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The tangent of a function curve affects the interpolated values between the keys of an animation. Most animation controllers use fixed tangents to define the function curve at a key location.

By default, 3ds Max Design assigns smooth tangents to the keys in a Position function curve. This is the reason that an animated object moves in smooth curves through the key frames. 3ds Max Design assigns smooth tangents because they usually provide the most natural motion.

Of course, you also need a way to add some corners and abrupt turns when you need them. The Linear controller uses a discontinuous tangent that points at the preceding and following keys, producing an abrupt change in motion at that key.

The two large flyout buttons at the bottom of the Key Info dialog provide five different types of predefined tangent types, plus a sixth type that lets you create your own custom tangents.

If you look at a single key dot and the line running through it, the line on the left side of the key dot is the incoming tangent, and the line on the right is the outgoing tangent. Using the tangent flyout buttons, you can assign a different tangent type to the incoming and the outgoing lines for each key dot.

The button on the left assigns the incoming tangent at the left side of the selected key dot, and the button on the right assigns the outgoing tangent on the right side of the selected key dot.