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The conic element defines a conic, without regard to which kind it is - a circle, an ellipse, a parabola or a hyperbola.

The conic is defined through the matrix of its associated quadratic form. For instance, the circle of center (1,3) and radius 2 has associated the form (x-1)^2+(y-3)^2-4, whose coefficient matrix is

( 1 0 -1 ) 
( 0 1 -3 ) 
( -1 -3 6 ).

Additionally, in the case of degenerate conics, the dual matrix is necessary; for non-degenerate conics this matrix is optional, and so it does not have to be saved.

The coefficients of the matrix are stored in this way:

    … nine complex or real numbers here …
There is no need to assume symmetry nor hermiticity. The coefficients of the optional dual matrix are stored in the same way within <dualmatrix>…</dualmatrix> tags.

The same format is used by the elements circle, ellipse, parabola and hyperbola, the other elements in the conic_family.

For the moment, it is assumed that the matrices have 9 entries, which are read from first row to last row, and within a row from the left to the right. It has been suggested that, in the future, when 3D geometry is tackled, 4x4 matrices could be also used; the difference would lie just in the number of entries.


  1. conic example: source JSXGraph