Fig.1
Fig.2

As seen in Fig.1, it is supposed that a point P moves on a line AB as an intermediate variable varies in the range of .
As the orthogonal coordinates of the point P is put with , the equation expressing such coordinates is assumed as the following with the use of the constants a, b and p.
. (1)
where Eq.(1) gives the curve shown in Fig.2.
In the next, vector which makes point P a cardinal point is assumed as the following with the use of the constants c, k and q.
, (2)
where i represents the imaginary unit.
Then, the coordinates is expressed as the following equations, and the point Q may display a curve which represents character S as the intermediate variable varies in the range of
, (3)
and
, (4)
where .
When the intermediate variable varies in the range of , the curves which Eqs.(3) and (4) display are shown in the following figures.
