Ports geometry/planar/Polygon.java (corner de-duplication and collinear
removal, winding number) and PolygonShape.java, including the recursive
split_to_convex that decomposes a simple polygon into convex Simplex
tiles by dividing at concave corners along minimal axis-parallel lines.
Orientation and convexity tests are exact; the division-point search is
approximate (float line evaluation, split point rounded to an integer
corner) as upstream. The concave-corner search starts deterministically
at corner 0 rather than a seeded PRNG; this only affects which valid
decomposition is produced.
Supporting additions: Simplex.from_corners (convex polygon to simplex)
and Line.function_value_approx / function_in_y_value_approx.
Invariant tests over L, plus, staircase and square polygons: tile areas
sum to the polygon area (no gaps, no overlap), a point is in the polygon
iff in some tile, and no point is strictly inside more than one tile
(interiors disjoint). Also covers Polygon normalization and orientation.
Ports geometry/planar/TileShape.java (the border-line-based containment,
area, and centre-of-gravity logic) and Simplex.java (a convex region as
the intersection of directed half-planes). Corners are exact
intersections of consecutive border lines; point containment uses exact
side_of. The remove_redundant_lines normalization — dropping lines that
do not contribute and detecting emptiness — is ported line-for-line.
Supporting additions: Line.compare_to/__lt__ (angular sort order),
Line.fast_equals, Line.side_of_intersection, Line.translate (perpendicular
offset), IntDirection.determinant, and IntBox.to_simplex.
offset is approximate (rounded translated lines, as upstream); enlarge
clips to the enlarged bounding box pending the IntOctagon port.
Since there is no JVM oracle, tests assert invariants: corners lie
exactly on their border lines (exact side_of == 0), IntBox -> Simplex
preserves the region over a sampled grid, intersection is contained in
both operands and a point is in the result iff in both, and get_instance
normalization drops redundant lines and detects empty half-plane pairs.
Ports Direction/IntDirection (equivalence classes of vectors, gcd-
normalized, exact angular compare) and Line. Line.side_of uses an exact
integer determinant; Line.intersection returns an IntPoint when the
crossing is integral and a RationalPoint otherwise, with the orthogonal
and 45-degree fast paths from the source preserved. Parallel lines yield
a point at infinity (z=0). BigIntDirection is folded into IntDirection
since unbounded int always fits.
Tests cover integral and rational intersections, parallel-line infinity,
exactness beyond double precision (verified via exact collinearity of the
result), and direction normalization/ordering.
rsp2k