You can use the line~ object to supply a changing speed value to the right inlet of the sfplay~ object. The second outlet of the function object sends out a list message intended to describe the function to a line~ object.
The function object can be used to create line segment functions that control a line~ object, and it can also be used as a lookup table. A number coming in its inlet will be treated as a point on the x-axis, and whatever y-axis value is shown on the line segment function at that point will be sent out the leftmost outlet. This example patch demonstrates that use of function.
Each MSP object (each object that has signal input and/or output) is always producing signal as long as audio is turned on. For example, signal generators like cycle~ (sinusoidal wave generator) and saw~ (band-limited sawtooth wave generator) are always producing a full-amplitude wave. You control the amplitude of that wave with multiplication, using *~ or some other object that performs a multiplication internally (such as gain~).
The function object assists you to make shapes composed of line segments. When you send a bang to the function, it sends out of its second outlet a list of destination value and ramp time pairs suitable for use as input to a line~ object. In that way, the shape shown in the function object serves as a function over time, the shape of which will be enacted by the signal coming out of the line~ object.
Simple linear motion in 2D animation is achieved by interpolating between two points and successively drawing an object at each intermediate point, as demonstrated in the example on Animating 2D graphics.
You can obtain values that change exponentially or logarithmically by using the pow object or by using the pow($f1,$f2) function in the expr object.
The real value of phasor~ is that it provides a very accurate way to read through (or mathematically calculate) some nonlinear shape to use as a control signal (or even as an audio signal). Among other things, it might be used to create a "window" shape that can serve as an amplitude envelope for a sound. This patch demonstrates five different ways to create window or waveform shapes with phasor~. We'll discuss them (in good Max fashion) from right to left.
The line~ object generates a signal that interpolates linearly from its current value to a new destination value in a specified amount of time. It receives messages specifying a new value and the amount of time (in milliseconds) in which to get there.
The line~ object is intended for use as a control signal for audio. You don't listen to line~ directly, but it's very effective as a controller/modifier/modulator of other signals. A pair of numbers (i.e. a two-item space-separated list of numbers) tells line~ a destination value and a time (in milliseconds) to get to that value.