Add pages to docs (#92)

* Explicit error for query:next * Add drain to docs * Fix next call * Add relationships page
2025-04-24 17:10:03 +00:00 · 2024-07-31 02:43:24 +02:00 · 2024-07-31 02:43:24 +02:00 · 51ed9e2173
commit 51ed9e2173
parent 24f9f5868b
18 changed files with 806 additions and 356 deletions
--- a/docs/.vitepress/config.mts
+++ b/docs/.vitepress/config.mts
@ -35,9 +35,9 @@ export default defineConfig({
                {
                    text: 'Concepts',
                    items: [
-                        { text: 'Entities', link: 'learn/concepts/entities' },
-                        { text: 'Static Components', link: 'learn/concepts/static-components' },
-                        { text: 'Queries', link: 'learn/concepts/queries' },
+                        { text: 'Entities and Components', link: 'learn/concepts/entities-and-components' },
+                        { text: 'Builtin Components', link: 'learn/concepts/builtin-components' },
+                        { text: 'Relationships', link: 'learn/concepts/relationships' },
                    ]
                },
                {
--- a/docs/api/jecs.md
+++ b/docs/api/jecs.md
@ -8,8 +8,31 @@ Jecs. Just an Entity Component System.
 ```luau
 jecs.World: World
 ```
+A world is a container of all ECS data. Games can have multiple worlds but component IDs may conflict between worlds. Ensure to register the same component IDs in the same order for each world.

 ### Wildcard
+```luau
+jecs.Wildcard: Entity
+```
+Builtin component type. This ID is used for [wildcard queries]().
+
+### Component
+```luau
+jecs.Component: Entity
+```
+Builtin component type. Every ID created with [world:component()](world.md#component()) has this type added to it. This is meant for querying every component ID.
+
+### ChildOf
+```luau
+jecs.ChildOf: Entity
+```
+Builtin component type. This ID is for creating parent-child hierarchies.
+
+:::
+### Rest
+```luau
+jecs.Rest: Entity
+```

 ## Functions

--- a/docs/api/query.md
+++ b/docs/api/query.md
@ -1,9 +1,21 @@
-# Query
+    # Query

 A World contains entities which have components. The World is queryable and can be used to get entities with a specific set of components.

 ## Functions

+### drain()
+```luau
+function query:drain(): Query
+```
+This function will impede it from being reset when the query is being iterated.
+
+### next()
+```luau
+function query:next(): Query
+```
+Get the next result in the query. Drain must have been called beforehand or otherwise it will error.
+
 ### with()
 ```luau
 function query:with(
--- a/docs/api/world.md
+++ b/docs/api/world.md
@ -133,4 +133,33 @@ for (const [id, position, velocity] of world.query(Position, Velocity) {

 :::info
 Queries are uncached by default, this is generally very cheap unless you have high fragmentation from e.g. relationships.
+
 :::
+### target()
+```luau
+function World:target(
+    entity: Entity, -- The entity
+    relation: Entity -- The relationship between the entity and the target
+): Entity? -- Returns the parent of the child
+```
+
+Get the target of a relationship.
+
+This will return a target (second element of a pair) of the entity for the specified relationship.
+
+If there is no pair with specified relationship, it will return nil.
+
+### parent()
+```luau
+function World:parent(
+    child: Entity -- The child ID to find the parent of
+): Entity? -- Returns the parent of the child
+```
+
+Get parent (target of ChildOf relationship) for entity. If there is no ChildOf relationship pair, it will return nil.
+
+This operation is the same as calling:
+
+```luau
+world:target(entity, jecs.ChildOf)
+```
--- a/docs/learn/concepts/builtin-components.md
+++ b/docs/learn/concepts/builtin-components.md
--- a/docs/learn/concepts/entities-and-components.md
+++ b/docs/learn/concepts/entities-and-components.md
@ -0,0 +1,109 @@
+# Entities and Components
+
+## Entities
+Entities represent things in a game. In a game there may be entities of characters, buildings, projectiles, particle effects etc.
