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从空间度量角度分析策略性关卡设计法则

发布时间:2012-09-30 08:20:00 Tags:,,,

作者:Luke McMillan

(何为出色的关卡设计?哲学博士兼教育家McMillan通过本文讨论了视角对玩家的影响,并展示可将玩家呈现不同策略性选择的一系列游戏场景。)

我们有许多方法可以理解游戏中的3D空间感是如何转变玩家的情感状态。

关卡设计中所使用的一个方法就是建筑透视图——即玩家在特定时间与其所在空间的关系。许多采用这种方法的设计并没有更多考虑到涉及玩家、其他代理和环境的动态关系。

本文将探讨3D空间中的动态关系,以便大家了解如何使用动态对象结合水平几何学去调整游戏难度和玩家情感状态。为达到这个目标,本文将通过评估玩家在现代3D第一人称射击游戏(以下简称3D FPS)中可用的策略进行说明。

目标

*通过了解如何让3D FPS关卡更困难或更简单,掌握为游戏虚拟空间调整难度的方法。

*探讨如何使用一系列不同方法实现富有层次感的难度设置。

空间度量

为了用理性方法设计3D游戏空间,我们需要鉴定一系列度量。可改变难度的一个主要度量就是玩家的视线。玩家视线越长,他们就越能够提前作好计划,以策略性思维应对游戏世界。

视线更长也意味着玩家将拥有更多可行的策略性选择,因为他们有更充裕的时间制定计划,并且对环境形势也更为了解。另一方面,削弱玩家视线将使其处于不利形势,因为他们对周围环境所知甚少,也没有足够时间应对特定问题。

我必须指出这种观察结果主要来自FPS游戏。如果用一个更宽泛的词汇来形容,我们也可以用玩家的“情境认知度”来下此结论,但本文主要以关卡设计为中心,所以我将用视线一词来剖析这个概念。

我们可以使用两个关键法则来衡量视线:几何视野所形成的角度(以下简称GFOV),以及图像分辨率保真度,这可以让我们知道玩家实际上可看到多远的东西(图1)。

图1(from gamasutra)

图1(from gamasutra)

几何视野 & 显示视野

处理3D空间渲染问题时,我们主要考虑的是几何视野(图2)。几何视野是最广为讨论的视野度量类型,这个视野就是玩家的摄像镜头。其广度就是衡量截头锥体水平跨度的角度,远处的截面就是游戏引擎可以停止渲染的结束点。这就是所谓的“绘制距离”概念。复杂渲染系统通常用“弧分”(游戏邦注:arc minutes,它是测量小角度的单位,常用于几何学、地图测量及天文学中,1弧分等于1度的六十分之一,可划分为60弧秒)来描述这种视敏度元素。

图2(from gamasutra)

图2(from gamasutra)

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。

图3(from gamaustra)

图3(from gamaustra)

入口 & 闭塞口,以及视线

入口是指可让玩家获得比正常情况更长视线的游戏装置。我们可以将围绕在一个工厂水平面更高层的构台视为一种入口,因为玩家在此可以使用开放的建筑平面图看到自己所处位置之下的状况(图4)。这也是我们常看到玩家在某个战略性场景中处于“高地”的原因,因为比起位居地图低处地带,位居高处更能让人们了解周围形势。窗户以及门廊也可作为游戏关卡的入口。

图4(from gamasutra)

图4(from gamasutra)

可让玩家掌握更多视野的游戏对象所持有的武器都有极为强大的作用。例如可以扩增视线的狙击步枪就是一个典型。但这种强大的能力也会在某些方面打些折扣。狙击步枪虽然可让玩家掌握更长视线,但却会减少玩家的GFOV(图5)。而《Unreal Tournament》中的归航火箭则容易让玩家在使用过程中遭受攻击。

图5(from gamaustra)

图5(from gamaustra)

闭塞口也能更改图像保真度,并随之限制周边视觉或者玩家的视距。《毁灭战士3》中使用的手电筒就是一个出色的闭塞装置典型,它兼具这两方面的特点(图6)。

图6(from gamaustra)

图6(from gamaustra)

从立体视图角度来看,手电筒效果也是一个很有趣的技巧,它让小型空间看起来被人为地扩大了,并促使玩家探索房间或关卡的各个部分(而如果整个房间/关卡被完全照亮时他们根本不会进行这种地毯式的搜索)。从表面上看,《毁灭战士3》的关卡设计与其早期版本相比极为线性化,但玩家却能在狭小的空间中逗留更久,因为这种闭塞设计迫使他们必须花更长时间熟悉每个房间的情况。

