This paper presents an application for semi-automatic
repositioning of bone fractures that allows the merging of several
fragments.
This application has been developed with regard to orthopaedic
surgeons who want to simulate the position and orientation of
bone fragments preoperatively.
The interactive algorithm includes volumetric collision detection
for intuitive navigation and coarse manual positioning.
Additionally, an optimization process for the mathematically exact
repositioning of the bone fragments is implemented.
In order to accelerate the volumetric collision detection, octree
structures are used that are efficiently implemented as an
hierarchy of oriented bounding boxes (OBB). The collision test
uses the separating axis theorem for a fast traversal of the
octree.
To improve the manual part of the repositioning process, the
principal axes of each fragment are precalculated initially.
Subsequently, the fragments are pre-justified by the user.
Finally, an optimization process is performed based on Powell's
algorithm for multidimensional minimization. The optimal position
of the bone fragments is determined by the use of a voxel-based
metric, that exploits the same bounding box hierarchy.
