体积云差分视差尺度及其在实时游戏渲染中的应用

摘要

体积云（volumetric clouds）在视觉上具有明显的三维体积感，但地面观察者在日常尺度内移动时，云的整体外观往往几乎不发生可察觉变化。本文以差分视差（differential parallax）为核心量，建立一个简化的几何尺度模型，说明云内部前后特征的相对角位移近似满足 $\Delta\theta \approx d \cdot \Delta L / [L(L+\Delta L)]$，在薄云与小角条件下进一步化为 $\Delta\theta \approx d \cdot \Delta L / L^2$。基于人眼角分辨率、代表性云体尺寸和玩家移动速度，本文估算出：要使典型低层积云的结构发生显著可见重排，观察者通常需要移动数百米到数公里。由此可以解释为何实时游戏中的远云可以大量依赖时间复用（temporal reprojection）、距离分级细节（level of detail, LOD）和相机中心化天空表示。进一步地，本文比较压缩有限世界、1:1 真实世界与无限程序化世界三种开放世界范式，讨论其云锚定方式、视差真实性、浮点精度和渲染成本之间的工程取舍。

关键词

体积云；差分视差；实时渲染；ray marching；temporal reprojection；LOD；开放世界尺度；浮点精度

1. 引言

云体在图像中常呈现出强烈的体积感。这种体积感并不主要来自双眼视差（binocular disparity），而更多来自体散射（volumetric scattering）、消光（extinction）、自遮挡（self-occlusion）、自阴影（self-shadowing）以及轮廓明暗等单眼线索。与此同时，一个日常经验是：观察者在地面步行或骑行时，远处云的形状几乎不因观察位置改变而发生明显变化。

本文讨论的问题是：观察者需要移动多远，才能使一团体积云的内部结构发生可见的“换角度”变化？这个问题不仅是几何光学问题，也直接关联到实时图形学中的体积云渲染优化。若玩家移动导致的云结构变化本来就低于感知阈值，那么渲染系统便可以在相当长的时间窗口内复用云的低频形状和光照结果。

本文不是气象云微物理模型，也不试图预测真实云的形成、湍流演化或降水过程。本文的目标更窄：用一个可计算的尺度模型解释云视觉视差，并把该模型转化为实时游戏渲染中的工程判断。

2. 几何模型：差分视差

设云中心到观察者的距离为 $L$，云沿视线方向的厚度为 $\Delta L$，云在垂直视线方向上的横向尺度为 $W$。为了估算云内部结构的相对错动，可取云的近侧特征点 $P_1$ 与远侧特征点 $P_2$，二者距离分别为 $L$ 与 $L+\Delta L$。观察者沿垂直于初始视线的方向横向移动 $d$，则两个特征点的角位移差为：

$$\Delta\theta(d) = \arctan(d/L) - \arctan(d/(L+\Delta L)) \tag{1}$$

2.1 小角近似与适用范围

式（1）是更精确的一维几何表达。若 $d \ll L$ 且 $\Delta L/L$ 不大，则 $\arctan x \approx x$，得到式（2）。原始博客式写法 $\Delta\theta \approx d \cdot \Delta L / L^2$ 是式（2）在 $\Delta L \ll L$ 时的进一步近似。因此，凡是 $\Delta L/L$ 达到 $1/3$ 或 $1/2$ 的浅近云场景，使用 $L^2$ 分母会系统性低估所需位移。本文后续表格统一采用 $L(L+\Delta L)$ 分母，以避免这一误差。

$$\Delta\theta \approx d \cdot \Delta L / [L(L+\Delta L)] \approx d \cdot \Delta L / L^2 \tag{2}$$

3. 可见性阈值与数值估算

正常 20/20 视力的最小分辨角（minimum angle of resolution, MAR）通常约为 1 弧分；这是高对比、中心视野、理想测试条件下的阈值 [1]。云边界低对比且持续演化，因此 1 弧分在本文中只作为理想可察觉下限，而非保证可稳定感知的阈值。

