--- /dev/null
+# Copyright 2023 highstreet technologies GmbH
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+# inspired by http://www.redblobgames.com/grids/hexagons/
+
+#!/usr/bin/python
+
+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()
Code Review / oam.git / commitdiff