# Generated code -- CC0 -- No Rights Reserved -- http://www.redblobgames.com/grids/hexagons/ from __future__ import division from __future__ import print_function import collections import math Point = collections.namedtuple("Point", ["x", "y"]) _Hex = collections.namedtuple("Hex", ["q", "r", "s"]) def Hex(q, r, s): assert not (round(q + r + s) != 0), "q + r + s must be 0" return _Hex(q, r, s) def hex_add(a, b): return Hex(a.q + b.q, a.r + b.r, a.s + b.s) def hex_subtract(a, b): return Hex(a.q - b.q, a.r - b.r, a.s - b.s) def hex_scale(a, k): return Hex(a.q * k, a.r * k, a.s * k) def hex_rotate_left(a): return Hex(-a.s, -a.q, -a.r) def hex_rotate_right(a): return Hex(-a.r, -a.s, -a.q) hex_directions = [Hex(1, 0, -1), Hex(1, -1, 0), Hex(0, -1, 1), Hex(-1, 0, 1), Hex(-1, 1, 0), Hex(0, 1, -1)] def hex_direction(direction): return hex_directions[direction] def hex_neighbor(hex, direction): return hex_add(hex, hex_direction(direction)) hex_diagonals = [Hex(2, -1, -1), Hex(1, -2, 1), Hex(-1, -1, 2), Hex(-2, 1, 1), Hex(-1, 2, -1), Hex(1, 1, -2)] def hex_diagonal_neighbor(hex, direction): return hex_add(hex, hex_diagonals[direction]) def hex_length(hex): return (abs(hex.q) + abs(hex.r) + abs(hex.s)) // 2 def hex_distance(a, b): return hex_length(hex_subtract(a, b)) def hex_round(h): qi = int(round(h.q)) ri = int(round(h.r)) si = int(round(h.s)) q_diff = abs(qi - h.q) r_diff = abs(ri - h.r) s_diff = abs(si - h.s) if q_diff > r_diff and q_diff > s_diff: qi = -ri - si else: if r_diff > s_diff: ri = -qi - si else: si = -qi - ri return Hex(qi, ri, si) def hex_lerp(a, b, t): return Hex(a.q * (1.0 - t) + b.q * t, a.r * (1.0 - t) + b.r * t, a.s * (1.0 - t) + b.s * t) def hex_linedraw(a, b): N = hex_distance(a, b) a_nudge = Hex(a.q + 1e-06, a.r + 1e-06, a.s - 2e-06) b_nudge = Hex(b.q + 1e-06, b.r + 1e-06, b.s - 2e-06) results = [] step = 1.0 / max(N, 1) for i in range(0, N + 1): results.append(hex_round(hex_lerp(a_nudge, b_nudge, step * i))) return results OffsetCoord = collections.namedtuple("OffsetCoord", ["col", "row"]) EVEN = 1 ODD = -1 def qoffset_from_cube(offset, h): col = h.q row = h.r + (h.q + offset * (h.q & 1)) // 2 if offset != EVEN and offset != ODD: raise ValueError("offset must be EVEN (+1) or ODD (-1)") return OffsetCoord(col, row) def qoffset_to_cube(offset, h): q = h.col r = h.row - (h.col + offset * (h.col & 1)) // 2 s = -q - r if offset != EVEN and offset != ODD: raise ValueError("offset must be EVEN (+1) or ODD (-1)") return Hex(q, r, s) def roffset_from_cube(offset, h): col = h.q + (h.r + offset * (h.r & 1)) // 2 row = h.r if offset != EVEN and offset != ODD: raise ValueError("offset must be EVEN (+1) or ODD (-1)") return OffsetCoord(col, row) def roffset_to_cube(offset, h): q = h.col - (h.row + offset * (h.row & 1)) // 2 r = h.row s = -q - r if offset != EVEN and offset != ODD: raise ValueError("offset must be EVEN (+1) or ODD (-1)") return Hex(q, r, s) DoubledCoord = collections.namedtuple("DoubledCoord", ["col", "row"]) def qdoubled_from_cube(h): col = h.q row = 2 * h.r + h.q return DoubledCoord(col, row) def qdoubled_to_cube(h): q = h.col r = (h.row - h.col) // 2 s = -q - r return Hex(q, r, s) def rdoubled_from_cube(h): col = 2 * h.q + h.r row = h.r return DoubledCoord(col, row) def