本文采用三个工程阈值：第一，$\Delta\theta$ 达到 $\alpha_{\min}=2.9\times10^{-4}$ rad（约 1 弧分）时，记为“理想可察觉”；第二，$\Delta\theta$ 达到云横向角尺度 $W/L$ 的 10% 时，记为“明显变化”；第三，达到 30% 时，记为“结构性重排”。10% 与 30% 不是视觉科学常数，而是用于工程估算的经验阈值。由式（2）反解可得：

$$d_{\mathrm{detect}} = \alpha_{\min} \cdot L(L+\Delta L)/\Delta L,\quad d_{\beta} = \beta \cdot W(L+\Delta L)/\Delta L \tag{3}$$

3.1 代表性云体场景

低层云通常位于地表至约 2 km 的低云层范围，积云（Cumulus）和积雨云（Cumulonimbus）均属于低云族或从低层向上发展的云类 [3][4]。表 1 中的 $L$、$W$ 与 $\Delta L$ 不是普适气象常数，而是用于尺度分析的代表性数量级。

表 1 基于 $L(L+\Delta L)$ 分母修正后的代表性位移阈值

注：表中“明显变化”和“结构性重排”分别采用云横向角尺度的 10% 与 30% 作为经验阈值。数值为数量级估算。

3.2 双眼视差的贡献

成年人瞳距（interpupillary distance, IPD）常取约 63 mm 作为数量级估计 [2]。对于 $L=3$ km、$\Delta L=1$ km 的云体，双眼产生的差分视差约为 $b \cdot \Delta L / [L(L+\Delta L)] \approx 5.3 \times 10^{-6}$ rad，即约 1.1 角秒。该量级远小于普通空间分辨阈值，也难以在自然云体这种低对比、非刚性纹理上提供稳定深度匹配。因此，数公里外云体的立体感主要来自单眼光照和遮挡线索，而不是双眼视差。

4. 时间尺度：玩家移动与风驱动变化

当观察者横向速度为 $v$ 时，玩家移动引入的差分视差角速度近似为式（4）。相对地，风导致的整团云平移在天空中的表观角速度近似为 $u/L$，其中 $u$ 是云体随风平移的水平速度。二者不是同一个量：前者描述云内部前后层的相对错动，后者描述云整体在天空坐标中的漂移。原始文档中将二者放在同一表格中比较是可行的，但必须明确它们的定义不同。

$$\omega_{\mathrm{parallax}} \approx v \cdot \Delta L / [L(L+\Delta L)],\quad \omega_{\mathrm{advection}} \approx u/L \tag{4}$$

表 2 玩家移动差分视差与风驱动整体漂移的角速度比较

## 5. 游戏世界尺度与云锚定方式

开放世界游戏通常同时包含叙事尺度、坐标尺度和渲染尺度。叙事尺度描述游戏想表现的地理范围；坐标尺度是引擎实际使用的米制距离；渲染尺度则决定天空、云层、雾和远景是否与世界坐标严格绑定。

若一朵真实高度约 1.5 km 的云被固定在世界坐标中，玩家横向移动 10 km 后，它的仰角将从接近头顶变为 $\arctan(1.5/10) \approx 8.5°$。这已不属于小角差分视差，而是明显的几何扫掠。因此，在压缩有限开放世界中，若地图只有十公里量级，却叙事上代表数百公里，远云通常不能简单采用真实高度的世界锚定（world-anchored）方案，否则会暴露尺度压缩。

公开逆向研究显示，Red Dead Redemption 2 的天空与云相关 GPU 计算非常显著，并且其环境 cubemap 会从相机位置生成 [7]。这并不等同于官方证明“所有主视图云内容都随相机平移”，但它支持一种保守判断：RDR2/GTA5 这类压缩开放世界至少在远云与天空表现上倾向于相机中心化或近似无穷远（camera-centered / effectively infinite-distance）的策略，以压制不合尺度的平移视差。

