Returns the positive real value of smallest magnitude
\epsilon which an element of a Transform should
contain. An element of a Transform may also contain
-\epsilon.
The value \epsilon is used for in the
function clean() (see Transform Reference; Cleaning).
It will also be used for comparing Transforms, when I've added
the equality operator Transform::operator==().
epsilon() returns different values, depending on whether
real is float or double:
If real is float (the default), epsilon()
returns 0.00001.
If real is double, it returns 0.000000001.
Please note: I haven't tested whether 0.000000001 is a good
value yet, so users should be aware of this if they set real to
double!1
The way to test this is to transform two different
Transforms
t_1 and t_2
using different rotations in such a way that the end
result should be the same for both Transforms.
Let \epsilon stand for the value returned by epsilon().
If for all sets of
corresponding elements E_1 and E_2 of t_1 and
t_2, ||E_1| - |E_2|| \le \epsilon, then
\epsilon is a good value.
It will be easier to test this when I've added
Transform::operator==().
Rotation causes a significant loss of precision to due to the use of the
sin() and cos() functions. Therefore, neither
Transform::epsilon() nor Point::epsilon()
(see Point Reference; Returning Information) can be as small as I'd like them to be. If they are two
small, operations that test for equality of Transforms and
Points will return false for objects that should be equal.
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