Convert Coordinates

The TransformBy method can translate a point or a displacement from one coordinate system to another. You use the AlignCoordinateSystem method to specify which coordinate system you are translating from and which coordinate system you are going to. The AlignCoordinateSystem method requires the following:

Origin point of the coordinate system you are translating from
Three 3D vectors that represent the X, Y and X axes of the coordinate system you are translating from
Origin point of the coordinate system you are translating to
Three 3D vectors that represent the X, Y and X axes of the coordinate system you are translating to

WCS: World coordinate system: The reference coordinate system. All other coordinate systems are defined relative to the WCS, which never changes. Values measured relative to the WCS are stable across changes to other coordinate systems. All points passed in and out of the methods and properties in the .NET API are expressed in the WCS unless otherwise specified.
UCS: User coordinate system (UCS): The working coordinate system. The user specifies a UCS to make drawing tasks easier. All points passed to AutoCAD commands, including those returned from AutoLISP routines and external functions, are points in the current UCS (unless the user precedes them with an * at the Command prompt). If you want your application to send coordinates in the WCS, OCS, or DCS to AutoCAD commands, you must first convert them to the UCS by calling the translating them and then transforming the Point3d or Point 2d object with the TransformBy method that represents the coordinate value.
OCS: Object coordinate system (also known as Entity coordinate system or ECS): Point values specified by certain methods and properties for the Polyline2d and Polyline objects are expressed in this coordinate system, relative to the object. These points are usually converted into the WCS, current UCS, or current DCS, according to the intended use of the object. Conversely, points in WCS, UCS, or DCS must be translated into an OCS before they are written to the database by means of the same properties. See the AutoCAD .NET Managed Class Guide for the methods and properties that use this coordinate system.

When converting coordinates to or from the OCS you must consider the normal of the OCS.
DCS: Display coordinate system: The coordinate system where objects are transformed before they are displayed. The origin of the DCS is the point stored in the AutoCAD system variable TARGET, and its Z axis is the viewing direction. In other words, a viewport is always a plan view of its DCS. These coordinates can be used to determine where something will be displayed to the user.
PSDCS: Paper space DCS: This coordinate system can be transformed only to or from the DCS of a Model space viewport. This is essentially a 2D transformation, where the X and Y coordinates are always scaled. Therefore, it can be used to find the scale factor between the two coordinate systems. The PSDCS can be transformed only into a Model space viewport.

Translate OCS coordinates to WCS coordinates

This example creates a polyline in Model space. The first vertex for the polyline is then displayed in both the OCS and WCS coordinates.

VB.NET

Imports Autodesk.AutoCAD.Runtime

Imports Autodesk.AutoCAD.ApplicationServices

Imports Autodesk.AutoCAD.DatabaseServices

Imports Autodesk.AutoCAD.Geometry

<CommandMethod("TranslateCoordinates")> _

Public Sub TranslateCoordinates()

  '' Get the current document and database, and start a transaction

  Dim acDoc As Document = Application.DocumentManager.MdiActiveDocument

  Dim acCurDb As Database = acDoc.Database

  Using acTrans As Transaction = acCurDb.TransactionManager.StartTransaction()

      '' Open the Block table for read

      Dim acBlkTbl As BlockTable

      acBlkTbl = acTrans.GetObject(acCurDb.BlockTableId, _

                                   OpenMode.ForRead)

      '' Open the Block table record Model space for write

      Dim acBlkTblRec As BlockTableRecord

      acBlkTblRec = acTrans.GetObject(acBlkTbl(BlockTableRecord.ModelSpace), _

                                      OpenMode.ForWrite)

      '' Create a 2D polyline with two segments (3 points)

      Dim acPoly2d As Polyline2d = New Polyline2d()

      '' Add the new object to the block table record and the transaction

      acBlkTblRec.AppendEntity(acPoly2d)

      acTrans.AddNewlyCreatedDBObject(acPoly2d, True)

      '' Before adding vertexes, the polyline must be in the drawing

      Dim acPts2dPoly As Point3dCollection = New Point3dCollection()

      acPts2dPoly.Add(New Point3d(1, 1, 0))

      acPts2dPoly.Add(New Point3d(1, 2, 0))

      acPts2dPoly.Add(New Point3d(2, 2, 0))

      acPts2dPoly.Add(New Point3d(3, 2, 0))

      acPts2dPoly.Add(New Point3d(4, 4, 0))

      For Each acPt3d As Point3d In acPts2dPoly

          Dim acVer2d As Vertex2d = New Vertex2d(acPt3d, 0, 0, 0, 0)

          acPoly2d.AppendVertex(acVer2d)

          acTrans.AddNewlyCreatedDBObject(acVer2d, True)

