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More generally, aquadric surfaceis the locus of the pointsPwhose coordinates satisfy the equation:

[tex]a_{200}x^2 + a_{110}xy + a_{020}y^2 + a_{011}yz + a_{002}z^2 + a_{101}xz + a_{100}x + a_{010}y + a_{001}z + a_{000} = 0 [/tex]

and it is straightforward to check that this condition is equivalent to

[tex]\bold{P}^TQ\bold{P} = 0, \qquad \text{where} \quad Q = \left( \begin{array}{cccc} a_{200} &\frac{1}{2}a_{110} &\frac{1}{2}a_{101} &\frac{1}{2}a_{100} \\

\frac{1}{2}a_{110} &a_{020} &\frac{1}{2}a_{011} &\frac{1}{2}a_{010} \\

\frac{1}{2}a_{101} &\frac{1}{2}a_{011} &a_{002} &\frac{1}{2}a_{001} \\

\frac{1}{2}a_{100} &\frac{1}{2}a_{010} &\frac{1}{2}a_{001} &a_{000} \end{array} \right ) [/tex]

In this equation,denotes the homogeneous coordinate vector ofPP.

I don't see any explanation of the subscripts. Anybody know what they represent?

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# What is this notation?

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