+
+By itself, an entity is just an unique identifier without any data
+
+### Creation
+
+## Components
+A component is something that is added to an entity. Components can simply tag an entity ("this entity is an `Npc`"), attach data to an entity ("this entity is at `Position` `Vector3.new(10, 20, 30)`") and create relationships between entities ("bob `Likes` alice") that may also contain data ("bob `Eats` `10` apples").
+
+### Operations
+Operation | Description
+----------|------------
+`get`     | Get a specific component or set of components from an entity.
+`add`     | Adds component to an entity. If entity already has the component, `add` does nothing.
+`set`     | Sets the value of a component for an entity. `set` behaves as a combination of `add` and `get`
+`remove`  | Removes component from entity. If entity doesn't have the component, `remove` does nothing.
+`clear`   | Remove all components from an entity. Clearing is more efficient than removing one by one.
+
+### Components are entities
+
+In an ECS, components need to be uniquely identified. In Jecs this is done by making each component is its own unique entity. If a game has a component Position and Velocity, there will be two entities, one for each component. Component entities can be distinguished from "regular" entities as they have a `Component` component. An example:
+
+:::code-group
+```luau [luau]
+local Position = world:component() :: jecs.Entity<Vector3>
+print(world:has(Position, Jecs.Component))
+```
+
+```typescript [typescript]
+const Position = world.component<Vector3>();
+print(world.has(Position, Jecs.Component))
+```
+
+All of the APIs that apply to regular entities also apply to component entities. This means it is possible to contexualize components with logic by adding traits to components
+
+:::code-group
+```luau [luau]
+local Networked = world:component()
+local Type = world:component()
+local Name = world:component()
+local Position = world:component() :: jecs.Entity<Vector3>
+world:add(Position, Networked)
+world:set(Posiition, Name, "Position")
+world:set(Position, Type, { size = 12, type = "Vector3" } ) -- 12 bytes to represent a Vector3
+
+for id, ty, name in world:query(Type, Name):with(Networked) do
+    local batch = {}
+    for entity, data in world:query(id) do
+        table.insert(batch, { entity = entity, data = data })
+    end
+    -- entities are sized f64
+    local packet = buffer.create(#batch * (8 + ty.size))
+    local offset = 0
+    for _, entityData in batch do
+        offset+=8
+        buffer.writef64(packet, offset, entityData.entity)
+        if ty.type == "Vector3" then
+            local vec3 = entity.data :: Vector3
+            offset += 4
+            buffer.writei32(packet, offset, vec3.X)
+            offset += 4
+            buffer.writei32(packet, offset, vec3.Y)
+            offset += 4
+            buffer.writei32(packet, offset, vec3.Z)
+        end
+    end
+
+    updatePositions:FireServer(packet)
+end
+```
+
+```typescript [typescript]
+const Networked = world.component()
+const Type = world.component()
+const Name = world.component()
+const Position = world.component<Vector3>();
+world.add(Position, Networked)
+world.set(Posiition, Name, "Position")
+world.set(Position, Type, { size: 12, type: "Vector3" } ) // 12 bytes to represent a Vector3
+
+for (const [id, ty, name] of world.query(Type, Name).with(Networked)) {
+    const batch = new Array<{ entity: Entity, data: unknown}>()
+
+    for (const [entity, data] of world.query(id)) {
+        batch.push({ entity, data })
+    }
+    // entities are sized f64
+    const packet = buffer.create(batch.size() * (8 + ty.size))
+    const offset = 0
+    for (const [_, entityData] of batch) {
+        offset+=8
+        buffer.writef64(packet, offset, entityData.entity)
+        if (ty.type == "Vector3") {
+            const vec3 = entity.data as Vector3
+            offset += 4
+            buffer.writei32(packet, offsetm, vec3.X)
+            offset += 4
+            buffer.writei32(packet, offset, vec3.Y)
+            offset += 4
+            buffer.writei32(packet, offset, vec3.Z)
+        }
+    }
+
+    updatePositions.FireServer(packet)
+}
+```
--- a/docs/learn/concepts/entities.md
+++ b/docs/learn/concepts/entities.md
@ -1 +0,0 @@
-
--- a/docs/learn/concepts/relationships.md
+++ b/docs/learn/concepts/relationships.md
@ -0,0 +1,228 @@
+# Relationships
+Relationships makes it possible to describe entity graphs natively in ECS.
