Hello,
I posted this message before,
but did not receive an answer. However, I was able to figure out this
myself. I'm posting my solution for others.
Task:
Determine the new location of a
point within a Transform group after the Transform group is
rotated.
example: Several
Cylinders are pickable - the program needs to know where the TOP of the
cylinders are located at any time after the user has rotated them
separately. (The transformgroup's center is the center of the
cylinder. The TOP is (0,cylinder_length/2,0) away from the
center.)
Solution:
You need to get information on
how the group was rotated. The transform group's rotation is stored in the
upper 3x3 section of a Matrix4d located in the Transform3d.
If one creates an AxisAngle4d
and uses .set(the_transfrom3d_Matrix4d), then the AxisAngle will have the x, y,
z components of a vector and an angle stored in it. This describes the
rotation from the original position of the transform group.
For instance, if one was to
rotate a cylinder 90 degrees clockwise, then they are essentially rotating -90
degrees about the vector (0,0,1) -the z-axis. The negative appears because
of the right hand rule dictating the angle is to be incremented in
counter-clockwise rotation.
Another way to look at it is
rotation +90 about the vector (0,0,-1).
This seems simple, but try
picturing an oddball rotation. The vector to describe the rotation would
have to be such that the cylinder would be perpendicular to it throughout the
rotation. So you could get some funky vectors back from you
AxisAngle4d.
The hard part is making the
vector mean something to you. The way it is done is as
follows:
The Smack-it-up-flip-it
Method:
Rotate the vector
counter-clockwise about the y-axis until the vector is in the y-z plane.
This requires some trigonometry to determine the angle between the original
vector and the y-z plane. The resulting equation is most easily written in
the form of a matrix-so you'll need a Matrix4d to store the rotation
information. (write me if you want the matrices involved). Note that
you are using the VECTORs x, y, z in these rotations. The coordinates of
interest are not factored in until you're done smacking and
flipping.
Next, rotate the vector around
the x-axis counter-clockwise until the vector lies on the +z axis. Once
again, use some trig. to determine the angle between the original vector and the
+z axis.
Now you can rotate around the
z-axis using the AxisAngle's angle returned.
To finish up, you rotate back
off the Z axis, and then rotate back to the original vector direction
(basically, reverse the process).
After doing this, you should
have a matrix for the y rotation, x rotation, z rotation, other y rotation, and
other x rotation. You now multiply the original coordinates (relative to
the center of the Transform) by the product of all those matrices and you have
the new coordinates position. (To multiply a matrix, you use
matrix1.mul(matrix2) ).
These coordinates are relative
to the center of the object (cylinder), to figure out where they are in the
scene, just add them to the objects center coordinates. This is actually
called a translation.
For a picture of what I just
said, go to http://graphics.cs.ucdavis.edu/GraphicsNotes/Rotation/Rotation.html
If anyone knows of a method I
missed that already performs this, let me know!!!
Thanks,
Sean
