Level Design

A Unity implementation of https://zhuanlan.zhihu.com/p/415025159

Definition

Stability Factor γ (稳定因子) [1]

A normalized and fast converging scalar that is calculated out from various orders of Cheeger constant.

$$\gamma_\infty=\lim_{m\to\infty}\frac{\sum_{i=1}^{m}\frac{1}{i!}\lambda_i}{\sum_{i=1}^{m}\frac{1}{i!}}=\frac{1}{e}\lim_{m\to\infty}\sum_{i=1}^{m}\frac{1}{i!}\lambda_i$$

where $\lambda_i$ is the $i$th order Cheeger constant.

Cheeger Constant

$$\lambda_k=1-\frac{n}{C_m^k}$$

Environment

Unity: 2022.1.0b16+

如何使用

Graph格式

例：

sample.txt

A>>B
B--C
C*>D
D->D

代表下图

连接符

符号	含义	英文
`--`	全连通路径	Undirected Path
`->`	单向路	Directed Path
`>>`	单向门	Shortcut
`*>`	机关门	Mechanism

图形化操作

打开 Window/Level Designer Shift+1 工具
点击打开并选择你的txt文件
计算3阶稳定因子

References

[1]尼莫. (2021). 如何设计一张有“魂味”的地图？——论“类魂”游戏关卡的拓扑结构. https://zhuanlan.zhihu.com/p/415025159
[2]https://en.wikipedia.org/wiki/Cheeger_constant_(graph_theory)

Credits

Tilemap assets: https://cainos.itch.io/pixel-art-top-down-basic

yatyricky/LevelDesign