+
+Adding/removing relationships is similar to adding/removing regular components, with as difference that instead of a single component id, a relationship adds a pair of two things to an entity. In this pair, the first element represents the relationship (e.g. "Eats"), and the second element represents the relationship target (e.g. "Apples").
+
+Relationships can be used to describe many things, from hierarchies to inventory systems to trade relationships between players in a game. The following sections go over how to use relationships, and what features they support.
+
+## Definitions
+
+Name      | Description
+----------|------------
+Id	      | An id that can be added and removed
+Component | Id with a single element (same as an entity id)
+Relationship | Used to refer to first element of a pair
+Target    | Used to refer to second element of a pair
+Source    | Entity to which an id is added
+
+## Relationship queries
+There are a number of ways a game can query for relationships. The following kinds of queries are available for all (unidirectional) relationships, and are all constant time:
+
+Test if entity has a relationship pair
+
+:::code-group
+```luau [luau]
+world:has(bob, pair(Eats, Apples)
+```
+```typescript [typescript]
+world.has(bob, pair(Eats, Apples)
+```
+:::
+
+Test if entity has a relationship wildcard
+
+:::code-group
+```luau [luau]
+world:has(bob, pair(Eats, jecs.Wildcard)
+```
+```typescript [typescript]
+world.has(bob, pair(Eats, jecs.Wildcard)
+```
+:::
+
+Get parent for entity
+
+:::code-group
+```luau [luau]
+world:parent(bob)
+```
+```typescript [typescript]
+world.parent(bob, pair(Eats, jecs.Wildcard)
+```
+:::
+
+Find first target of a relationship for entity
+
+:::code-group
+```luau [luau]
+world:target(bob, Eats)
+```
+```typescript [typescript]
+world.target(bob, Eats)
+```
+:::
+
+
+Find first target of a relationship for entity
+
+:::code-group
+```luau [luau]
+world:target(bob, Eats)
+```
+```typescript [typescript]
+world.target(bob, Eats)
+```
+:::
+
+Find all entities with a pair
+
+:::code-group
+```luau [luau]
+for id in world:query(pair(Eats, Apples)) do
+    -- ...
+end
+```
+```typescript [typescript]
+for (const [id] of world.query(pair(Eats, Apples)) {
+    // ...
+}
+```
+:::
+
+Find all entities with a pair wildcard
+
+:::code-group
+```luau [luau]
+for id in world:query(pair(Eats, jecs.Wildcard)) do
+    local food = world:target(id, Eats) -- Apples, ...
+end
+```
+```typescript [typescript]
+for (const [id] of world.query(pair(Eats, jecs.Wildcard)) {
+    const food = world.target(id, Eats) // Apples, ...
+}
+```
+:::
+
+Iterate all children for a parent
+
+:::code-group
+```luau [luau]
+for child in world:query(pair(jecs.ChildOf, parent)) do
+    -- ...
+end
+```
+```typescript [typescript]
+for (const [child] of world.query(pair(jecs.ChildOf, parent)) {
+    // ...
+}
+```
+:::
+
+Relationship components
+
+Relationship pairs, just like regular component, can be associated with data.
