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integrated last points from Efis review

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Sven Oesau 2025-11-20 14:31:06 +01:00
parent 9b224e2d71
commit 03b459c8a4
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6
Barycentric_coordinates_3/doc/Barycentric_coordinates_3/Barycentric_coordinates_3.txt
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@ -133,7 +133,7 @@ We adopt the simple formula below to compute tetrahedron coordinates of the quer
\f$w_i = \frac{V_i}{V}\f$
</center>
where \f$V_i\f$ is the signed volume of the sub-tetrahedron opposite to the vertex \f$i\f$ and \f$V\f$
where \f$V_i\f$ is the signed volume of the sub-tetrahedron opposite to the vertex \f$i\f$, i.e., the tetrahedron where the vertex \f$i\f$ is replaced by the query point `q`. \f$V\f$
is the total volume of the tetrahedron, that is \f$V = V_0 + V_1 + V_2 + V_3\f$.
These coordinates can be computed exactly if an exact number type is chosen, for any query point and with respect to any non-degenerate tetrahedron. No special cases are handled.
@ -193,8 +193,8 @@ star-shaped polyhedron.
Efficiency is crucial in this implementation.
These coordinates are used in applications that require
calculations for millions of points; thus developing metrics
to evaluate performance is absolutely necessary. In this section,
calculations for millions of points; thus, developing metrics
to evaluate performance is necessary. In this section,
we present benchmark results for each algorithm.
The benchmark and runtimes are evaluated by regularly sampling