在过去几年中，我发现游戏行业似乎乐于将建筑学作为辅助我们执行设计的一个潜在领域。作为拥有两个建筑学位的游戏开发者，我当然也看到了这两个领域之间的联系。我在还是一名建筑学本科生时就开始与朋友制作小型电子游戏——使用我在课堂上所用的设计软件来绘制游戏的美术内容。因我一些工作室伙伴的建议，我开始在自己的课堂在项目上运用我所学到的游戏设计知识。我认为建筑学与游戏一样，与其用户之间具有象征性的关系，并且设计精良的游戏关卡与建筑大师Frank Lloyd Wright、Le Corbusier、I.M. Pei等人的作品也有异曲同工之妙。我在这两个领域的研究集中体现在一篇关于游戏与建筑学交集的毕业论文中。毕业之后我成了一名游戏开发者，并继续研究建筑理论对关卡设计的运用。这项工作令我撰写出了多篇论文，展开了多次大会演讲，并且现在还出版了一本书。
《An Architectural Approach to Level Design》这本书由CRC Press于6月12日出版，整合了建筑学和关卡设计领域的空间设计理论。本书通过建筑学情境和历史探索了关卡设计原则，为学者和游戏开发专业人士提供了有用的信息。
美国建筑师Louis Sullivan常被誉为摩天大厦的创造者，他曾说过“形式要遵从功能”。Sullivan以这个格言确立了一个建筑学现代派的主导原则。现代派是二十世纪早期强调创造形式源自功能的建筑这一主张所定义的建筑学运动。在现代建筑中，装饰物通常是建筑本身或者具有某项用途的产品，而不只是纯粹为了美学效果而存在。与Sullivan相同，Le Corbusier也曾说过，“房子是居住的机器。”他的许多建筑设计与Frank Lloyd Wright、Walter Gropius、Louis Sullivan等人的作品一样，关注的是有目的地为居住者创造一种体验。
游戏设计可以通过核心机制这个理念来表现形式遵从功能。核心机制通常被定义为玩家在整个游戏过程中所执行的基本操作。游戏设计师Aki Jarvinen在自己的博士论文中曾创造了一个以核心机制为中心，即设计师从动词入手的设计方法。如果你将核心机制视为玩家在游戏中的基本动作，就能够理解构造每款游戏独特体验的基本元素了。例如，《超级马里奥》就可以说是关于跳跃的游戏。而《塞尔达传说》的主题就是探索，《Katamari Damacy》就是翻滚，《愤怒的小鸟》就是弹射。从这个核心开始，其他添加的动作定义了最终游戏产品的规则。
在这个关卡中，游戏的Builders League United（或称BLU）队必须通过一辆轨道上的矿车向对手Reliable Excavation Demolition（或称RED)队的基地投掷一个炸弹。Payload模式的矿车机制采用了《军团要塞2》基于团队的第一人称射击机制的标准并进行了一些调整。这不但改变了玩法机制，还改变了关卡空间几何条件。
Edmund McMillan在《Indie Game:The Movie》关卡设计讨论中指出，当设计师创造出环境机制时，即与玩法相关的关卡交互环节，它们就必须具有多种可用性。在e4 Software的手机游戏《SWARM》（玩家必须将敌人引进陷陆的平台游戏），程序员/设计师Taro Omiya创造了电子栅栏陷陆的多张草图来形象化它们的不同用途。此外，Omiya等人还在电脑和纸张上制作正式的方法论以便形象化关卡的空间方向（例如下坡、漂浮岛以及平台区域）。
游戏与建筑学的区别就在于现实世界的建筑必须遵从现实规则。例如，现实世界的建筑必须同时具有内部和外部设计——其中一者必然影响另一者。同理，现实世界的建筑学必须考虑到气候、地质、分区管制以及构造现实状况。而游戏领域却没有这些必须处理的情况。这可能意味着像Atelier Ten Architects和GMO Tea-cup Communications Inc.的地球博物馆（一个漂浮在太空的大型椭圆建筑）或者巴西建筑师Oscar Niemeyer生活中的Hidenori Watanave的探索数据雕像——这两者都是存在于虚拟世界《第二人生》中的建筑结构。这会产生基于玩家行动模式、叙事事件或游戏机制等更为自由的空间布局。的确，“内部”和“外部”不过是基于运用于装饰游戏空间的美术元素的描述。
（这是Atelier Ten建筑和GMO Tea Cup Communication Inc的地球博物馆的一张草图。因为该建筑是在虚拟世界中创造，它并不需要任何构架来支撑组成其主体的成百上千个立方体。设计师是用微软Excel表格设计该建筑形式，之后再用一个自动建模程序生成其几何图形）
Frederick还指出，在利用Figure-ground理论时，figure元素和空间都可以通过区分结构元素的空间，或者创造与附近figure相似的形式的消极空间进行暗示。这与理论神经系统科学家Gerd Sommerhoff引述建筑师Grant Hildebrand所谈的观念相呼应：
正如figure-ground是用大量元素组成空间的空间布局一样，form-void是通过添加堆块或减除空间来进行的空间布局。这与我们在第二章：关卡设计的工具与技巧所描述的许多游戏引擎的操作方法一样。与之相似，3D美术程序也允许形式之间通过精心建模或Voolean操作实现交互，可用数学方程式以增加或减少的方式来结合3D模型。 Peter Zumthor的Therme Vals或Mario Botta的Casa Bianchi（两者均位于瑞士）等建筑就能够说明form-void关系可运用于塑造露台、门廊、窗户、卧室和其他用途的空间。在游戏中，这种增减方法可用于创造隐藏性的空地、秘密走廊、伏击点甚至是关卡目标。
（来自Peter Zumthor和Mario Botta的草图表明形式和虚无可以用于确定空间。）
我们主要通过到达某空间来向玩家传递信息。这也正是空间促使玩家走向下一个目的地或为玩家提供其路径选择的方式。你进入一个空间的体验来自之前空间所提供的空间条件：如果你进入一个大型空间，那么引你进入其中的之前空间应该是狭窄的，这样才能让新空间显得更大；同理，明亮的空间之前对应的应该是阴暗的空间。建筑师Donlyn Lindon和Charles W. Moore在其著作《Chambers For A Memory Palace》中称John Portman & Associates的Hyatt Regency Atlanta酒店就是这种典型。它又被评论者称为“Jesus Chris Spot”，该酒店落成后商人们从较低的天花板空间进入22层的中庭并向上看时，嘴里都在喃喃着“天哪！”类似的空间体验还可见于基于探索的游戏，例如《塞尔达传说》或《合金装备》系列中进入重要敌人遭遇战，道具获取或故事事件的时候（见下图）。
（许多游戏使用对比鲜明的空间条件来突出进入boss房间或目标等重要玩法空间的路径。这是来自《塞尔达：时之笛》中的Temple of Time图表，玩家在此会收到重要的宝剑，这显示了对比鲜明的空间，其拜占庭式的大厅布局则强调了宝剑房间的重要性。）
最后一个建筑学空间经验与布局的关系较小，但与设计空间的另一个目标关系更为密切。这个经验就是Spirit of Place。这个术语来自一个罗马信仰，即灵魂会扮演城市精灵的角色，保护城镇或其他有人口居住的地方。这个术语被20世纪末的建筑师所采纳，并用于描述一个地方的标识或情感体验。
在第二章节，我们讨论了关卡任天堂力量方法，即设计师创造一个宏观层面的方法或者其关卡的规划，然后分配玩法的高潮时刻 ，就像为游戏杂志创造地图一样。每个玩法的高潮时刻，可以是敌人遭遇战，行动谜题，或者有帮助的阻塞点，都有它们自己的Genius Loci。这些地方是用于休息还是战斗？玩家在这些游戏空间是否该感到放松、紧张或思考？这些问题的答案取决于你所创造的游戏，但却有助于确定你想为关卡创造的体验类型。
除了每个玩法遭遇战，关卡设计师还可以在其游戏空间中植入Genius Loci，并将其作为一种将玩家从一个点转移到另一个点的工具。Genius Loci可以通过光线、阴影、空间布局以及空间大小的操控来创建。如果你为恐怖游戏创造关卡，你所创建的Genius Loci就应该是通过对场景艺术、光照、音效和其他资产的精不挑细选而创造出来的。同理，仅有一点或没有Genius Loci的游戏空间就可能是一个流通空间，也就是玩家转移到下一个目的地的空间。根据你所创造玩法的情况，流通空间可能是激烈遭遇战之间的一次休息机会，或者玩家进入下一个难忘玩法时刻前创造悬念的工具。
几何视野 & 显示视野
较少被人提及的概念是显示视野，或称DFOV（图3）。这个视野由玩家到显示器之间的距离，以及他们所玩游戏设备的显示器大小所决定。有趣的是，DFOV在导航以及3D空间的后续难度中发挥了极端重要的作用，但这只是针对女性玩家而言。据Tan, Czerwinski和Robertson (2006) 所执行的一项调查结果显示，当DFOV和GFOV角度比例为1：1时，女性玩家会最占据优势。而即使这一比例显著变化，男性玩家在3D空间中的导航能力也甚少受到影响。
入口 & 闭塞口，以及视线
水平几何 & 玩家战术
理解动态关系并非本文话题，我们需要了解迫使玩家移动并同水平几何体接触的动力。我想，这里所提到的3D FPS游戏难度升级方法应该也很容易运用于你自己的游戏设计概念。如果在设计游戏空间时考虑到了玩家的情境认知度，那么我们就可以开始植入其他设计工具，例如Jesse Schell的兴趣曲线，以便进一步提升我们的设计。
如果我们在设计时采用领土理论，那么我们就能使用领土来确保我们不会强迫玩家进入连续的、高密度的游戏区域。也就是说，我们希望用分子设计来确保在不同区域之间，玩家有足够的情绪“冷却”时间。我认为这些冷却区域类似于音乐的动态。在《The Clarinet and Clarinet Playing》一书中，音乐家和作者David Pino将这个概念总结如下：
Dan Cook和Chris Crawford等人研究了人们玩游戏的动机，启发我们产生学习和改进这些新技术的想法。Raph Koster进一步细化这个概念；人类是寻找模式的机器，当我们在游戏中识别并学会它的模式时，我们就能从游戏中收获快乐。因此，基于模式的分子设计法来定义游戏空间直接迎合了人类天性，的确有实用价值。
值得一提的是，使用绘图理论概念化和分析游戏空间并不是什么新思路，事实上很多人都以各种形式讨论了这个想法。这个研究的灵感最初来源于Raph Koster和他的“游戏数学”展示。我向所有对设计感兴趣的人推荐他的工作。Joris Dormans也写了一些与绘图理论相关的文章，关卡设计师可以当作参考。Dormans的《Adventures in Level Design》和《Level Design as Model Transformation》都很不错，清楚地说明了这个工具的广泛用途。
篇目1，Excerpts from An Architectural Approach to Level Design
by Christopher Totten
In the past few years, I have noticed a fascination in the game industry with architecture as a field that could be potentially helpful to the way we design. As a game developer with two degrees in architecture I have likewise seen the connections between the two fields. As an undergraduate architecture student I began making small video games with friends – creating art with the design software I used for classes. On the suggestion of some of my studio-mates, I began utilizing what I learned about game design in my class projects. I felt that architecture, like games, had a symbiotic relationship with its users and that well designed game levels had much in common with the work of architects like Frank Lloyd Wright, Le Corbusier, I.M. Pei, and others. Eventually, my work with both fields culminated in a graduate thesis on the intersections between games and architecture. After grad school, I became a game developer and continued my research into the ways architectural theory could be applied to level design. This work has allowed me to write several articles, give a few conference talks, and now publish a book.
