Version 1.5
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Subsubsection 3.9.4.1: Area Calculator Up Subsection 3.9.4: The Tools Panel Section 3.10: The Repository Panel

#### 3.9.4.2 Quadric Fit

This tool fits a quadric surface to the selected faces. Quadrics include ellipsoids, cylinders and cones. The general equation fitted to the data is This equation may be rewritten in matrix form as Once the coefficients are obtained, the principal axes of the quadric may be found by evaluating the eigenvalues and eigenvectors of the coefficient matrix, where Then, in the basis of these eigenvectors, the equation of the quadric may be rewritten as where The different types of quadric surfaces are described on Wikipedia (https://en.wikipedia.org/wiki/Quadric). To reduce the above equation to one of the forms presented there, we find the origin of the quadric and consider three cases:
1. If and and , where
2. If and and , where
3. If and and , where
When , may be divided across by .
Once we find in the basis of eigenvectors, we can convert these coordinates back to the reference coordinate system using
The output of the quadric fit tool corresponds to the following values:
 Quadric Type Best guess to cases in https://en.wikipedia.org/wiki/Quadric Center A max eigenvalue, () or () B mid eigenvalue, () or () C min eigenvalue, () or () U should be for cases 1, 2, 3 V should be 0 for cases 1 and 2, and () or () for case 3 W should be 0 for case 1, and () or () for cases 2 and 3 c evaluated as or , should be , , or Axis 1 normalized eigenvector for max eigenvalue Axis 2 normalized eigenvector for mid eigenvalue Axis 3 normalized eigenvector for min eigenvalue
Subsubsection 3.9.4.1: Area Calculator Up Subsection 3.9.4: The Tools Panel Section 3.10: The Repository Panel