This example shows fitting of faces in a volume mesh to a given set of data points. The Volume elements in the mesh are decomposed into faces. These faces are treated as area(2d) elements. Data points are then projected on to the faces such that the distance between a data point to the face is minimum. If the data point is within the purview of the face, the projection is 'orthogonal', otherwise it is non-orthogonal resulting the projection on to a side or on to a vertex of the face. For each face, an objective function is defined as the summation of the distances between each data point to its projection onto the face. Necessary number of linear equations are generated by differentiating the objective function wrt each nodal parameter (i.e. nodal value and derivatives of x,y and z) and equating the resulting expression to zero. In addition to this, Sobelov smoothing is also incorporated to control the arc curvature, arc length and the surface curvature of the face. Once face(element) equations are formulated, they are then assembled to give mesh (global)equations. The assembling is done to satisfy the continuity of the nodal values and nodal derivatives at the nodes common to different elements. For more details of the geometric fitting see Geometric modeling of the human torso using cubic hermite elements, Bradley et. al.
Created by : Kumar Mithraratne. Aug. 2002.
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Initial Mesh RMS Error = 7.427 mm |
First Fit RMS Error = 1.400 mm Sobelov weights |
Second Fit RMS Error = 1.038 mm Sobelov weights |
Third Fit RMS Error = 0.857 mm Sobelov weights |