diff --git a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt index a1a2f03a7c0..f6143e50d7d 100755 --- a/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt +++ b/Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt @@ -2149,7 +2149,7 @@ point type, i.e., `Point_2` from the substituted line-segment traits, and defines the nested types `Curve_2` and `X_monotone_curve_2`, which are used to represent polylines and \f$ x\f$-monotone polylines, respectively. A curve of one of these two type is stored as a vector -of `SegmentTraits::X_monotone_curve_2` objects (namely line segments). +of `SegmentTraits::X_monotone_curve_2` objects (namely line segments). The nested `X_monotone_curve_2` type inherits from the nested type `Curve_2`. @@ -2194,8 +2194,8 @@ directly. Instead, it solely relies on the functionality of the substituted segment-traits class. For example, when we need to determine the position of a point with respect to an \f$x\f$-monotone polyline, we use binary search to locate the relevant segment that -contains the point in its $x$-range. Then, we compute the position of -the point with respect to this segment. Thus, operations on $x$-monotone +contains the point in its \f$x\f$-range. Then, we compute the position of +the point with respect to this segment. Thus, operations on \f$x\f$-monotone polylines of size \f$m\f$ typically take \f$O(\log m)\f$ time. You are free to choose the underlying line-segment traits class. Your