Add Navigation AStar Hexagonal demo

AStar hexagonal pathfinding
Format corrections with A Thousand Ships <[email protected]> review
Corrections format with  external linter

```yml
default_install_hook_types: [pre-commit]
repos:

-   repo: https://github.com/pre-commit/pre-commit-hooks
    rev: v4.5.0
    hooks:
    -   id: check-added-large-files
    -   id: check-case-conflict
    -   id: check-merge-conflict
    -   id: end-of-file-fixer
    -   id: trailing-whitespace
    -   id: check-json
    -   id: check-symlinks

-   repo: https://github.com/Scony/godot-gdscript-toolkit
    rev: 4.2.2
    hooks:
        - id: gdlint
          exclude: .*screenshots/
        - id: gdformat
          exclude: .*screenshots/

```

2d/navigation_astar_hexagonal/README.md

@@ -0,0 +1,15 @@
+# Tile-based navigation on hexagonal Tilemap (2D)
+
+Example of using 2D navigation (tile based) on a hexagonal map, using :
+- [`TileMap`](https://docs.godotengine.org/en/stable/classes/class_tilemap.html)
+- [`AStar2D`](https://docs.godotengine.org/en/stable/classes/class_astar2d.html)
+
+Language: GDScript
+
+Renderer: Compatibility
+
+Use mouse left click to interact.
+
+## Screenshots
+
+![Screenshot](screenshots/Hexagon_Navigation_2D.png)

2d/navigation_astar_hexagonal/astar_hex_2d.gd

@@ -0,0 +1,28 @@
+class_name AStarHex2D
+extends AStar2D
+
+var map: TileMap
+
+
+# Final cost used for pathfinding would be weight * cost.
+# See https://docs.godotengine.org/fr/4.x/classes/class_astar3d.html#class-astar3d
+func _compute_cost(_from_id: int, _to_id: int):
+	return 1
+
+
+func _estimate_cost(_from_id: int, _to_id: int):
+	return 1
+
+# Euclidian distance heuristic would not work on hexagonal map with global position because
+# we are not using regular hexagon.
+# https://github.com/godotengine/godot/issues/92338
+
+#func _compute_cost( from_id:int, to_id:int ):
+#var position_from = get_point_position(from_id)
+#var position_to = get_point_position(to_id)
+#return (position_to - position_from).length_squared()
+
+#func _estimate_cost( from_id:int, to_id:int ):
+#var position_from = get_point_position(from_id)
+#var position_to = get_point_position(to_id)
+#return (position_to - position_from).length_squared()

2d/navigation_astar_hexagonal/debug/debug_astar.gd

@@ -0,0 +1,139 @@
+extends Node2D
+
+const BASE_LINE_WIDTH = 3.0
+const DRAW_COLOR: Color = Color.WHITE
+const OFFSET_POSITIONS = Vector2(10, 30)
+const OFFSET_WEIGHT = Vector2(10, -10)
+
+@export var map: Map
+
+var _debug_connections = false
+var _debug_position = false
+var _debug_weights = false
+var _debug_costs = false
+var _debug_path = true
+
+@onready var _font: Font = ThemeDB.fallback_font
+
+
+func _process(_delta):
+	queue_redraw()
+
+
+func draw_arrow(src, dst, color, width, aa = true):
+	var angle = 0.6
+	var size_head = 20
+	var head: Vector2 = (dst - src).normalized() * size_head
+	draw_line(src, dst - head / 2, color, width, aa)
+	draw_polygon(
+			[dst, dst - head.rotated(angle), dst - head.rotated(-angle)], [color, color, color]
+		)
+
+
+func _draw():
+	if _debug_connections:
+		_draw_connections()
+	if _debug_position:
+		_draw_positions()
+	if _debug_weights:
+		_draw_weights()
+	if _debug_costs:
+		_draw_costs()
+	if _debug_path:
+		_draw_path()
+
+
+func _draw_path():
+	if not map._point_path:
+		return
+	var point_start: Vector2i = map._point_path[0]
+	var point_end: Vector2i = map._point_path[len(map._point_path) - 1]
+
+	var last_point = point_start
+	for index in range(1, len(map._point_path)):
+		var current_point = map._point_path[index]
+		draw_line(last_point, current_point, DRAW_COLOR, BASE_LINE_WIDTH, true)
+		draw_circle(current_point, BASE_LINE_WIDTH * 2.0, DRAW_COLOR)
+		last_point = current_point
+
+
+func _draw_weights():
+	for id in map.astar_node.get_point_ids():
+		var position_weight = map.astar_node.get_point_position(id)
+		var cost = map.astar_node.get_point_weight_scale(id)
+		draw_string(
+				_font,
+				position_weight + OFFSET_WEIGHT,
+				str(cost),
+				HORIZONTAL_ALIGNMENT_FILL,
+				-1,
+				16,
+				Color.RED
+			)
+
+
+func _draw_positions():
+	for id in map.astar_node.get_point_ids():
+		var position_label = map.astar_node.get_point_position(id)
+		var position_map = map.local_to_map(map.to_local(map.astar_node.get_point_position(id)))
+		draw_string(
+				_font,
+				position_label + OFFSET_POSITIONS,
+				str(position_map),
+				HORIZONTAL_ALIGNMENT_FILL,
+				-1,
+				16,
+				Color.RED
+			)
+
+
+func _draw_connections():
+	for id in map.astar_node.get_point_ids():
+		for id_con in map.astar_node.get_point_connections(id):
+			var position_start = map.astar_node.get_point_position(id)
+			var position_end = map.astar_node.get_point_position(id_con)
+			var direction = position_end - position_start
+			draw_arrow(
+					position_start,
+					position_end - direction / 4.0,
+					Color(0.0, 1.0, 1.0, 1.0),
+					BASE_LINE_WIDTH * 2,
+					true
+				)
+
+
+func _draw_costs():
+	for id in map.astar_node.get_point_ids():
+		for id_con in map.astar_node.get_point_connections(id):
+			var position_cost_start = map.astar_node.get_point_position(id)
+			var position_cost_end = map.astar_node.get_point_position(id_con)
+			var cost = map.astar_node._compute_cost(id, id_con)
+			draw_string(
+					_font,
+					(position_cost_start + position_cost_end) / 2.0,
+					str("%.2f" % cost),
+					HORIZONTAL_ALIGNMENT_CENTER,
+					-1,
+					16,
+					Color.PINK
+				)
+
+
+func _on_d_path_toggled(toggled_on):
+	_debug_path = toggled_on
+
+
+func _on_d_costs_toggled(toggled_on):
+	_debug_costs = toggled_on
+
+
+func _on_d_positions_toggled(toggled_on):
+	_debug_position = toggled_on
+
+
+func _on_d_connections_toggled(toggled_on):
+	_debug_connections = toggled_on
+
+
+func _on_d_weights_toggled(toggled_on):
+	_debug_weights = toggled_on

2d/navigation_astar_hexagonal/icon.svg.import

@@ -0,0 +1,37 @@
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+
+[deps]
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+editor/scale_with_editor_scale=false
+editor/convert_colors_with_editor_theme=false

2d/navigation_astar_hexagonal/icon.webp.import

@@ -0,0 +1,34 @@
+[remap]
+
+importer="texture"
+type="CompressedTexture2D"
+uid="uid://bnujvgksdtkex"
+path="res://.godot/imported/icon.webp-e94f9a68b0f625a567a797079e4d325f.ctex"
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+
+[deps]
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