> 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/conic-surface.md).
# Conic Surface
Conic Surfaces are rotationally symmetric surfaces whose profile varies from a Sphere with a κ=0 to Parabola κ=-1, and Oblate and Prolate ellipsoids. They have two properties. R is the base radius for the sphere, and κ is the conic constant. The benefit of spheres is that they can be manufactured quite reliably - driving down manufacturing cost, where other conic constants take more effort, but are significantly easier to manufacture than other aspheres. They have the following sag:
$$
z(x,y) = \frac{r^2}{R \left(1+\sqrt{1-(1+κ)\frac{r^2}{R^2}} \right)},\quad r^2 = x^2+y^2
$$
Example of Conic Surface, where κ=0 and R = 15mm
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