There are eight nodes in the Treil
maxillo-facial frame [4, 5]. Only one shape function will be evaluated in the
Consider a pre-assigned field
The aforementioned relation will be exactly satisfied in terms of the coordinate variables
The following code generates the coefficient matrix
A Symmetric Case
The anatomical points are symmetrically located on the left and right side of the face. The canonical maxillo-facial frame is then symmetric about x-axis. Hence the following is a specialization for which a symmetric frame is generated according to the rule.
Now the coefficient matrix and the right-hand side vector,
Before attempting to solve for the unknown shape functions, the consistency of the assumption of the interpolated field should be established.
In general, the nonzero determinant signifies that the assumption:
could be acceptable and the matrix
For given numerical data for the nodal coordinates, the shape functions will be obtained from the expression below, after
removing the comments
Failure to Interpolate: --An Example of Inconsistent Data
The Symmetric Maxillo-facial Frame
Hence the following evaluation is not attempted since the coefficient matrix is not invertible.
Copyright © 2001 Wolfram Media, Inc. All rights reserved.