diff --git a/Barycentric_coordinates_3/doc/Barycentric_coordinates_3/Barycentric_coordinates_3.txt b/Barycentric_coordinates_3/doc/Barycentric_coordinates_3/Barycentric_coordinates_3.txt index 63e37d1db31..c14489503c9 100644 --- a/Barycentric_coordinates_3/doc/Barycentric_coordinates_3/Barycentric_coordinates_3.txt +++ b/Barycentric_coordinates_3/doc/Barycentric_coordinates_3/Barycentric_coordinates_3.txt @@ -133,7 +133,7 @@ We adopt the simple formula below to compute tetrahedron coordinates of the quer \f$w_i = \frac{V_i}{V}\f$ -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