Ardour offers two modes for interpolating automation control points: Linear and Discrete. The mode is changed by a Right click on the automation lane header and choosing the mode from the mode menu.
Linear mode interpolates values between control points in a given automation curve by connecting them with straight lines; the values played back are derived from the points that lie on the lines thus defined. Typically, this is what is desired and is the default mode for all automation lanes.
Discrete mode does no interpolation between control points in a given automation curve. The values set by the control points do not change until the following control point is reached at which time the value is then set to its value; this continues on until there are no more control points. Typically this is used for parameters such as mute or sustain pedal (e.g., on a MIDI piano track).
When recording automation via MIDI (e.g., pitch bend from a MIDI keyboard), Ardour always uses discrete mode.