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Microstructure Characterization 79
FIGURE 3.16 Tangent plane, contact normal vector, and branch vector.
contact point. Ideally, the tangent plane could be uniquely determined by using the
curvature plane that passes through the contact point and best fits the surrounding
points. In real implementation, the tangent plane is approximated by the plane that has
its normal equal to the mean normal of the four planes comprised of the contact point
and its four surrounding points (Figure 3.17). As demonstrated in Figure 3.17, the con-
tact point (o 1 ) and its nearest left side point (a), its right side point (c), the closest point
FIGURE 3.17 Defi nition of the contact normal vector O 1 O 1 ’ (obtained from the contact point O1
and its neighbor points, a, b, c, and d).