# 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:

$$
z(x,y) = \frac{r^2}{R \left(1+\sqrt{1-(1+κ)\frac{r^2}{R^2}} \right)},\quad r^2 = x^2+y^2
$$

<figure><img src="/files/2jPnRMLRM8HKnFkT7Ztm" alt=""><figcaption><p>Example of Conic Surface, where κ=0 and R = 15mm</p></figcaption></figure>


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