ABSTRACT
Quadrics are algebraic surfaces of the second degree. They can be represented implicitly as the set of points satisfying a general second-degree equation in coordinates x, y, and z as
for real coefficients A, B, C, D, E, F, G, H, K, and L, where at least one of A, B, C, D, E, F is nonzero. Again, a soft analysis of this equation is fruitful. Although the 10 coefficients in Eq. (4.2) can take arbitrary real values, the equation remains unaltered if the coefficients are multiplied by the same factor. Hence only the ratios of these 10 coefficients are significant. This means that a quadric can have, in general, nine independent parameters (or degrees of freedom), out of which six-three translational and three rotational-are accounted for rigid motion in space. So, intrinsically, a quadric surface has a maximum of three independent parameters.
