Recall that the smoothed position of a vertex node is only accepted if the quality of its ball did not get worse. In analogy, the smoothed position of a mnidnode will only be accepted if the quality of its shell does not get worse. For the quality measure of a quadratic element the largest difference of the Jacobian determinant at the integration points will be taken as measure. Recall that the 10-node tetrahedral element has 4 integration points. The quality of quadratic element is now defined as:
where if and if . The second term in the above equation takes precedence as soon as any Jacobian determinant in the element is negative.