#
Virtual Forestry Generation: Evaluating Models for Tree Placement in Games^{ †}

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## Abstract

**:**

## 1. Introduction

**Hypothesis**

**1**(H1)

**.**

**Hypothesis**

**2**(H2)

**.**

## 2. Background

**Symmetric competition:**When considering the competition between two plants, resources are split evenly between the two. This infers that the two plants are of the same size, and pose an equal threat to one another:$$\begin{array}{c}\hfill I(a,b)\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}\frac{C(a,b)}{2}\end{array}$$**Asymmetric competition:**In the case of two plants, resources are split unevenly between the two, based on which FON is larger. This means that the tree with the smaller FON will be dominated by its competitor, resulting in no access to resources and its eventual death:$$\begin{array}{c}\hfill I(a,b)\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}\left(\right)open="\{"\; close>\begin{array}{cc}C(a,b)\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{a}_{\mathrm{FON}}{b}_{\mathrm{FON}}\hfill \\ C(a,b)\phantom{\rule{4.pt}{0ex}}\mathrm{or}\phantom{\rule{4.pt}{0ex}}0\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{a}_{\mathrm{FON}}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}{b}_{\mathrm{FON}}\hfill \\ 0\hfill & \phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}{a}_{\mathrm{FON}}{b}_{\mathrm{FON}}\hfill \end{array}\end{array}$$

**Self-thinning:**A similar notion to asymmetric competition—plants which are in competition with larger ones are dominated, and are subsequently culled from the population. Competition is also detected in a similar method to the FON model [31]. That is, if the radii of two trees overlap, the two plants are in competition with one another.**Succession:**Trees grow over time and have a random probability of dying at each step once they reach a certain age. This ensures that old trees are culled from the population.**Plant propagation:**Trees reproduce in a similar method proposed by Alsweis and Deussen [31], in which seeds are sown locally around the tree chosen for reproduction. This helps to cluster trees together which are of the same species.

## 3. Forest Generation Approaches

#### 3.1. Method 1: Naive

#### 3.2. Method 2: Propagation

**Succession**: In each simulation iteration, every tree ages (and grows) until it reaches a mature age. Once a tree reaches a certain age, it dies and is culled from the population.**Plant propagation**: Once trees have reached a mature age, they can reproduce by sowing seeds locally to their position.**Self-thinning**: If a tree is growing close to another tree, then the oldest (and largest) tree will outgrow the other, thereby killing it and culling it from the environment. This is an approximation of asymmetric plant competition.

#### 3.3. Method 3: Clustering

## 4. First Study: 2D Evaluation

#### 2D Study Results

## 5. Second Study: 3D and Density Evaluation

#### 5.1. Algorithm Chosen

#### 5.2. Forest Density

- ‘Based on these images, which is the most realistic forest?’
- ‘Based on these images, which is the least realistic forest?’
- ‘If you were to play a game in one of these forests, which environment would you select to play within based on these top-down images?’
- ‘If you were to play a game in one of these forests, which environment would you not select to play within based on these top-down images?’

