Ports IntBox, the simplest concrete convex tile (RegularTileShape): exact
integer-corner rectangle with contains (border-inclusive and interior),
intersection, union, intersects/overlaps, offset (round half up),
horizontal/vertical offset, shrink, box containment, translate, and
dimension. Adds the package __init__ exporting the geometry API.
The general convex machinery beyond IntBox — TileShape/Simplex/IntOctagon
and polygon split_to_convex — is deferred to the next geometry phase.
Tests cover boundary vs interior containment, degenerate tiles
(empty/point/segment), edge-touching intersects-vs-overlaps, rational
point on a border, and half-up offset rounding.
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.
Ports the point/vector foundation of geometry/planar: Side and Signum
(three-valued signs), Limits, FloatPoint (approximate), and the exact
IntPoint/IntVector plus projective RationalPoint/RationalVector.
Arithmetic model per type is documented in each module. The key
simplification over the Java source: Python's unbounded int makes the
exact orientation determinants and rational (x,y,z) coordinates trivial,
so side_of is kept exact (upstream uses a double for speed) and no
BigInteger or CRIT_INT overflow promotion is needed. Rational points use
the projective triple with z=0 denoting the point at infinity.
Tests cover collinearity, determinants beyond Java long range, rational
equality/reduction, and integer/rational promotion.
rsp2k