5.1 三种世界范式

第一类是压缩有限世界，例如 RDR2/GTA5。它们为了叙事密度压缩地理尺度，因而更适合把远云视为低视差天空内容，由天气、风场和昼夜光照驱动变化。

第二类是 1:1 真实世界，例如 Microsoft Flight Simulator。其世界重建依赖 Bing 卫星/航拍数据与 Azure 云端流式数据 [8]，并提供实时天气模式，包括风速、温度、湿度、降水等 [9]。在这种尺度自洽的世界中，真实高度云层、飞机速度和世界锚定云场之间是兼容的。

第三类是无限程序化世界，例如 Minecraft。原版云是客户端图形效果（client-side graphical effect），在 192 至 196 层之间向西移动，并非服务器物理天气实体；但其位置在视觉上由坐标和时间决定，而不是将云图案作为内容绑定到相机 [10]。因此 Minecraft 不需要通过内容相机锚定来隐藏世界尺度矛盾。它真正需要处理的是大坐标下的浮点精度问题。

6. 体积云渲染方法与成本

实时体积云通常以云盒（cloud volume）或大气体积域的形式表示。渲染时，视线从相机出发穿过体积区域，沿光线进行步进采样（ray marching），每个采样点查询三维噪声（3D noise，如 Perlin/Worley/fBm 组合）或气象密度场，并累积消光与散射。Guerrilla Games 在 Horizon Zero Dawn 的体积云方案中明确提出了可美术控制、天气集成和约 2 ms GPU 预算等目标 [5]。后续研究也强调，体积云之所以昂贵，主要因为 ray marching 步数和时间复用策略之间存在直接权衡 [6]。

若采用直观的主光线步进与简化太阳方向步进模型，单帧成本可粗略表示为：

$$\mathrm{Cost} \approx P \times N \times (1+M) \times c_{\mathrm{noise}} \tag{5}$$

其中 $P$ 为参与体积云计算的像素数，$N$ 为主光线采样步数，$M$ 为每个采样点用于估算太阳方向遮蔽或散射的附加步数，$c_{\mathrm{noise}}$ 为噪声查询与相函数计算的单位成本。式（5）不是所有引擎的严格成本公式，而是用于说明 ray marching 嵌套采样为何昂贵的近似模型。

表 3 三类实时云渲染方案的成本与锚定方式

### 6.1 三个实现层级

层级 0 是几何或伪体积云，例如 Minecraft 原版云段。其主要成本来自几何绘制与简单透明处理，不进行真实体积积分。

层级 1 是薄层噪声云（2D or slab-based shader clouds）。这类方法在固定高度附近对噪声层进行少量采样，能表现云层明暗和边缘变化，但缺少充分的深度自遮挡。

层级 2 是真体积云（fully volumetric clouds）。它在一定高度范围内执行多步 ray marching，并可加入多次散射近似、太阳方向自阴影或预积分查找表。该层级质量最高，但也最依赖半分辨率渲染、时间重投影、抖动采样、空步跳跃（empty-space skipping）和提前终止（early ray termination）。

7. 由标度律导出的优化策略

第一，时间重投影。当地面玩家慢速移动时，$\omega_{\mathrm{parallax}}$ 很小，十几帧内云内部结构的相对角位移可能仍低于一个像素。因此，半分辨率或四分辨率渲染加 temporal reprojection 是有物理依据的，而不仅是经验优化。

第二，距离 LOD。差分视差随距离近似按 $1/L^2$ 衰减。近场云需要完整步进，中场可降低采样率并依赖重投影，远场可退化为 impostor、天空穹顶纹理或低频体积表示。

