Automated Generation of Kempe Linkages for ... - Alexander Kobel

4.4 Presentation of Our Simulation of Kempe Linkages
Figure 4.8: The graphical user interface of our implementation
For a deeper insight to the construction, we log all steps done throughout the construction
in the CindyScript instruction format. Thus the user can redo the operations
in a stand-alone instance of Cinderella and examine the simulation in every detail,
although without our interface to Xalci. For short requests, the user can also use a
CindyScript command line inside our application.
4.4.2 Animations
Sadly, a printout cannot express the dynamic nature of an animation very well. At least
we can give some screenshots throughout a simulation (figures 4.10 and 4.11). We
trace the motion of S while P moves along the curve C = V(y 2 + x 3 − x 2 ); our setup
uses m = n = 1. In the trigonometric form of the polynomial, no offset by constant
terms occurs, so the line S stays on is the y-axis.
When P enters the viewport into the second quadrant, S comes along from above.
Through the self-intersection of the curve in the origin, S continuously passes (0, 1),
to oscillate around the origin while P describes the loop of C. When P leaves the
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