Explanation of the Corrected Implementation

Oct 13, 2025 by magicalceylontours.com 130 views

Introduction

In computational geometry, an arrangement is a collection of geometric objects, such as points, curves, and surfaces, that intersect each other. The do_intersect function is used to determine whether a given curve intersects with an arrangement of geometric objects. In this article, we will discuss the do_intersect function on arrangement with curves and x-monotone curves, and provide a corrected implementation.

Understanding the `do_intersect` Function

The do_intersect function takes four arguments:

arr: an instance of the Arrangement_on_surface_2 class, which represents the arrangement of geometric objects.
c: a curve that we want to check for intersection with the arrangement.
pl: a point location object that is used to locate points in the arrangement.
std::is_same<int, double>::type: a type trait that is used to check the type of the curve.

The function returns a boolean value indicating whether the curve intersects with the arrangement.

Corrected Implementation of the `do_intersect` Function

The original implementation of the do_intersect function has a bug. The argument type should be Curve_2 instead of X_monotone_curve_2 because they are not the same. Additionally, there is a bug fix at std::get_if<Face_const_handle>.

Here is the corrected implementation of the do_intersect function:

template <typename GeometryTraits_2, typename TopologyTraits,
          typename PointLocation>
bool
do_intersect(Arrangement_on_surface_2<GeometryTraits_2, TopologyTraits>& arr,
             const typename GeometryTraits_2::Curve_2& c,
             const PointLocation& pl, std::is_same<int, double>::type)
{
  typedef GeometryTraits_2                              Gt2;
  typedef TopologyTraits                                Tt;

  // Obtain an arrangement accessor.
  typedef Arrangement_on_surface_2<Gt2, Tt>             Arr;

  // Break the input curve into x-monotone subcurves and isolated points.
  typedef Arr_traits_adaptor_2<Gt2>                     Traits_adaptor_2;

  typedef typename Gt2::Point_2                         Point_2;
  typedef typename Gt2::Curve_2                         Curve_2;
  typedef std::variant<Point_2, Curve_2>               Make_x_monotone_result;
  typedef typename Arr::Face_const_handle               Face_const_handle;

  const Traits_adaptor_2* traits =
    static_cast<const Traits_adaptor_2*>(arr.geometry_traits());

  std::list<Make_x_monotone_result> x_objects;
  traits->make_x_monotone_2_object()(c, std::back_inserter(x_objects));

  // Insert each x-monotone curve into the arrangement.
  for (const auto& x_obj : x_objects) {
    // Act according to the type of the current object.
    const Curve_2* curve = std::get_if<Curve_2>(&x_obj);
    if (curve != nullptr) {
      // Check if the x-monotone subcurve intersects the arrangement.
      if (do_intersect(arr, *curve, pl) == true) return true;
      continue;
    }

    const Point_2* iso_p = std::get_if<Point_2>(&x_obj);
    CGAL_assertion(iso_p != nullptr);

    // Check whether the isolated point lies inside a face (otherwise,
    // it coincides with a vertex or an edge).
    auto obj = pl.locate(*iso_p);
    if (std::get_if<Face_const_handle>(&obj) != nullptr) return true;
  }

  // If we reached here, the curve does not intersect the arrangement.
  return false;
}

Explanation of the Corrected Implementation

The corrected implementation of the do_intersect function uses the Curve_2 type instead of X_monotone_curve_2 as the argument type. This is because Curve_2 is the correct type for the curve that we want to check for intersection with the arrangement.

Additionally, the corrected implementation fixes the bug at std::get_if<Face_const_handle>. This bug was caused by the incorrect use of the std::get_if function, which is used to retrieve the value of a variant object.

Example Use Case

Here is an example use case of the do_intersect function:

int main() {
  // Create an arrangement of geometric objects.
  Arrangement_on_surface_2<Bezier_curve_traits_2, Topology_traits_2> arr;

  // Create a curve that we want to check for intersection with the arrangement.
  Bezier_curve_2 curve;

  // Create a point location object.
  Point_location_2 pl;

  // Check if the curve intersects with the arrangement.
  if (do_intersect(arr, curve, pl)) {
    std::cout << "The curve intersects with the arrangement." << std::endl;
  } else {
    std::cout << "The curve does not intersect with the arrangement." << std::endl;
  }

  return 0;
}

Introduction

In our previous article, we discussed the do_intersect function on arrangement with curves and x-monotone curves. We also provided a corrected implementation of the do_intersect function. In this article, we will answer some frequently asked questions about the do_intersect function.

