Fig. 3
From: Development of a dental handpiece angle correction device
Calculation of tooth axis (a), tooth height (b), and tooth axis angulation (c). When observed from a fixed view point, the line between the centers of gravity at the top (red spot) and bottom (yellow spot) surfaces was defined as the tooth axis of the abutment. When the center of gravity of the top and bottom surfaces is (xt, yt, zt) and (xb, yb, zb), respectively, the tooth axis is \( \overrightarrow {Axis} = \left( {x_{t} - x_{b} ,\,y_{t} - x_{b} ,\,z_{t} - z_{t} } \right) \) (a). The height of the abutment was defined as the distance from the upper abutment margin to the bucco-mesial cusp tip (b). Tooth axis angulation was obtained for each direction using the inverse tangent function (c)