《寂静岭2》(图7)所使用的“嘈杂”效果也是一种闭塞装置的替代性方法,它可用于减少玩家视线,从而让他们提高警惕。值得一提的是,这种效果通常还有重要的技术性用意,因为它可以减少制作大型、开放式场景所需的绘制距离,但同时又能给人造成一种大场景的错觉。通常还可以使用雨天、迷雾以及降雪等天气模拟效果来达到同样的目标。

图7(from gamasutra)

图7(from gamasutra)

关卡设计师可根据游戏情景,使用入口和闭塞法则去调整游戏虚拟空间的难度。图8呈现了有关使用闭塞方法的不同难度情况。在未使用闭塞方法的左图中,玩家具有高度的情境认知度,因为他们可以看透墙面,所有事物一览无余。这意味着他们随时可以应对任何敌人。

图8(from gamasutra)

图8(from gamasutra)

而在使用了闭塞方法的右图中,玩家的情境认知度受到限制,因此他们在探索新空间时将经历一个紧张的过程,他们必须迅速掌握空间布局以便针对一系列可能发生的情况部署战略。这些机制含有许多心理学原理,但我们在本文主要探讨如何使用闭塞和入口方法来解决3D空间中的难度升级问题。

二级度量:行动的能力,以及行动的可能性

解决3D空间的合理设计问题时,设计师需要清楚控制界面是如何让人们3D空间中的行动变得更为困难或简单。

图9(from gamasutra)

图9(from gamasutra)

当玩家掌握了大量的空间情况时,他们就有更多机会决定究竟要与敌人交战或是逃避敌人。空间也是塑造游戏过程必要情感的基础。最好是通过水平几何空间大小的变化,让玩家看到自己所处环境的反差。

空间需与前面的主要度量——视线相结合起来使用。

即使更大的空间可为玩家创造更多机会,有限的视线也会让这一空间所带来的优势荡然无存,这一点类似于手电筒在《毁灭战士3》中的使用(图9)

当玩家视野的截锥足够大时,他们就会掌握更多优势(图10)。将这两种元素结合在一起,要考虑到游戏空间的大小总会被玩家视野截锥所过滤。因此从难度的度量分级来看,虚拟空间总是居于次位,毕竟玩家最终是通过摄像机系统来感知游戏世界。

图10(from gamasutra)

图10(from gamasutra)

接近向量

虚拟空间是玩家判断行动可能性及埋伏可能性的一个权衡途径。理解这个权衡方法的最简单方式就是考虑视线、虚拟空间和敌人接近向量之间的关系。

有三个方法有助于我们理解接近向量如何对游戏难度产生影响。接近向量的难度取决于敌人是否占据玩家当前视野的截锥,玩家是否需要移动视野,或者他们是否需要移动视野并改变所处位置与敌人交战。

*最容易的接近向量:这是指玩家无需调整所在位置或视野,就能直接通过视野看到敌人(图11)

图11(from gamasutra)

图11(from gamasutra)

*中级接近向量:指玩家需改变自己在3D世界中的视野位置,但不一定改变所处世界位置,就可以看到敌人(图12)。

图12(from gamaustra)

图12(from gamaustra)

*最困难的接近向量:需要玩家改变当前位置,最大化地调整视野才能看到敌人(图13)。

图13(from gamasutra)

图13(from gamasutra)

当一个敌人接近向量需要玩家改变视野和所处位置时,玩家就会有犯错的可能。这也就增加了我们提高游戏难度的可能性。但为了更深入理解这个度量,我们还需要掌握一点玩家心理。

玩家心理:矫正循环

人类是杰出的“瞎猜者”。我们倾向于通过持续猜测、观察和更正,反复瞎猜解决问题的方法。想象下你打算去取一杯咖啡。你得移动手,观察它所在位置,然后更改移动量以到达目标所在。在你达到目标前,这个过程每秒都会发生好几次(图14)。

图14(from gamasutra)

图14(from gamasutra)

从根本上说,我们越是要求玩家更改所在位置或视线,他们就越需要执行大量矫正循环。而矫正循环次数越少,玩家就越容易直达目标。

图14就是我们面对一个静态目标而进行瞎猜过程的一个典型。红色的大三角形代表每个猜测阶段的误差限度,三角形越大,就意味着犯错的可能性越高。

当我们通过移动、观察和更正(更新)而接近目标时,我们会逐渐减少误差限度。然而,如果一个对象持续移动,直达目标的可能性并不会以线性方式减少,正如图14那样。

再举一例,让我们假设玩家正执行针对静态目标的移动、观察、更新等相同过程——他们试图调整自己的准星以便瞄准对象。他们会逐步移动准星直至误差限度越来越小。

现在,假如目标突然对玩家作出回应,并且试图通过扫射而逃脱(图15)。玩家就需要极大更正自己的猜测过程,考虑更多可能性,因此就增加了误差限度,直到他们再次瞄准敌人。