rdoubled_to_cube(h): q = (h.col - h.row) // 2 r = h.row s = -q - r return Hex(q, r, s) Orientation = collections.namedtuple("Orientation", ["f0", "f1", "f2", "f3", "b0", "b1", "b2", "b3", "start_angle"]) Layout = collections.namedtuple("Layout", ["orientation", "size", "origin"]) layout_pointy = Orientation(math.sqrt(3.0), math.sqrt(3.0) / 2.0, 0.0, 3.0 / 2.0, math.sqrt(3.0) / 3.0, -1.0 / 3.0, 0.0, 2.0 / 3.0, 0.5) layout_flat = Orientation(3.0 / 2.0, 0.0, math.sqrt(3.0) / 2.0, math.sqrt(3.0), 2.0 / 3.0, 0.0, -1.0 / 3.0, math.sqrt(3.0) / 3.0, 0.0) def hex_to_pixel(layout, h): M = layout.orientation size = layout.size origin = layout.origin x = (M.f0 * h.q + M.f1 * h.r) * size.x y = (M.f2 * h.q + M.f3 * h.r) * size.y return Point(x + origin.x, y + origin.y) def pixel_to_hex(layout, p): M = layout.orientation size = layout.size origin = layout.origin pt = Point((p.x - origin.x) / size.x, (p.y - origin.y) / size.y) q = M.b0 * pt.x + M.b1 * pt.y r = M.b2 * pt.x + M.b3 * pt.y return Hex(q, r, -q - r) def hex_corner_offset(layout, corner): M = layout.orientation size = layout.size angle = 2.0 * math.pi * (M.start_angle - corner) / 6.0 return Point(size.x * math.cos(angle), size.y * math.sin(angle)) def polygon_corners(layout, h): corners = [] center = hex_to_pixel(layout, h) for i in range(0, 6): offset = hex_corner_offset(layout, i) corners.append(Point(center.x + offset.x, center.y + offset.y)) return corners # Tests def complain(name): print("FAIL {0}".format(name)) def equal_hex(name, a, b): if not (a.q == b.q and a.s == b.s and a.r == b.r): complain(name) def equal_offsetcoord(name, a, b): if not (a.col == b.col and a.row == b.row): complain(name) def equal_doubledcoord(name, a, b): if not (a.col == b.col and a.row == b.row): complain(name) def equal_int(name, a, b): if not (a == b): complain(name) def equal_hex_array(name, a, b): equal_int(name, len(a), len(b)) for i in range(0, len(a)): equal_hex(name, a[i], b[i]) def test_hex_arithmetic(): equal_hex("hex_add", Hex(4, -10, 6), hex_add(Hex(1, -3, 2), Hex(3, -7, 4))) equal_hex("hex_subtract", Hex(-2, 4, -2), hex_subtract(Hex(1, -3, 2), Hex(3, -7, 4))) def test_hex_direction(): equal_hex("hex_direction", Hex(0, -1, 1), hex_direction(2)) def test_hex_neighbor(): equal_hex("hex_neighbor", Hex(1, -3, 2), hex_neighbor(Hex(1, -2, 1), 2)) def test_hex_diagonal(): equal_hex("hex_diagonal", Hex(-1, -1, 2), hex_diagonal_neighbor(Hex(1, -2, 1), 3)) def test_hex_distance(): equal_int("hex_distance", 7, hex_distance(Hex(3, -7, 4), Hex(0, 0, 0))) def test_hex_rotate_right(): equal_hex("hex_rotate_right", hex_rotate_right(Hex(1, -3, 2)), Hex(3, -2, -1)) def test_hex_rotate_left(): equal_hex("hex_rotate_left", hex_rotate_left(Hex(1, -3, 2)), Hex(-2, -1, 3)) def test_hex_round(): a = Hex(0.0, 0.0, 0.0) b = Hex(1.0, -1.0, 0.0) c = Hex(0.0, -1.0, 1.0) equal_hex("hex_round 1", Hex(5, -10, 5), hex_round(hex_lerp(Hex(0.0, 0.0, 0.0), Hex(10.0, -20.0, 10.0), 0.5))) equal_hex("hex_round 2", hex_round(a), hex_round(hex_lerp(a, b, 0.499))) equal_hex("hex_round 3", hex_round(b), hex_round(hex_lerp(a, b, 0.501))) equal_hex("hex_round 4", hex_round(a), hex_round(Hex(a.q * 0.4 + b.q * 0.3 + c.q * 0.3, a.r * 0.4 + b.r * 0.3 + c.r * 0.3, a.s * 0.4 + b.s * 0.3 + c.s * 0.3))) equal_hex("hex_round 