Released on June 12th by CRC Press, An Architectural Approach to Level Design integrates architectural and spatial design theory with the field of level design. The book explores the principles of level design through the context and history of architecture, providing information useful to both academics and game development professionals.
Presenting architectural techniques and theories for level designers to use in their own work, practical elements of how designers construct space are addressed along with experiential elements of how and why humans interact with this space. Throughout the text, readers learn skills for spatial layout, evoking emotion through gamespaces, and creating better levels through architectural theory.
This article contains several excerpts from the book showing basic architectural elements that can be applied to practical level design applications along with illustrations from the book taken from my own gameplay and design journals. These sections prepare the reader for further explorations of methods for visual communication, producing emotional responses in players, encouraging social interaction, and other things important to game worlds. I hope you enjoy reading it as much as I have enjoyed researching and writing it. The book can be purchased at http://www.crcpress.com/product/isbn/9781466585416
Ways of Seeing for Level Design – from Chapter 1: A Brief History of Architecture and Level Design
In order to fully understand spatial design principles for level design, it is necessary to analyze precedents from both real world architecture and video games. Hal Box, FAIA, Professor Emeritus and former Dean of the School of Architecture at the University of Texas at Austin argues for an educated form of seeing architecture based on study and analysis. In this case, “seeing” is not used to only describe using the visual senses, but also to process the spatial, formal, contextual, and historical elements that make a building unique.
For level designers, this type of “seeing” can be transformative for how we learn from the levels of previous games – both good and bad. Doing this may involve breaking some habits common to game players. For example, there is a saying that “gamers don’t look up” when playing games. As designers, the verticality of gamespaces can be an important element in establishing the grandiosity of a setting or for communicating direction with players. Likewise, as players, it is common to run directly to the next action scene rather than pause to explore game environments. Designers should look for ways to direct the pacing of a game environment in subtle ways – placing narrative elements in the way of player pathways or incentivizing exploration with rewards.
In his book, Think Like an Architect, Box proposes ten ways for exploring and understanding a building:
1. Learn why a building was built, what it was for, and what it is now.
2. Look up as you walk around – noticing visual elements, layering of forms, and materials.
3. Sense the space by its size, shape, and how it interacts with light, sound, and other spaces.
4. Train your eye to understand the structure of the building and how it holds the building up.
5. Determine how materials are working – in compression or tension – or if they feel heavy or light.
6. Determine how the building was constructed and from what materials.
7. Examine the historical precedents of the building.
8. Analyze the composition, proportions, and rhythms of building elements.
9. Observe the appropriateness of the building to its setting.
10. Analyze what makes the building special from others[i].
Obviously, not all of these apply to game levels. While the environment art of a level can represent structures that are in compression or tension, the game art itself will not be. Likewise, many game levels are held up by the fact that they are not defined as rigidbody objects in the game engine and thus, do not fall according to the engine’s physics system. However, many of these proposed ways of seeing are applicable to game levels in their current form, or may be modified slightly to fit our own purposes. In this way, we may say that level designers can modify their ways of seeing with these methods:
1. Identify what gameplay occurs in the space. What are the game mechanics supported?
2. Look up as you walk around – noticing visual elements, especially art that contrasts the rest of the environment or somehow calls attention to itself. Also look down – is the spaces’s verticality used in reverse to make you feel in danger?
3. Sense the space by its size, shape, and how it interacts with light, sound, and other spaces. How do the lighting or sound conditions make you feel?
4. Analyze the pacing of the level. Does the level usher you through itself quickly or are there opportunities to explore? Are these required or bonuses for extra curiosity?
5. Is there one gameplay style reflected in this level, or are multiple supported? (For example, does a deathmatch map have places for snipers, offensive players, defensive players, etc.? Does a game level play well for barbarians but poorly for mages?)
6. How does the space express the narrative of the game? Is it a backdrop or does exploring the level tell you about the game world in some way? Are narrative events scripted to occur around the player or are there cutscenes?
7. Examine any historical or gameplay precedents? What kinds of spatial experiences were in those games?
8. Analyze the composition, proportions, and rhythms of environment art elements.
9. How does level geometry compare with the movement abilities of your avatar? Is everything well within their capabilities or does the level space challenge these measurements? Is there anything that is outside of these capabilities? If so, does the game offer any way to expand these abilities?
10. What environment art elements are repeated? Are they interactive? If so, do they correspond to a specific gameplay mechanic?
These ways of seeing for level design, as well as the architectural and gamespace precedents found in the rest of this chapter, will guide our explorations of spatial design principles for level design.
Level Design Workflows – from Chapter 2: Tools and Techniques for Level Design
The American architect Louis Sullivan, often credited as the creator of the skyscraper, once famously said, “Form ever follows function.” This was shortened to the famous design idiom, “Form follows function.” With this phrase, Sullivan stated one of the driving principles of architectural modernism. Modernism was an architectural movement of the early twentieth century defined by an emphasis on creating buildings whose form was derived from their purpose. In modernist architecture, ornament was generally a product of the building itself or applied for a purpose, rather than simply for the sake of aesthetics. Similarly to Sullivan, Le Corbusier stated, “The house is a machine for living in.” Much of his architecture, as with the architecture of Frank Lloyd Wright, Walter Gropius, Louis Sullivan, and others was focused on purposefully creating an experience for the occupants.
As we have seen, the same can be said of level design. In level design, developers often design with a specific experiential goal in mind. In a 2008 interview, Valve level designer Dario Casali argued that “experience is key” when creating level design ideas[ii]. Earlier in this chapter, we discussed some goals of level design that related to how users use gamespace and how we as designers communicate to the user through the space. These experiential goals should dictate how we as level designers construct space: form follows function.
In this section, we will discuss some workflow processes that involve these same tools, beginning with how “form follows function” fits into game design.
Form Follows Core Mechanics
The tenants of form follows function thrive in game design through a concept known as the core mechanic. A core mechanic is often defined as the basic action that a player makes throughout the course of a game. In his doctoral dissertation, game designer Aki Jarvinen similarly created a core mechanic-centered design method where designers began from verbs[iii]. If one looks at core mechanics as the basic verb of what a player does in a game, they can understand the foundational elements of what builds each game’s unique experience. For example, Super Mario Bros[iv]. can be said to be about jumping, The Legend of Zelda[v] is about exploring, Katamari Damacy[vi] is about rolling, Angry Birds[vii] is about flinging, and so on. Beginning from this core, other actions are added that define the rules of the final game product.
When designing levels, having a similar core mechanic idea in mind is necessary. While many new designers assume that individual levels should simply follow the core mechanic of the game, it is possible to define level core mechanics to make each unique. An example is the Badwater Basin level (figure 2.43) of Valve’s Team Fortress 2 (TF2)[viii].
Figure 2.43 A plan diagram of Badwater Basin from Team Fortress 2. RED and BLU team bases are marked on the map, as are major circulation areas and BLU checkpoints between the two bases.
In this level, the game’s Builders League United (or BLU) team must push a bomb into their opponent’s, the Reliable Excavation Demolition (or RED) team’s, base via a mine cart on a track. The mine cart mechanic of Payload mode, which Badwater Basin is a map for, takes TF2’s standard team-based first person shooter mechanics and adds a twist. Not only does this change the mechanics of gameplay, but also the conditions of the levels spatial geometry.
One example cited by Casali, who helped design the level, was the level’s tunnel. In the first prototypes of the level, designers made the mine tunnels a standard width that they had used for other basic maps. However, upon playtesting the level with the mine cart-pushing mechanic in place, they realized that tunnels had to be widened to accommodate both players and cart. This seems like a small change, but it prevented a lot of aggrivation from players that had been getting blocked out of tunnels by the cart (figure 2.44.)
Figure 4.44 Modifying the width of the tunnel in Badwater Basin allowed for better circulation of both the player and mine cart through the level and made gameplay less aggravating for the offensive team.
As level designers, it is our job to design to the realities of how player avatars and other gameplay elements move through levels. Traversing levels is comfortable when level spaces comfortably accommodate metrics. As we will explore in later chapters, gameplay drama can be achieved when we create spaces that push metrics to the limit. Such spaces include gaps that require the farthest possible jump a character can do such as the one found in world 8-1 of Super Mario Bros. (figure 2.45) or tight corridors that restrict movement in horror games, such as Resident Evil[ix] (figure 2.46.)