Q: What is the purpose of the `do_intersect` function?

A: The do_intersect function is used to determine whether a given curve intersects with an arrangement of geometric objects.

Q: What are the arguments of the `do_intersect` function?

A: The do_intersect function takes four arguments:

arr: an instance of the Arrangement_on_surface_2 class, which represents the arrangement of geometric objects.
c: a curve that we want to check for intersection with the arrangement.
pl: a point location object that is used to locate points in the arrangement.
std::is_same<int, double>::type: a type trait that is used to check the type of the curve.

Q: What is the difference between `Curve_2` and `X_monotone_curve_2`?

A: Curve_2 and X_monotone_curve_2 are two different types of curves. Curve_2 is a general type of curve, while X_monotone_curve_2 is a type of curve that is x-monotone, meaning that it does not intersect with itself.

Q: Why is the `do_intersect` function using `Curve_2` instead of `X_monotone_curve_2`?

A: The do_intersect function is using Curve_2 instead of X_monotone_curve_2 because Curve_2 is the correct type for the curve that we want to check for intersection with the arrangement. X_monotone_curve_2 is a specific type of curve that is x-monotone, but it is not the correct type for the curve that we want to check for intersection with the arrangement.

Q: What is the purpose of the `std::get_if` function in the `do_intersect` function?

A: The std::get_if function is used to retrieve the value of a variant object. In the do_intersect function, the std::get_if function is used to retrieve the value of a variant object that represents a curve or a point.

Q: What is the difference between `std::get_if` and `std::get`?

A: std::get_if and std::get are two different functions that are used to retrieve the value of a variant object. std::get_if returns a pointer to the value of the variant object, while std::get returns a reference to the value of the variant object.

Q: Why is the `do_intersect` function using `std::get_if` instead of `std::get`?

A: The do_intersect function is using std::get_if instead of std::get because std::get_if returns a pointer to the value of the variant object, which is the correct type for the curve that we want to check for intersection with the arrangement.

Q: What is the purpose of the `CGAL_assertion` macro in the `do_intersect` function?

A: The CGAL_assertion macro is used to check if a condition is true. In the do_intersect function, the CGAL_assertion macro is used to check if the curve is not null.

Q: What is the difference between `CGAL_assertion` and `assert`?

A: CGAL_assertion and assert are two different macros that are used to check if a condition is true. CGAL_assertion is a macro that is specific to the CGAL library, while assert is a macro that is part of the C++ standard library.

Q: Why is the `do_intersect` function using `CGAL_assertion` instead of `assert`?

A: The do_intersect function is using CGAL_assertion instead of assert because CGAL_assertion is a macro that is specific to the CGAL library, and it provides more information about the assertion failure.

Example Use Case

Here is an example use case of the do_intersect function:

int main() {
  // Create an arrangement of geometric objects.
  Arrangement_on_surface_2<Bezier_curve_traits_2, Topology_traits_2> arr;

  // Create a curve that we want to check for intersection with the arrangement.
  Bezier_curve_2 curve;

  // Create a point location object.
  Point_location_2 pl;

  // Check if the curve intersects with the arrangement.
  if (do_intersect(arr, curve, pl)) {
    std::cout << "The curve intersects with the arrangement." << std::endl;
  } else {
    std::cout << "The curve does not intersect with the arrangement." << std::endl;
  }

  return 0;
}

In this example, we create an arrangement of geometric objects using the Arrangement_on_surface_2 class. We then create a curve that we want to check for intersection with the arrangement using the Bezier_curve_2 class. We also create a point location object using the Point_location_2 class. Finally, we use the do_intersect function to check if the curve intersects with the arrangement. If the curve intersects with the arrangement, we print a message indicating that the curve intersects with the arrangement. Otherwise, we print a message indicating that the curve does not intersect with the arrangement.