How can we calculate the intersection between the plane and the penetrating line?

[휴엔]

Hello Everyone,
I have a question about the way to calculate intersection point.
We have four points which we know its coordinates.
and let's assume we can create plane with these points.
When there is a line penetrating the plane, I guess there are one intersection point which the plane and the line meet.

How can we calculate the coordinates of the intersection point?

Thank you in advance.

[jeremytammik]

You will only need three points to uniquely define the face, so the fourth point can actually be used to verify that all four are co-planar.

Calculating the intersection between a straight line and a plane is pretty easy, so the most efficient method to achieve this may possibly be to do it yourself:

• https://duckduckgo.com/?q=line+plane+intersect
• https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection
• https://youtu.be/_W3aVWsMp14
• https://rosettacode.org/wiki/Find_the_intersection_of_a_line_with_a_plane
• https://stackoverflow.com/questions/5666222/3d-line-plane-intersection

If you prefer to use the official Revit API, you can refer to the Face.Intersect method taking a Curve argument:

• https://www.revitapidocs.com/2020/3513f5e2-a274-4f60-4d8f-78145930a9e3.htm

I do not understand why you prefer to ask this question here instead fo searching for these results yourself.

It took me much longer to write them down than to find them.

[jeremytammik · Accepted solution]

I went ahead and implemented a line-plane intersection method for you in The Building Coder samples:

https://github.com/jeremytammik/the_building_coder_samples/blob/master/BuildingCoder/BuildingCoder/U...

Here is the code:

    /// <summary>
    /// Return the 3D intersection point between
    /// a line and a plane.
    /// https://forums.autodesk.com/t5/revit-api-forum/how-can-we-calculate-the-intersection-between-the-plane-and-the/m-p/9785834
    /// https://stackoverflow.com/questions/5666222/3d-line-plane-intersection
    /// Determine the point of intersection between 
    /// a plane defined by a point and a normal vector 
    /// and a line defined by a point and a direction vector.
    /// planePoint - A point on the plane.
    /// planeNormal - The normal vector of the plane.
    /// linePoint - A point on the line.
    /// lineDirection - The direction vector of the line.
    /// lineParameter - The intersection distance along the line.
    /// Return - The point of intersection between the 
    /// line and the plane, null if the line is parallel 
    /// to the plane.
    /// </summary>
    public static XYZ LinePlaneIntersection(
      Line line,
      Plane plane,
      out double lineParameter )
    {
      XYZ planePoint = plane.Origin;
      XYZ planeNormal = plane.Normal;
      XYZ linePoint = line.GetEndPoint( 0 );

      XYZ lineDirection = (line.GetEndPoint( 1 ) 
        - linePoint).Normalize();

      // Is the line parallel to the plane, i.e.,
      // perpendicular to the plane normal?

      if( IsZero( planeNormal.DotProduct( lineDirection ) ) )
      {
        lineParameter = double.NaN;
        return null;
      }

      lineParameter = (planeNormal.DotProduct( planePoint ) 
        - planeNormal.DotProduct( linePoint )) 
          / planeNormal.DotProduct( lineDirection );

      return linePoint + lineParameter * lineDirection;
    }

[휴엔]

Thank you for offering sample code. Actually I intended to find solution only with Revit Official API.

[NonicaTeam]

Thanks @jeremytammik . It was really helpful for us!