#### 5.3. Image Perspectives

## 6. Results

#### 6.1. Top-Down 2D Perspective

#### 6.2. Top-Down 3D Perspective

#### 6.3. First-Person 3D Perspective

## 7. Frequency Analysis of Selection Counts

#### 7.1. Forest Density and Believability

#### 7.2. Forest Density and Playability

#### 7.3. Generation Algorithm and Believability

#### 7.4. Generation Algorithm and Playability

#### 7.5. Summary

## 8. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Condit, R.; Ashton, P.S.; Baker, P.; Bunyavejchewin, S.; Gunatilleke, S.; Gunatilleke, N.; Hubbell, S.P.; Foster, R.B.; Itoh, A.; LaFrankie, J.V.; et al. Spatial patterns in the distribution of tropical tree species. Science
**2000**, 288, 1414–1418. [Google Scholar] [CrossRef] [PubMed] - Williams, B.; Ritsos, P.; Headleand, C. Evaluating Models for Virtual Forestry Generation and Tree Placement in Games. In Computer Graphics and Visual Computing (CGVC); Vidal, F.P., Tam, G.K.L., Roberts, J.C., Eds.; The Eurographics Association: Aire-la-Ville, Switzerland, 2019. [Google Scholar] [CrossRef]
- Togelius, J.; Kastbjerg, E.; Schedl, D.; Yannakakis, G.N. What is procedural content generation?: Mario on the borderline. In Proceedings of the 2nd International Workshop on Procedural Content Generation in Games, Bordeaux, France, 8 June 2011; p. 3. [Google Scholar]
- Yannakakis, G.N.; Togelius, J. Experience-driven procedural content generation. IEEE Trans. Affect. Comput.
**2011**, 2, 147–161. [Google Scholar] [CrossRef][Green Version] - Hastings, E.J.; Guha, R.K.; Stanley, K.O. Automatic content generation in the galactic arms race video game. IEEE Trans. Comput. Intell. AI Games
**2009**, 1, 245–263. [Google Scholar] [CrossRef][Green Version] - Parish, Y.I.; Müller, P. Procedural modeling of cities. In Proceedings of the 28th annual conference on Computer Graphics and Interactive Techniques, Los Angeles, CA, USA, 12–17 August 2001; pp. 301–308. [Google Scholar]
- Togelius, J.; Champandard, A.J.; Lanzi, P.L.; Mateas, M.; Paiva, A.; Preuss, M.; Stanley, K.O. Procedural content generation: Goals, challenges and actionable steps. Dagstuhl Follow-Ups
**2013**, 6. [Google Scholar] [CrossRef] - Doran, J.; Parberry, I. Controlled procedural terrain generation using software agents. IEEE Trans. Comput. Intell. AI Games
**2010**, 2, 111–119. [Google Scholar] [CrossRef] - Cordonnier, G.; Braun, J.; Cani, M.P.; Benes, B.; Galin, E.; Peytavie, A.; Guérin, E. Large Scale Terrain Generation from Tectonic Uplift and Fluvial Erosion. In Computer Graphics Forum; Wiley Online Library: Hoboken, NJ, USA, 2016; Volume 35, pp. 165–175. [Google Scholar]
- Shaker, N.; Togelius, J.; Nelson, M.J. Fractals, noise and agents with applications to landscapes. In Procedural Content Generation in Games; Springer: Berlin/Heidelberg, Germany, 2016; pp. 57–72. [Google Scholar]
- Choroś, K.; Topolski, J. Parameterized and Dynamic Generation of an Infinite Virtual Terrain with Various Biomes using Extended Voronoi Diagram. J. Univers. Comput. Sci.
**2016**, 22, 836–855. [Google Scholar] - Hahn, E.; Bose, P.; Whitehead, A. Persistent realtime building interior generation. In Proceedings of the 2006 ACM SIGGRAPH symposium on Videogames, Boston, MA, USA, 30–31 July 2006; pp. 179–186. [Google Scholar]
- Martin, A.; Lim, A.; Colton, S.; Browne, C. Evolving 3d buildings for the prototype video game subversion. In European Conference on the Applications of Evolutionary Computation; Springer: Berlin/Heidelberg, Germany, 2010; pp. 111–120. [Google Scholar]
- Shaker, N.; Togelius, J.; Yannakakis, G.N.; Weber, B.; Shimizu, T.; Hashiyama, T.; Sorenson, N.; Pasquier, P.; Mawhorter, P.; Takahashi, G. The 2010 Mario AI championship: Level generation track. IEEE Trans. Comput. Intell. AI Games
**2011**, 3, 332–347. [Google Scholar] [CrossRef][Green Version] - Williams, B.; Headleand, C.J. A Time-Line Approach for the Generation of Simulated Settlements. In Proceedings of the 2017 International Conference on Cyberworlds (CW), Chester, UK, 20–22 September 2017; pp. 134–141. [Google Scholar]
- Bauer, S.; Berger, U.; Hildenbrandt, H.; Grimm, V. Cyclic dynamics in simulated plant populations. Proc. R. Soc. Lond. B Biol. Sci.
