Simulate forest trees by integrating L-system and 3D CAD files (2001.04530v1)

Abstract: In this article, we propose a new approach for simulating trees, including their branches, sub-branches, and leaves. This approach combines the theory of biological development, mathematical models, and computer graphics, producing simulated trees and forest with full geometry. Specifically, we adopt the Lindenmayer process to simulate the branching pattern of trees and modify the available measurements and dimensions of 3D CAD developed object files to create natural looking sub-branches and leaves. Randomization has been added to the placement of all branches, sub branches and leaves. To simulate a forest, we adopt Inhomogeneous Poisson process to generate random locations of trees. Our approach can be used to create complex structured 3D virtual environment for the purpose of testing new sensors and training robotic algorithms. We look forward to applying this approach to test biosonar sensors that mimick bats' fly in the simulated environment.

• The paper presents a hybrid method combining L-systems with CAD-derived geometry to generate detailed tree structures.
• It employs an inhomogeneous Poisson process to simulate forest layouts with varying density and natural randomness.
• The approach enables realistic virtual environments for advanced sensor testing and robotic algorithm training.

This paper presents a method for simulating realistic 3D forest trees by combining Lindenmayer systems (L-systems) with geometry data from 3D Computer-Aided Design (CAD) files (2001.04530). The goal is to overcome limitations of existing tree simulation methods, which often lack detailed geometry or are difficult to modify, by creating trees with full geometric information for branches, sub-branches, and leaves.

Methodology:

1. Branching Structure (L-systems): The core branching pattern of a tree is generated using an L-system. An L-system is defined by an axiom (initial state) and production rules that recursively rewrite symbols to create a string representing the tree's structure. The paper provides examples of rules generating trees with 4, 6, or 8 main branches emerging from the trunk.
   • Implementation: Define an axiom (e.g., g) and rules (e.g., P(g) -> d(d)+d)[d(d)+d)). Each symbol corresponds to a drawing command (e.g., draw branch, turn, push/pop state). Recursively applying the rules generates the branching topology.
2. Geometric Detail (CAD Files): While L-systems define the topology, they often produce overly simplistic geometry. To add realism, the method integrates geometric information extracted from existing 3D CAD files (specifically mentioning STL files). These files contain detailed mesh data (vertices, normals) describing the surfaces of trunks, branches, sub-branches, and leaves.
   • Implementation:
     • Parse STL or other CAD files to extract vertex coordinates and face information (triangular meshes).
     • Map this geometric data onto the structure generated by the L-system. For instance, use the length, thickness, and curvature information from CAD branches to render the branches defined by the L-system rules.
     • Randomize placement: Introduce randomness in the angles and positions of branches, sub-branches, and leaves when attaching them based on the CAD geometry to create more natural variation. For leaves represented by triangular meshes, their placement can be randomized around attachment points on sub-branches.
3. Forest Generation (Inhomogeneous Poisson Process - IPP): To simulate a forest, the locations of individual trees within a 2D region ($D$) are determined using an IPP. The IPP allows for varying tree densities across the region, controlled by an intensity function $\lambda(s)$.
   • Implementation:
     • Define a region $D$ and an intensity function $\lambda(s)$.
     • Simulate the number of trees $n$ using a Poisson distribution with mean $\int_D \lambda(s) ds$.
     • Generate the $(x, y)$ coordinates for $n$ trees within $D$ according to the intensity function, potentially using a thinning algorithm.
     • Place a simulated tree (generated using L-system + CAD) at each sampled location.

Results and Applications:

The paper demonstrates the process by simulating trees with varying numbers of branches (8, 12, 16), showing the stages from the basic L-system structure to the final model with CAD-based branches, sub-branches, and leaves (visualized as center points of meshes). It also shows examples of forest layouts generated using the IPP with different tree densities.

The primary application discussed is the creation of complex, realistic 3D virtual environments. Such environments are valuable for:

• Testing Sensors: Specifically mentioned is testing biosonar sensors mimicking bat navigation in cluttered environments.
• Training Robotic Algorithms: Simulating scenarios for robot navigation, path planning, and obstacle avoidance in natural settings.

Implementation Considerations:

• Software: Requires tools for parsing CAD files (e.g., libraries for handling STL), implementing L-systems, and 3D rendering. FreeCAD is mentioned for visualization.
• Data: Relies on the availability of suitable 3D CAD models of trees or tree parts.
• Computational Cost: Generating highly detailed trees and large forests can be computationally intensive, especially regarding rendering complex mesh geometries. Visualizing leaves as points instead of full meshes is suggested as a way to manage complexity.

In conclusion, the paper proposes a practical, hybrid approach to generate detailed and randomized 3D tree models and forests by integrating the topological generation power of L-systems with the geometric realism derived from CAD files, suitable for various simulation tasks in robotics and sensor development.