2 General Description of a Quadric surface and a Plane
Alternatively, we sometimes write a quadric surface in the scalar form of:
In the above deducing process, we do not make any assumptions on the intrinsic parameters, and the rank of dual absolute quadric surface
is three and is used as constraint factor which guarantees the robustness of the solving process.
The expression for Im(y), as shown in Equation (6), is also that of a general quadric surface, with many similarities to surface A.
These figures show a general quadric surface in contrast to the bi-linear (degenerate) case which resulted from purely real coefficients.
Geometric Approaches to Nonplanar Quadric Surface Intersection
Quadric surfaces occur frequently in the design of discrete piece parts in mechanical CAD/CAM.
It is a quadric surface, since no term or combination of terms in Equation (5) exceeds degree 2.
Since there are 14 different types of quadric surface (Clapham, 1996), it is useful to investigate further the exact nature of the surface A.
Another problem, solved by Schubert in his book  is: find the number of twisted cubics, tangent to 12 quadric surfaces
. Schubert won a gold medal from the Royal Danish Academy in 1875 for the solution of this problem which is the number 5,819,539,783,680.
CAD models mainly consist of planes and quadric surfaces
, and functional features generally lie on a few surfaces, an extended Gaussian image and geodesics approach for local shape representation and extraction is proposed.
But these previous experiments in quadric surfaces
perversely reappeared in derelict fashion: The glossy polycarbonate curve of Philippe Starck's Ero/s/ Chair, 2001, for Kartell, now upturned and deposited atop Geschwister (Brothers and Sisters), 2004, seemed like so much modernist design on layaway.
In general, two quadric surfaces
intersect in a nonsingular quartic space curve.