+
+:::code-group
+```luau [luau]
+local Position = world:component()
+local Eats = world:component()
+local Apples = world:entity()
+local Begin = world:entity()
+local End = world:entity()
+
+local e = world:entity()
+world:set(e, pair(Eats, Apples), { amount = 1 })
+
+world:set(e, pair(Begin, Position), Vector3.new(0, 0, 0))
+world:set(e, pair(End, Position), Vector3.new(10, 20, 30))
+
+world:add(e, jecs.ChildOf, Position)
+
+```
+```typescript [typescript]
+const Position = world.component()
+const Eats = world.component()
+const Apples = world.entity()
+const Begin = world.entity()
+const End = world.entity()
+
+const e = world.entity()
+world.set(e, pair(Eats, Apples), { amount: 1 })
+
+world.set(e, pair(Begin, Position), new Vector3(0, 0, 0))
+world.set(e, pair(End, Position), new Vector3(10, 20, 30))
+
+world.add(e, jecs.ChildOf, Position)
+```
+:::
+
+## Relationship wildcards
+
+When querying for relationship pairs, it is often useful to be able to find all instances for a given relationship or target. To accomplish this, an application can use wildcard expressions. Consider the following example, that queries for all entities with a `Likes` relationship:
+
+:::code-group
+```luau [luau]
+for id in world:query(pair(Likes, jecs.Wildcard)) do
+    local rel = get_name(ecs_pair_relation(world.entityIndex, id))
+    local obj = get_name(ecs_pair_object(world.entityIndex, id))
+    print(`entity {id} has relationship {rel} {obj}`)
+end
+
+```
+```typescript [typescript]
+for (const [id] of world.query(pair(Likes, jecs.Wildcard))) {
+    const rel = get_name(ecs_pair_relation(world.entityIndex, id))
+    const obj = get_name(ecs_pair_object(world.entityIndex, id))
+    print(`entity ${id} has relationship ${rel} ${obj}`)
+}
+```
+:::
+
+Wildcards may used for the relationship or target part of a pair
+
+```c
+"pair(Likes, jecs.Wildcard)" // Matches all Likes relationships
+"pair(jecs.Wildcard, Alice)" // Matches all relationships with Alice as target
+```
+
+## Relationship performance
+This section goes over the performance implications of using relationships.
+
+### Introduction
+The ECS storage needs to know two things in order to store components for entities:
+- Which IDs are associated with an entity
+- Which types are associated with those ids
+Ids represent anything that can be added to an entity. An ID that is not associated with a type is called a tag. An ID associated with a type is a component. For regular components, the ID is a regular entity that has the builtin `Component` component.
+
+### Storing relationships
+Relationships do not fundamentally change or extend the capabilities of the storage. Relationship pairs are two elements encoded into a single 53-bit ID, which means that on the storage level they are treated the same way as regular component IDs. What changes is the function that determines which type is associated with an id. For regular components this is simply a check on whether an entity has `Component`. To support relationships, new rules are added to determine the type of an id.
+
+Because of this, adding/removing relationships to entities has the same performance as adding/removing regular components. This becomes more obvious when looking more closely at a function that adds a relationship pair.
+
+### Id ranges
+Jecs reserves entity ids under a threshold (HI_COMPONENT_ID, default is 256) for components. This low id range is used by the storage to more efficiently encode graph edges between archetypes. Graph edges for components with low ids use direct array indexing, whereas graph edges for high ids use a hashmap. Graph edges are used to find the next archetype when adding/removing component ids, and are a contributing factor to the performance overhead of add/remove operations.
+
+Because of the way pair IDs are encoded, a pair will never be in the low id range. This means that adding/removing a pair ID always uses a hashmap to find the next archetype. This introduces a small overhead.
+
+### Fragmentation
+Fragmentation is a property of archetype-based ECS implementations where entities are spread out over more archetypes as the number of different component combinations increases. The overhead of fragmentation is visible in two areas:
+- Archetype creation
+- ueries (queries have to match & iterate more archetypes)
+Applications that make extensive use of relationships might observe high levels of fragmentation, as relationships can introduce many different combinations of components. While the Flecs storage is optimized for supporting large amounts (hundreds of thousands) of archetypes, fragmentation is a factor to consider when using relationships.
+
+Union relationships are planned along with other improvements to decrease the overhead of fragmentation introduced by relationships.
+
+### Archetype Creation
+
+When an ID added to an entity is deleted, all references to that ID are deleted from the storage. For example, when the component Position is deleted it is removed from all entities, and all archetypes with the Position component are deleted. While not unique to relationships, it is more common for relationships to trigger cleanup actions, as relationship pairs contain regular entities.
+
+The opposite is also true. Because relationship pairs can contain regular entities which can be created on the fly, archetype creation is more common than in applications that do not use relationships. While Jecs is optimized for fast archetypes creation, creating and cleaning up archetypes is inherently more expensive than creating/deleting an entity. Therefore archetypes creation is a factor to consider, especially for games that make extensive use of relationships.
