Hey there! Avoiding reinventing the wheel for geometric computations is totally the way to go—edge cases like parallel planes or numerical precision issues can be tricky to handle correctly on your own. Here are some battle-tested libraries that have this functionality built-in:

C++ Options #

• Eigen: This popular linear algebra library has a robust geometry module. You can use the Plane class from Eigen/Geometry to represent your two planes, then call the intersection method to get a Line object. To get two points on the line, you can take the line's origin plus/minus its direction vector, or use scaled versions of the direction to create distinct points. Example snippet:

  #include <Eigen/Geometry>
  using namespace Eigen;
  
  Plane<double> plane1(A1, B1, C1, D1);
  Plane<double> plane2(A2, B2, C2, D2);
  Line<double, 3> intersection_line;
  if (plane1.intersection(plane2, intersection_line)) {
      Vector3d point1 = intersection_line.origin();
      Vector3d point2 = intersection_line.origin() + intersection_line.direction();
      // Use point1 and point2 for your line representation
  } else {
      // Handle parallel or coincident planes here
  }
  

• CGAL: The Computational Geometry Algorithms Library is purpose-built for these kinds of problems. Use the Plane_3 class from the Core module, then call the intersection function to get a Line_3 object. You can retrieve two distinct points directly with line.point(0) and line.point(1), or generate your own by adding the direction vector to a base point. CGAL prioritizes numerical precision, which is a huge win for real-world use cases.

Python Options #

• SciPy: If you're working in Python, SciPy's scipy.spatial.geometry module has a Plane class that simplifies this task. Create two Plane instances, then call the intersection method to get a Line object. Generate two points by taking the line's base point plus/minus its direction vector. Example:

  from scipy.spatial import Plane, Line
  
  plane1 = Plane([A1, B1, C1], D1)
  plane2 = Plane([A2, B2, C2], D2)
  intersection_result = plane1.intersection(plane2)
  if isinstance(intersection_result, Line):
      point1 = intersection_result.point
      point2 = intersection_result.point + intersection_result.direction
      // Use point1 and point2 for your line representation
  else:
      // Handle parallel or coincident planes here
  

All these libraries handle edge cases gracefully, either returning a boolean success flag or a non-line result for parallel planes, so you don't have to implement those error checks from scratch.

内容的提问来源于stack exchange，提问作者Stepan Yakovenko