# Planes, quadric surfaces and then …?

If planes are described as: $\mathbf{n} \cdot (\mathbf{r}-\mathbf{r_0})=0$

And quadric surfaces can be described as: $\mathbf{x}^T\mathbf{A}\mathbf{x} = 0$ (with $\mathbf{x} = \begin{bmatrix} x && y && z && 1\end{bmatrix}^T$ and $\mathbf{A}$ is a symmetric matrix)

Then what is the name and compact form for a surface in the form of $Ax^3 + By^3 + Cz^3 + Dx^2z + \ldots = 0$

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Cubic hypersurface. –  user27126 May 4 '13 at 23:40
@Sanchez, is cubic hypersurface still applicable when the polynomial is still an implicit function of three variables? –  Damien May 8 '13 at 22:45
Oh, I forgot to add - @Sanchez, if you answer the above comment, and provide a compact form for the equations, add it an an answer and you'll have yourself a nice easy accepted solution. –  Damien May 8 '13 at 22:48