Wrote a shader

building.gd

@@ -0,0 +1,27 @@
+class_name Building extends Node2D
+
+var location : Vector2i # x is the angle, y is the height in the grid
+var dimension : Vector2i = Vector2.ONE # same as above
+@onready var grid : Grid = get_parent()
+
+# make sure location is set before adding a building to the scene tree
+# also make sure that the buildings are instantiated as children of the grid
+func _ready() -> void:
+	var angle = location.x * TAU / grid.num_collumns; # currently assumes anchor is bottom left
+	var height = grid.ground_radius + location.y * grid.cell_height;
+	position = height * Vector2.from_angle(angle)
+	print(angle, "   ", height, "   ", position)
+
+func overlaps(other : Building):
+	# heights don't overlap
+	if location.y >= other.location.y + other.dimension.y: return false # other is below
+	if location.y + dimension.y <= other.location.y: return false # other is above
+	
+	# angles overlap. We can now assume heights overlap
+	var relative_other_loc = (other.location.x - location.x + grid.num_collumns) % grid.num_collumns
+	if dimension.x > relative_other_loc: return true
+	if relative_other_loc + other.dimension > grid.num_collumns: return true
+	
+	# If we get here, angles do not overlap
+	return false
+	

building.gd.uid

@@ -0,0 +1 @@
+uid://b2ji03ekijjnn

building.gdshader

@@ -0,0 +1,34 @@
+shader_type canvas_item;
+
+uniform ivec2 location;
+uniform ivec2 dimension = ivec2(1,1);
+
+uniform float ground_height = 3000.;
+uniform float cell_height = 300.;
+uniform int num_cells = 60;
+
+varying vec2 world_position;
+
+void vertex()
+{
+    world_position = (MODEL_MATRIX * vec4(VERTEX, 0.0, 1.0)).xy;
+}
+
+void fragment() {
+	float radius = sqrt(world_position.x * world_position.x + world_position.y * world_position.y);
+	float angle = atan(world_position.y, world_position.x);
+
+	float sample_y = 1. - ((radius - ground_height) / cell_height - float( location.y)) / float(dimension.y);
+	float sample_x = mod(fract(angle / TAU + 1.) * float(num_cells) - float(location.x) + float(num_cells), float(num_cells)) / float(dimension.x);
+
+	if(sample_y > 1. || sample_y < 0. || sample_x > 1. || sample_x < 0.) {
+		discard;
+	}
+	COLOR = texture(TEXTURE, vec2(sample_x, sample_y));
+
+}
+
+//void light() {
+//	// Called for every pixel for every light affecting the CanvasItem.
+//	// Uncomment to replace the default light processing function with this one.
+//}

building.gdshader.uid

@@ -0,0 +1 @@
+uid://c7gb1nqwvkr37

building.tscn

@@ -0,0 +1,22 @@
+[gd_scene load_steps=5 format=3 uid="uid://djawvtdwp423v"]
+
+[ext_resource type="Script" uid="uid://b2ji03ekijjnn" path="res://building.gd" id="1_5j34s"]
+[ext_resource type="Texture2D" uid="uid://cy70quh6k3s1j" path="res://icon.svg" id="2_2yopf"]
+[ext_resource type="Shader" uid="uid://c7gb1nqwvkr37" path="res://building.gdshader" id="2_f1gjg"]
+
+[sub_resource type="ShaderMaterial" id="ShaderMaterial_qnfc1"]
+resource_local_to_scene = true
+shader = ExtResource("2_f1gjg")
+shader_parameter/location = Vector2i(45, 0)
+shader_parameter/dimension = Vector2i(1, 1)
+shader_parameter/ground_height = 3000.0
+shader_parameter/cell_height = 300.0
+shader_parameter/num_cells = 60
+
+[node name="Building" type="Node2D"]
+script = ExtResource("1_5j34s")
+
+[node name="Sprite2D" type="Sprite2D" parent="."]
+material = SubResource("ShaderMaterial_qnfc1")
+scale = Vector2(7, 7)
+texture = ExtResource("2_2yopf")

draw_circle.gd

@@ -1,4 +1,4 @@
-extends Sprite2D
+extends Node2D
 @export var radius : float;
 
 func _draw():

earth.tscn

@@ -1,8 +1,8 @@
 [gd_scene load_steps=5 format=3 uid="uid://33k5v6skcbsm"]
 
-[ext_resource type="Texture2D" uid="uid://cy70quh6k3s1j" path="res://icon.svg" id="1_qbwya"]
 [ext_resource type="Script" uid="uid://b5fhsy1xlreco" path="res://draw_circle.gd" id="2_2bhor"]
 [ext_resource type="Script" uid="uid://m3vyyfk8gnma" path="res://grid.gd" id="3_2bhor"]
+[ext_resource type="PackedScene" uid="uid://djawvtdwp423v" path="res://building.tscn" id="3_5i67w"]
 
 [sub_resource type="CircleShape2D" id="CircleShape2D_5i67w"]
 radius = 3000.0
@@ -14,8 +14,7 @@ radius = 3000.0
 [node name="CollisionShape2D" type="CollisionShape2D" parent="Ground"]
 shape = SubResource("CircleShape2D_5i67w")
 
-[node name="Sprite2D" type="Sprite2D" parent="Ground"]
+[node name="GroundVisual" type="Node2D" parent="Ground"]
-texture = ExtResource("1_qbwya")
 script = ExtResource("2_2bhor")
 radius = 3000.0
 
@@ -29,3 +28,9 @@ cell_height = 300.0
 num_collumns = 60
 debug = true
 metadata/_custom_type_script = "uid://m3vyyfk8gnma"
+
+[node name="Building" parent="." instance=ExtResource("3_5i67w")]
+position = Vector2(-5212, -1497)
+
+[node name="Building2" parent="." instance=ExtResource("3_5i67w")]
+position = Vector2(49, 25)

grid.gd

@@ -5,6 +5,8 @@ class_name Grid extends Node2D
 @export var num_collumns : int
 @export var debug : bool
 
+var buildings : Array[Building] = []
+
 func _draw() -> void:
 	if !debug:
 		return
@@ -16,8 +18,20 @@ func _draw() -> void:
 		var angle = i * TAU / num_collumns;
 		draw_line(Vector2.ZERO, 10000 * Vector2.from_angle(angle), Color.SKY_BLUE);
 
-#func cart_to_sphere(cart : Vector2):
+func add_building_to_collumn(building : Building, collumn : int):
-	#var x = cart.x; var y = cart.y;
+	# find the height of the top building in the buildings list:
-	#var radius = sqrt(x*x + y*y);
+	building.location = Vector2(collumn, 0)
-	#var angle = tan(y/x)
+	var height = 0
-	## TODO
+
+	# TODO: support other dimensions for buildings
+	
+	# add the new building one higher than the previous
+	height += 1
+	building.location = Vector2i(collumn, height);
+
+# for testing
+func _ready() -> void:
+	var packed : PackedScene = preload("res://building.tscn")
+	var test_building = packed.instantiate()
+	test_building.location = Vector2(45, 1)
+	add_child(test_building)