Figure 2.45 This section of Super Mario Bros.’s level 8-1 pushes Mario’s jumping metrics to their limit. The gap is 10 blocks wide, 1 block longer than Mario’s running jump distance of 9 blocks, so using the 1-block-wide middle island is necessary. Most strategies for crossing this gap call for a running jump to the middle island, and then another quick one off the 1-block-wide island so Mario’s landing inertia doesn’t launch the player into the pit.
Figure 2.46: Many hallways in Resident Evil are barely wide enough for two characters standing shoulder to shoulder. In this way, a single zombie in these hallways can become a significant threat for players trying to get past. This spatial condition also gives the game a claustrophobic atmosphere.
Designing to gameplay does not solely have to involve measurements either. It can also mean designing to specific character abilities such as special attacks or movement modes. Stealth games, like Metal Gear Solid[x] provide a great example of how to construct levels based on different types of character movement. In Metal Gear Solid, the player character, Solid Snake, has the ability to hide behind walls and look around corners. This vastly changes the meaning of ninety-degree corners when compared with other action games – they are strategic hiding places rather than just level geometry. As such, the nuclear weapons facility that makes up Metal Gear Solid’s environments has lots of these corners so players can sneak from place to place, looking around corners to find their next refuge. While not measurement or metric based, these kinds of layouts are based on the character’s own mechanics, the gameplay actions that form the range of possibilities for how a character may act or interact with their environment.
Level Design Parti
Earlier in the chapter, we discussed the architect’s parti, basic formal explorations that architects utilize to determine what shape or orientation they want their building to take. For level designers coming off of determining the core mechanics of their level, a parti is another valuable tool for developing the spatial layout of your level.
Designing with parti is quite different than designing on graph paper or computer. Partis are meant to be sketches, and therefore will lack measurement. Sketching exercises allow designers to form ideas quickly before spending the time to plan measured versions of their designs. The key to a level designer’s parti is to sketch gameplay ideas as spatial diagrams. For example, a level design parti of the previously mentioned Badwater Basin level would be two large masses (representing the team’s base areas) with thinner zones of circulation in between the two to represent the mine cart track, and some smaller bases for BLU players to capture, similar to the diagram shown in 2.43.
In his discussions of level design from Indie Game: The Movie, Edmund McMillan argues that once a designer has created environmental mechanics, that is, interactive parts of a level that factor into gameplay, they should be usable in many different ways in order to be valuable. For the e4 Software’s mobile game, SWARM![xi], a ball-roller/platformer game where players had to lure enemies into traps, programmer/designer Taro Omiya created many sketches of the electric fence traps to visualize the different uses they could have (figure 2.47.) Likewise, Omiya and others working on the game made formal Partis on the computer and on paper to visualize spatial orientations of levels such as downhill slides, floating islands, and platforming areas (figure 2.48.)
Figure 2.47 Once designers for SWARM! created the electric fence traps, they sketched many gameplay partis of them to visualize how they could be utilized through different levels.
Figure 2.48 Formal partis for SWARM! show the visualization of different spatial orientations such as hills, tilted ledges, and others.
Digital Prototypes with Whiteblocking
When developers have moved from prototyping off the computer to prototyping in digital form, they create test levels through a process known as Whiteblocking. Whiteblocking is when a level designer creates a level out of simple geometry, most often white or simply-textured blocks (thus the name), to test whether levels accomplish the gameplay goals they want. Early on in the design process, when designers are trying to define gameplay metrics of player characters and other things, Whiteblocking can help determine what gameplay measurements should be. Likewise, designers can draft the spatial characteristics of their levels in a parti-like way, testing the sizes and shapes of certain environments for different gameplay experiences, before specific environmental art is added to a level (figure 2.51.)
Figure 2.51 Whiteblocking done for SWARM! shows how an important section of a level meant to teach players how to kill enemies was thoroughly tested in simple geometry before environment art was added.
The geometry used to Whiteblock level spaces is usually the simplest needed to simulate the colliders that will be used in the eventual final level design. Colliders are a component of objects in game engines that simulate the interaction between physical objects. A box collider attached to a piece of level geometry, for example, will cause that object to interact with other objects as though it is the shape of a six-sided box, regardless of the shape of the actual environmental art (figure 2.52.) Colliders can be simple geometric shapes or can be made to tightly fit organic shapes.
Figure 2.52: This plant has a box collider attached to it. Though its 3D model has an organic shape, player objects in a game will interact with it as though it were a rectangular solid.
Valve uses Whiteblocking extensively in its level design process. The construction rules for engine primitives in their level editor, Hammer, allows rapid 3D level prototyping through simple and precise building. Hammer’s primitives, called “brushes”, are used to roughly define level spaces, which are then playtested to see if the intended experience is created. Level designers see what worked properly and what did not, and then change the spaces by editing the brushes. When the designers find themselves editing little of major spaces and instead focusing on smaller details, the level is ready for environment art.
As an iterative process, Whiteblocking begins with almost parti-like interactive forms of levels and moves designers towards more art and ornament-centric design decisions that are not unlike interior design. As level geometries become better defined, standard pieces of environment art can be defined as well, eventually becoming the building blocks of levels.
Architectural Spatial Arrangements – from Chapter 3: Basic Gamespaces
As with the previous chapter, we will begin with lessons from Architecture. Where last time we focused on tools and techniques that were useful in game engine environments, this time we will discuss spatial arrangements that can be utilized in games.
Games and architecture differ in the fact that real-world Architecture must conform to real-world rules. For example, real-world buildings must both have an interior and exterior – with the shape of one influencing the other. Likewise, real-world architecture must take into consideration weather, geology, zoning regulations, and structural realities. Conversely, these are not things that gamespaces must deal with. To one extreme, this can mean experimental structures such as Atelier Ten Architects and GMO Tea-cup Communications Inc.’s Museum of the Globe[xii], a large elliptical structure formed from cubes floating in space (figure 3.1) or Hidenori Watanave’s explorable database sculpture on the life of Brazilian architect Oscar Niemeyer[xiii] – both former structures within the virtual world Second Life[xiv]. For more day-to-day level design, however, this means gamespaces that are free from interior/exterior requirements. This results in more freeform spatial layouts based on player movement patterns, narrative events, or game mechanics (figure 3.2.) Indeed, “interior” and “exterior” are little more than descriptions based on the art used to decorate the gamespace.
Figure 3.1 A sketch of Atelier Ten architects and GMO Tea Cup Communication, Inc’s Museum of the Globe. Since the building is built within a virtual world, it does not require any structure to hold up the hundreds of cubes making up its main body. The designers designed the buildings form in Microsoft Excel and then generated the geometry in an automatic modeling program.
Figure 3.2 Parti diagram sketches of level plans. Game levels can take on unusual forma characteristics because they do not have to conform to a corresponding interior and exterior as real buildings do.
With these differences in mind, spatial designers for games can take advantage of architectural lessons within the freedom of game design environments. Some of these lessons even have conceptual links to how levels are constructed in many modern game engines.
The first architectural spatial arrangement we will explore is that of figure-ground. Figure-ground is derived from artistic notions of the positive and negative space of a composition, where positive space describes the area inhabited by the subject of a piece and negative space describes space outside of or in-between subjects (figure 3.3.)
Figure 3.3 This illustration, known as Rubin’s vase, shows the concept of positive and negative space and how they can be reversed. Based on whether the viewer is interpreting the black or white portions of the image as the negative space, this is either an illustration of two faces looking at one another or of a vase.
Figure-ground theory in architecture comes from the arrangement of positive space figures, often poche’d building masses, within a negative space ground. When viewed in plan, the designer can see how the placement of building figures begins to form spaces out of the ground. Indeed, the formation of such spaces in figure-ground drawings is as important as the placement of the figures themselves (figure 3.4.) According to architectural designer Matthew Frederick, spaces formed by arranged figures become positive space in their own right, since they now have a form just as the figures do[xv]. From an urban design standpoint, these framed spaces are often squares, courtyards, parks, nodes, and other meeting areas where people can “dwell”, while remaining negative spaces are for people to move through[xvi].
Figure 3.4 When mapping out spaces with figure-ground drawing, it is important to observe how the positive space figures create spaces out of the negative space ground. These spaces, having forms of their own, are considered positive space.
Frederick also points out that when utilizing figure-ground, both figural elements and spaces can be implied[xvii], either by demarcating a space with structural elements or by creating negative spaces that resemble the form of nearby figures (figure 3.5.) This echoes theoretical neuroscientist Gerd Sommerhoff who, as quoted by architect Grant Hildebrand, said,
The brain expects future event-and-image sets to be event-and-image sets previously experienced. When repetition of previous experience seems likely, the brain readies itself to reexperience the set. If expectances are confirmed, the model is reinforced, with a resultant sensation of pleasure.[xviii]
In this way, we can see how figure-ground becomes a powerful tool for level designers to create additive and subtractive spaces within many game engines. Many engines allow for the creation of additive figure elements to be arranged within negative 2D or 3D space. Gamespaces are often based on mechanics of movement through negative space, using positive elements as ledges or supports for a player’s journey. Under other mechanics, forming spaces in-between solid forms allows for the creations of rooms, corridors, and other spaces that players can run, chase and hide in. Additionally, designers can communicate with players via implied boundaries or highlighted spaces that use figure-ground articulations like those described by Sommerhoff (figure 3.6.)
Figure 3.5 This illustration shows how figure-ground arrangements can be used to imply spaces or elements.
Figure 3.6 These illustrations show ways that figure-ground relationships can be utilized in many gamespaces, implying spatial relationships can be an effective way of relaying spatial messages to players.
Form-Void (also called solid-void) is in many ways a 3-dimensional evolution of figure-ground. Indeed, it is the natural application of figure-ground in games where the gamespace will be viewed from a non-top-down perspective (figure 3.7.) In form-void theory, spaces that are carved out of solid forms are implied to have a form of their own.
Figure 3.7 Some examples of form-void relationships between forms.