第三，形状与光照解耦。远云的体积感主要由单眼线索提供，因此密度形状场可以低频更新，光照查找表或大气散射项可按太阳高度、天气状态等更低频变量更新。

第四，速度自适应采样。在 Minecraft 鞘翅飞行或飞行模拟中，玩家速度从步行量级跃迁到航空量级，$\omega_{\mathrm{parallax}}$ 不再可忽略。渲染器应根据相机速度、云高、云厚和屏幕残差提高近场采样率。

第五，坐标精度管理。Minecraft Wiki 记载，Bedrock Edition 的许多位置计算使用 32 位浮点数，并在高坐标处产生明显精度问题；Java Edition 对实体位置等使用 64 位浮点数，但渲染阶段仍需面对 GPU float32 限制 [11][12]。因此，渲染器通常应在相机相对空间中步进，同时在噪声采样时采用世界坐标取模、分块原点或双精度 CPU / 单精度 GPU 混合策略。

8. 局限性

本文模型忽略了云体的非刚性演化、湍流、光照多次散射、遮挡复杂性和实际天气系统的空间相关性。表格中的云体尺寸和风速仅用于数量级分析，不应解读为气象分类标准。对于具体游戏引擎，本文基于公开资料与视觉推断进行讨论；除非有官方技术论文或 RenderDoc 帧捕获证据，不能把这些推断视为对引擎内部实现的最终证明。

9. 结论

体积云“看起来立体但不随人走几步而明显变形”的核心原因，是云内部前后特征的差分视差随距离平方快速衰减。对地面慢速观察者，玩家移动造成的云结构重排通常弱于风、密度演化和光照变化。这个物理事实为实时图形学中的 temporal reprojection、距离 LOD、形状/光照解耦与速度自适应采样提供了定量依据。

在游戏世界中，云的物理真实性并非只由渲染技术决定，还取决于世界尺度是否自洽。压缩有限世界倾向于使用相机中心化的远云表示来隐藏尺度矛盾；1:1 真实世界可以承受真实高度的世界锚定体积云；无限程序化世界则可以保留真实视差，但必须解决大坐标浮点精度问题。

参考文献

[1] M. Kalloniatis and C. Luu, “Visual Acuity,” Webvision: The Organization of the Retina and Visual System. University of Utah / Webvision, 2007. https://www.webvision.pitt.edu/book/part-viii-psychophysics-of-vision/visual-acuity/

[2] Cleveland Clinic, “Pupillary Distance: What It Is & How To Measure,” 2026. https://my.clevelandclinic.org/health/articles/pupillary-distance

[3] World Meteorological Organization, International Cloud Atlas: “Levels.” https://cloudatlas.wmo.int/some-useful-concepts-levels.html

[4] NOAA JetStream, “The Four Core Types of Clouds,” National Oceanic and Atmospheric Administration, 2023. https://www.noaa.gov/jetstream/clouds/four-core-types-of-clouds

[5] Guerrilla Games, “The Real-Time Volumetric Cloudscapes of Horizon Zero Dawn,” 2015. https://www.guerrilla-games.com/read/the-real-time-volumetric-cloudscapes-of-horizon-zero-dawn

[6] A. Toft, H. Bowles, and D. Zimmermann, “Optimisations for Real-Time Volumetric Cloudscapes,” arXiv:1609.05344, 2016. https://arxiv.org/abs/1609.05344

[7] imgEs, “Graphics Study: Red Dead Redemption 2,” 2020. https://imgeself.github.io/posts/2020-06-19-graphics-study-rdr2/

[8] Xbox Wire, “See the World in Microsoft Flight Simulator,” Microsoft / Xbox, 2019. https://news.xbox.com/en-us/2019/09/30/microsoft-flight-simulator-preview/

[9] Xbox Wire, “The Biggest World Update Ever for Microsoft Flight Simulator Is Also Its Best Yet,” Microsoft / Xbox, 2024. https://news.xbox.com/en-us/2024/07/24/biggest-world-update-ever-microsoft-flight-simulator-best-yet/