+
+### Indexing
+
+To improve the speed of evaluating queries, Jecs has indices that store all archetypes for a given component ID. Whenever a new archetype is created, it is registered with the indices for the IDs the archetype has, including IDs for relationship pairs.
+
+While registering a archetype for a relationship index is not more expensive than registering a archetype for a regular index, a archetype with relationships has to also register itself with the appropriate wildcard indices for its relationships. For example, an archetype with relationship `pair(Likes, Apples)` registers itself with the `pair(Likes, Apples)`, `pair(Likes, jecs.Wildcard)` and `pair(jecs.Wildcard, Apples)` indices. For this reason, creating new archetypes with relationships has a higher overhead than a archetype without relationships.
+
+This page takes wording and terminology directly from Flecs, the first ECS with full support for [Entity Relationships](https://www.flecs.dev/flecs/md_docs_2Relationships.html).
--- a/docs/learn/concepts/static-components.md
+++ b/docs/learn/concepts/static-components.md
@ -1,3 +0,0 @@
-## TODO
-
-This is a TODO stub.
--- a/src/init.luau
+++ b/src/init.luau
@ -739,7 +739,7 @@ do
    local lastArchetype: number
    local archetype: Archetype
    local queryOutput: { any }
-
+    local queryLength: number
    local entities: { number }
    local i: number

@ -748,7 +748,6 @@ do
    local columns

    local A, B, C, D, E, F, G, H
-    local I -- tombstone
    local a, b, c, d, e, f, g, h

    local init
@ -768,6 +767,7 @@ do
       	end

       	queryOutput = {}
+        queryLength = #ids

        entities = archetype.entities
       	i = #entities
@ -809,7 +809,7 @@ do
            e = columns[records[E]]
            f = columns[records[F]]
            g = columns[records[G]]
-        elseif not I then
+        elseif H then
            a = columns[records[A]]
            b = columns[records[B]]
            c = columns[records[D]]
@ -872,7 +872,7 @@ do
                    e = columns[records[E]]
                    f = columns[records[F]]
                    g = columns[records[G]]
-                elseif not I then
+                elseif H then
                    a = columns[records[A]]
                    b = columns[records[B]]
                    c = columns[records[D]]
@ -886,22 +886,22 @@ do
      		local row = i
      		i-=1

-      		if not B then
+      		if queryLength == 1 then
     			return entityId, a[row]
-      		elseif not C then
+      		elseif queryLength == 2 then
     			return entityId, a[row], b[row]
-      		elseif not D then
+      		elseif queryLength == 3 then
     			return entityId, a[row], b[row], c[row]
-      		elseif not E then
+      		elseif queryLength == 4 then
     			return entityId, a[row], b[row], c[row], d[row]
-      		elseif not F then
+      		elseif queryLength == 5 then
     			return entityId,
        				a[row],
        				b[row],
        				c[row],
        				d[row],
        				e[row]
-      		elseif not G then
+      		elseif queryLength == 6 then
     			return entityId,
     			        a[row],
        				b[row],
@ -909,7 +909,7 @@ do
        				d[row],
        				e[row],
                        f[row]
-      		elseif not H then
+      		elseif queryLength == 7 then
     			return entityId,
                        a[row],
        				b[row],
@ -918,7 +918,7 @@ do
        				e[row],
                        f[row],
                        g[row]
-      		elseif not I then
+      		elseif queryLength == 8 then
     			return entityId,
                        a[row],
        				b[row],
@ -930,12 +930,12 @@ do
        				h[row]
      		end

-   	        local field = archetype.records
+   	    local field = archetype.records
            for j, id in ids do
                queryOutput[j] = columns[field[id]][row]
            end

-      		return entityId, unpack(queryOutput)
+      		return entityId, unpack(queryOutput, 1, queryLength)
    end

    local function world_query_without(self, ...)
