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434 Chapter 12: Animation
The parent space of the IK chain contains a rotation when
the IK solver is assigned.
Parent A contains a rotation of 90 degrees. This is
an abstract ion of the case when a user creates four
bones without an IK solver and later assig ns an IK
solver from Bone2 to Bone4. If we parent the chain
directly to world, it would appear as shown in the
right figure: the solver plane becomes horizontal.
• A: ParentSpaceisStartJoint. Thesphereis
mountedaftertherotationofAandtherefore
the “ hori zontal plane” coincides with the chain
planeasshownintheviewport. Thesingular
points are perpendicular to the Start Joint with
regard to the plane. When the goal/end effector
is moved on the plane, it will never hit the
singular points and flip.
• B: Parent Space is IK Goal. Again, we assume
that the parent space of the goal is the world.
The“horizontalplane”ofthespherebecomes
horizontal, as shown in the rig ht figure. The
singular points, the poles, are on the plane that
joints are laid out. Therefore, when users move
the goal/end effector left to right, or the other
around, the end effector wil l move across the
singular point and flip.
A problem of B is that the figure on the right is
never shown to the user. They have to envision it
in order to understand the flipping.
Example 3
This example describes what happened when Start
Joint is reassigned. Suppose we have an IK chain
of four bone nodes.
1. Bone01
2. Bone02
3. Bone03
4. Bone04
The Star t and End Joints are Bone01 and B one04,
respectively. Suppose the pose shown in the
figure is the preferred pose and Bone01 contains a
rotation. If we parent B one02 directly to the world,
the hierarchy from Bone02 will appear as in the
right figure.
When we reassign Start Joint to Bone02, the
Zero Plane Map sphere will be based on the
configuration on the right.
• A: Parent Space is Start Joint. In this case, the
sphere that is fixed to the right configuration is
to be parented to Bone01 together. This will
bethesameastheonebasedonBone01to
Bone04. Therefore, we get the same norma l
and chain stays stationary.
• B: Parent Space is IK Goal. In this case, the
sphere stays in the world while Bone02 is
parented to Bone01. When Bone04 is moved
towhereitisshownontheleftduetothe
transformation of Bone01, the observer who is
fixed to the sphere that is fixed to the world will