[10] Minecraft Wiki, “Cloud.” https://minecraft.wiki/w/Cloud

[11] Minecraft Wiki, “Java Edition distance effects.” https://minecraft.wiki/w/Java_Edition_distance_effects

[12] Minecraft Wiki, “Bedrock Edition distance effects.” https://minecraft.wiki/w/Bedrock_Edition_distance_effects

Abstract

Volumetric clouds exhibit strong three-dimensional appearance, yet their visible shape usually changes very little when a ground observer walks or cycles over everyday distances. This paper formalizes the phenomenon with a differential-parallax model. For two cloud features separated along the view direction by a depth $\Delta L$ at range $L$, the relative angular displacement caused by a lateral observer displacement $d$ is $\Delta\theta(d)=\arctan(d/L)-\arctan(d/(L+\Delta L))$. Under small-angle conditions this becomes $\Delta\theta \approx d \cdot \Delta L / [L(L+\Delta L)]$, and, for $\Delta L \ll L$, the familiar scaling $\Delta\theta \approx d \cdot \Delta L / L^2$. Using representative cloud dimensions, visual-acuity thresholds, and player speeds, the model shows that visually significant restructuring of typical low-level cumulus clouds generally requires observer motion on the order of hundreds of meters to several kilometers. The result provides a physical rationale for temporal reprojection, distance-based level of detail, shape/lighting decoupling, and camera-centered sky representations in real-time rendering. The paper then compares three world-scale paradigms: compressed finite worlds, 1:1 real-world simulations, and infinite procedural worlds.

Keywords

volumetric clouds; differential parallax; real-time rendering; ray marching; temporal reprojection; level of detail; open-world scale; floating-point precision

1. Introduction

Clouds often appear volumetric because of monocular cues such as volumetric scattering, extinction, self-occlusion, self-shadowing, and luminance gradients. In contrast, binocular disparity contributes little for cloud structures several kilometers away. A common observation follows: when a ground observer moves a few meters or even tens of meters, the visible shape of a distant cloud remains nearly unchanged.

This paper asks a narrow scaling question: how far must an observer move before the internal structure of a volumetric cloud changes visibly due to parallax? The answer is relevant not only to geometric optics but also to real-time graphics. If player-motion-induced cloud restructuring is below perceptual thresholds over many frames, a renderer can reuse low-frequency cloud shape and lighting information with limited visual penalty.

The discussion is not a cloud microphysics model. It does not predict turbulence, condensation, precipitation, or the life cycle of a real cloud. Its purpose is to derive a tractable geometric scale law and translate it into rendering decisions.

2. Geometric Model: Differential Parallax

Let $L$ be the distance from the observer to a near cloud feature, $\Delta L$ the cloud depth along the view direction, and $W$ the transverse cloud width. Consider two internal features: $P_1$ at distance $L$ and $P_2$ at distance $L+\Delta L$. When the observer moves laterally by $d$, their relative angular displacement is

$$\Delta\theta(d) = \arctan(d/L) - \arctan(d/(L+\Delta L)) \tag{1}$$

2.1 Small-Angle Approximation

Equation (1) is the more exact one-dimensional geometric expression. When $d \ll L$ and $\Delta L/L$ is modest, $\arctan x \approx x$ and

$$\Delta\theta \approx d \cdot \Delta L / [L(L+\Delta L)] \approx d \cdot \Delta L / L^2 \tag{2}$$

The last form is valid only when $\Delta L \ll L$. For shallow nearby clouds where $\Delta L/L$ may be $1/3$ or larger, using $L^2$ in the denominator underestimates the displacement required for a given perceptual threshold. Therefore the numerical estimates below use $L(L+\Delta L)$.

3. Visibility Thresholds and Numerical Estimates

A standard 20/20 visual acuity threshold corresponds to a minimum angle of resolution of roughly one arc minute under high-contrast foveal viewing conditions [1]. Natural clouds are low-contrast, deforming, and visually ambiguous, so one arc minute should be treated as an ideal lower bound rather than a robust detection guarantee.