图15(from gamasutra)

图15(from gamasutra)

逃脱向量

虽然开放空间给玩家带来了更多被敌人夹击或接近的可能性(游戏邦注:因为敌人可以从更多方向接近玩家),但同时也为玩家创造了许多脱险的机会。

在图16中,玩家的优势在于,他所掌握的逃脱向量要多于敌人的接近向量。我曾在过去的文章中将这些向量称为“扩张向量”,这个元素可以减缓玩家因敌人侵袭而产生的紧张感。

图16(from gamasutra)

图16(from gamasutra)

在多数情况下,玩家在第一人称视角的游戏中会首先选择调整自己所处位置,以便将大量敌人尽收眼底——观察人们玩《Serious Sam》时就会发现,他们通常习惯于后退,以便在自己的视野中都能看到敌人。改变所处位置是优于改变视野的良策。在多数时候,玩家会优先选择后退,最小限度地改变视野位置(图17)。

图17(from gamasutra)

图17(from gamasutra)

在战略性场景中,向敌人扫射总会很有优势,因为比起那些简单地逃离或接近他们的目标,敌人需要更多矫正循环应对扫射目标。你可以从在游戏中移动准星这个情况来考虑。如果玩家朝向敌人后退,虽然目标会变得更小,但却可大量减少调整准星所需的矫正循环(图18)。

图18(from gamasutra)

图18(from gamasutra)

当敌人以这种方式移动时,玩家就需要极大更改自己的视野,这种情形就会因为增加误差限度而变得更为困难(图19)。

图19(from gamasutra)

图19(from gamasutra)

水平几何 & 玩家战术

现在我们已经掌握了一些基本度量和玩家心理元素,可以开始观察水平几何如何从难度及情感层面改变这些关系。

图20简单描述了水平几何如何通过影响视野来改变玩家的情感状态和策略。图20的第1帧显示了玩家视野的模拟表现,而第2帧则是闭塞之后的实际视野。

图20(from gamasutra)

图20(from gamasutra)

在图20中引入一个敌人后,我们可以开始评估水平几何如何改变玩家视线、视角以及逃脱/接近向量。图21展示了玩家通过一个狭窄的走廊走向一个开放空间。

图21(from gamasutra)

图21(from gamasutra)

由于摄像镜头截锥已被水平几何体所闭塞,玩家无从知晓前方有敌人在巡逻。在这种情况中,玩家形势最为不利。水平几何体减少了他们的可行逃脱向量。由于玩家此时已无法扫射,敌人就掌握了优势,他们可以用较少的矫正循环来锁定玩家。

在这一情况中,玩家需要闯入未知空间与敌人交战。他们不会冒然行事,因为交战需要改变GFOV和所处位置。除此之外,由于房间已经被阻塞,他们对周围环境情况所知甚少——他们甚至可能认为自己正进入另一个狭小的过道。

但这也有一个好处,密闭的空间有时候也会有利于玩家,因为它减少了敌人的接近向量。然后这一形势有利必有弊,玩家逃脱敌人的移动向量也相应减少,所以评估这种场景时需要玩家对敌人行为更为了解。

图22(from gamasutra)

图22(from gamasutra)

如果我们将玩家与敌人的位置对换,形势就会大为逆转——玩家此时就会掌握敌人之前所拥有的优势,而敌人则处于劣势(图22)。

像图22所描绘的这种走廊就是会对玩家产生压迫感的堵塞点,玩家受到压迫时就会觉得异常紧张,并迅速前行以期早点脱离这种环境,在死亡模式类型的场景中尤其如此。

图23(from gamasutra)

图23(from gamasutra)

图23展示了我们如何通过引入特定水平几何体来改变玩家的战略能力以及随后的情感状态。在图23的第1帧中,玩家正在前行过程中,有两个敌人从玩家视线之外的对角线方向接近他。这种情况类似于图21,但玩家要与敌人交战时就必须改变自己的视野(或所处位置),并将自己逼到一个角落,这样等于是减少了逃脱敌人的可用空间(图24)。

图24(from gamasutra)

图24(from gamasutra)

迫使敌人穿过堵塞点总会对玩家更为有利。图25改变了图24的场景,将玩家更具有战略优势。图25的第2帧展示闭塞装置在战略角度上为何对玩家更为有利。在这种例子中,玩家有两个可监视的接近向量。当时只有一个敌人,因此他可以使用任意一个接近向量作为逃脱向量,从而迫使敌人进入另一个阻塞点。

图25(from gamaustra)

图25(from gamasutra)

