First of all, thanks to Carl and Niklas for thier hints and help.
I ended up with the following approach. (Which seems to work in all the
test data I can find.)
The folloing code/math/hidden errors is/are GPL. Use/abuse as you feel the need.
This started out as the "Arrow" class I found on j3d.org. If the author of
that class wants to use it and post an uppdate on j3d.org, feel free. :)
Also, I realize that it should throw an illegal argument exception instead of
returning identity, but it works.
/**
* creates a rotation/translation suitable for placing an object between
* two points with its "top" and "bottom" oriented twards the first and
* second points respectively.
**/
public static void getTwoPointTransform(Tuple3d stPt,
Tuple3d endPt,
Transform3D transform) {
if(stPt.equals(endPt)) {
transform.setIdentity();
return;
}
Vector3d unitVect = new Vector3d((endPt.x - stPt.x),
(endPt.y - stPt.y),
(endPt.z - stPt.z));
unitVect.normalize();
// find rotation about X axis
double angle_x = Math.acos( unitVect.y );
// find rotation about Y axis
double angle_y = Math.PI/2.0;
if(unitVect.z != 0.0) {
angle_y = Math.atan( unitVect.x/unitVect.z );
}
if(unitVect.z <= 0) {
angle_y += Math.PI;
}
// determine the transform matrix for X.Y axis rotation
// and translation to the midpoint of the line segment.
Matrix4d rotMat = new Matrix4d();
double A = Math.cos(angle_x);
double B = Math.sin(angle_x);
double C = Math.cos(angle_y);
double D = Math.sin(angle_y);
rotMat.m00 = C;
rotMat.m01 = B*D;
rotMat.m02 = A*D;
rotMat.m03 = stPt.x + (endPt.x - stPt.x)/2.0f;
rotMat.m10 = 0.;
rotMat.m11 = A;
rotMat.m12 = -B;
rotMat.m13 = stPt.y + (endPt.y - stPt.y)/2.0f;
rotMat.m20 = -D;
rotMat.m21 = B*C;
rotMat.m22 = A*C;
rotMat.m23 = stPt.z + (endPt.z - stPt.z)/2.0f;
rotMat.m30 = 0.;
rotMat.m31 = 0.;
rotMat.m32 = 0.;
rotMat.m33 = 1.;
transform.set(rotMat);
}
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