Three engineering thresholds are used: an ideal detection threshold $\alpha_{\min}=2.9\times10^{-4}$ rad; a clearly visible shape change when the relative displacement reaches 10% of the cloud’s angular width $W/L$; and a structural rearrangement when it reaches 30%. Solving Eq. (2) gives

$$d_{\mathrm{detect}} = \alpha_{\min} \cdot L(L+\Delta L)/\Delta L,\quad d_{\beta} = \beta \cdot W(L+\Delta L)/\Delta L \tag{3}$$

3.1 Representative Cloud Scenarios

Low clouds generally occupy the surface-to-2 km layer, and Cumulus and Cumulonimbus are low-level or vertically developing cloud genera [3][4]. The values of $L$, $W$, and $\Delta L$ in Table 1 are representative order-of-magnitude scenarios, not meteorological constants.

Table 1. Representative displacement thresholds using the $L(L+\Delta L)$ denominator

The main conclusion is robust: everyday walking or cycling distances are far below the scale required to make a typical cloud structure visibly rotate or unfold. Motion on the order of hundreds of meters to kilometers is usually needed.

3.2 Binocular Disparity

Adult pupillary distance is often approximately 63 mm, with substantial individual variation [2]. For $L=3$ km and $\Delta L=1$ km, binocular differential parallax is approximately $b \cdot \Delta L / [L(L+\Delta L)] \approx 5.3 \times 10^{-6}$ rad, or about 1.1 arc seconds. This is far below ordinary spatial-resolution thresholds and is difficult to exploit in natural low-contrast, non-rigid cloud textures. Thus, the perceived depth of distant clouds is dominated by monocular lighting and occlusion cues.

4. Time Scale: Player Motion Versus Wind-Driven Change

For a lateral observer speed v, the differential-parallax angular velocity is approximately

$$\omega_{\mathrm{parallax}} \approx v \cdot \Delta L / [L(L+\Delta L)],\quad \omega_{\mathrm{advection}} \approx u/L \tag{4}$$

Here $\omega_{\mathrm{parallax}}$ describes the relative motion of front and back cloud layers due to player movement, whereas $\omega_{\mathrm{advection}}$ describes the apparent angular drift of the entire cloud as it is transported by wind speed $u$. They are not the same quantity; comparing them is useful only if the distinction is explicit.

Table 2. Player-induced differential parallax versus wind-driven apparent drift

5. World Scale and Cloud Anchoring in Games

An open-world game often contains three scales at once: narrative scale, engine-coordinate scale, and rendering scale. Narrative scale is the geographic extent the game wants to suggest; coordinate scale is the metric distance used by the engine; rendering scale determines whether sky, clouds, fog, and distant vistas are strictly tied to world coordinates.

If a cloud at a realistic height of 1.5 km is fixed in world coordinates, a 10 km lateral player displacement changes its elevation angle from nearly overhead to $\arctan(1.5/10) \approx 8.5°$. This is not subtle differential parallax; it is a strong geometric sweep. Therefore a compressed open world spanning only tens of kilometers in coordinates cannot naively place all far clouds at realistic heights without exposing the scale compression.

A public reverse-engineering study of Red Dead Redemption 2 reports substantial GPU work related to sky, clouds, fog, and volumetrics, and states that the game generates environment cubemaps from the camera position [7]. This is not an official proof that every cloud visible in the main view is camera-anchored, but it supports a conservative interpretation: in compressed open worlds such as RDR2 or GTA5, distant sky and cloud systems tend to behave as camera-centered or effectively infinite-distance content to suppress implausible translational parallax.

5.1 Three World-Scale Paradigms

The first paradigm is the compressed finite world, represented by games such as RDR2/GTA5. These worlds compress geography for narrative density and therefore benefit from treating distant clouds as low-parallax sky content driven by weather, wind, and time-of-day lighting.

