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Celeritas
0.5.0-86+4a8eea4
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Celeritas
0.5.0-86+4a8eea4
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Return a simplified version of a transformation. More...
#include <TransformSimplifier.hh>
Public Member Functions | |
| TransformSimplifier (Tolerance<> const &tol) | |
| Construct with tolerance. | |
| VariantTransform | operator() (NoTransformation const &nt) |
| No simplification can be applied to a null transformation. | |
| VariantTransform | operator() (Translation const &nt) |
| Translation may simplify to no transformation. | |
| VariantTransform | operator() (Transformation const &nt) |
| Simplify, possibly to translation or no transform. More... | |
Return a simplified version of a transformation.
Like surface simplification, we want to consider whether two different transformations will result in a distance change of \(\epsilon\) for a point that's at the length scale from the origin. Setting the length scale to unity (the default), we use the relative tolerance.
A translation can be deleted if its magnitude is less than epsilon.
For a translation, we use the fact that the trace (sum of diagonal elements) of any proper (non-reflecting) rotation matrix has an angle of rotation
\[ \mathrm{Tr}[R] = 2 \cos \theta + 1 \]
about an axis of rotation. Applying the rotation to a point at a unit distance will yield an iscoceles triangle with sides 1 and inner angle \(\theta\). For the displacement to be no more than \(\epsilon\) then the angle must be
\[ \sin \theta/2 \le \epsilon/2 \]
which with some manipulation means that a "soft zero" rotation has a trace
\[ \mathrm{Tr}[R] \ge 3 - \epsilon^2 \,. \]
Note that this means no rotational simplifications may be performed when the geometry tolerance is less than the square root of machine precision.
| VariantTransform celeritas::TransformSimplifier::operator() | ( | Transformation const & | t | ) |
Simplify, possibly to translation or no transform.
See the derivation in the class documentation.
1.9.1