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Pyramid2

A truncated pyramid with rectangular base.

Constructor

Pyramid2(L, W, H, alpha_L, alpha_W)

Parameters:

  • L, edge length of the base
  • W, edge width of the base
  • H, height
  • alpha_L, dihedral angle of the two faces that taper the length $L$
  • alpha_W, dihedral angle of the two faces that taper the width $W$

Each angle must satisfy

$$0 < \alpha_L,\alpha_W < 180^\circ.$$

For an angle below $90^\circ$, the corresponding top-face dimension must remain positive:

$$L > \dfrac{2H}{\tan\alpha_L}, \qquad W > \dfrac{2H}{\tan\alpha_W}.$$

For an angle at least $90^\circ$, there is no additional constraint in that direction and the upper face has the same or a larger extent than the base.

Usage

As for any other Form factor.

Implementation

Class Pyramid2 inherits from the interface class Formfactor.

Form factor computation is based on the generic form factor of a polyhedron provided by libformfactor .

Volume has been validated against $$ V=H\left[LW-\dfrac{WH}{\tan\alpha_L}-\dfrac{LH}{\tan\alpha_W} +\dfrac{4H^2}{3\tan\alpha_L\tan\alpha_W}\right]. $$

More special:

  • Pyramid4, if $L=W$ and $\alpha_L=\alpha_W$.
  • Box, if $\alpha_L=\alpha_W=90^{\circ}$.

Example

Scattering by uncorrelated, oriented pyramids for horizontal incidence. Rotation around $z$ axis:

Generated by Examples/sas/sas-ff.py (particle_geometry=Pyramid2).

History

Was named “AnisoPyramid” up to BornAgain 1.19.

Agrees with the “In plane anisotropic pyramid” form factor of IsGISAXS Lazzari, IsGISAXS manual v2.6 (2006), Eq. 2.38-2.39; Renaud et al, Surf Sci Rep 64, 255 (2009), Eq. 216-217, except for different parametrization. This is not the “Anisotropic pyramid” of FitGISAXS, which is a true pyramid with an off-center apex Babonneau, FitGISAXS v130531 (2013).