5", hex_round(c), hex_round(Hex(a.q * 0.3 + b.q * 0.3 + c.q * 0.4, a.r * 0.3 + b.r * 0.3 + c.r * 0.4, a.s * 0.3 + b.s * 0.3 + c.s * 0.4))) def test_hex_linedraw(): equal_hex_array("hex_linedraw", [Hex(0, 0, 0), Hex(0, -1, 1), Hex(0, -2, 2), Hex(1, -3, 2), Hex(1, -4, 3), Hex(1, -5, 4)], hex_linedraw(Hex(0, 0, 0), Hex(1, -5, 4))) def test_layout(): h = Hex(3, 4, -7) flat = Layout(layout_flat, Point(10.0, 15.0), Point(35.0, 71.0)) equal_hex("layout", h, hex_round(pixel_to_hex(flat, hex_to_pixel(flat, h)))) pointy = Layout(layout_pointy, Point(10.0, 15.0), Point(35.0, 71.0)) equal_hex("layout", h, hex_round(pixel_to_hex(pointy, hex_to_pixel(pointy, h)))) def test_offset_roundtrip(): a = Hex(3, 4, -7) b = OffsetCoord(1, -3) equal_hex("conversion_roundtrip even-q", a, qoffset_to_cube(EVEN, qoffset_from_cube(EVEN, a))) equal_offsetcoord("conversion_roundtrip even-q", b, qoffset_from_cube(EVEN, qoffset_to_cube(EVEN, b))) equal_hex("conversion_roundtrip odd-q", a, qoffset_to_cube(ODD, qoffset_from_cube(ODD, a))) equal_offsetcoord("conversion_roundtrip odd-q", b, qoffset_from_cube(ODD, qoffset_to_cube(ODD, b))) equal_hex("conversion_roundtrip even-r", a, roffset_to_cube(EVEN, roffset_from_cube(EVEN, a))) equal_offsetcoord("conversion_roundtrip even-r", b, roffset_from_cube(EVEN, roffset_to_cube(EVEN, b))) equal_hex("conversion_roundtrip odd-r", a, roffset_to_cube(ODD, roffset_from_cube(ODD, a))) equal_offsetcoord("conversion_roundtrip odd-r", b, roffset_from_cube(ODD, roffset_to_cube(ODD, b))) def test_offset_from_cube(): equal_offsetcoord("offset_from_cube even-q", OffsetCoord(1, 3), qoffset_from_cube(EVEN, Hex(1, 2, -3))) equal_offsetcoord("offset_from_cube odd-q", OffsetCoord(1, 2), qoffset_from_cube(ODD, Hex(1, 2, -3))) def test_offset_to_cube(): equal_hex("offset_to_cube even-", Hex(1, 2, -3), qoffset_to_cube(EVEN, OffsetCoord(1, 3))) equal_hex("offset_to_cube odd-q", Hex(1, 2, -3), qoffset_to_cube(ODD, OffsetCoord(1, 2))) def test_doubled_roundtrip(): a = Hex(3, 4, -7) b = DoubledCoord(1, -3) equal_hex("conversion_roundtrip doubled-q", a, qdoubled_to_cube(qdoubled_from_cube(a))) equal_doubledcoord("conversion_roundtrip doubled-q", b, qdoubled_from_cube(qdoubled_to_cube(b))) equal_hex("conversion_roundtrip doubled-r", a, rdoubled_to_cube(rdoubled_from_cube(a))) equal_doubledcoord("conversion_roundtrip doubled-r", b, rdoubled_from_cube(rdoubled_to_cube(b))) def test_doubled_from_cube(): equal_doubledcoord("doubled_from_cube doubled-q", DoubledCoord(1, 5), qdoubled_from_cube(Hex(1, 2, -3))) equal_doubledcoord("doubled_from_cube doubled-r", DoubledCoord(4, 2), rdoubled_from_cube(Hex(1, 2, -3))) def test_doubled_to_cube(): equal_hex("doubled_to_cube doubled-q", Hex(1, 2, -3), qdoubled_to_cube(DoubledCoord(1, 5))) equal_hex("doubled_to_cube doubled-r", Hex(1, 2, -3), rdoubled_to_cube(DoubledCoord(4, 2))) def test_all(): test_hex_arithmetic() test_hex_direction() test_hex_neighbor() test_hex_diagonal() test_hex_distance() test_hex_rotate_right() test_hex_rotate_left() test_hex_round() test_hex_linedraw() test_layout() test_offset_roundtrip() test_offset_from_cube() test_offset_to_cube() test_doubled_roundtrip() test_doubled_from_cube() test_doubled_to_cube() if __name__ == '__main__': test_all()