The second paradigm is the 1:1 real-world simulation, represented by Microsoft Flight Simulator. Microsoft describes the simulator as using Bing satellite and aerial data plus Azure cloud streaming to recreate the planet [8], and its live weather mode includes wind, temperature, humidity, rain, and related variables [9]. In this scale-consistent setting, real cloud heights, aircraft speeds, and world-anchored volumetric weather can coexist.

The third paradigm is the infinite procedural world, represented by Minecraft. Vanilla Minecraft clouds are client-side graphical effects, moving westward between layers 192 and 196; they are not server-side meteorological entities [10]. However, their apparent placement is determined by coordinates and time rather than by attaching the cloud content to the camera. Minecraft therefore does not need content anchoring to hide a world-scale contradiction; its major technical issue is instead floating-point precision at large coordinates.

6. Volumetric-Cloud Rendering and Cost

Real-time volumetric clouds are commonly represented by a cloud volume or atmospheric density domain. A ray is marched from the camera through the volume; each sample queries a 3D density field, often built from Perlin, Worley, and fBm-like noise, and accumulates extinction and scattering. Guerrilla Games’ Horizon Zero Dawn cloud work explicitly targeted art direction, weather integration, and a GPU budget of approximately 2 ms [5]. Related research emphasizes that volumetric clouds are expensive because image quality depends strongly on ray-marching steps and temporal reuse [6].

For an intuitive main-ray plus approximate sun-ray model, per-frame cost can be written as

$$\mathrm{Cost} \approx P \times N \times (1+M) \times c_{\mathrm{noise}} \tag{5}$$

where $P$ is the number of pixels processed, $N$ is the number of primary ray-marching samples, $M$ is the number of auxiliary samples for shadowing or scattering, and $c_{\mathrm{noise}}$ is the unit cost of density lookup and phase-function evaluation. Equation (5) is not a universal engine formula; it is a scaling model illustrating why nested ray marching is expensive.

6.1 Implementation Levels

Level 0: geometric or pseudo-volumetric clouds, such as vanilla Minecraft cloud prisms. The cost is dominated by geometry and transparency, not by volumetric integration.

Level 1: thin-layer or slab-based shader clouds. These sample noise near a fixed altitude and can create lighting and edge variation, but they lack full volumetric self-occlusion.

Level 2: fully volumetric clouds. These use multi-step ray marching over a height interval and may include approximate multiple scattering, sun-direction self-shadowing, or preintegrated lookup tables. They achieve the highest quality but depend heavily on half-resolution rendering, temporal reprojection, jittered sampling, empty-space skipping, and early ray termination.

Table 3. Cost and anchoring of three real-time cloud-rendering levels

7. Optimization Strategies Implied by the Scale Law

Temporal reprojection. When a ground player moves slowly, $\omega_{\mathrm{parallax}}$ remains small; over many frames the relative angular displacement of cloud layers can remain below a pixel. Half-resolution or quarter-resolution rendering plus temporal reprojection therefore has a physical basis.

Distance-based LOD. Differential parallax decays approximately as $1/L^2$. Near clouds require full sampling; mid-range clouds can use lower sampling and temporal accumulation; distant clouds can become impostors, sky-dome textures, or low-frequency volumetric fields.

Shape/lighting decoupling. Distant cloud depth is perceived mainly through monocular cues. Density shape can be updated slowly, while lighting lookup tables or atmospheric terms can be updated on lower-frequency drivers such as solar elevation and weather state.

Speed-adaptive sampling. Elytra flight in Minecraft or aircraft motion in a flight simulator moves the camera from walking speed to aviation speed; $\omega_{\mathrm{parallax}}$ is no longer negligible. Sampling rates should adapt to camera velocity, cloud altitude, cloud depth, and projected reprojection residual.

