Tekla API Matrix Transformations explained

Key Take Out

WorldCoordinateSystem

The world Coordinate system is a Coordinate System with Origin defined as (0,0,0) and the XAxis defined as (1,0,0) and the YAxis as: (0,1,0).

FromCoordinateSystem

FromCoordinateSystem(beamCS) is the same as ByCoordinateSystems(beamCS, worldCS)

true == MatrixFactory.FromCoordinateSystem(beamCS) == MatrixFactory.ByCoordinateSystems(beamCS, worldCS) == True

// use unit tests if you want to explore this avenue
  [Test]
  public void TestMatrixEquivalentsFrom()
  {
      CoordinateSystem beamCS = getCoordinateSystemFromBeam(new Point(0, 0, 0), new Point(-50, 100, 200)); // helper method but you can use your own
      CoordinateSystem worldCS = new CoordinateSystem();

      Matrix m1 = MatrixFactory.FromCoordinateSystem(beamCS);
      Matrix m2 = MatrixFactory.ByCoordinateSystems(beamCS, worldCS);

      for (int i = 0; i < 4; i++)
      {
          for (int j = 0; j < 3; j++)
          {
              ClassicAssert.AreEqual(m1[i, j], m2[i, j], Double.Epsilon);
          }
      }
  }

ToCoordinateSystem

And on the flip side:

ToCoordinateSystem(beamCS) is the same as: ByCoordinateSystems(worldCS, beamCS)

MatrixFactory.ToCoordinateSystem(beamCS) == MatrixFactory.ByCoordinateSystems(worldCS, beamCS) == True;

  [Test]
  public void TestMatrixEquivalentsTo()
  {
      CoordinateSystem beamCS = getCoordinateSystemFromBeam(new Point(0, 0, 0), new Point(-50, 100, 200)); // // helper method but you can use your own
      CoordinateSystem worldCS = new CoordinateSystem();

      Matrix m1 = MatrixFactory.ToCoordinateSystem(beamCS); // from world to BeamCS
      Matrix m2 = MatrixFactory.ByCoordinateSystems(worldCS, beamCS);

      for (int i = 0; i < 4; i++)
      {
          for (int j = 0; j < 3; j++)
          {
              ClassicAssert.AreEqual(m1[i, j], m2[i, j], Double.Epsilon);
          }                    
      }
  }

From the docs (which is plane wrong):

ToCoordinateSystem: Returns a coordinate transformation matrix defined by the given coordinate system. With the returned matrix points can be transformed from the current work plane coordinate system to the given coordinate system.
FromCoordinateSystem Returns a coordinate transformation matrix defined by the given coordinate system. With the returned matrix points can be transformed from the given coordinate system to the current work plane coordinate system.

They are really transformations from and to the world coordinate system. (I checked the source code).

benkoshy/tekla-api-matrix-transformations-summary.md

Select an option