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Quadric Surfaces
Moritz currently supports such triangularization for all surfaces, including the special (SQ) and general (GQ) quadrics (or quadratics), and all solid bodies. Polygonalization of the quadric surfaces (except aligned ellipsoids and elliptical cylinders) is new as of Moritz version 1.04 and may need further refinement; several quadric surfaces are shown. An orange elliptical paraboloid is at upper left. A blue 1 sheet hyperboloid is at upper right. Below at right is a green hyperbolic paraboloid.
The surfaces are analyzed to find the specific surface type: elliptical cone, ellipsoid, elliptical cylinder, 1 or 2 sheet hyperboloid, elliptical paraboloid, parabolic cylinder, or hyperbolic paraboloid. For GQ surfaces, the transformation from a simpler SQ shape must be calculated.
Some quadric surfaces are very sensitive to the number of significant digits entered for the coefficients and to the accumulation of numerical imprecision in the calculations to analyze, convert, and transform the surface. The inaccuracies can result in crossings of closely spaced surfaces such as the thin skin layer on the legs of the MIRD anthropomorphic models (one is shown here) where the inner and outer skin surfaces are tilted elliptical cones described as GQ surfaces. When the same MIRD model was translated and written to a file, an insufficient number of significant digits used for the heart surfaces caused that organ to extend beyond the chest cavity.
The use of a transformed simpler shape (if the transformation does not have a large translation) will usually result in a better 3D representation than the equivalent GQ surface. Macrobodies can be used to introduce tilted cylinders (RCC, REC) and cones (TRC); these also give better results than a GQ definition.
 White Rock Science http://www.whiterockscience.com/wrs.html 505 672 1105 |
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