Research on Modeling the Super-illuminated Area of Apple Tree Canopies Based on Ray Tracing and Multi-swarm Particle Swarm Optimization

Abstract

In the gully region of the Loess Plateau, the efficient utilization of solar energy within apple tree canopies is crucial for optimizing fruit yield and quality. To address the challenge of optimizing the light use efficiency of apple tree canopies, this paper proposes a cross-scale modeling framework that integrates ray tracing and improved particle swarm optimization. By establishing a dual coordinate system of ground-light cone and a dynamic light cone equation, combined with Monte Carlo random sampling and ray equation solving, efficient determination of points receiving more than eight hours of light is achieved. With the objective of maximizing the canopy over-illuminated area (COA) under surface area constraints, as shown in Equation (17),a multi-swarm cooperative PSO algorithm is used for morphological parameter optimization. The results indicate that the COA of apple tree canopies is influenced by factors such as season, terrain, and canopy shape. The COA is larger in summer and almost zero in winter, and the slope of the terrain also affects the duration of sunlight exposure. Conical canopies have a slightly larger COA than spherical canopies under the same surface area. This paper provides theoretical basis and technical support for the morphological optimization of apple tree canopies.