A Rust library for exploring symmetry in 2D space with tolerance intervals for floating-point comparisons.
Add this to your Cargo.toml:
[dependencies]
rust-symm = "0.1"See main.rs for example usage.
Given a set of points S_p, a line of symmetry for the set is defined
as a line for which, given any point p_1 in the set, there exists a
point p_2 in S_p that is the reflection of p_1 across the
line. If p_1 is on the line, it is its own reflection.
The problem is to find the set of all lines of symmetry S_ls given a
set of points S_p. Intuitively, the set of all lines that are
equidistant from pairs of different points in S_p (perpendicular
bisectors of point pairs), with the possible addition of a line that
goes through all the points (if there is such a line), forms a set
S_lc (set of candidate lines) that is a superset of S_ls. The
basic proof for this is that if there is a line l_i for which a
point in S_p is both not on the line, and does not have a reflection
across it that is also in S_p, then l_i is simply not a line of
symmetry.
As a first step, the algorithm creates a set of all distinct, order-
insensitive pairs of different points in S_p, called
e_line_generators. Then, a random pair is repeatedly picked from
this set, the perpendicular bisector line is calculated for it, and
all points in the set are checked for symmetry across this candidate
line.
Any pair of points found to constitute a reflection across a candidate
line is removed from e_line_generators, as the pair would generate
the same line being examined. In addition, when a point is found
without a reflection across a particular candidate line, that is when
the candidate line is not a line of symmetry, the algorithm possibly
continues checking points in the input set for reflections across this
line, so that problematic point pairs can potentially be removed from
the generator set. This is an optimization for input sets in which a
high degree of partial symmetry is expected (parameter
high_degree_expected: Option<bool>).
Finally, the existence of a line going through all the points is checked.