A Displacement represents a geometric position along a line segment, expressed in terms of two quantities: a relative position called a, and an absolute offset called b. The length of the line segment is not known in advance --- the idea is that the Displacement object encapsulates a rule for determining a location along ANY line segment. The Displacement has methods which take the line segment length as an argument and return the computed final position.

There are two different position-calcuating methods, corresponding to two different interpretations of the relative value a:

relative length: a is a number between 0 and 1, representing a fraction of the total length of the line segment; the relative position determined by a is the fraction a of the total length of the segment. In this case, the position-calculating method calculateLength(L) returns the number a * L + b, which corresponds to moving a of the way along the length L, then adding b:

        [--------------------------------X------------]
        |<---- a * L --->|<---- b ------>|
        |<------------------  L  -------------------->|

relative coordinate: a is a number between -1 and 1, representing a coordinate value in a [-1,1] coordinate system along the line segment. In this case, the position-calculating method calculateCoordinate(L) returns the number (a+1) * L/2 + b. which corresponds to moving to the position determined by the a coordinate, then adding b:

        [------------------------------------X--------]
        |<--- (a+1) * L/2 --->|<---- b ----->|
        |<------------------  L  -------------------->|