Grid-Based Collision Detection for Orthodontic Tooth Simulation

The simulation space is divided into a grid structure where each cell can independently store tooth model data. This segmentation allows the collision detection system to only check for overlaps between teeth in the same or adjacent grid cells, rather than performing comprehensive pairwise comparisons across all teeth, thereby reducing computational complexity while maintaining detection accuracy.

A grid-based spatial index is introduced as an intermediary data structure between the tooth models and the collision detection logic. This grid acts as a mediator that organizes tooth positions in space and enables efficient querying of potential collision candidates, reducing the computational burden of direct collision detection between all tooth pairs.

The computational domain is segmented into discrete grid cells, allowing the system to process only relevant spatial regions. Teeth are mapped to grid cells based on their positions, and collision detection is performed only within cells containing multiple teeth or at cell boundaries, significantly reducing the number of computational operations required while maintaining complete collision detection coverage.

The system performs collision detection checks selectively based on grid cell occupancy. Rather than checking all possible tooth pairs, the system only performs collision checks for teeth located in the same or adjacent grid cells, applying partial action only where collisions are physically possible, thus reducing computational resource consumption while maintaining detection completeness.

The grid-based approach segments the collision detection process into hierarchical levels: first checking grid cell occupancy (coarse level), then performing detailed tooth model intersection tests only for teeth in overlapping cells (fine level). This multi-level segmentation enables fast initial filtering while ensuring accurate collision detection for relevant tooth pairs, balancing processing speed and accuracy.

The system performs preliminary spatial indexing of teeth into grid cells before executing collision detection. This preliminary organization of data by spatial location enables the subsequent collision detection algorithm to quickly identify and process only those tooth pairs that have the potential to collide, avoiding unnecessary computational operations on distant teeth and thereby improving processing speed without sacrificing detection accuracy.