Wondering how you can get a mirroring plane from a matrix passed into transformBy( ) during a MIRROR command?

Here I present one way to calculate a mirroring plane from a matrix passed into transformBy( ) during a MIRROR command. This is done using vector algebra.

if [M] is a transformation matrix passed in during a mirroring operation, then the mirror of an arbitrary point P will be [M]P.

We know that a mirroring plane is midway between the point P and its mirror [M]P,

so any point on the mirroring plane = ( 1/2) .(P+ [ M ]P ). This by the way is the same as a vector P projected on this plane.

This can also be written as:

Point on mirroring plane = ( 1/2) .([I]P+ [ M ]P)

Or

Point on mirroring plane = ( 1/2) .([I]+ [ M ]) x P

Here [ I ] is the identity matrix.

So the transformation matrix applied to find the projection on this plane is ( 1/2) .( [ I ] + [ M ] ). You may then take two arbitrary vectors to find projections on this plane - so you have 2 coplanar vectors. You may then find the cross product of these two to find a vector normal to them. You then take an origin, say (0,0,0) and transform with the above transformation matrix to find a point on this plane.

So now you have a point on the mirroring plane and a vector normal to it. With these you can construct a mirroring plane. The code below shows how to do this.

xform is the transformation matrix passed into transformBy during a mirroring operation (you can do this with an editor reactor checking to see when "MIRROR" happens)

AcGePoint3d origin(0,0,0);

AcGeVector3d normal, Axis1, Axis2, Axis3,

XAxis(1,0,0), YAxis(0,1,0), ZAxis(0,0,1);

AcGeMatrix3d Identity, Temp;

AcGePlane MirrorPlane;

AcGeMatrix3d Mirror;

Identity.setToIdentity();

for(int i=0; i<4; i++) {

for(int j=0; j<4; j++) {

Temp(i,j) = 0.5*(Identity(i,j) + xform(i,j));

}

}

Axis1 = (XAxis.transformBy(Temp)).normalize();

Axis2 = (YAxis.transformBy(Temp)).normalize();

Axis3 = (ZAxis.transformBy(Temp)).normalize();

origin = origin.transformBy(Temp);

// Choose two vectors out of the three Axis1,

// Axis2 and Axis3 to find the cross product.

// Make sure that the two selected vectors are of

// unit length and are not parallel

if (Axis1.length() == 1 && Axis2.length() == 1 &&

fabs(Axis1.dotProduct(Axis2)) != 1) {

normal = (Axis1.crossProduct(Axis2)).normalize();

} else if (Axis2.length() == 1 && Axis3.length() == 1 &&

fabs(Axis2.dotProduct(Axis3)) != 1) {

normal = (Axis2.crossProduct(Axis3)).normalize();

} else if (Axis3.length() == 1 && Axis1.length() == 1 &&

fabs(Axis3.dotProduct(Axis1)) != 1) {

normal = (Axis3.crossProduct(Axis1)).normalize();

}

MirrorPlane.set(origin, normal); // This is the mirroring plane