From(adsbygoogle = window.adsbygoogle || []).push({}); Computer Vision, A Modern Approachby Forsyth & Ponce:

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?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# What is this notation?

Loading...

Similar Threads - notation | Date |
---|---|

I Diagonalization and change of basis | Jan 16, 2018 |

I Basic Notation for Field Extensions ... | Apr 10, 2017 |

I Notation N(H) for a subgroup | Oct 28, 2016 |

B Bracket notation problem | Oct 14, 2016 |

**Physics Forums - The Fusion of Science and Community**