# Virtual Reality Collision Detection Based on Improved Ant Colony Algorithm
## 3 An Improved Ant Colony Algorithm Based on Random Collision Detection
### Random Collision Detection in the 3D Model  
For three-dimensional models, selecting points as the feature pairs of random collision detection can improve the operational efficiency of the algorithm. Therefore, the combinations of feature points of the model are usually selected as the feature pairs to be detected in random collision detection. In practical applications, because the three-dimensional model is a three-dimensional structure, its position is generally determined by the vertex coordinates of the model, so the distance between the models will generally be transformed into the distance between the vertex coordinates or geometric primitives. Therefore, the collision distance threshold (\(\delta\)) mentioned above was used to judge the distance between the three-dimensional models [18; 19; 20; 21].  
The nonlinear optimization problem requires an objective function to be selected as the fitness function to be optimized. For collision detection, precise detection is described as the test of a junction between patches. Therefore, the centroid of the triangular patch of the three-dimensional model was selected as the feature point of the sampling algorithm. When the centroids' spacing is lower than a certain value, the patches intersect, and the model intersects. Let the two centroid coordinates be \((x_{1},y_{1},z_{1}),\ (x_{2},y_{2},z_{2})\). The centroid spacing is as follows:  
\[\begin{split} d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}+(z_{1} -z_{2})^{2}}\end{split} \tag{6}\]  
When the distance between the centroids is less than the collision distance threshold, collision occurs between the models.  
In the stage of accurate collision detection, the geometric primitives that may collide in the preliminary detection stage are selected for feature sampling, and the sampled feature points are used as the set to be detected for detecting a collision. The three-dimensional model to be detected in the space is mapped to the two-dimensional space. The problem of detecting a collision in the three-dimensional model is transformed into a nonlinear optimization problem of the distance between the feature pairs in the discrete two-dimensional space. An intelligent algorithm is needed to solve this problem.  
Intelligent algorithms are inspired by the laws of nature. According to their principles, they imitate algorithms for solving problems, such as genetic algorithms, simulated annealing algorithms and artificial neural network algorithms. There are many intelligent algorithms. To be applied to the field of collision detection, we first need to understand the problems that the optimization algorithm can solve and analyze the essence of the collision problem and then design and improve the optimization method that can be applied to detect collisions.  
Researchers have generally introduced the particle swarm optimization algorithm to solve optimization problems, but because of the low search efficiency of the particle swarm optimization algorithm, it cannot be applied to complex search spaces. The robustness of the algorithm is not good, it can easily miss the interference elements and the spatial adjacency of the points is not easy to determine. Therefore, this study used the ant colony algorithm to solve the optimization problem. The ant colony algorithm uses distributed computing in the search process, and multiple individuals perform parallel computations at the same time, which greatly improves the computing power and operating efficiency of the algorithm [22; 23].