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Added some notes to indicate that inexact constructions are tolerated for do_intersect() when applied to (linear) polygons

This commit is contained in:
Efi Fogel 2025-09-07 00:28:11 +03:00
parent 4a6d766d8c
commit 1d62c37822
2 changed files with 88 additions and 8 deletions
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30
Boolean_set_operations_2/doc/Boolean_set_operations_2/Boolean_set_operations_2.txt
View File

@ -700,15 +700,29 @@ swap its source and target points).
The traits classes `Arr_segment_traits_2`,
`Arr_non_caching_segment_traits_2`, `Arr_circle_segment_traits_2`,
`Arr_conic_traits_2` and `Arr_rational_function_traits_2`, which are
bundled in the `Arrangement_2` package and distributed with \cgal,
are all models of the refined concept
`AosDirectionalXMonotoneTraits_2`.\cgalFootnote{The \cgalFootnoteCode{Arr_polyline_traits_2} class is <I>not</I> a model of the, \cgalFootnoteCode{AosDirectionalXMonotoneTraits_2} concept, as the \f$ x\f$-monotone curve it defines is always directed from left to right. Thus, an opposite curve cannot be constructed. However, it is not very useful to construct a polygon whose edges are polylines, as an ordinary polygon with linear edges can represent the same entity.}
bundled in the `Arrangement_2` package and distributed with \cgal, are
all models of the refined concept
`AosDirectionalXMonotoneTraits_2`.\cgalFootnote{The
\cgalFootnoteCode{Arr_polyline_traits_2} class is <I>not</I> a model
of the, \cgalFootnoteCode{AosDirectionalXMonotoneTraits_2} concept, as
the \f$ x\f$-monotone curve it defines is always directed from left to
right. Thus, an opposite curve cannot be constructed. However, it is
not very useful to construct a polygon whose edges are polylines, as
an ordinary polygon with linear edges can represent the same entity.}
Just as with the case of computations using models of the
`AosXMonotoneTraits_2` concept, operations are robust only
when exact arithmetic is used. When inexact arithmetic is used,
(nearly) degenerate configurations may result in abnormal termination
of the program or even incorrect results.
Operations on polygons (or general polygons) are guaranteed to be
robust only if the operations of the geometry traits used to carry out
the high-level operations are robust. Most operations on polygons use
geometry traits constructors, as they generate new polygons; such
constructors are guaranteed to be robust only if the kernel in use
supports exact constructions, such as the EPEC (Exact Predicate Exact
Construction) kernel. The `do_intersect()` overloaded predicates that
operate on (linear) polygons are exceptions, as they only use geometry
traits predicates; such predicates are guaranteed to be robust only if
the kernel in use supports exact predicates, such as the EPIC (Exact
Predicate Inexact Construction) kernel. When inexact arithmetic is
used, (nearly) degenerate configurations may result in abnormal
termination of the program or even incorrect results.
\subsection bso_sseccirc_seg Operating on Polygons with Circular Arcs

66
Boolean_set_operations_2/doc/Boolean_set_operations_2/CGAL/Boolean_set_operations_2.h
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@ -723,6 +723,11 @@ namespace CGAL {
//////// Traits-less
/*! determines whether two polygons intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@ -733,6 +738,11 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
const Polygon_2<Kernel, Container>& pgn2);
/*! determines whether two polygons intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@ -743,6 +753,11 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
const Polygon_with_holes_2<Kernel, Container>& pgn2);
/*! determines whether two polygons intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@ -753,6 +768,11 @@ bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
const Polygon_2<Kernel, Container>& pgn2);
/*! determines whether two polygons with holes intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \return `true` if `pgn1` and `pgn2` intersect in their interior and `false`
@ -814,6 +834,13 @@ bool do_intersect(const General_polygon_with_holes_2<Polygon>& pgn1,
* of general polygons or a range of general polygons with holes) determines
* whether the open polygons (respectively general polygons) in the range have a common
* point.
*
* When the operation is applied to linear polygons (that is, the value type of
* the input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
* kernel used to instantiate the type of the input polygons must support exact
* predicates to guarantee correct results; however, inexact constructions are
* tolerated.
*
* \param begin the first iterator of the input range. Its value type is
* either `Polygon_2` (respectively `General_polygon_2`) or
* `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
@ -830,6 +857,13 @@ bool do_intersect(InputIterator begin, InputIterator end);
/*! Given a range of polygons (respectively general polygons) and a range of polygons
* with holes (respectively general polygons with holes) determines whether the open
* polygons (respectively general polygons) in the two ranges have a common point.
*
* When the operation is applied to linear polygons (that is, the value type of
* any input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
* kernel used to instantiate the type of the input polygons must support exact
* predicates to guarantee correct results; however, inexact constructions are
* tolerated.
*
* \param begin1 the first iterator of the 1st input range. Its value type is
* `Polygon_2` (respectively `General_polygon_2`).
* \param end1 the past-the-end iterator of the 1st input range. Its value
@ -850,6 +884,11 @@ bool do_intersect(InputIterator1 begin1, InputIterator1 end1,
//////// With Traits
/*! determines whether two polygons intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \param traits a traits object.
@ -863,6 +902,11 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
const GpsTraits& traits);
/*! determines whether two polygons intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \param traits a traits object.
@ -876,6 +920,11 @@ bool do_intersect(const Polygon_2<Kernel, Container>& pgn1,
const GpsTraits& traits);
/*! determines whether two polygons intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \param traits a traits object.
@ -889,6 +938,11 @@ bool do_intersect(const Polygon_with_holes_2<Kernel, Container>& pgn1,
const GpsTraits& traits);
/*! determines whether two polygons with holes intersect in their interior.
*
* The kernel used to instantiate the type of the input polygons must support
* exact predicates to guarantee correct results; however, inexact constructions
* are tolerated.
*
* \param pgn1 the 1st input polygon.
* \param pgn2 the 2nd input polygon.
* \param traits a traits object.
@ -967,6 +1021,12 @@ bool do_intersect(const General_polygon_with_holes_2<Polygon>& pgn1,
* of general polygons or a range of general polygons with holes) determines
* whether the open polygons (respectively general polygons) in the range have a common
* point.
*
* When the operation is applied to linear polygons (that is, the value type of
* the input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
* traits parameter `GpsTraits` must support exact predicates to guarantee
* correct results; however, inexact constructions are tolerated.
*
* \param begin the first iterator of the input range. Its value type is
* either `Polygon_2` (respectively `General_polygon_2`) or
* `Polygon_with_holes_2` (respectively `General_polygon_with_holes_2`).
@ -986,6 +1046,12 @@ bool do_intersect(InputIterator begin, InputIterator end,
/*! Given a range of polygons (respectively general polygons) and a range of polygons
* with holes (respectively general polygons with holes) determines whether the open
* polygons (respectively general polygons) in the two ranges have a common point.
*
* When the operation is applied to linear polygons (that is, the value type of
* any input iterator is either `Polygon_2` or `Polygon_with_holes_2`), the
* traits parameter `GpsTraits` must support exact predicates to guarantee
* correct results; however, inexact constructions are tolerated.
*
* \param begin1 the first iterator of the 1st input range. Its value type is
* `Polygon_2` (respectively `General_polygon_2`).
* \param end1 the past-the-end iterator of the 1st input range. Its value