Just as figure-ground is spatial arrangement by marking off spaces with massive elements, form-void is spatial arrangement by adding masses or subtracting spaces from them. This further resembles the operation of many of the game engines described in Chapter 2: Tools and Techniques for Level Design, in how these engines allow for the placement of geometric forms or for their carving out of an endless mass. Similarly, 3D art programs allow for intersections between forms to be realized through either careful modeling or Boolean operations, where mathematical equations are used to combine 3D models in additive or subtractive ways. Buildings such as Peter Zumthor’s Therme Vals or Mario Botta’s Casa Bianchi, both in Switzerland, show how form-void relationships can be used to carve out spaces for balconies, doorways, windows, private rooms, and other functions (figure 3.8.) In games, such additions and subtractions can be used for hidden alcoves, secret passages, sniping spots, or even highlighted level goals.
Figure 3.8 Sketches from Therme Vals by Peter Zumthor and Casa Bianchi by Mario Botta show how forms and voids can be used to define space.
Level design is an art of contrasts. It is also an art of sight lines, pathways, dramatic lead-ups, and ambiguity about the nature of where you are going. All of these elements contribute to the experience of an arrival, the way in which you come into a space for the first time.
Much of how we will communicate with the player is through arrivals in space. It is also in how that space ushers the player towards their next destination or provides the means for players to choose their own path. Much of how you experience a space when you arrive in it comes from the spatial conditions of the spaces that preceded it: if you are arriving in a big space, spaces leading up to it should be enclosed so the new space seems even bigger, light spaces should be preceded by dark, etc. In their book, Chambers For A Memory Palace, architects Donlyn Lindon and Charles W. Moore highlight John Portman & Associates’ Hyatt Regency Atlanta Hotel as featuring such arrival in its atrium space. Dubbed the “Jesus Chris Spot” by critics, it was not uncommon soon after the hotel was built for businessmen to arrive in the twenty-two-story atrium from the much lower-ceilinged spaces preceding it and mutter “Jee-sus Christ!” as they looked upward[xix] Similar spatial experiences are common in exploration-based games such as those in the Legend of Zelda or Metroid series for leading up to important enemy encounters, item acquisitions, or story events (figure 3.9.)
Figure 3.9 Many games use contrasting spatial conditions to highlight the approaches to gameplay-important spaces such as boss rooms or goals. This diagram of the Temple of Time from The Legend of Zelda: Ocarina of Time, where the player receives a narrative-important sword, shows how contrasted spaces and a Byzantine-esque basilica plan emphasize the importance of the sword chamber.
Another important element of how players arrive at spaces is their point of view from the arrival point. As we will see later in the chapter, camera angles in games have a great deal of influence with how a player understands space. However, dramatic reveals and arrivals are possible regardless of the chosen point-of-view. In classical architecture, the procession-like approach to the Parthenon in Athens, Greece shows how an occupant’s point of view is steered towards dramatic reveals. Visitors climbing up the steps of the Acropolis would first see the Parthenon from below. Then, passing through the Propylaea, the portico-like entrance building of the Acropolis, they would be greeted by a three-quarters view of the Parthenon from its Northwestern corner rather than a more 2-dimensional view from straight on. The path then forced visitors to walk around the building before they would wind back to the entrance of the Parthenon itself. From this forced path, visitors got a more theatric approach to the Parthenon than if they had walked straight up to its entrance (figure 3.10.)
Figure 3.10 Diagram of the entry procession to the Parthenon. Visitors did not approach from the entryway side, but from a corner. They then had to walk around the building. Since all elevations of the building were equally intricate, it could be enjoyed from all sides as visitors walked around to the entrance.
A last architectural spatial lesson is less of an arrangement and more of another goal for designing your own spaces. This lesson is known as Genius Loci, also known as Spirit of Place. This term comes from a Roman belief that spirits would protect towns or other populated areas, acting as the town’s Genius. This term was adopted by late 20th century architects to describe the identifying qualities or emotional experience of a place. Some call designing to the concept of Genius Loci placemaking, that is, creating memorable or unique experiences in a designed space.
In Chapter 2, we discussed the Nintendo Power Method of level design, where the designer creates a macro-scaled parti or plan of their level, then distributes highlighted moments of gameplay as though developing a map for a game magazine. Each of these highlighted moments of gameplay; be they enemy encounters, movement puzzles, or helpful stopping points; have potential for their own Genius Loci. Are these places for rest or for battle? Should the player feel relaxed, tense, or meditative in these gamespaces? The answers to these questions depend highly on the game you are building, but can help you determine the kind of feel you want for your levels.
Beyond individual gameplay encounters, level designers can implant Genius Loci within the entirety of their gamespaces and use it as a tool for moving players from one point to another. Genius Loci can be built through manipulations in lighting, shadows, spatial organization, and the size of spaces – which will all be discussed in detail later in the book. If you are building a level for a horror game, for example, the Genius Loci you build should be one of dread, created through careful selection of environmental art, lighting, sound effects, and other assets. Likewise, spaces in a game with little or no Genius Loci can be circulation spaces, that is, spaces for the player to move through to get to their next destination. Depending on the gameplay you are creating, circulation spaces may be a chance to rest between intensive encounters or tools for building suspense before a player gets to the next memorable gameplay moment.
篇目2，The Metrics of Space: Tactical Level Design
by Luke McMillan [Design]
What makes good level design? PhD and educator McMillan — who’s worked with Ubisoft to create a curriculum for game design — examines how point of view effects players, showcasing a variety of gameplay scenarios which show different tactical choices players may be confronted with.
There are various means of understanding how the perception of 3D spaces in games changes the player’s emotional state.
One methodology used in level design is that of architectural perspective — the relationship of the player and the spaces that they occupy at any given time. Many implementations of this approach do not consider more dynamic relationships involving the player, other agents and the environment.
This article looks at dynamic relationships within 3D space in order to understand how we can use dynamic objects in conjunction with level geometry to adjust game difficulty and the player’s emotional state. To achieve this goal, this article will take the novel approach of evaluating the tactics of players in the context of modern, 3D FPS games.
•An understanding of how we can tailor the difficulty level of virtual spaces in games through a better understanding of what makes 3D FPS levels more or less difficult.
•A look at how difficulty ramping can be achieved using a number of different approaches.
The Metrics of Space
In order to take a rational approach to the design of 3D game spaces, we need to identify a number of metrics. The primary metric that alters difficulty is player line of sight. The greater a player’s line of sight, the more able they are to plan ahead and think strategically about the game world.
Greater line of sight also allows the possibilities for a larger amount of tactical options, as the player will have more time to plan and also a greater situational awareness. On the other hand, reducing the player’s line of sight will result in disadvantaging the player, as they will have less situational awareness and less time to act to certain problems.
I must point out that this observation is in relation primarily to the FPS genre. If we were to phrase this in broader terms, we could make the same conclusions by citing a player’s “situational awareness”; however, as this article is level design-centric, I will instead dissect this notion of line of sight.
We can measure line of sight using two key principles: the angle created by geometric field of view (GFOV) as well as the fidelity of graphical resolution, which will tell us how far the player can accurately see. (Figure 1)
Geometric Field of View & Display Field of View
When dealing with the rendering of 3D spaces, we are primarily concerned with the geometric field of view (Figure 2). The GFO is the most commonly discussed type of field of view metric, as this field of view is that of the player’s camera. The width is represented as an angle that measures the horizontal span of the frustum. The far clipping plane is the point at which the game engine stops rendering. We sometime hear this referred to as “draw distance”. Complex rendering systems will express this element of visual acuity in “arc minutes.”
Less discussed is the concept of display field of view, or DFOV (Figure 3). This is the field of view dictated by the player’s distance to display and the size of the display that they are playing the game with. Interestingly, the DFOV plays an exceedingly important role in the navigation and subsequent difficulty of 3D space, but only for female gamers. Research conducted by Tan,Czerwinski, and Robertson (2006) suggests that female players have the most to gain when the DFOV and GFOV angle is a 1:1 relationship. Interestingly, males seem to be far less affected in their navigation of 3D spaces when this relationship is changed, even dramatically.
Portals & Occluders, and Line of Sight
A portal is any game device that allows for greater-than-usual line of sight. We could consider a gantry that surrounds an upper level of a factory level as a type of portal, as the player is able to use the open floor plan to gain a view of the floor beneath them (Figure 4). This is why we often see players taking the “high ground” in a tactical scenario, as the height elevation allows for a greater situational awareness as opposed to if the player remained on the lower parts of the map. Windows and doorways also constitute portals within game levels.
Any type of weapon of game object that allows the player to have greater control over their view of the virtual world is extremely powerful. Weapons like the sniper rifle, which its ability to increase line of sight, are extremely powerful as a consequence. These powerful abilities, however, are usually compromised in some way. The sniper rifle, although giving the player greater line of sight, will always reduce the player’s GFOV (Figure 5). Or the homing rocket used in Unreal Tournament will leave the player exposed to attack whilst in use.
Occluders can also modify graphical fidelity, and subsequently limit peripheral vision, or the player’s view distance. The flashlight used in Doom 3 is one of the best examples of an occluding device that does both of these things (Figure 6).
The flashlight technique is also interesting from a spatial perspective, as it makes small spaces seem artificially larger, and encourages the player to explore parts of a room or level that they wouldn’t otherwise do if it were fully lit. On face value, Doom 3′s levels have an extremely linear design when compared to the franchise’s earlier titles; however, the player is kept in the smaller spaces longer, as the use of occlusion means that they need to spend longer gaining a situational awareness of each room.
The “noise” effect used in Silent Hill 2 (Figure 7) is also another alternative occluding device, used to reduce the player’s line of sight and subsequently make them feel more cautious. It is also important to note that effects like this often serve an important technical purpose, as they reduce the draw distance required in large, open environments whilst also giving the illusion that the environment is larger than what it seems. We often see simulated weather effects such rain, fog and simulated snow used to achieve a similar goal.
