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Celeritas
0.5.0-86+4a8eea4
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Celeritas
0.5.0-86+4a8eea4
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Axis-aligned cylinder. More...
#include <CylAligned.hh>
Public Member Functions | |
| CELER_FUNCTION | CylAligned (Real3 const &origin, real_type radius) |
| Construct from origin and radius. | |
| template<class R > | |
| CELER_FUNCTION | CylAligned (Span< R, StorageSpan::extent >) |
| Construct from raw data. | |
| CylAligned (CylCentered< T > const &other) noexcept | |
| Promote from a centered axis-aligned cylinder. | |
| CELER_FUNCTION real_type | origin_u () const |
| Get the origin vector along the 'u' axis. | |
| CELER_FUNCTION real_type | origin_v () const |
| Get the origin vector along the 'v' axis. | |
| CELER_FUNCTION real_type | radius_sq () const |
| Get the square of the radius. | |
| CELER_FUNCTION StorageSpan | data () const |
| Get a view to the data for type-deleted storage. | |
| Real3 | calc_origin () const |
| Get the origin as a 3-vector. | |
| CELER_FUNCTION SignedSense | calc_sense (Real3 const &pos) const |
| Determine the sense of the position relative to this surface. | |
| CELER_FUNCTION Intersections | calc_intersections (Real3 const &pos, Real3 const &dir, SurfaceState on_surface) const |
| Calculate all possible straight-line intersections with this surface. | |
| CELER_FUNCTION Real3 | calc_normal (Real3 const &pos) const |
| Calculate outward normal at a position. | |
Static Public Member Functions | |
| static CylAligned | from_radius_sq (Real3 const &origin, real_type rsq) |
| Construct from the square of the radius and the origin. More... | |
Type aliases | |
| using | Intersections = Array< real_type, 2 > |
| Surface type identifier. | |
| using | StorageSpan = Span< real_type const, 3 > |
| Surface type identifier. | |
| static CELER_CONSTEXPR_FUNCTION SurfaceType | surface_type () |
| Surface type identifier. | |
| static CELER_CONSTEXPR_FUNCTION bool | simple_safety () |
| Safety is intersection along surface normal. | |
| static CELER_CONSTEXPR_FUNCTION Axis | t_axis () |
| static CELER_CONSTEXPR_FUNCTION Axis | u_axis () |
| Surface type identifier. | |
| static CELER_CONSTEXPR_FUNCTION Axis | v_axis () |
| Surface type identifier. | |
Axis-aligned cylinder.
The cylinder is centered about the template parameter Axis.
For a cylinder along the x axis:
\[ (y - y_0)^2 + (z - z_0)^2 - R^2 = 0 \]
The axis-aligned cylinder is used to calculate a tolerance for the second-order coefficient on the quadratic equation, where a small value is approximately zero.
Basing the intersection tolerance on a particle traveling nearly parallel to the cylinder, the angle \(\theta \) between the particle's direction and the center axis of the cylinder needed to give an intersection distance of \( 1/\delta \) when a distance of 1 from the cylinder (or equivalently, an intersection of 1 when a distance \( \delta \) away) is
\[ \sin \theta = \frac{1}{1/\delta} \;. \]
Letting \( \mu = \cos \theta = \Omega \cdot t \) we have
\[ \mu^2 + \delta^2 = 1 \;. \]
The quadratic intersection for an axis-aligned cylinder where the particle is at \( R + \delta \) is
\[ 0 = ax^2 + bx + c = (1 - \mu^2)x^2 + 2 \sqrt{1 - \mu^2} (R + 1) x + (R + 1)^2 - R^2 \]
so the quadric coefficient when a particle is effectively parallel to a cylinder is:
\[ a = (1 - \mu^2) = \delta^2 \;. \]
Because a is calculated by subtraction, this puts a hard limit on the accuracy of the intersection distance: the default value of a=1e-10 corresponds to a tolerance of 1e-5, not the default tolerance 1e-8.
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Construct from the square of the radius and the origin.
This is used for surface simplification.
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inlinestatic |
Axes
1.9.1