Digital collision checking and scraping tooth by dental bar

In this paper, we present digital checking and scraping algorithms for an intersection volume between tooth and dental bit. For this purpose, we firstly represent each human tooth and dental bit by an octree (a set of voxels) and a set of points, respectively. A tooth or bit is converted from STL (triangular patch polyhedron) by Z-buffer and parallel processing of all the pixels, and each STL is captured from a dental CT-scanner. Using the digital checking algorithm, we quickly detect the intersection between digital tooth and bit. Each tooth consists of decayed tooth, enamel, ivory, dental pulp material parts. It individually has elasticity, viscosity, hardness to scrape. On the other hand, each bit has its ability to scrape a part of tooth. Therefore, by the binary search per sampling time based on the digital collision checking, we efficiently determine an adequate position of a bit to scrape a tooth. In addition to this, according to the penetration volume between all parts and dental bit, we calculate an artificial force by the Kelvin-Voigt model based on penalty function. Finally, if a dental bit starts to touch or scrape a human tooth, they are contact with each other and consequently the binary search is useless. To solve this problem, we propose a new digital scraping algorithm. The algorithm consists of three procedures: calculation of an approximated normal vector around a digital tooth, slight movement along the normal vector, and revisit of the binary search.