In the context of games, level designers can use the principle of portals and occluders to adjust the difficulty of a game’s virtual space. Figure 8 demonstrate the difference in difficulty associated with using occlusion. In the example of the left, the player has a significantly heightened sense of situational awareness, as they can see through the walls. This will mean that they will be on the “front foot” when it comes to engaging any enemies.
In the example on the right, occlusion is used to limit the player’s situational awareness. By doing so, the player will undergo moments of anxiety when exploring new spaces, as they will need to quickly familiarize themselves with the layout of the space so that they can plan strategically for a number of possibilities. Although there are many psychological outcomes from these mechanisms, in the context of this article, we are dealing primarily with occluders and portals as a function of difficulty ramping using 3D spaces.
Secondary Metric: The Ability to Move, and Possibilities for Movement
When dealing with the rational design of 3D spaces, the designer needs to be aware of how control interfaces can make movement in a 3D space more or less difficult.
When the player has a greater amount of space to operate in, they have increased opportunities for either enemy engagement or enemy evasion. Space also forms the basis of essential emotions of game play. Size variations in level geometry should be used in a way in which the player can observe contrasts in their environment.
The use of space needs to be analyzed with the addition of the primary metric, line of sight.
Even though a large space may offer the player greater amounts of opportunity, a limited line of sight will override any advantage that the space brings with it, and this is similar to the use of the flashlight in Doom 3. (Figure 9)
Alternatively, when the player’s view frustum is sufficiently large enough in comparison to the virtual space, they will be the most empowered (Figure 10). A simple way of thinking about the combination of these two elements is to consider that the size of a game space is always filtered through the player’s view frustum; hence, in terms of a hierarchy of difficulty metrics, virtual space will always be secondary, as the world is ultimately communicated to the player via the camera system.
Virtual space is a trade-off for the player between possibility for movement and possibility for ambush. The easiest way to understand this trade-off is by considering the relationship of line of sight, virtual space, and enemy approach vectors.
There are three ways of understanding how approach vectors affect the game’s difficulty. Difficulty of approach vectors is dictated by whether an enemy occupies the players existing view frustum,whether they have to move view frustum, or if they have to move view frustum and change world position to engage.
•Easiest Approach Vectors: Those which the player can see in their immediate view frustum without the need to adjust their position or view. (Figure 11)
•Intermediate Approach Vectors are those where the player must change their view position of the 3D world, but not necessarily their world position. (Figure 12)
•Most Difficult: Any approach vector that requires the player to shift their view the most from its current position.
When an enemy approach vector requires the player to change their view frustum and world position, we are creating the potential for the player to make mistakes. This added possibility for mistakes is what ramps our difficulty. However, in order to understand this metric further, we need to know a little more about player psychology.
Player Psychology: Correction Cycles
Humans are excellent “guesstimaters.” We tend to iteratively guesstimate our way to the solution of problem by continually guessing, observing, and correcting. Imagine you are reaching out for your cup of coffee. You will move your hand, observe its new position, and then update the amount of movement required to meet with the target. This will happen many times per second until you reach your goal. (Figure 14) (This is akin to Steve Swink’s “delicious cupcake” example in Game Feel.)
Basically, the more we expect the player to change their position or line of sight, the more correction cycles we are forcing them to undertake. The lower the number of correction cycles, the easier it is for the player to hone in on their target.
Figure 14 is an example of our guesstimation process when honing in on a static target. The large red triangles represent the margin for error in any guesstimation phase; the larger the triangle, the more room for error in that guesstimation step.
As we hone in on our target via movement, observation, and correction (update), we gradually reduce our margin of error. However, if an object continues to move, then the amount of possibilities will not reduce in a linear fashion, like Figure 14 suggests.
To give another example, let’s assume that the player is undertaking the same process of move, observe, update for a static object — say they are trying to adjust their crosshair so it is over a target. They will gradually move the crosshair until the margin of error becomes lower and lower via this process of refinement.
Now, imagine of the target suddenly reacts to the player and attempts to evade them via strafing away (Figure 15). The player will now need to significantly update their process of guesstimation, bringing more possibilities, and hence a greater margin for error, until they eventually hone in on the enemy again.
Although open spaces open up the possibility for the player to be flanked or approached from many more approach vectors by enemies, more open spaces also allow the opportunity for evasive maneuvers by the player.
In Figure 16, the player has the advantage, as there are more evasion vectors than enemy approach vectors. In a previous article where I dealt with the notion of compression and funnelling, I refer to these vectors as “expansion vectors” — an element which can alleviate the tension caused by compression via enemy encroachment on the player.
In the majority of cases, players in first person perspective games will choose to firstly adjust their world position so that as many enemies as possible can be kept in the current view perspective — watch someone play Serious Sam and they will usually prefer to backpedal away from enemies so they can keep their view frustum on them. World movement change is preferred above excessive view frustum changes. In most cases, a player will choose to backpedal first with minimal changes to view position. (Figure 17)
In a tactical scenario, strafing around an enemy will always be advantageous, as enemies require more correction cycles to attack a strafing target as opposed to one that is simply moving away or towards them. You can think of this in terms of the movement of a crosshair in game. If a player backpedals away from their enemy, then although they are becoming a smaller target, the amount of correct cycles required to adjust the cross-hair is significantly less. (Figure 18)
When an enemy moves in such a way that it causes the player to frequently update their view frustum, the scenario is much more difficult due to the margin of error which is being introduced into the scenario. (Figure 19)
Level Geometry and Player Tactics
Now that we have an understanding of the essential metrics and player psychology, we can now look at how level geometry begins to modify these relationships from both a difficulty perspective as well as an emotional perspective.
Figure 20 is a simple depiction of how level geometry begins to modify the player’s the emotional state and strategy by affecting the view frustum. Frame 1 of Figure 20 shows an artificial representation of the player’s view frustum, whilst frame 2 depicts the actual view frustum after occlusion.
By introducing an enemy into the example used in Figure 20, we can begin to evaluate how the level geometries modify line of sight, view angle and evasion / approach vectors. Figure 21 is an example of the player moving forward along a tight corridor into an open space.
As the camera frustum has been occluded by the level geometry, the player is unaware of the patrolling enemy ahead. In this example, the player is the most disadvantaged. The level geometry is reducing their possible evasion vectors. By removing the player’s possibility to strafe, the enemy has the advantage of requiring fewer correction cycles to target the player.
In this example, the player will need to rush into unknown space in order to engage the enemy. They will be hesitant to do this, as it will require changes to GFOV and world position in order to engage. Further to this, as the room has been occluded, they will have not situational awareness in this environment — they may even believe that they are moving into another tight hallway.
There is, however, an upside; confined spaces are sometimes beneficial for the player, as it reduces the possible amount of approach vectors that an enemy can use against them. The trade-off, though, will always be a reduction in the possible evasive movement vectors, so evaluating this particular scenario requires more knowledge of the enemies’ behaviors.
If we change the player’s position with the enemy’s position, we have a significantly different type of encounter — one that favors the player for all of the same reasons that the enemy was favored in the previous encounter (Figure 22). This is another extension of the notion of compression and funneling that I have discussed previously.
Corridors like those depicted in Figure 22 are choke points which cause compression on the player — when compressed, the player will feel extremely anxious, and move quickly to get out of this environment, especially in deathmatch type scenarios where human players will exploit these choke points.
Figure 23 is a demonstration of how we can modify the player’s tactical abilities and subsequent emotional state by introducing certain level geometries. In frame 1 of Figure 23, the player is moving forward through the frame, and has two enemies approaching them from a diagonal vector, just outside of their line of sight. This example is similar to that of Figure 21; however, when the player goes to engage enemies by changing their view frustum (and/or their world position) they have reoriented themselves into a corner, hence compromising the available space that they have for evasive maneuvers. (Figure 24)
Forcing enemies through choke points will always be advantageous for the player. Figure 25 modifies the scenarios depicted in Figure 24 to turn the tactical advantage towards the player. Frame 2 of Figure 25 demonstrates how an occluding device can be beneficial for the player from a strategic perspective. In this example, the player has two approach vectors to monitor. As there is only one enemy, they can use the either one of the two approach vectors as an evasion vector to force to the enemy into another choke point if they need to.
Figure 25 can be further modified with level geometry to add additional choke points (Figure 26). However, this will start to work against the player, as they have far too many possible approach vectors. We can think of this scenario in terms of “closing off space” — a tactic that players use as a type of checklist to ensure that that they systematically closed off possible ambush vectors before moving onto the next game space.
In Figure 27, we have the same amount of choke points as in Figure 26; however, the player is able to systematically close each one of these off as they move through. In Figure 26, the player needs to manage three different potential approach vectors at any one time, whilst in the linear space of Figure 27, they only every have to manage two at a time. Further to this, they can incrementally close off these spaces to reduce this number further.
As the player moves through the environment as depicted in Figure 27, they begin to close off space, preventing possible ambush (under normal circumstances at least). Games such as Dead Space purposely break this rule in order to keep the player in a constant stage of anxiety:
Multiplayer maps are also a notable exception to this rule. Figure 29 is an example of a deathmatch type space that purposely prevents the player from being able to close off spaces. This type of spatial design is intended to be strictly non-linear, and force confrontation as much as possible.
Just as planar objects affect the metrics of space, so to do height elements. Earlier in the article, we considered how gantries could be used as an advanced type of occluder, allowing the player to gain an advantage as they have greater situational awareness.
It is also important to once again demonstrate how line of sight takes priority over virtual space in terms of metrics that determine difficulty.
Although the player will have limited evasion vectors, a gantry like the one depicted in Figure 30 will give the player strafing abilities whilst they are targeting enemies on the lower floor. The combination of these two elements combined give the player the most advantageous position in this scenario.
To demonstrate this point even further, let us consider the player in the inverse position. Whilst close to the gantry ledge, the player will have a significantly occluded view of the position above them. Further to this, the only way they have of removing this occlusion is to backpedal. As demonstrated in earlier examples, if the player is backpedaling away from the gantry, any enemy attempting to target them will require fewer correct cycles to gain an accurate hit.
