.. _doc_interpolation: Interpolation ============= Interpolation is a very basic operation in graphics programming. It's good to become familiar with it in order to expand your horizons as a graphics developer. The basic idea is that you want to transition from A to B. A value ``t``, represents the states in-between. As an example if ``t`` is 0, then the state is A. If ``t`` is 1, then the state is B. Anything in-between is an *interpolation*. Between two real (floating-point) numbers, a simple interpolation is usually described as: :: interpolation = A * (1 - t) + B * t And often simplified to: :: interpolation = A + (B - A) * t The name of this type of interpolation, which transforms a value into another at *constant speed* is *"linear"*. So, when you hear about *Linear Interpolation*, you know they are referring to this simple formula. There are other types of interpolations, which will not be covered here. A recommended read afterwards is the :ref:`Bezier ` page. Vector interpolation -------------------- Vector types (:ref:`Vector2 ` and :ref:`Vector3 `) can also be interpolated, they come with handy functions to do it :ref:`Vector2.linear_interpolate() ` and :ref:`Vector3.linear_interpolate() `. For cubic interpolation, there are also :ref:`Vector2.cubic_interpolate() ` and :ref:`Vector3.cubic_interpolate() `, which do a :ref:`Bezier ` style interpolation. Here is simple pseudo-code for going from point A to B using interpolation: .. tabs:: .. code-tab:: gdscript GDScript var t = 0.0 func _physics_process(delta): t += delta * 0.4 \$Sprite.position = \$A.position.linear_interpolate(\$B.position, t) .. code-tab:: csharp private float _t = 0.0f; public override void _PhysicsProcess(float delta) { _t += delta * 0.4f; Position2D a = GetNode("A"); Position2D b = GetNode("B"); Sprite sprite = GetNode("Sprite"); sprite.Position = a.Position.LinearInterpolate(b.Position, _t); } It will produce the following motion: .. image:: img/interpolation_vector.gif Transform interpolation ----------------------- It is also possible to interpolate whole transforms (make sure they have either uniform scale or, at least, the same non-uniform scale). For this, the function :ref:`Transform.interpolate_with() ` can be used. Here is an example of transforming a monkey from Position1 to Position2: .. image:: img/interpolation_positions.png Using the following pseudocode: .. tabs:: .. code-tab:: gdscript GDScript var t = 0.0 func _physics_process(delta): t += delta \$Monkey.transform = \$Position1.transform.interpolate_with(\$Position2.transform, t) .. code-tab:: csharp private float _t = 0.0f; public override void _PhysicsProcess(float delta) { _t += delta; Position3D p1 = GetNode("Position1"); Position3D p2 = GetNode("Position2"); CSGMesh monkey = GetNode("Monkey"); monkey.Transform = p1.Transform.InterpolateWith(p2.Transform, _t); } And again, it will produce the following motion: .. image:: img/interpolation_monkey.gif Smoothing motion ---------------- Interpolation can be used to smooth movement, rotation, etc. Here is an example of a circle following the mouse using smoothed motion: .. tabs:: .. code-tab:: gdscript GDScript const FOLLOW_SPEED = 4.0 func _physics_process(delta): var mouse_pos = get_local_mouse_position() \$Sprite.position = \$Sprite.position.linear_interpolate(mouse_pos, delta * FOLLOW_SPEED) .. code-tab:: csharp private const float FollowSpeed = 4.0f; public override void _PhysicsProcess(float delta) { Vector2 mousePos = GetLocalMousePosition(); Sprite sprite = GetNode("Sprite"); sprite.Position = sprite.Position.LinearInterpolate(mousePos, delta * FollowSpeed); } Here is how it looks: .. image:: img/interpolation_follow.gif This useful for smoothing camera movement, allies following you (ensuring they stay within a certain range), and many other common game patterns.