Coordinate precision management. Minecraft Wiki documents that many Bedrock Edition position calculations use 32-bit floating-point numbers and show visible precision problems at large coordinates, whereas Java Edition uses 64-bit floating-point precision for entity positions and related calculations [11][12]. Rendering still commonly relies on GPU float32, so cloud ray marching should use camera-relative space while density sampling uses modular world coordinates, tiled origins, or mixed CPU double/GPU float strategies.

8. Limitations

The model ignores non-rigid cloud evolution, turbulence, multiple scattering, complex occlusion, and the spatial correlation of weather systems. The cloud dimensions and wind speeds used here are order-of-magnitude examples, not meteorological definitions. For specific game engines, the analysis relies on public documentation, reverse-engineering reports, and visual inference; without official technical papers or frame captures, such conclusions should be treated as engineering interpretations rather than definitive implementation claims.

9. Conclusion

The reason volumetric clouds can look three-dimensional yet remain visually stable as a person walks is that differential parallax between front and back cloud features decays rapidly with distance. For slow ground observers, player-motion-induced cloud restructuring is usually weaker than wind, density evolution, and lighting change. This physical fact supports temporal reprojection, distance-based LOD, shape/lighting decoupling, and speed-adaptive sampling in real-time rendering.

In games, cloud realism is not determined by shader sophistication alone; it also depends on whether the game’s world scale is internally consistent. Compressed finite worlds tend to use camera-centered distant clouds to hide scale contradictions. A 1:1 world simulation can support world-anchored volumetric clouds. An infinite procedural world can preserve true parallax, but it must solve large-coordinate floating-point precision problems.

References

[1] M. Kalloniatis and C. Luu, “Visual Acuity,” Webvision: The Organization of the Retina and Visual System. University of Utah / Webvision, 2007. https://www.webvision.pitt.edu/book/part-viii-psychophysics-of-vision/visual-acuity/

[2] Cleveland Clinic, “Pupillary Distance: What It Is & How To Measure,” 2026. https://my.clevelandclinic.org/health/articles/pupillary-distance

[3] World Meteorological Organization, International Cloud Atlas: “Levels.” https://cloudatlas.wmo.int/some-useful-concepts-levels.html

[4] NOAA JetStream, “The Four Core Types of Clouds,” National Oceanic and Atmospheric Administration, 2023. https://www.noaa.gov/jetstream/clouds/four-core-types-of-clouds

[5] Guerrilla Games, “The Real-Time Volumetric Cloudscapes of Horizon Zero Dawn,” 2015. https://www.guerrilla-games.com/read/the-real-time-volumetric-cloudscapes-of-horizon-zero-dawn

[6] A. Toft, H. Bowles, and D. Zimmermann, “Optimisations for Real-Time Volumetric Cloudscapes,” arXiv:1609.05344, 2016. https://arxiv.org/abs/1609.05344

[7] imgEs, “Graphics Study: Red Dead Redemption 2,” 2020. https://imgeself.github.io/posts/2020-06-19-graphics-study-rdr2/

[8] Xbox Wire, “See the World in Microsoft Flight Simulator,” Microsoft / Xbox, 2019. https://news.xbox.com/en-us/2019/09/30/microsoft-flight-simulator-preview/

[9] Xbox Wire, “The Biggest World Update Ever for Microsoft Flight Simulator Is Also Its Best Yet,” Microsoft / Xbox, 2024. https://news.xbox.com/en-us/2024/07/24/biggest-world-update-ever-microsoft-flight-simulator-best-yet/

[10] Minecraft Wiki, “Cloud.” https://minecraft.wiki/w/Cloud

[11] Minecraft Wiki, “Java Edition distance effects.” https://minecraft.wiki/w/Java_Edition_distance_effects

[12] Minecraft Wiki, “Bedrock Edition distance effects.” https://minecraft.wiki/w/Bedrock_Edition_distance_effects