Interpolation

The basic idea is that you want to transition from A to B. A value , represents the states in-between.

As an example if is 0, then the state is A. If 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:

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And often simplified to:

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which is exactly the same.

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.

Vector types ( and Vector3) can also be interpolated, they come with handy functions to do it and Vector3.linear_interpolate().

For cubic interpolation, there are also and Vector3.cubic_interpolate(), which do a style interpolation.

Here is simple pseudo-code for going from point A to B using interpolation:

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It will produce the following motion:

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 Transform.interpolate_with() can be used.

Here is an example of transforming a monkey from Position1 to Position2:

Using the following pseudocode:

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And again, it will produce the following motion:

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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Here is how it looks: