Z-aligned Elliptical Toroid. More...

#include <Toroid.hh>

Type aliases
using	Intersections = Array< real_type, 4 >
	Location of center of toroid.

using	StorageSpan = Span< real_type const, 6 >
	Location of center of toroid.

using	Real3 = Array< real_type, 3 >
	Location of center of toroid.

using	Real4 = Array< real_type, 4 >
	Location of center of toroid.

using	Real5 = Array< real_type, 5 >
	Location of center of toroid.

static SurfaceType	surface_type ()
	Location of center of toroid.

static constexpr bool	simple_safety ()
	Safety distance is calculable w/xy of normal and ellipse safety distance, but this is out of scope at first and might not be trivially calculable https://web.archive.org/web/20170829172516/https://www.spaceroots.org/documents/distance/distance-to-ellipse.pdf.

	Toroid (Real3 const &origin, real_type major_radius, real_type ellipse_xy_radius, real_type ellipse_z_radius)
	Construct toroid from origin point and radii.

template<class R >
	Toroid (Span< R, StorageSpan::extent >)
	Construct from raw data.

Real3 const &	origin () const
	Center of the toroid (in the donut hole)

real_type	major_radius () const
	Radius from origin to center of revolved ellipse.

real_type	ellipse_xy_radius () const
	Radius of revolved ellipse along xy plane.

real_type	ellipse_z_radius () const
	Radius of revolved ellipse along z axis.

StorageSpan	data () const
	View of data for type-deleted storage.

SignedSense	calc_sense (Real3 const &pos) const
	Determine the sense of the position relative to this surface.

Intersections	calc_intersections (Real3 const &pos, Real3 const &dir, SurfaceState on_surface) const
	Calculate all possible straight-line intersections between the given ray and this surface.

Real3	calc_normal (Real3 const &pos) const
	Calculate outward facing normal at a position on or close to the surface.

Detailed Description

Z-aligned Elliptical Toroid.

An elliptical toroid is a shape created by revolving an axis-aligned ellipse around a central axis. This shape can be used in everything from pipe bends to tokamaks in fusion reactors. It possesses a major radius r, and ellipse radii a and b, as shown in the below diagram:

    ___   _________   ___
  /  |  \           /     \
 /   b   \         /       \
|    |    |       |         |
|-a--+    |   o-----r--+    |
|         |       |         |
 \       /         \       /
  \...../...........\...../

This torus can be defined with the following quartic equation:

\[ (x^2 + y^2 + p*y^2 + B_0) - A_0 * (x^2 + y^2) = 0 \]

where \(p = a^2/b^2 \), \(A_0 = 4 r^2 \), and \( B_0 = (r^2-a^2)\).

The intersection is calculated using an algorithm from [arvo-graphicsgems-1995].

Constructor & Destructor Documentation

◆ Toroid()

celeritas::Toroid::Toroid	(	Real3 const &	origin,
		real_type	major_radius,
		real_type	ellipse_xy_radius,
		real_type	ellipse_z_radius
	)

explicit

Construct toroid from origin point and radii.

Parameters

origin	3d origin of the toroid.
major_radius	Radius from origin to the center of revolved ellipse.
ellipse_xy_radius	Radius of ellipse in xy plane, aka 'a'.
ellipse_z_radius	Radius of ellipse aligned with z axis, aka 'b'.

Member Function Documentation

◆ calc_sense()

SignedSense celeritas::Toroid::calc_sense ( Real3 const & pos ) const

inline

Determine the sense of the position relative to this surface.

For a toroid, being inside the toroid (i) counts as inside, outside (including in the 'hole' region) (o) as outside, and on the surface exactly as on (s).

    ___   _________   ___
  /     \           /     \
 /       \     o   /       \
|         |       |         | o
|         |       |    i    s
 \       /         \       /
  \     /           \     /
    ⁻⁻⁻   ⁻⁻⁻⁻⁻⁻⁻⁻⁻   ⁻⁻⁻

The documentation for this class was generated from the following files:

Type aliases

Detailed Description

Constructor & Destructor Documentation

◆ Toroid()

Member Function Documentation

◆ calc_sense()