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

4.1 Some Design Aspects of Cinderella
(a) Euclidean view
(b) spherical view
Figure 4.2: The intersection of two parallel lines at infinity
are considered to be invalid by other applications.
Automatical input generation benefits in additional extent, because a design can be
done in one go and moved to a nonsingular position later. The treatment of degenerate
cases in R 2 is left to Cinderella and cannot cause any inconsistencies.
4.1.2 Continuity
As the term “dynamic geometry” suggests, constructions can be modified once they
are established. The users then expect a construction to behave “nicely” when input
elements are moved, which means that no sudden jumps occur when the input is
changed continuously. The situation in figure 4.3 serves as an example for the behaviour
of a continuous geometry system versus so called deterministic approaches. The black
line is defined as the angular bisector of the blue and red line, a geometric primitive
offered by any system.
(a) starting position
(b) situation after a rotation of the
red line by 180 degrees
Figure 4.3: The angular bisector in continuous and deterministic geometry systems
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