Transformation Constraints Using Approximate Spherical Regression

Journal of Computer Graphics Techniques (JCGT), vol. 11, no. 3, pp.1-22, 2022.

Authors: Tomohiko Mukai

Link: Journal of Computer Graphics Techniques (open access) , Maya 2020 Implementation (GitHub)

Abstract: Transformation constraint is a standard tool to control a transformation of a 3D object according to the other transformations. For example, a character rig in realtime applications is often built using the transformation constraints to control many skeletal joints with fewer handles simultaneously. However, conventional example-based methods suffer from artifacts such as flipping due to the complexity of 3D transformation, especially for rotation-rotation constraints. We propose an approximate regression scheme for data-driven transformation constraints. Our method uses a spherical basis function interpolation technique whose computations are linearly approximated in Lie algebra. The nonlinearities and ambiguities in 3D transformation spaces are handled with several extensions such as automated example duplication and regression weight constraints. Our approximate regression scheme provides smooth and predictable interlocking control among multiple transformations in realtime.

Acknowledgements: We thank PlatinumGames Inc. for providing valuable suggestions and experimental assets. This work was supported by Grant-in-Aid for Research from the Faculty of Systems Design, Tokyo Metropolitan University, and JSPS KAKENHI Grant Number 18K11607, 19H04231, and 21K2193.

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