**2002**, 269, 2443–2450. [Google Scholar] [CrossRef] [PubMed] - Lindenmayer, A. Adding continuous components to L-systems. In L Systems; Springer: Berlin/Heidelberg, Germany, 1974; pp. 53–68. [Google Scholar]
- Prusinkiewicz, P. Graphical applications of L-systems. In Proceedings of the Graphics Interface, Montreal, QC, Canada, 15–18 May 1986; Volume 86, pp. 247–253. [Google Scholar]
- Pradal, C.; Boudon, F.; Nouguier, C.; Chopard, J.; Godin, C. PlantGL: A Python-based geometric library for 3D plant modelling at different scales. Graph. Model.
**2009**, 71, 1–21. [Google Scholar] [CrossRef][Green Version] - Shlyakhter, I.; Rozenoer, M.; Dorsey, J.; Teller, S. Reconstruction of Plausible 3D Tree Models from Instrumented Photographs. Available online: https://www.researchgate.net/publication/2816859_Reconstruction_of_Plausible_3D_Tree_Models_from_Instrumented_Photographs (accessed on 13 March 2020).
- Tan, P.; Fang, T.; Xiao, J.; Zhao, P.; Quan, L. Single image tree modeling. ACM Trans. Graph. (TOG)
**2008**, 27, 108. [Google Scholar] [CrossRef] - Tan, P.; Zeng, G.; Wang, J.; Kang, S.B.; Quan, L. Image-based tree modeling. In Proceedings of the ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, San Diego, CA, USA, 5–9 August 2007; Volume 26, p. 87. [Google Scholar]
- Livny, Y.; Yan, F.; Olson, M.; Chen, B.; Zhang, H.; El-Sana, J. Automatic reconstruction of tree skeletal structures from point clouds. ACM Trans. Graph. (TOG)
**2010**, 29, 151. [Google Scholar] [CrossRef][Green Version] - Dale, H.; Runions, A.; Hobill, D.; Prusinkiewicz, P. Modelling biomechanics of bark patterning in grasstrees. Ann. Bot.
**2014**, 114, 629–641. [Google Scholar] [CrossRef] [PubMed][Green Version] - Desbenoit, B.; Vanderhaeghe, D.; Galin, E.; Grosjean, J. Interactive modeling of mushrooms. In Proceedings of the Eurographics Conferences, Grenoble, France, 30 August–3 September 2004; pp. 37–40. [Google Scholar]
- Desbenoit, B.; Galin, E.; Akkouche, S. Simulating and modeling lichen growth. In Computer Graphics Forum; Wiley Online Library: Hoboken, NJ, USA, 2004; Volume 23, pp. 341–350. [Google Scholar]
- Reeves, W.T.; Blau, R. Approximate and Probabilistic Algorithms for Shading and Rendering Structured Particle Systems. SIGGRAPH Comput. Graph.
**1985**, 19, 313–322. [Google Scholar] [CrossRef] - Gain, J.; Long, H.; Cordonnier, G.; Cani, M.P. EcoBrush: Interactive Control of Visually Consistent Large-Scale Ecosystems. In Computer Graphics Forum; Wiley Online Library: Hoboken, NJ, USA, 2017; Volume 36, pp. 63–73. [Google Scholar]
- Emilien, A.; Vimont, U.; Cani, M.P.; Poulin, P.; Benes, B. Worldbrush: Interactive example-based synthesis of procedural virtual worlds. ACM Trans. Graph. (TOG)
**2015**, 34, 106. [Google Scholar] [CrossRef] - Ecormier-Nocca, P.; Memari, P.; Gain, J.; Cani, M.P. Accurate Synthesis of Multi-Class Disk Distributions. In Computer Graphics Forum; Wiley Online Library: Hoboken, NJ, USA, 2019; Volume 38, pp. 157–168. [Google Scholar]
- Alsweis, M.; Deussen, O. Modeling and visualization of symmetric and asymmetric plant competition. In Proceedings of the Eurographics, Dublin, Ireland, 29 August–2 September 2005; pp. 83–88. [Google Scholar]
- Hu, B.G.; De Reffye, P.; Zhao, X.; Yan, H.; Kang, M. Greenlab: A new methodology towards plant functional-structural model–structural part. In Plant Growth Modelling and Applications; TsingHua University Press: Beijing, China; Springer: Berlin/Heidelberg, Germany, 2003; pp. 21–35. [Google Scholar]
- Cournede, P.H.; Guyard, T.; Bayol, B.; Griffon, S.; De Coligny, F.; Borianne, P.; Jaeger, M.; De Reffye, P. A forest growth simulator based on functional-structural modelling of individual trees. In Proceedings of the 2009 Third International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA), Beijing, China, 9–13 November 2009; pp. 34–41. [Google Scholar]
- Lane, B.; Prusinkiewicz, P. Generating spatial distributions for multilevel models of plant communities. In Proceedings of the Graphics Interface 2002 Conference, Calgary, AB, Canada, 27–29 May 2002; pp. 69–80. [Google Scholar]

