> For the complete documentation index, see [llms.txt](https://docs.kostacloud.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.kostacloud.com/kostacloud/geometric-surface-types/radial-asphere-surface.md).
# Radial Asphere Surface
Radial Aspheres have a base Conic Surface with radial polynomial terms. There are several ways to specify these terms. There are four coefficient modes in KostaCLOUD: "Even Only", "Odd Only", "Even + Odd" and Arbitrary. By default the Even, Odd, and Even + Odd increment coefficients starting at the 3rd or 4th order coefficient by 1 or 2. There is also a checkbox for enabling the second order coefficient in even mode, although is is not recommended because the Conic Constant should suffice for this purpose. If working in arbitrary coefficient mode, then the user can supply any power that they like including irrational numbers such as pi, or fractional powers. The normalization radius by default is disabled \[i.e. it equals 1], but can be enabled, and set to some normalization radius.
$$
z(x,y) = \frac{r^2}{R \left(1+\sqrt{1-(1+κ)\frac{r^2}{R^2}} \right)} + \sum\_i \text{coeff}*i \cdot \left(\frac{r}{r*\text{norm}}\right)^{\text{order}\_i},\quad r^2 = x^2+y^2
$$
Example of Radial Asphere , where κ=0 and R = 15mm and a single 4th order coefficient 1e-6 with no normalization radius.
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