From BlenderWiki

Keyframing and Ipo Curves

The concept of Interpolation

Quite obviously, something is "animated" when it changes over time.
In Blender, animating an object means changing its properties as its X location, or the Red channel value of its material diffuse color, and so on, during a certain amount of time.

As mentioned, Blender's fundamental unit of time is the "frame", which usually lasts just a fraction of a second, depending on the frame rate of the scene.

As animation is composed of incremental changes spanning multiple frames, usually these properties ARE NOT manually modified frame by frame, because:

• it would take ages!
• it would be very difficult to get smooth variations of the property (unless you compute mathematical functions and type a precise value for each frame, which would be crazy).

This is why nearly all direct animation is done using interpolation.

The idea is simple: you define a few “control points”, called "keyframes", which are multiple frames apart.
Between these keyframes, the properties' values are computed (interpolated) by Blender and filled in. Thus, the animators' workload is significantly reduced.

For example, if you have:

• a control point of value 0 at frame 0,
• another one of value 10 at frame 25,
• linear interpolation,

then, at frame 5 we get a value of 2.

The same goes for all intermediate frames: with just two points, you get a smooth growth from 0 to 10 along the 25 frames. Obviously, if you’d like the frame 15 to have a value of 9, you’d have to add another control point (or keyframe)…

Ipo curve

Definition

In Blender, all standard direct animation uses “Ipo curves”, which stands for “InterPOlation curves”. An Ipo curve is a curve that control the value of a property, based on time, or, technically, it maps the time to the value.

The Ipo Curve Editor is where you edit Ipo curves.

Types of interpolation

Despite of the name “curve”, it might be a set a linear segments, or even a set of discrete values (materialized as a “stairway curve”), depending on the interpolation mode chosen.

Direction of time

Altough Ipo curves are very similar to Bézier curves, there are some important differences.

For obvious reasons, a property represented by an Ipo Curves cannot have more than one value at a given time, hence:

• when you move a control point ahead of a control point that was previously ahead of the point that you are moving, the two control points switch their order in the edited curve, to avoid that the curve goes back in time
• for the above reason, it's impossible to have a closed Ipo curve

Two control points switching: the curve can't go back in time!

Before moving the second keyframe

After moving the second keyframe

Keyframes

This a bit a fuzzy word, as depending on the context, it might designate two different (even though related) things:

Referred to a single Ipo curve

Each of its control points is often called "a keyframe".

Referred to a set of Ipo curves or Actions

All control points of different properties that have exactly the same time value.