BornAgain-git-develop HorizontalCylinder

HorizontalCylinder

A horizontal truncated circular cylinder along x-axis

Constructor

Full form

HorizontalCylinder(R, H, t, b)

and short form

HorizontalCylinder(R, H) == HorizontalCylinder(R, H, 0, 0)

Parameters:

$ R $, radius
$ H $, height
$ t $, cut from top
$ b $, cut from bottom

Constraint:

$ 2R - t - b \ge 0 $

Usage

As for any other Form factor.

Implementation

Class HorizontalCylinder inherits from the interface class IFormfactor.

Form factor is computed as

$$ F(\mathbf{q})=2 L \space \text{sinc}\Big(q_x\dfrac{L}{2}\Big) \exp[iq_z(R-b)] \int_{-R+b}^{R-t} \text{d}z \space \sqrt{R^2-z^2} \space \text{sinc}(q_y\sqrt{R^2-z^2}) \exp[iq_z z] , $$

Volume has been validated against $$V=L \Big( (R-t)\sqrt{2Rt-t^2}- (R-b)\sqrt{2Rb-b^2} + R^2 \Big[\text{asin}\Big(1-\frac{t}{R}\Big) + \text{asin}\Big(1-\frac{b}{R}\Big) \Big] \Big).$$

More general: