddChild(canvas);
        bool ru = TranslationServer.GetLocale().StartsWith("ru");
        var title = new Label { Position = new Vector2(24, 20), Text = ru
            ? "Локальная точка и мировая плоскость" : "A local point and a world-space plane" };
        title.AddThemeFontSizeOverride("font_size", 22); canvas.AddChild(title);
        canvas.AddChild(new Label { Position = new Vector2(24, 58), Text = ru
            ? "Синий куб: local (1,1,0). Белая метка: проекция на Y = 0."
            : "Blue cube: local (1,1,0). White marker: projection onto Y = 0." });
        ReckfellApi.Print("TRANSFORM local=" + Pivot.ToLocal(Marker.GlobalPosition));
    }

    public static bool TryTransformNormal(Basis basis, Vector3 normal, out Vector3 result)
    {
        result = Vector3.Zero;
        if (!basis.IsFinite() || !normal.IsFinite() || normal.LengthSquared() < 0.000001f ||
            MathF.Abs(basis.Determinant()) < 0.000001f) return false;
        Vector3 transformed = basis.Inverse().Transposed() * normal;
        if (!transformed.IsFinite() || transformed.LengthSquared() < 0.000001f) return false;
        result = transformed.Normalized();
        return true;
    }
}