@ -977,23 +977,23 @@ do
          		local columns = archetype.columns
                local tr = archetype.records
          		for row in archetype.entities do
-              		if not B then
+              		if queryLength == 1 then
             			local va = columns[tr[A]]
             			local pa = fn(va[row])

             			va[row] = pa
-              		elseif not C then
+              		elseif queryLength == 2 then
             			local va = columns[tr[A]]
             			local vb = columns[tr[B]]

             			va[row], vb[row] = fn(va[row], vb[row])
-              		elseif not D then
+              		elseif queryLength == 3 then
             			local va = columns[tr[A]]
             			local vb = columns[tr[B]]
             			local vc = columns[tr[C]]

             			va[row], vb[row], vc[row] = fn(va[row], vb[row], vc[row])
-              		elseif not E then
+              		elseif queryLength == 4 then
             			local va = columns[tr[A]]
             			local vb = columns[tr[B]]
             			local vc = columns[tr[C]]
@ -1088,7 +1088,7 @@ do
    	local length = 0

        local components = { ... } :: any
-        A, B, C, D, E, F, G, H, I = ...
+        A, B, C, D, E, F, G, H = ...
    	local archetypes = world.archetypes

    	local firstArchetypeMap: ArchetypeMap
@ -1107,12 +1107,12 @@ do

    	for id in firstArchetypeMap.cache do
    		local compatibleArchetype = archetypes[id]
-    		local tr = compatibleArchetype.records
+    		local archetypeRecords = compatibleArchetype.records

    		local skip = false

    		for i, componentId in components do
-    			local index = tr[componentId]
+    			local index = archetypeRecords[componentId]
    			if not index then
    				skip = true
    				break
--- a/test/tests.luau
+++ b/test/tests.luau
@ -208,7 +208,6 @@ TEST("world:add()", function()
    end
 end)

-
 TEST("world:query()", function()
    do CASE "query single component"
        do
@ -805,7 +804,7 @@ do
                    break
                end

-                id, new, old = q:next()
+                id, new, old = q.next()
            end

            add[id] = new
--- a/thesis/drafts/1/paper.aux
+++ b/thesis/drafts/1/paper.aux
@ -17,10 +17,10 @@
 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{Research Approach}}{3}{subsection.2.1}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{Research Process}}{3}{subsection.2.2}\protected@file@percent }
 \@writefile{toc}{\contentsline {section}{\tocsection {}{3}{Theory}}{3}{section.3}\protected@file@percent }
+\citation{Nystrom}
 \citation{Flecs}
 \citation{Flecs}
-\citation{Flecs}
-\citation{Anderson}
+\citation{ABC}
 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{Entity Component System Architecture}}{4}{subsection.3.1}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{Cache Locality}}{4}{subsection.3.2}\protected@file@percent }
 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{Data Layouts}}{4}{subsection.3.3}\protected@file@percent }
@ -34,6 +34,7 @@
 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.7}{Sparse Set}}{6}{subsection.3.7}\protected@file@percent }
 \newlabel{Fig 2: Sparse Set}{{3.7}{6}{Sparse Set}{subsection.3.7}{}}
 \citation{Caini}
+\citation{Luau}
 \newlabel{Fig 3: Removing Entity}{{3.7}{7}{Sparse Set}{subsection.3.7}{}}
 \@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Implementation}}{7}{section.4}\protected@file@percent }
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 \bibcite{Martin}{1}
 \bibcite{Muratori}{2}
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-\bibcite{Anderson}{4}
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+\bibcite{matter}{9}
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--- a/thesis/drafts/1/paper.fdb_latexmk
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-\OT1/cmr/m/n/8 Part 1. [][]$\OT1/cmtt/m/n/8 https : / / t-[]machine . org / index . php / 2007 / 09 / 03 / entity-[]systems-[]are-[]the-[]future-[]of-[]mmog-[]development-[]part-[]1/$[][] 
- []
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-[]\OT1/cmr/m/n/8 Michele Caini (2020, Au-gust). ECS back and forth. [][]$\OT1/cmtt/m/n/8 https : / / skypjack . github . io /
- []
-
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--- a/thesis/drafts/1/paper.pdf
+++ b/thesis/drafts/1/paper.pdf