图25可以利用水平几何体进一步改变,并添加额外阻塞点(图26)。但这种形势会对玩家不利,因为他们此时拥有过多可能的接近向量。我们可以用“封锁空间”一词来考虑这种场景——玩家在进入下一个游戏空间时就可用这种“封锁空间”策略来确保自己有组织地堵死了潜在埋伏向量。

图26(from gamasutra)

图26(from gamasutra)

图27拥有与图26相同数量的阻塞点,但玩家可以在进前过程中较有条理地封锁各个点。在图26中,玩家任何时候都需要同时警惕三个不同的潜在接近向量,而在图27的线性空间中,他们一次只需考虑两个接近向量。另外,他们还可以渐进性地封锁这些空间以减少接近向量。

图27(from gamaustra)

图27(from gamaustra)

随着玩家在图27中的前行,他们开始封闭空间,以免遭遇埋伏。《死亡空间》等游戏就是为了让玩家时时处于紧张和焦虑中而有意打破了这一规则。

图28(from gamasutra)

图28(from gamasutra)

多人模式地图也是这一规则的例外情况。图29是一个死亡模式类型的空间,它有意阻止玩家封锁空间。这类空间设计故意采用非线性模式,迫使玩家频频遭遇险境。

图29(from gamasutra)

图29(from gamasutra)

高度元素

正如平面物体一样,高度元素也会影响空间度量。在上文内容中,我们已经提到构台如何作为高级的闭塞器,让玩家掌握更多情境认知优势。

这里需要再次强调,从确定难度的度量角度来看,视线的重要性超过了虚拟空间。

虽然玩家所拥有的逃脱向量较为有限,但图30中所描绘的构台却有利于玩家扫射处于较低地势的敌人。将这两种元素结合起来可以让玩家获得最有利的位置。

图30(from gamaustra)

图30(from gamaustra)

为进一步解释这一点,让我们想象玩家处于相反位置的情况(图31)。玩家靠近这个构台边缘时,他们对自己上方位置的视野就会极大受阻。另外,他们要想移除这种闭塞性,唯一可行的方法就是后退。而他们越是后退,离构台就越远,就越容易撞上敌人的枪口,因为此时敌人瞄准玩家开火所需的矫正循环就会越少。

图31(from gamasutra)

图31(from gamasutra)

玩家此时若是采取后退行动,并与处于更高位置的敌人交战,就会让自己身陷险境(图32)。虽然最终结果意味着占据构台的敌人不会脱离玩家视野,但玩家自己也更易于成为攻击目标。骨灰级玩家则会意识到要这种情况下后退,需要伴随大量的随机扫射移动才有胜算。

图32(from gamasutra)

图32(from gamasutra)

这种场景的最困难情况可见于图33。如果我们移除了玩家扫射的能力,并在玩家的路径中添加了一个悬伸出的平台,那么这就会变成一个最困难的空间。玩家的视线受阻,其掌握的情境认知度也更少,更不利于制定行动计划。除此之外,玩家的逃脱选择也非常不利——他们只可能后退而无法采取更有效率的边扫射边撤退行动。

图33(from gamasutra)

图33(from gamasutra)

如果我们发现图33中的情况对玩家来说太困难了,我们可以使用合理方法调整水平几何体,逐渐降低难度。例如,在图34中让走廊的高度再高一点,以便玩家看到前面有一个构台。这至少可以让他们知道这个接近向量的潜在危险,这样他们就可以调整自己的视野以适应当前环境,而非被迫增加矫正循环的次数。

图34(from gamasutra)

图34(from gamasutra)

总结

从空间对游戏难度及玩家心理影响的层面来看,本文所涉内容还只是冰山一角。理解虚拟空间的下一步就是要认识到在游戏几何学中,我们还要考虑到大量的引力和斥力。我曾在另一篇文章探讨压迫感和漏斗理论的文章中提到了这类元素。

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。(本文为游戏邦/gamerboom.com编译,拒绝任何不保留版权的转载,如需转载请联系:游戏邦

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.

Objectives:

•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)

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.”

Figure 2

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.

Figure 3

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.

Figure 4

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.

Figure 5

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).

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.

Figure 7

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.

Figure 8

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.

Figure 9

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.

Figure 10

Approach Vectors

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)

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)

Figure 12

•Most Difficult: Any approach vector that requires the player to shift their view the most from its current position.

Figure 13

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.)

Figure 14

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.

Figure 15

Evasion Vectors

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.

Figure 16

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)

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)

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)

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.

Figure 21

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.

Figure 22

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

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)

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

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.

Figure 26

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.

Figure 27

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.

Figure 29

Height Elements

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.

Figure 30

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.

Figure 31

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.

Figure 32

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.

Figure 33

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.

Figure 34

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.(source:gamasutra

 


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