9. Csound
argument mapping
When
three pairs of input/output values are supplied, BP2 attempts to define a
quadratic mapping from the input (x) to the output (y). Fig.20 is an example
of a successful mapping.
Fig.20
A simple quadratic mapping
BP2
expects the mapping function to be monotonous, i.e. the three values (x1, x2,
x3) supplied as the input and the ones supplied as the output (y1, y2, y3) must
be strictly ordered. Even in this case a proper quadratic mapping may not be
possible. See for instance Fig.21.
Fig.21
An incorrect mapping
Here
the quadratic function is not monotonous even though the input values are
ordered properly. In this case, BP2 replaces the incorrect part (the one
containing an extremum) with a linear function, and changes the other part to
make the curve tangent to the linear part. This yields the graph shown Fig.22.
Fig.22
The correct mapping