To demonstrate this point even further, let us consider the player in the inverse position (Figure 31). Whilst close to the gantry ledge, the player will have a significantly occluded view of the position above them. Further to this, the only way they have of removing this occlusion to backpedal. As demonstrated in earlier examples, if the player is backpedaling away from the gantry, any enemy attempting to target them will require fewer correct cycles to gain an accurate hit.
The player in this scenario takes a risk by undertaking a backpedaling action to engage a potential enemy that is higher than them (Figure 32). Although the eventual outcome will mean that an enemy occupying the ledge gantry will be contained within their view frustum, the player is also making himself or herself an easier target. Ideally, advanced players will begin to learn that any backpedaling in this type of scenario should also be accompanied by large amounts of random strafing movements.
The most difficult iteration of this scenario can be seen in Figure 33. If we remove the player’s ability to strafe and also add an overhanging ledge over the player’s path, then this represents the most difficult iteration of the space. The player has reduced line of sight, hence they are less able to gain situational awareness and plan their actions and possible alternatives. Further to this, the player has had their evasion options compromised in the worst possible way — they only have the possibility for backpedaling rather than the more effective strafing type movements.
If we find that the example given in Figure 33 is too difficult for the player, we can use rational approach to start modifying the level geometry in such a way that we incrementally reduce difficulty. For example, Figure 34 makes the height of the corridor much higher, so that the player can see that there is a gantry ahead of them. This, then, at least lets them know of a potential hazard on this approach vector and they can then adjust their view frustum to accommodate this portion of the environment as they approach, instead of being forced to add multiple correction cycles.
A Conclusion, of Sorts
The term “conclusion” is misleading; in terms of understanding the impacts of space on difficulty and player psychology, what is presented here is merely the tip of the iceberg. The next step in understanding virtual space is to consider that within game geometries, we have a number of attractive and repulsive forces. I have previously discussed the theoretical components of this in another article, which deals with the notion of compression and funneling, and I have hinted at its benefits throughout this article.
Understanding dynamic relationships is the next piece of the puzzle. We need to understand the dynamic forces that compel the player to move and engage with the level geometries. For now, though, this rational approach to difficulty ramping in 3D FPS games can be easily applied to your own design concepts. If spaces are designed with the player’s situational awareness in mind, then we can begin to incorporate other design tools, such as Jesse Schell’s interest curves, to further improve our designs.
篇目3，The Metrics of Space: Molecule Design
by Luke McMillan, Nassib Azar
Game spaces provide a context for the game’s rules and systems, and a space for the game agents to perform mechanics. When we go about designing game spaces, sometimes thinking in pure spatial terms clouds what a designer needs to achieve with a certain game space.
For FPS games, sitting yourself down with your favorite prototyping tool kit and drawing corridors and rooms is a recipe for disaster. It is difficult to design interesting spatial puzzles when you are creating game spaces using the rules of reality. How many office blocks are fun to navigate?
Molecule design is a way of applying graphing theory for concepting and fine-tuning of various types of game spaces. This rational approach to design is a means to design spaces without thinking about the representational elements of space itself. This article still accepts the importance of planar maps; however, we need better tools to help us create these first.
This article will examine some useful tools gathered from the field of graphing theory that designers can use to conceptualize various game components. The latter half of this article will examine a real-world application of these tools. By doing so, we will examine how iterations of a level design benefited from this abstracted means of realizing space.
The Basics of Graphing
Graphing theory is a broad and diverse field of mathematics; however, this article discusses graphs that can explain spatial relationships. Core to graphs that explain spatial relationships are nodes and edges (Figure 1). Nodes can represent game spaces / rooms, pickups, spawn points and AI pathing nodes. Edges define relationships between nodes.
Figure 2 is a simple molecule consisting of several nodes, linked by edges. In this example, we have defined a set of tokens around the players spawn point. This is a literal depiction of space using a graphing approach. Nodes become linked by edges, and these define the shortest possible distance between the player and other node. The more powerful a token is, the longer the edge should become.
This approach works well for PvP games — to create a game space with roughly similar distributions of pickups, to achieve game balance. Repeating and rotating a molecule leads to symmetrical distributions throughout the game space. Edges are abstract ways of defining relationships but not necessarily hallways or any other level geometry. To explain this further, we need to look at weighted and directed graphs.
We can manipulate the physical appearance of our edges to help communicate different types of relationships between the nodes. In Figure 3, the edge between nodes A and C is thicker than the rest. If we are using graphing theory to create spaces, and the nodes represent particular game spaces, then the larger edge does not imply a bigger space between the two nodes, but rather a more direct route.
Figure 4 takes our molecule from Figure 3 and uses weighted edges as a guideline to place out level geometry. In this example, heavy weighted edges create a path between nodes A and C that is direct and unimpeded. Alternatively, the thin edge connecting nodes A and B results in a meandering pathway that is complex in nature. This example shows that edges do not depict geometry, but rather the relationship between nodes.
We can further increase the information that an edge communications by adding direction. Figure 5 is an example of a graph that has directed and weighted edges. Figure 5 uses directed and weighted edges to communicate two different ways to get between node A and node B. The thicker edge is more direct than the other. Linking nodes B and C is an indirect one-way gate. The thick edge linking nodes A and C is another one-way gate. The thickness of this edge shows a direct and unimpeded relationship between the nodes.
Nodes and edges can represent nearly any feature of game level design. For example, we could use a system whereby the weight of the lines also tells us about the difficulty of getting between nodes. By using edges to depict vertical space, we could say that node C is the highest point of the map. Node C is then transitive in the sense that it can only be accessed from node B. The one-way direction between nodes B and C might be achieved by having a “jump pad” at node B, pointing towards node C, but not in the opposite direction. It is really at the discretion of the designer and their team to define a key for their particular molecule system.
To further explain the concept of using spatial molecules to create play spaces, let us consider one example molecule and how it should and should not be implemented. The molecule represented in Figure 6 is a simple spatial molecule that defines a linear level progression, suitable for single player type maps. Weighted edges have not been used in this example; however directed edges have been used to create interesting spatial puzzles.
Figure 7 is an example of what not to do with a spatial molecule. The reason to use a molecule-based approach is to free your creative process from thinking in purely spatial terms, and instead think about creating interesting spatial relationships. Although the planar map in Figure 7 does follow the spatial relationships of the molecule, it is a boring, linear space.
There are also a number of other flaws that demonstrate why designing maps from a planar perspective is problematic. First, the linear, room-by-room layout of the map is a direct product of drawing maps out in planar space. When your imaginative space is two-dimensional, your maps will be two-dimensional also. As such, there are no interesting vertical spaces and, more importantly, the objective is not clearly visible from the beginning of the map.
Figure 8 is a better implementation of the same spatial molecule. This example treats each node as a “play space” and uses the edges of the molecule to define how these play spaces can interact with each other. Below is a hypothetical playthrough:
In this example, the player starts on a ledge overlooking a valley (node A). Beside them they can see play area F, a large manmade structure towering over the environment. This is the final objective and its size and scale immediately compels the player to wonder how they can get inside the structure. The player notices that the entry to the tower is locked, but they can see another structure in the distance, a large pyramid in section E of the map. The pyramid has a grand entryway that draws the player’s attention — it is the only other major point of interest in the landscape and as such acts to draw the player towards it.
Between their starting point at section A and the pyramid, the player sees a number of obstacles that they need to overcome: a large wall, a bridge with a closed gate and a canyon filled with water. The player has time to survey the landscape from their elevated position and gain situational awareness. From node A the player begins to plan their route.
The player jumps down from the elevated platform of node A — this is a one way gate. In section B, they need to make their way to the open gate. Initially they will be drawn to the bridge that crosses the canyon, but they soon realize that it is blocked off and can only be open from the other side. Close to the bridge, the player notices that there is a section of rocks which they can use to jump into the river below without taking damage.
Once in the river, they follow it downstream towards a large open section. Here the player finds a set of stairs that will take them up to the plateau containing the pyramid. Once inside the pyramid, there is an underground road which links back to the objective at section F. This road will collapse behind them once they get close to section F so it acts as a one-way gate.
The hidden room, “a”, is connected to F and to E, however it is also a one-way gate and can only be accessed from F. The room will flood once entered, causing it to be blocked off from F, and forcing the player back up into section E.
Section F is the objective, and once inside, the player can continue onwards. Note that because section A is a one-way gate and section F is closed off, the player should not be allowed to return back into the open-area space.
Figure 9 is another interpretation of the same molecule, this time using a more traditional room-based approach.
In this playthrough, the player starts in section A, a large room with two doors, one open and one closed. The player goes through the only open door into a large arena section — B. There is a door in this room, but it is blocked in such a way that the player knows that it is broken and they cannot get through it. Inside B are a number of containers that the player needs to jump between in order to get out of the room.
Above this tall room is a gantry, suspended high above the floor. The player can also see a room overlooking the arena — section E. The player jumps from container to container, slowly exploring the vertical space. Once they are in the highest position they enter a network of small service tunnels (section C) that gradually descend.
After navigating the tunnels, the player drops down into an outdoor section — section D. From here, they can go between D and E via the stair. Once inside E, they can cross the suspended bridge that they saw earlier to their objective. On the way to F, they notice a pickup, situated on a container that they previously could not access via section B. If they player decided to jump down onto this container, then they need to backtrack via, B, C, and D.
Figure 8 and Figure 9 demonstrate how creating a planar map based on a molecule can be an excellent way to creatively problem-solve spatial design. This method of concepting forces the designer to create interesting spatial options at the planar map stage of level design. From my own experiences, designing levels starting at the planar stage more often than not leads to boring, linear progressions which are a consequence of trying to create interesting 3D spaces in a purely 2D creative space.