--- a/thesis/drafts/1/paper.synctex.gz
+++ b/thesis/drafts/1/paper.synctex.gz
--- a/thesis/drafts/1/paper.tex
+++ b/thesis/drafts/1/paper.tex
@ -2,7 +2,10 @@
 \usepackage{mathrsfs,comment}
 \usepackage[usenames,dvipsnames]{color}
 \usepackage[normalem]{ulem}
-\usepackage{url}
+\usepackage[hyphens]{url}
+\usepackage{breakurl}
+\usepackage[utf8]{inputenc} % Ensure proper encoding
+\usepackage{hyperref} % For clickable links
 \usepackage{listings}
 \usepackage[all,arc,2cell]{xy}
 \UseAllTwocells
@ -259,7 +262,7 @@ The Entity Component System (ECS) architecture provides infrastructure for repre
 \subsection{Cache Locality}
 When a CPU loads data from Random Access Memory it is stored in a cache tier (i.e. L1, L2, L3), 
 where the lower tiers are allowed to operate faster relatively to how closely 
-embedded it is to the CPU.\cite{Flecs} When a program requests some memory, the CPU grabs a whole slab, usually from around 64 to 128 bytes starting from the requested address, and puts it in the CPU cache, i.e. cache line. If the next requested data is in the same slab, the CPU reads it straight from the cache, which is faster than hitting RAM. Inversely, when there is a cache miss, i.e. it is not in the same slab then the CPU cannot process the next instruction because it needs said data and waits a couple of CPU cycles until it successfully fetches it. (Nystrom, 2011). 
+embedded it is to the CPU.\cite{Nystrom} When a program requests some memory, the CPU grabs a whole slab, usually from around 64 to 128 bytes starting from the requested address, and puts it in the CPU cache, i.e. cache line. If the next requested data is in the same slab, the CPU reads it straight from the cache, which is faster than hitting RAM. Inversely, when there is a cache miss, i.e. it is not in the same slab then the CPU cannot process the next instruction because it needs said data and waits a couple of CPU cycles until it successfully fetches it. (Nystrom, 2011). 

 \subsection{Data Layouts}

@ -298,7 +301,7 @@ Vectorization is where code meets the requirements to use SIMD instructions. Tho

 \subsection{Archetype}
 Storing data in contiguous arrays to maximize vectorization and SIMD is the ideal situation, 
-however it is a very complex problem in implementation. Below the ABC problem\cite{Anderson} 
+however it is a very complex problem in implementation. Below the ABC problem\cite{ABC} 
 is demonstrated where 3 entities all have the component \texttt{A} which can be stored in a single 
 column:

@ -363,7 +366,8 @@ references to the next archetype based on component types (see Figure 1).
 Each edge in the graph corresponds to a component that can be added, akin to an 
 intersection operation on the archetype set. \[A \cap \left( B \cap C \right)\] 
 Removal of a component from the archetype is akin to a subtraction operation from the set. \[A \cap \left( B \cap C \right) - {C}\]`. 
-This archetype graph facilitates $\mathsf{O}(1)$ transitions between adjacent archetypes to mitigate the cost of fragmentation.
+This archetype graph facilitates $\mathsf{O}(1)$ transitions between adjacent archetypes to 
+mitigate the cost of structual changes.

 \begin{figure}[htbp]
 \centering
@ -401,7 +405,7 @@ This method ensures that the dense array remains tightly packed.\cite{Caini}
 The sparse set structure is beneficial for programs that frequently manipulate the component structures of entities. However, querying multiple components can become less efficient due to the need to load and reference each component array individually. In contrast to archetypes, which only needs to iterate over entities matching their query. 

 \section{Implementation}
-The decision to use Lua scripting language for the ECS implementation was ultimately chosen because
+The decision to use Luau\cite{Luau} for the ECS implementation was ultimately chosen because
 a pure Lua implementation confers distinct advantages in terms 
 of compatibility and portability. By eschewing reliance on external C or C++ libraries 
 or bindings, we ensure that our ECS framework remains platform-agnostic and 
@ -422,11 +426,11 @@ The ECS utilize several key data structures to organize and manage entities and
    
    \item \textbf{EntityIndex:} Maps entity IDs to their corresponding records.