**Figure 1.**A diagram illustrating the field-of-neighbourhood (FON) model as described by Bauer et al. [16]. The top-most image shows arbitrary competition between two plants with different FON radii. The bottom-most image similarly shows two separate trees, but with no competition between them.

**Figure 2.**(

**a**) An example of a top-down virtual forest generated with the Naive algorithm, implemented in Unity 3D; (

**b**) an example in 2D.

**Figure 3.**(

**a**) An example of a top-down forest image created using the Propagation algorithm, in a 3D environment; (

**b**) another image generated using the same algorithm, but in a 2D environment. Both (

**a**) and (

**b**) were generated over a total of 13 iterations.

**Figure 4.**(

**a**) an example of top-down virtual forest generated with the Clustering algorithm, in a 3D environment; (

**b**) a similar forest generated with the same algorithm, but in a 2D environment.

**Figure 5.**The normalized number of responses from participants when asked to choose the most realistic and playable forest. The letters in this figure correspond to each algorithm used.

**Figure 6.**The normalized number of responses from participants when asked to choose the most unrealistic and unplayable forest. The letters in this figure correspond to each algorithm used.

**Figure 7.**The overall performance of each algorithm. Here the metrics used are the difference between positive and negative ratings.

**Figure 8.**(

**a**) an example of a top-down 2D perspective; (

**b**) an example of a top-down 3D perspective; (

**c**) an example of a first-person 3D perspective.

**Figure 9.**(

**a**) overall performance of all algorithm and densities for top-down 2D images, realistic rating vs. playability rating; (

**b**) magnitude of ratings for realistic/unrealistic responses; and (

**c**) magnitude of ratings for playable/unplayable responses.

**Figure 10.**(

**a**) overall performance of all algorithm and densities for top-down 3D images, realistic rating vs playability rating; (

**b**) magnitude of ratings for realistic/unrealistic responses; and (

**c**) magnitude of ratings for playable/unplayable responses.

**Figure 11.**(

**a**) overall performance of all algorithm and densities for first-person images, realistic rating vs. playability rating; (

**b**) magnitude of ratings for realistic/unrealistic responses; and (

**c**) magnitude of ratings for playable/unplayable responses.

**Table 1.**A table showing the number of times each type of forest density was selected as most or least believable. Notice that columns are categorised by image perspective for clarity. The labels +B and −B respectively correspond to the count of most and least believable selections. In contrast, the label U (Unrated) represents the number of times it was not selected as either.

First-Person | Aerial (2D) | Aerial (3D) | |||||||
---|---|---|---|---|---|---|---|---|---|

+B | −B | U | +B | −B | U | +B | −B | U | |

Low | 22 | 37 | 12 | 4 | 48 | 19 | 14 | 41 | 16 |

Medium | 23 | 13 | 35 | 38 | 2 | 31 | 31 | 11 | 29 |

High | 26 | 20 | 25 | 29 | 17 | 25 | 26 | 16 | 29 |

**Table 2.**A table showing the number of times each type of forest density was selected as most or least playable. Notice that columns are categorised by image perspective for clarity. The labels +P and −P respectively correspond to the count of most and least playable selections. In contrast, the label U (Unrated) represents the number of times it was not selected as either.

First-Person | Aerial (2D) | Aerial (3D) | |||||||
---|---|---|---|---|---|---|---|---|---|

+P | −P | U | +P | −P | U | +P | −P | U | |

Low | 21 | 28 | 22 | 7 | 41 | 23 | 19 | 30 | 22 |

Medium | 27 | 11 | 33 | 46 | 2 | 23 | 33 | 8 | 30 |

High | 23 | 31 | 17 | 18 | 27 | 26 | 19 | 32 | 20 |

**Table 3.**A table showing the number of times each type of generation algorithm was selected as most or least believable. The labels +B and −B respectively correspond to the count of most and least believable selections. The label U (Unrated) represents the number of times it was not selected as either.

First-Person | Aerial (2D) | Aerial (3D) | |||||||
---|---|---|---|---|---|---|---|---|---|

+B | −B | U | +B | −B | U | +B | −B | U | |

Naive | 28 | 18 | 25 | 28 | 22 | 21 | 24 | 21 | 26 |

Clustering | 19 | 31 | 21 | 24 | 18 | 29 | 35 | 11 | 25 |

Propagation | 24 | 21 | 26 | 19 | 29 | 23 | 12 | 38 | 21 |

**Table 4.**A table showing the number of times each type of generation algorithm was selected as most or least playable. The labels +P and −P respectively correspond to the count of most and least playable selections. In contrast, the label U (Unrated) represents the number of times it was not selected as either.

First-Person | Aerial (2D) | Aerial (3D) | |||||||
---|---|---|---|---|---|---|---|---|---|

+P | −P | U | +P | −P | U | +P | −P | U | |

Naive | 21 | 28 | 22 | 24 | 21 | 26 | 24 | 22 | 25 |

Clustering | 22 | 23 | 26 | 25 | 15 | 31 | 34 | 11 | 26 |

Propagation | 29 | 19 | 24 | 22 | 34 | 15 | 13 | 37 | 21 |

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## Share and Cite

**MDPI and ACS Style**

Williams, B.; Ritsos, P.D.; Headleand, C.
Virtual Forestry Generation: Evaluating Models for Tree Placement in Games. *Computers* **2020**, *9*, 20.
https://doi.org/10.3390/computers9010020

**AMA Style**

Williams B, Ritsos PD, Headleand C.
Virtual Forestry Generation: Evaluating Models for Tree Placement in Games. *Computers*. 2020; 9(1):20.
https://doi.org/10.3390/computers9010020

**Chicago/Turabian Style**

Williams, Benjamin, Panagiotis D. Ritsos, and Christopher Headleand.
2020. "Virtual Forestry Generation: Evaluating Models for Tree Placement in Games" *Computers* 9, no. 1: 20.
https://doi.org/10.3390/computers9010020