Question

I have two line curves that are not parallel and that do not intersect. How can I find the intersection of them?

Answer

You can find the intersection of two non-parallel line curves using the ON_Intersect function.

C++

  CRhinoCommand::result CCommandTest::RunCommand( const CRhinoCommandContext& context )
  {
    CRhinoGetObject go;
    go.SetCommandPrompt( L"Select lines" );
    go.SetGeometryFilter( ON::curve_object );
    go.GetObjects( 2, 2 );
    if( go.CommandResult() != success )
      return go.CommandResult();


    if( go.ObjectCount() != 2 )
      return failure;


    const ON_LineCurve* crv0 = ON_LineCurve::Cast( go.Object(0).Geometry() );
    const ON_LineCurve* crv1 = ON_LineCurve::Cast( go.Object(1).Geometry() );
    if( 0 == crv0 || 0 == crv1 )
      return failure;  


    ON_Line line0 = crv0->m_line;
    ON_Line line1 = crv1->m_line;


    ON_3dVector v0 = line0.to - line0.from;
    v0.Unitize();


    ON_3dVector v1 = line1.to - line1.from;
    v1.Unitize();


    if( v0.IsParallelTo(v1) != 0 )
    {
      RhinoApp().Print( L"Selected lines are parallel.\n" );
      return nothing;
    }


    ON_Line ray0( line0.from, line0.from + v0 );
    ON_Line ray1( line1.from, line1.from + v1 );


    double s = 0, t = 0;
    if( !ON_Intersect(ray0, ray1, &s, &t) )
    {
      RhinoApp().Print( L"No intersection found.\n" );
      return nothing;
    }


    ON_3dPoint pt0 = line0.from + s * v0;
    ON_3dPoint pt1 = line1.from + t * v1;


    // pt0 and pt1 should be equal, so we will 
    // only add pt0 to the document
    context.m_doc.AddPointObject( pt0 );
    context.m_doc.Redraw();


    return CRhinoCommand::success;
  }

C# (Rhino 4)

  public override IRhinoCommand.result RunCommand(IRhinoCommandContext context)
  {
    MRhinoGetObject go = new MRhinoGetObject();
    go.SetCommandPrompt( "Select lines" );
    go.SetGeometryFilter( IRhinoGetObject.GEOMETRY_TYPE_FILTER.curve_object );
    go.GetObjects( 2, 2 );
    if( go.CommandResult() != IRhinoCommand.result.success )
      return go.CommandResult();
    if( go.ObjectCount() != 2 )
      return IRhinoCommand.result.failure;


    IOnLineCurve crv0 = OnLineCurve.ConstCast( go.Object(0).Geometry() );
    IOnLineCurve crv1 = OnLineCurve.ConstCast( go.Object(1).Geometry() );
    if( crv0 == null || crv1 == null )
      return IRhinoCommand.result.failure;


    OnLine line0 = new OnLine(crv0.m_line);
    OnLine line1 = new OnLine(crv1.m_line);


    On3dVector v0 = line0.to - line0.from;
    v0.Unitize();
    On3dVector v1 = line1.to - line1.from;
    v1.Unitize();


    if( v0.IsParallelTo(v1) != 0 )
    {
      RhUtil.RhinoApp().Print( "Selected lines are parallel.\n" );
      return IRhinoCommand.result.nothing;
    }


    OnLine ray0 = new OnLine( line0.from, line0.from + v0 );
    OnLine ray1 = new OnLine( line1.from, line1.from + v1 );


    double s = 0.0, t = 0.0;
    if( !OnUtil.ON_Intersect(ray0,ray1,ref s, ref t) )
    {
      RhUtil.RhinoApp().Print( "No intersection found.\n" );
      return IRhinoCommand.result.nothing;
    }


    On3dPoint pt0 = line0.from + v0 * s;
    On3dPoint pt1 = line1.from + v1 * t;


    // pt0 and pt1 should be equal, so we will 
    // only add pt0 to the document
    context.m_doc.AddPointObject( pt0 );
    context.m_doc.Redraw();


    return IRhinoCommand.result.success;
  }

VB.NET (Rhino 4)

  Public Overrides Function RunCommand(ByVal context As RMA.Rhino.IRhinoCommandContext) _
    As RMA.Rhino.IRhinoCommand.result
    Dim go As New MRhinoGetObject()
    go.SetCommandPrompt("Select lines")
    go.SetGeometryFilter(IRhinoGetObject.GEOMETRY_TYPE_FILTER.curve_object)
    go.GetObjects(2, 2)
    If (go.CommandResult() <> IRhinoCommand.result.success) Then
      Return go.CommandResult()
    End If
    If (go.ObjectCount() <> 2) Then Return IRhinoCommand.result.failure


    Dim crv0 As IOnLineCurve = OnLineCurve.ConstCast(go.Object(0).Geometry())
    Dim crv1 As IOnLineCurve = OnLineCurve.ConstCast(go.Object(1).Geometry())
    If (crv0 Is Nothing Or crv1 Is Nothing) Then
      Return IRhinoCommand.result.failure
    End If


    Dim line0 As New OnLine(crv0.m_line)
    Dim line1 As New OnLine(crv1.m_line)


    Dim v0 As On3dVector = line0.to - line0.from
    v0.Unitize()
    Dim v1 As On3dVector = line1.to - line1.from
    v1.Unitize()


    If (v0.IsParallelTo(v1) <> 0) Then
      RhUtil.RhinoApp().Print("Selected lines are parallel." + vbCrLf)
      Return IRhinoCommand.result.nothing
    End If


    Dim ray0 As New OnLine(line0.from, line0.from + v0)
    Dim ray1 As New OnLine(line1.from, line1.from + v1)


    Dim s As Double = 0.0, t As Double = 0.0
    If (Not OnUtil.ON_Intersect(ray0, ray1, s, t)) Then
      RhUtil.RhinoApp().Print("No intersection found." + vbCrLf)
      Return IRhinoCommand.result.nothing
    End If


    Dim pt0 As On3dPoint = line0.from + v0 * s
    Dim pt1 As On3dPoint = line1.from + v1 * t


    ' pt0 and pt1 should be equal, so we will 
    ' only add pt0 to the document
    context.m_doc.AddPointObject(pt0)
    context.m_doc.Redraw()


    Return IRhinoCommand.result.success
  End Function