More Advanced Toolsets
Now that the basics of graphing theory have been discussed, it is time to move on examine some of the tools that designers have at fingertips when going about designing game spaces. It is important to note that these are just some of the concepts available for designers. As this article is appropriating some of these ideas, there are instances where it is necessary to deviate from some of the pure mathematical interpretations of these concepts. This article will explore the following graphing concepts:
Dominion / Domination Theory
Domination Theory is a way to understand how nodes can have an area of effect (AOE) and how this AOE might overlap with other nodes. This tool is especially useful to analyze your existing maps from the perspective of player experience. Using this method, each node represents “zones of play” and the intensity of play that happens within each space.
This notion of “zones of play” is something that was originally explored during the design of Half-Life and is referred to as “Experiential Density”. Experiential Density is a term coined by Valve’s designers during the creation of Half-Life. The concept refers to play experience being distance-based, rather than time-based. The basic concept is that a player should always opt-in to the next section of the play experience. They should be given as much time as they need in order to accumulate loot or simply explore before being placed in a situation of high intensity.
Figure 10 is an example taken from Half-Life 2 that demonstrates how dominion theory can be used to promote Experiential Density. In this map, we have three distinct section of high-intensity play represented by nodes, A, B, and C. The area of effect around the nodes is meant to represent the intensity of play in each of these sections. The greater the AOE, the greater the challenge posed to the player.
If we are designing with Experiential Density in mind, then we can use Dominion to ensure that we are not forcing the player into consecutive, high intensity play zones. Quite literally we are looking at molecule design to ensure that we have enough emotional “cool-down” time for the player between zones. I like to think of these cool-down zones as being similar to dynamics in music. In his book The Clarinet and Clarinet Playing, musician and author David Pino sums this notion up well:
Think of it this way: If you look out from the shore upon a great expanse of ocean, you may become very quickly bored. If however the ocean is enlivened by the sudden appearance of an interesting ship, the view is more likely to hold your attention. Similarly, if your view is suddenly filled with hundreds of ships, not any single one of them will hold interest for very long. The same principle holds for the performance of music: If the listener perceives no subtleties he becomes bored; if he detects nothing but subtleties he becomes disorientated and bored… the most important element in any piece of music is its rhythmic flow.
To better demonstrate how Dominion Theory works, let us use the same example from Half-Life 2, but let’s intentionally break the Experiential Density (Figure 11). In Figure 11, the overlapping play sections are represented by the overlapping, red AOEs. From a player experience perspective, this is like trying to read a book with no punctuation. The game experience lacks a satisfactory blend of emotional states as the player “detects nothing but subtleties,” in Pino’s words.
This map, therefore, is a prime candidate to apply dominion theory to in order to solve the problem of Experiential Density. Depending on the amount of cool-down space you wish the player to have you can adjust your rules for “dominion-overlap” to suit. For example, you could remove overlapping nodes from your molecule so there was no-overlap (as per Figure 10) or you could revise your zones of play so that the play intensity is lower, yet more frequent (as in Figure 12).
From a level concepting perspective, Dominion can also be used to define a “spawn exclusion zone” or any other type of “exclusion zone.” An exclusion zone can define an area in which something should not happen — i.e., there should not be an overlap with the dominion of another node. In this application of Dominion Theory, a node can represent a pickup or a player spawn point. The red AOE is therefore a visual representation of the spatial metric that you have decided to use to represent minimum distances to a spawn event.
Figure 13 is an example of using Dominion to define an exclusion zone. The node represents an actual player spawn point, but could be any game token. The red AOE around the node is a visual representation of the minimum distance that another spawn can occur. For example, if we are working within the confines of UDK, then we might say that based on the size of our map, each spawn point must be at least 1024UU away from another if it occupies the same vertical space. The rules of your dominion zones are flexible; however, for this example, the rule is that no other spawns are to happen within the Dominion Zone — at least from a planar perspective.
Figure 14 is a dominion problem that needs to be resolved. The problem may be a result of overlapping spawns or pickups that are too close. We can remove the overlap in dominion by placing these nodes further apart or by simply using level geometry to mitigate overlap, as in Figure 15.
It is important though to use common sense when implementing Domination Theory. Once you start to add in level geometry, you are adding another layer of complexity to your designs that will call for revising some of your rules.
In this example, Figure 16, I have used the spawn exclusion system to spread spawn locations in an asymmetric environment. One thing to note is that spawn point 3 has been intentionally moved further away from spawns 1 and 2.
The reason for this is due to the fact that spawns 1 and 2 have fewer approach vectors — i.e. the player can see any oncoming enemy in their view frustum upon spawn. Spawn point 3, on the other hand, has a wide arc of approach vectors which the player cannot possibly cover within the same view frustum, hence the need to compensate by moving it further away from the other spawn points.
You can apply this same spawn exclusion system to other pickups — the more powerful the pickup, the larger the spawn exclusion should be. As mentioned earlier though, level geometry and other factors such as pickups and the player’s ability to move within the game space will necessitate the use of more sophisticated analytical tools — namely Spanning Trees and Steiner Points.
Using Graphing Theory to Understand Player Choice and Strategy
All game levels provide some type of spatial problem-solving puzzle. These puzzles take a number of forms, but one type of puzzle which can be improved via the application of graphing theory are puzzles relating to optimum movement strategies seen in all well-designed deathmatch style maps.
Players thrive on choice; however, too much choice can be just as bad as too little choice. Further to this, players take great pride in achieving victories via the execution of “good” strategic choices. So far we have used graphing theory to examine the construction of play spaces; however, graphing theory is especially useful when we examine our level designs with human cunning and strategy as our primary concern. The principles of Steiner trees, spanning trees, and maximum and minimum cutting are integral to understanding these human factors.
Figure 17 is an example of a hypothetical level. Each node, designated A-H, represents a different type of play space, and each edge represents how many different ways a player can move from space to space. Note that each edge does not represent a corridor, but rather the player’s options. The length of the edge is short or long based on how complex that particular route is — i.e., the longer an edge, the more time it should take to use that option. In the case of Figure 17, each space (node) has between three to five different options for the player to consider when exploring the space. The graph also communicates how the player needs to move through spaces in order to traverse the map.
Spanning trees can be used to define the most optimal connection of nodes in a graph. This tool can also be useful when we are trying to understand player behavior in a map and look for aspects of the design that may be unfair or unbalanced. We can use spanning trees such as those seen in Figure 18 to help disperse item pickups, define spawn points, and place level geometry to help counteract any significantly overpowered (OP) movement strategies that might emerge in a PvP map.
Although mapping out specific permutations of the optimal movement strategy for a level is a good way to start defining your play spaces, it is essential that we give further consideration for players’ desire to exercise cunning and emergence. A good example of this point is considering the pride that people (not just players) take in identifying shortcuts. A shortcut is a set of strategic choices that sit outside of the norm. Players will look for opportunities like this in any game environment and their discovery and exploitation of this can be very satisfying on an emotional level. A great way of planning for an understanding this behavior comes from the theory of Steiner trees.
A Steiner tree is a type of spatial problem that looks for the shortest interconnection between a number of nodes. The example that Raph Koster gives in his “Games are Math” presentation is a good way to understand the application of Steiner trees in games. In his presentation, Koster states “If you have three nodes and you need to create the shortest possible route between them, what is the shortest amount of edges required?” Koster states that most people will answer something similar to Figure 19.
The answer to this problem is slightly more devious, as it requires adding another node in the puzzle — a Steiner point. Via introducing the Steiner point in Figure 20, we have created the most optimal solution to this puzzle. Steiner points and the edges that they create can be treated just like any other type of graph. In the context of games, we can use weighted and directed edges to help define how a Steiner point might be a height element of a map or may be another one-way gate, like a teleporter or jump pad.
A Steiner Point is a shortcut. It is that element of a level’s design that players will seek out in order to exploit. The secret for level designers is to make the Steiner points in your map seem less obvious than the spanning tree routes. Borderlands is a good example of this. Within the maps, spanning tree paths are clearly defined and for the most part, appear as clearly defined paths and gantries.
Steiner points exist within the game in the form of height elements which allow the player to skip large sections of the spanning trees by jumping down to certain parts of the map, therefore avoiding large path traversal. Krom’s Canyon in Borderlands is just one example where the player can jump down from raised platforms to quickly move to another point in the map, therefore creating a Steiner point (see Figure 21).
Figure 22 (taken from Krom’s Canyon above) is an example of how spanning trees and Steiner points work from a level design perspective. In this example, in order for the player to get from node A to node F, they must enact a spanning tree solution. This relationship is represented in the level design by a set of gradually ascending platforms which are interconnected via bridges. A number of bonus items are implemented in this section of the map via Steiner points.
In Figure 23, two Steiner points have been added. Although there are actually several other Steiner points in this spatial molecule, these nodes are pickups placed on high platforms, only accessible from the nodes above them. As such, not only are these considered to be Steiner points as they offer the player a shortcut, but they are important points of interest for the player that allow them to explore the environment as a spatial puzzle.
Figure 24 expands this particular section of play into an even more defined molecule and adds two other major Steiner nodes that show how the player can traverse the space when they are either ascending or descending.
Now that we have taken a look at how Steiner points operate from a spatial puzzle perspective, lets revisit our spanning tree molecule originally introduced in Figure 17. If we applied Steiner points to link nodes in close proximity, then we would have something similar to what is seen in Figure 25.
These Steiner nodes could take many forms. They could be teleporters, actual level geometry, or even height elements that allow for faster path traversal. Figure 25 shows how many Steiner points we could possibly have in this spatial design. According to Koster, too many Steiner points are bad for human players, because you have provided so much opportunity; there really isn’t much scope to exercise what I like to call “skillful strategy.” Basically, there is no pleasure to be derived from creating shortcuts in this environment because there are so many of them.
If we begin to use level geometry to reduce the amount of possible Steiner points, we are beginning to ask much more of the player. By giving them fewer options (Figure 26), we are asking the player to exercise better strategy than the other players on the map. The upside to this is that players who do well in this environment will take much more satisfaction from its successful completion, as they perceive the lack of options to be indicative of a more complex problem. To demonstrate how a reduction in Steiner points relates to increased difficulty, we need look no further than the Steiner tree problem that we see in the lower, east quadrant of the Fallout 3 overworld (see Figure 27.)
