Finding Transformation matrix for aligning two entities

By Balaji Ramamoorthy

In AutoCAD API, entities are transformed (Moved / Rotated / Scaled) using transformation matrices.

Here is a sample code snippet that demonstrates aligning two entities (say two lines oriented in space) by finding the required transformation matrix.

Document activeDoc 
= Application.DocumentManager.MdiActiveDocument;
 
Database db = activeDoc.Database;
Editor ed = activeDoc.Editor;
 
PromptEntityResult per 
= ed.GetEntity
(
new PromptEntityOptions("Select an entity : ")
);
 
if (per.Status != PromptStatus.OK)
return;
ObjectId oid = per.ObjectId;
 
PromptPointResult ppr1 
= ed.GetPoint
(
new PromptPointOptions("Select src point 1")
);
 
if (ppr1.Status != PromptStatus.OK)
return;
Point3d sp1 = ppr1.Value;
 
PromptPointResult ppr2 
= ed.GetPoint
(
new PromptPointOptions("Select src point 2")
);
 
if (ppr2.Status != PromptStatus.OK)
return;
Point3d ep1 = ppr2.Value;
 
PromptPointResult ppr3 
= ed.GetPoint
(
new PromptPointOptions("Select dest point 1")
);
 
if (ppr3.Status != PromptStatus.OK)
return;
Point3d sp2 = ppr3.Value;
 
PromptPointResult ppr4 
= ed.GetPoint
(
new PromptPointOptions("Select dest point 2")
);
 
if (ppr4.Status != PromptStatus.OK)
return;
Point3d ep2 = ppr4.Value;
 
Matrix3d resMat = Matrix3d.Identity;
 
Matrix3d trans1 = Matrix3d.Displacement(sp2-sp1);
sp1 = sp1.TransformBy(trans1);
ep1 = ep1.TransformBy(trans1);
resMat = resMat.PreMultiplyBy(trans1);
 
// Rotation about Z axis
Vector3d dir1 = ep1 - sp1;
Vector3d dir2 = ep2 - sp2;
Plane xy = new Plane(Point3d.Origin, Vector3d.ZAxis);
Matrix3d trans2 
= Matrix3d.Rotation
(
dir2.AngleOnPlane(xy)-dir1.AngleOnPlane(xy),
Vector3d.ZAxis, 
sp1
);
sp1 = sp1.TransformBy(trans2);
ep1 = ep1.TransformBy(trans2);
resMat = resMat.PreMultiplyBy(trans2);
 
// Rotation about X axis
dir1 = ep1 - sp1;
dir2 = ep2 - sp2;
Plane yz = new Plane(Point3d.Origin, Vector3d.XAxis);
Matrix3d trans3 
= Matrix3d.Rotation
(
dir2.AngleOnPlane(yz)-dir1.AngleOnPlane(yz), 
Vector3d.XAxis, 
sp1
);
sp1 = sp1.TransformBy(trans3);
ep1 = ep1.TransformBy(trans3);
resMat = resMat.PreMultiplyBy(trans3);
 
// Rotation about Y axis
dir1 = ep1 - sp1;
dir2 = ep2 - sp2;
Plane xz = new Plane(Point3d.Origin, Vector3d.YAxis);
Matrix3d trans4 
= Matrix3d.Rotation
(
dir2.AngleOnPlane(yz)-dir1.AngleOnPlane(xz), 
Vector3d.YAxis, 
sp1
);
sp1 = sp1.TransformBy(trans4);
ep1 = ep1.TransformBy(trans4);
resMat = resMat.PreMultiplyBy(trans4);
 
// Scaling
dir1 = ep1 - sp1;
dir2 = ep2 - sp2;
Matrix3d trans5 
= Matrix3d.Scaling
(
dir2.Length / dir1.Length, 
sp1
);
sp1 = sp1.TransformBy(trans5);
ep1 = ep1.TransformBy(trans5);
resMat = resMat.PreMultiplyBy(trans5);
 
using (Transaction tr 
= db.TransactionManager.StartTransaction())
{
Entity ent = (Entity)tr.GetObject(oid, OpenMode.ForWrite);
ent.TransformBy(resMat);
tr.Commit();
}