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 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.
rsp2k