Algorithms to Measure Area and Volume on 3D Face Models for Facial Surgeries

The increased availability and affordability of 3D scanning technology due to recent advancements have made pre and post-operative analysis for facial surgeries more convenient and accurate through the use of 3D patient scans. However, to perform a more comprehensive analysis using area and volume measurements, it is necessary to develop new software tools that include the appropriate algorithms. Without the right algorithms, any software tool cannot perform its intended tasks effectively. In this study, we introduce two algorithms along with their open-source code to calculate the surface area and volume of a specific subsection of a 3D model. The first algorithm partitions the area/volume into smaller segmentations and applies raycasting to find the points on the face surface, and then finds an approximate measurement depending on the resolution selected. In contrast, the second algorithm utilizes the vertex information stored in the 3D model file to calculate the area and volume measurements for the designated region. The advantage of the second algorithm is that it examines every point in the model, resulting in the highest degree of precision possible. We have also used ChatGPT to generate the code for area/volume calculation and found that the logic of the ChatGPT-generated code is surprisingly similar to the second algorithm. We have presented the results of the measurements on certain regions of the face for both of the algorithms and compared the temporal performance of the algorithms.