Find Angles of Intersection of line segments drawn

Questions & Answers
1

I was wondering if I draw two intersecting lines like in the picture below, how would I find the top and bottom angles of intersection of the two lines?

42485-angle-of-intersection.png
42485-angle-of-intersection.png391×562 8.09 KB

2

the angle is the same if you calculate the intersection or not:

   /// <summary>
   /// Angle between vectors from -179 to 180.
   /// </summary>
   /// <returns>From -179 to 180.</returns>
   /// <param name="one">One.</param>
   /// <param name="two">Two.</param>
   public static float AngleBetweenVectors(Vector3 one, Vector3 two)
   {
      float a = one.sqrMagnitude;
      float b = two.sqrMagnitude;
      if (a > 0.0f && b > 0.0f)
      {
         float angle = Mathf.Acos(Vector3.Dot(one, two) / Mathf.Sqrt(a * b)) * 180.0f / Mathf.PI;
         
         Vector3 cross = Vector3.Cross(one, two);
         //float sign = Mathf.Min( Mathf.Min(cross.x, cross.y), cross.z );
         float sign = cross.y;
         if (sign < 0.0f)
            return -angle;
         else
            return angle;
      }
      return 0.0f;
   }

this function calculates the angle between two vectors on the x-z plane (no y component)

if you want to calculate the intersection, you need this function:

   // Finds the intersection of two lines, or returns false.
   // The lines are defined by (o1, p1) and (o2, p2).
   public static bool LineIntersection(Vector3 one1, Vector3 two1, Vector3 one2, Vector3 two2, ref Vector3 point)
   {
      Vector3 seg1 = two1 - one1;
      Vector3 seg2 = two2 - one2;
      
      float cross = seg1.x*seg2.z - seg1.z*seg2.x;

      if (Mathf.Abs(cross) < 1e-8)
         return false;

      Vector3 one12 = one2 - one1;
      
      float t = (one12.x * seg2.z - one12.z * seg2.x)/cross;
      point = one1 + seg1 * t;

      return true;
   }