      Next

      '' Set the normal of the 2D polyline

      acPoly2d.Normal = New Vector3d(0, 1, 2)

      '' Get the first coordinate of the 2D polyline

      Dim acPts3d As Point3dCollection = New Point3dCollection()

      Dim acFirstVer As Vertex2d = Nothing

      For Each acObjIdVert As ObjectId In acPoly2d

          acFirstVer = acTrans.GetObject(acObjIdVert, _

                                         OpenMode.ForRead)

          acPts3d.Add(acFirstVer.Position)

          Exit For

      Next

      '' Get the first point of the polyline and

      '' use the eleveation for the Z value

      Dim pFirstVer As Point3d = New Point3d(acFirstVer.Position.X, _

                                             acFirstVer.Position.Y, _

                                             acPoly2d.Elevation)

      '' Translate the OCS to WCS

      Dim mWPlane As Matrix3d = Matrix3d.WorldToPlane(acPoly2d.Normal)

      Dim pWCSPt As Point3d = pFirstVer.TransformBy(mWPlane)

      Application.ShowAlertDialog("The first vertex has the following " & _

                                  "coordinates:" & _

                                  vbLf & "OCS: " + pFirstVer.ToString() & _

                                  vbLf & "WCS: " + pWCSPt.ToString())

      '' Save the new objects to the database

      acTrans.Commit()

  End Using

End Sub

using Autodesk.AutoCAD.Runtime;

using Autodesk.AutoCAD.ApplicationServices;

using Autodesk.AutoCAD.DatabaseServices;

using Autodesk.AutoCAD.Geometry;

[CommandMethod("TranslateCoordinates")]

public static void TranslateCoordinates()

  // Get the current document and database, and start a transaction

  Document acDoc = Application.DocumentManager.MdiActiveDocument;

  Database acCurDb = acDoc.Database;

  using (Transaction acTrans = acCurDb.TransactionManager.StartTransaction())

      // Open the Block table record for read

      BlockTable acBlkTbl;

      acBlkTbl = acTrans.GetObject(acCurDb.BlockTableId,

                                   OpenMode.ForRead) as BlockTable;

      // Open the Block table record Model space for write

      BlockTableRecord acBlkTblRec;

      acBlkTblRec = acTrans.GetObject(acBlkTbl[BlockTableRecord.ModelSpace],

                                      OpenMode.ForWrite) as BlockTableRecord;

      // Create a 2D polyline with two segments (3 points)

      Polyline2d acPoly2d = new Polyline2d();

      // Add the new object to the block table record and the transaction

      acBlkTblRec.AppendEntity(acPoly2d);

      acTrans.AddNewlyCreatedDBObject(acPoly2d, true);

      // Before adding vertexes, the polyline must be in the drawing

      Point3dCollection acPts2dPoly = new Point3dCollection();

      acPts2dPoly.Add(new Point3d(1, 1, 0));

      acPts2dPoly.Add(new Point3d(1, 2, 0));

      acPts2dPoly.Add(new Point3d(2, 2, 0));

      acPts2dPoly.Add(new Point3d(3, 2, 0));

      acPts2dPoly.Add(new Point3d(4, 4, 0));

      foreach (Point3d acPt3d in acPts2dPoly)

          Vertex2d acVer2d = new Vertex2d(acPt3d, 0, 0, 0, 0);

          acPoly2d.AppendVertex(acVer2d);

          acTrans.AddNewlyCreatedDBObject(acVer2d, true);

      // Set the normal of the 2D polyline

      acPoly2d.Normal = new Vector3d(0, 1, 2);

      // Get the first coordinate of the 2D polyline

      Point3dCollection acPts3d = new Point3dCollection();

      Vertex2d acFirstVer = null;

      foreach (ObjectId acObjIdVert in acPoly2d)

          acFirstVer = acTrans.GetObject(acObjIdVert,

                                         OpenMode.ForRead) as Vertex2d;

          acPts3d.Add(acFirstVer.Position);

          break;

      // Get the first point of the polyline and

      // use the eleveation for the Z value

      Point3d pFirstVer = new Point3d(acFirstVer.Position.X,

                                      acFirstVer.Position.Y,

                                      acPoly2d.Elevation);

      // Translate the OCS to WCS

      Matrix3d mWPlane = Matrix3d.WorldToPlane(acPoly2d.Normal);

      Point3d pWCSPt = pFirstVer.TransformBy(mWPlane);

      Application.ShowAlertDialog("The first vertex has the following " +

                                  "coordinates:" +

                                  "\nOCS: " + pFirstVer.ToString() +

                                  "\nWCS: " + pWCSPt.ToString());

      // Save the new objects to the database

      acTrans.Commit();

VBA/ActiveX Code Reference