Quaternion Rotation Output from RBF Solvers

Feb 21, 2020

In my previous post, I described how driving an RBF solver with quaternion values for rotational inputs is more reliable than driving with euler inputs. In this post, I will describe a method to output rotational values from an RBF solver.
As described in my last post, euler rotations suffer from gimbal lock and multiple solutions to the same rotation. If we were to solve directly to these euler angles, we would see a lot of undesirable flipping depending on the sample inputs.

Quaternion Rotation Input to RBF Solvers

Feb 3, 2020

In my previous post, I described how to create an RBF solver using regularized linear regression. While the solver works well for most independent input values, it does not work so well if we want to drive it with euler rotations. Euler rotations are susceptible to gimbal lock and can have multiple solutions for the same rotation.
These two joints look like they have the same rotation. But looking at their animation curves tells a different story:

Regularized Linear Regression with Radial Basis Functions

Feb 2, 2020

RBF solvers are systems used to interpolate from values in one space to another set of values in another space. Basically a set driven key with arbitrary inputs and arbitrary outputs. This has many applications such as driving corrective shapes, retargeting meshes, or training systems in machine learning to predict values based on a set of known samples.
There are several demo implementations and explanations of RBF solvers scattered around the internet:

Swing Twist Decomposition to Offset Parent Matrix

Jan 25, 2020

Decomposing a rotation into separate swing and twist components has many useful applications. Maya's pose interpolator toolset allows shapes to be driven with isolated twist and/or swing components of rotations. This allows a corrective shape in the pectorals driven by the raising of the arm to be independent from the twist motion of the arm. Also, the twist component can be used to drive twist joints more reliably than the euler twist axis by itself, as demonstrated in the video below.

Trig Functions in Maya without Third-Party Plug-ins

Jan 7, 2020

By default Maya does not ship with any nodes to calculate trig functions. If you want to use a plug-in, you can use the great plug-in Maya Math Nodes written by Serguei Kalentchouk. If you want or have to use default Maya, there is still hope. I recently added trig function support to dge, my library that converts string math equations to Maya node networks. Using math and trig knowledge, we can recreate these functions with the nodes that come with Maya.

Space Switch Using Offset Parent Matrix

Jan 1, 2020

Maya 2020 introduced the offsetParentMatrix attributes to transform nodes. This attribute allows transforms to be driven directly with a matrix and can cut down the number of nodes and connections in your set ups. In this post I'll show how to set up space switching using the offsetParentMatrix attribute instead of constraints and extra transform nodes.
A parent-child relationship is a simple matrix multiplication and can be replicated with a multMatrix node: