In my master's degree project I worked with lidar point cloud classification models in a forestry context. One of the problems I encountered was to get labelled datasets with the characteristics I wanted (leaves, branches and ground labelled with mixtures of tree species) and a sufficient size to be able to train deep learning models. While playing Elden Ring I realised that the synthetic trees used to create the maps could be the solution to my lack of real quality data so I decided to employ the methods used in game development to generate my own point clouds.
To build the synthetic trees I implemented a Lindenmayer system generator (https://en.wikipedia.org/wiki/L-system) and a function to translate the L-system instructions into point clouds sampled on the branches (cylinders) and leaves (flat surfaces) with the desired density.
The componets of a L-system are an afabet or set of characters with asociated production meanings, an axiom or initial state and the rules to modify the initial axiom by substitution in an iterative way. The alfabet used has the folowing actions:
- F Grow forward
- [ Save last state
- ] Pop last state, and return to last state saved
-
$+$ Positive rotation in z axis with angle_1 -
$-$ Negative rotation in z axis with angle_1 - & Positive rotation in y axis with angle_1
- ^ Negative rotation in y axis with angle_1
- \ Positive rotation in x axis with angle_1
- / Negative rotation in x axis with angle_1
- +2 Positive rotation in z axis with angle_2
- -2 Negative rotation in z axis with angle_2
- &2 Positive rotation in y axis with angle_2
- ^2 Negative rotation in y axis with angle_2
- \2 Positive rotation in x axis with angle_2
- /2 Negative rotation in x axis with angle_2
- | Turn 180º
- d Rotate main branch with angle_3
- X Do nothing
- 0 Terminal branch
- . Decrease length and width with f1 and f2 factors
- r Random rotation
The following is an example of a set of rules and an axiom for generating a plant.
b1 = function() c('F','+','[','.','[','.','X',']',
'-','X',']','-','F','[','.','-',
'F','X',']','+','X')
b2 = function() c('F','F')
plant1 = list(axiom='X', # Axiom
rules=list(r1=list(a='X', # First rule
b=b1),
r2=list(a='F', # Second rule
b=b2)))Once the rule set is defined, we can use the evolve() function to transform the axiom with these rules and obtain the final instruction set. The produce() function uses this instructions set to sample the resulting point cloud. This function requires specifying the origin, the initial length and width of the branches, the branching angles and the decrement factor.
instructions = evolve(plant1, # lsystem rules
n=4, # number of iterations
terminal.leafs = 10 # number of leafs in each terminal branch
)
out=produce(instructions,
alfabet, # dictionary of functions to interpretate the instructions
# this alfabet is a list contained in the lSystem.R file
origin=c(0,0,0),
size1=2, # initial width
size2=20, # initial lenght
factor1=0.707, # decreasing width factor
factor2=0.9, # decreasing length factor
density=1,
angle=(pi/6), # z axis branching angle
angle2=(pi/6), # y axis branching angle
angle3=(pi/6) # main branch rotation angle
) A terrain modelling tool is available. This tool uses perlin noise (https://en.wikipedia.org/wiki/Perlin_noise) to create noise artefacts that mimic the irregularities of the terrain. It is possible to recreate surfaces that closely mimic the irregularities of real terrain by stacking several layers of perlin noise at diferent scales.
The perlin_noise.R file contains the functions dedicated to terrain simulation using perlin noise and the lSystem.R file contains the implementations for tree creation. An example of how to use these tools can be found in the simulation.R file. The landscape of the previous image is a snapshot of the point cloud generated with this script.
This repository is currently in a prototype phase. In the near future I intend to add rules to generate trees with various base phenotypes of real trees and rewrite these functions in c++ to parallelise and speed up the computation time.