-    \item \textbf{ComponentIndex}: Maps IDs to archetype records. 
-
-    \item \textbf{ArchetypeIndex}: Maps type hashes to archetype. 
+    \item \textbf{ComponentIndex}: Maps IDs to archetype maps. 

    \item \textbf{ArchetypeMap:} Maps archetype IDs to archetype records which is used to find the column for the corresponding component.
+
+    \item \textbf{ArchetypeIndex}: Maps type hashes to archetype. 
    
    \item \textbf{Archetypes:} Maintains a collection of archetypes indexed by their IDs.
 \end{itemize}
@ -634,45 +638,53 @@ meticulous evaluations of the minimal ECS implementation iterations.
 My thanks also extend to Eryn L. K. and Lucien Greathouse for their invaluable 
 guidance and contributions to the Matter project.

-\begin{thebibliography}{9}
+\sloppy
+\tolerance=2000
+\hbadness=10000
+\begin{thebibliography}{10000}

 \bibitem{Martin}
-Adam Martin (2007, September).
-Entity Systems are the future of MMOG development - \\ Part 1.
+Martin, Adam (2007). 
+\textit{Entity Systems are the future of MMOG development - Part 1}. 
 \url{https://t-machine.org/index.php/2007/09/03/entity-systems-are-the-future-of-mmog-development-part-1/}

 \bibitem{Muratori}
-Casey Muratori (2014, June). 
-Semantic Compression.
+Muratori, Casey (2014). 
+\textit{Semantic Compression}. 
 \url{https://caseymuratori.com/blog_0015}

-\bibitem{Flecs}
-Sanders Mertens (2019). 
-Flecs. 
-\url{https://github.com/SanderMertens/flecs}
+\bibitem{ABC} 
+Mertens, Sanders (2022). \texttt{Building Games in ECS with Entity Relationships. See the ABC problem, component index.}
+\url{https://ajmmertens.medium.com/building-an-ecs-1-where-are-my-entities-and-components-63d07c7da742}
+
+\bibitem{Archetypes} 
+Mertens, Sanders (2022). \texttt{Building an ECS \#2: Archetypes and Vectorization.}
+\url{https://ajmmertens.medium.com/building-an-ecs-2-archetypes-and-vectorization-fe21690805f9}

 \bibitem{Anderson}
-Carter Anderson (2022).
-Bevy. 
-\url{https://github.com/bevyengine/bevy}
+Anderson, Carter (2022). 
+\textit{Bevy}. 
+Available at: \url{https://github.com/bevyengine/bevy}

 \bibitem{Caini}
-Michele Caini (2020, August). 
-ECS back and forth. 
-\url{https://skypjack.github.io/2020-08-02-ecs-baf-part-9/}
+Caini, Michele (2020). 
+\textit{ECS back and forth}. 
+Available at: \url{https://skypjack.github.io/2020-08-02-ecs-baf-part-9/}

 \bibitem{Nystrom}
-Robert Nystrom (2011). 
-Game Programming Patterns.
+Nystrom, Robert (2011). 
+\textit{Game Programming Patterns}.

 \bibitem{gdc}
-Scott Bilas (2002). 
-A Data-Driven Object System (GDC 2002 Talk by Scott Bilas). 
-\url{https://www.youtube.com/watch?v=Eb4-0M2a9xE}
+Bilas, Scott (2002). 
+\textit{A Data-Driven Object System} (GDC 2002 Talk by Scott Bilas). 
+Available at: \url{https://www.youtube.com/watch?v=Eb4-0M2a9xE}

 \bibitem{matter}
-Matter, an archetypal ECS for Roblox
-https://matter-ecs.github.io/matter/
+\textit{Matter, an archetypal ECS for Roblox}. 
+Available at: \url{https://matter-ecs.github.io/matter/}
+
+\bibitem{luau}

 \end{thebibliography}