Figure 27 (Click for larger version.)
Spatial navigation problems in the early parts of Fallout 3 are negotiated via simple spanning trees where you have many possible Steiner points. This is most noticeable in the areas to the south of main Vault as this is the first (and easiest) part of the map that the player is expected to explore. As difficulty increases, though, these Steiner points are vastly reduced; this can be seen in the subway system of DC, which the player encounters later in the main quest of Fallout 3.
A Practical Implementation
So far we have examined the basic principles of graphing theory and applied this to the analysis of a number of commercial examples, but how does graphing theory stack up as a tool to concept game spaces? The following is an example of a practical implementation of the theory of molecule design created by Nassib Azar.
In this example, a molecule concept is tested, implemented, and refined in order to create a balanced, multiplayer space, which despite its simplicity, offers players with a significant amount of interesting strategic possibilities to explore.
The core idea Nassib decided to explore was a map design which had three layers of experience, represented as three concentric circles. The game space is a deathmatch style map within the default game type of Unreal Development Kit. The outer layer comprises low intensity zones designed to “feed” players into the innermost section of the game space.
For the purposes of this design, “intensity” is measured by the amount of players actively trying to kill each other within each zone. Figure 28 is one of the preproduction sketches of the map. This diagram explores how choke points, intersections, spawn points and weapon pickups could be used to increase the intensity of the play experience as the player nears the center of the map.
After some initial paper prototypes and feedback, the core idea of three concentric play spaces of varying intensity eventually developed into a more concrete molecule which defines the space as a whole. Figure 29 is an iteration of the early concept. In this iteration, we still have the same set of concentric circles representing intensity of play; however, edges have been added to describe how the outer sections feed into the middle.
To achieve this goal, Nassib applied the notion of Compression and Funnelling, a simple tool which looks at how forcing the player around a game space using various game elements can create heightened emotional states. In Figure 29, each edge represented additional vectors of compression on the nodes they led to. In the case of this example, the nodes represented spaces for conflict; the more the edges leading into a node the higher the compression on that node (and as a result, the higher the intensity of game experience). In this application, node size was used to represent increased compression, and subsequently, intensity of play.
Figure 29 (Click for larger version.)
Although the application of molecule design is meant to create a distinction between play experience and level geometry, Nassib chose to explore whether pure geometrical representations of space have inherent player experience value. The hexagonal attributes of Nassib’s molecule prototypes were worthy of further investigation. The question was: Would the molecule translate to actual level geometry and still retain the original design intent?
The prototype molecule used to define the overall game space went through a number of iterations in the form of grey box levels developed within UDK. It was clear through prototyping that the experiment had merit; the intensity of the player’s experience increases as they work their way towards the center of the map. Nodes became generic play spaces (rooms) and edges became corridors that would feed into these spaces.
Figure 30 is one of the more advanced iterations of the grey box. It shows the implementation of the original molecule into a playable space. During testing, it was found that for intensity of play to increase, the room sizes needed to increase in order to accommodate the increased play intensity.
Room sizes are designed to create the most optimal zone sizes for the desired amount of play intensity. The original molecule design translated well in this regard. Play zones became progressively larger as they player moves towards the center of the map, yet the zones are also small enough to force the players into close proximity combat, hence increasing play intensity.
In order to create a syphoning of players towards the center of the map, a molecule was designed to aid in the placement of various weapon pickups. There are two main molecules used to define token placement. Weapon pickups were embedded in a molecule that forced the player to move quickly towards the center of the map. Health pickups were embedded in a molecule that forced the player to explore the circular boundaries of each play zone. The differing nature of these two molecules not only adds to creating clearly defined and different movement tactics for offensive and defensive play, but also aids spreading play over the entirety of the map rather than the central most zones.
Figure 31 (Click for larger version.)
Figure 31 breaks down the graphing further. In the close up of the medium node (upper left), a differentiation is made between two different edge types leading into it. Edges 1 and 2 come from the spawn point while 3 and 4 are fed from other medium nodes. This suggests a difference in danger level and is therefore represented by expressing the edges differently. Although the initial design hypothesis suggested that there would be some type of discernable difference between edges one and two AND three and four, it took several revisions of the grey box to observe this hypothesis the real world, seen in Figure 32.
Early iterations of the grey box demonstrated a fundamental flaw in the design. Although play was becoming intensified as it reached the center of the map, a secondary mechanic was emerging; players became aware that it was possible to farm the outer ring of the map and rack up numerous spawn kills. As a result of testing, edges [corridors] 1 and 2 were raised to create one-way gates, allowing them to feed players into the map but not allowing players already within the map to access the spawn points. The elevated corridors were re-conceptualized in the physical space as maintenance shafts, as can be seen below in Figure 33.
The placement of pickups also benefited from the molecule design approach and followed a similar symmetrical layout to the level geometry. Although the use of symmetrical molecules creates an easy workflow for designing the map, too much symmetry is often boring and even confusing for players.
To address this issue, asymmetry was used to create navigation landmarks for the players as well rooms that highlighted different types of weapons and game mechanics. Differences in each room’s layout served two purposes: to aid with player navigation and to create “perceived” advantages to each room. Perceived unfairness suggests no matter how fair or balanced a system is, players will be drawn to elements of the game that they believe are broken, even if they are not.
In essence, each room in the second ring contained a different type of spatial molecule. The molecules differed by varying choke points and cover elements. The result of this can be seen in the comparison between Figure 34 and Figure 35; both are rooms in the second ring and both offer different types of play experience within them.
After further iteration and testing, it was found that players were entering the primary room more than the second ring / medium rooms, but not at the expected proportion. The intensity of the play experience needed to be very high in the center room and there simply was not enough player traffic to achieve the desired experience. Of course, this could have been addressed with revising the space to make it smaller, however as much of the level art had already gone into production, it became necessary to look at alternative option.
To amplify this experience, a second ring of player spawn points where created on the mezzanine floor of the secondary ring. The walking distance to the center room from the upper spawns was shorter than the ground floor and therefore encouraged far more traffic to the central room and as such created the desired effect.
The two stacked spawns in Figure 36 did not have the same spawn-to-engagement times to the mid rooms. In other words, the edges above were not equal to those below when they should have been. By changing the position of the spawns in line with the revised molecule design, time to engagement was negligible when compared with the existing spawn points.
Symmetrical molecules create fair distribution of stairs and elevators in the map; however, the actual design of each of these three elevators is varied intentionally (Figure 37). The rationale for this approach was to highlight the psychology of perceived unfairness. Via testing, it was shown that most players thought that the stairs near their spawn point gave them the advantage, and that this advantage was not used against them. Asymmetry was also used in the design of stairs themselves, again this served two functions: to assist with navigation and vary the play experience in the medium rooms.
Another strategy that was used for balancing was not in the graphing theory itself, but highlights how graphing theory can help read player behavior. A Kismet script was created where every three minutes the game would compare the number of players that have passed through each of the six medium rooms and determine which one had the least traffic. The room with the least activity would then spawn a trigger.
When pressed by a player, this trigger would vent every other player into space, killing them and scoring multiple kills for the instigator. (Figure 38 is a view from above the map, and the last thing a player would see before dying.) This encourages “heat” where there is least, therefore creating a dynamic balancing system through mechanics rather than the static graphing. When presented with this scenario, players are given a choice to exercise Steiner point solutions to resolve the spatial problem — what is the shortest route to the target.
Once the script had identified the room with the least traffic, all players in the map receive both an auditory and a console announcement letting them know which medium room the trigger is available in. Depending on the player’s current location, they are presented with two main choices. They can use the risky, but shortest path through the center OR they can navigate the longer, but safer path through the medium rooms, avoiding the central conflict area.
By doing so, we have created two different strategies for players; they can use the middle room as a Steiner node or use the outer rooms as a spanning tree solution (Figure 39). These strategic options play to a player’s sense of accomplishment. The player feels a sense of pride, as they feel they are outwitting the rest by taking a shortcut to the proper room. Level assets used to populate the various rooms also served to reduce the total amount of possible Steiner points, creating higher intrinsic value for finding one of the limited solutions.
The final published map went through eight major revisions, resulting in updates to either the grey box or the molecules themselves to achieve the final product. Underpinning each revision was a revised molecule concept that would then be converted into a grey box. As such, each revision had clear objectives and goals and the final product benefited greatly from this, as time was extremely limited.
People like Dan Cook and Chris Crawford look at how people’s motivation to play games stems from our need to learn and prove these new gained skills. Raph Koster takes this notion further by being even more specific; people are pattern-finding machines and we take pleasure from games when we identify patterns and pre-empt them. It therefore stands to reason that using the pattern-based approach of molecule design to define play spaces immediately plays to this desire.
There is one main consideration to keep in mind; the player doesn’t perceive the game as a planar map; they sense it from their own camera frustum. As such, the scale and “identifiability” of the molecules you want to implement is very much limited by how much of the game world the player can perceive at any one point in the game.
Too often designers create labyrinth type maps, which — although being easily understand from a planar perspective — are absolutely impossible to traverse when viewed through the limited perspective of the player. As such, molecules and the patterns that they create need not necessarily be complex in order for them to be “fun” for the player.
Instead, well designed game spaces tend to have a number of nested molecules, rather than a molecule that defines the space as a whole. The practical example created by Nassib Azar is relatively simple from a graphing perspective, however the amount of molecule permutations created by the dynamic game elements create a diverse, yet manageable set of strategies for the players to explore.
It is important to point out the use of graphing theory to conceptualize and analyze game spaces is not a new idea, but rather one that has been discussed in various forms by different authors. The original inspiration for this research came from Raph Koster and his Games are Math presentation, and I would recommend Koster’s work to anyone interested in rational approaches to design. Joris Dormans also has a few informative articles that deal with how graphing theory can be a powerful tool for level designers. Dormans’ Adventures in Level Design and Level Design as Model Transformation [pdf links] are excellent and display the malleability of this toolset.