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99 lines
3.4 KiB
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99 lines
3.4 KiB
ReStructuredText
.. _doc_interpolation:
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Interpolation
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=============
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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.
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The basic idea is that you want to transition from A to B. A value ``t``, represents the states in-between.
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For 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*.
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Between two real (floating-point) numbers, an interpolation can be described as:
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.. tabs::
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.. code-tab:: gdscript GDScript
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interpolation = A * (1 - t) + B * t
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And often simplified to:
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.. tabs::
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.. code-tab:: gdscript GDScript
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interpolation = A + (B - A) * t
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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 formula.
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There are other types of interpolations, which will not be covered here. A recommended read afterwards is the :ref:`Bezier <doc_beziers_and_curves>` page.
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Vector interpolation
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--------------------
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Vector types (:ref:`Vector2 <class_Vector2>` and :ref:`Vector3 <class_Vector3>`) can also be interpolated, they come with handy functions to do it
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:ref:`Vector2.linear_interpolate() <class_Vector2_method_linear_interpolate>` and :ref:`Vector3.linear_interpolate() <class_Vector3_method_linear_interpolate>`.
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For cubic interpolation, there are also :ref:`Vector2.cubic_interpolate() <class_Vector2_method_cubic_interpolate>` and :ref:`Vector3.cubic_interpolate() <class_Vector3_method_cubic_interpolate>`, which do a :ref:`Bezier <doc_beziers_and_curves>` style interpolation.
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Here is example pseudo-code for going from point A to B using interpolation:
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.. tabs::
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.. code-tab:: gdscript GDScript
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func _physics_process(delta):
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t += delta * 0.4
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$Sprite2D.position = $A.position.linear_interpolate($B.position, t)
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It will produce the following motion:
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.. image:: img/interpolation_vector.gif
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Transform interpolation
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-----------------------
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It is also possible to interpolate whole transforms (make sure they have either uniform scale or, at least, the same non-uniform scale).
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For this, the function :ref:`Transform.interpolate_with() <class_Transform_method_interpolate_with>` can be used.
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Here is an example of transforming a monkey from Position1 to Position2:
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.. image:: img/interpolation_positions.png
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Using the following pseudocode:
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.. tabs::
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.. code-tab:: gdscript GDScript
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var t = 0.0
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func _physics_process(delta):
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t += delta
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$Monkey.transform = $Position1.transform.interpolate_with($Position2.transform, t)
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And again, it will produce the following motion:
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.. image:: img/interpolation_monkey.gif
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Smoothing motion
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----------------
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Interpolation can be used to smooth movement, rotation, etc. Here is an example of a circle following the mouse using smoothed motion:
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.. tabs::
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.. code-tab:: gdscript GDScript
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const FOLLOW_SPEED = 4.0
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func _physics_process(delta):
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var mouse_pos = get_local_mouse_position()
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$Sprite2D.position = $Sprite2D.position.linear_interpolate(mouse_pos, delta * FOLLOW_SPEED)
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Here is how it looks:
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.. image:: img/interpolation_follow.gif
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This useful for smoothing camera movement, allies following you (ensuring they stay within a certain range), and many other common game patterns.
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