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The matrix interpolation function `interp_m3_m3m3()` decomposes the matrices into rotation and scale matrices, converts the rotation matrices to quaternions, SLERPs the quaternions, and converts the result back to a matrix. Since quaternions cannot represent axis flips, this results in interpolation problems like described in T77154. Our interpolation function is based on "Matrix Animation and Polar Decomposition", by Ken Shoemake & Tom Duff. The paper states that it produces invalid results when there is an axis flip in the rotation matrix (or negative determinant, or negative scale, those all indicate the same thing). Their solution is to multiply the rotation matrix with `-I`, where `I` is the identity matrix. This is the same as element-wise multiplication with `-1.0f`. My proposed solution is to not only do that with the rotation matrix `R`, but also with the scale matrix `S`. This ensures that the decomposition of `A = R * S` remains valid, while also making it possible to conver the rotation component to a quaternion. There is still an issue when interpolating between matrices with different determinant. As the determinant represents the change in volume when that matrix is applied to an object, interpolating between a negative and a positive matrix will have to go through a zero determinant. In this case the volume collapses to zero. I don't see this as a big issue, though, as without this patch Blender would also produce invalid results anyway. Reviewed By: brecht, sergey Differential Revision: https://developer.blender.org/D8048
.. Keep this document short & concise, linking to external resources instead of including content in-line. See 'release/text/readme.html' for the end user read-me. Blender ======= Blender is the free and open source 3D creation suite. It supports the entirety of the 3D pipeline-modeling, rigging, animation, simulation, rendering, compositing, motion tracking and video editing. .. figure:: https://code.blender.org/wp-content/uploads/2018/12/springrg.jpg :scale: 50 % :align: center Project Pages ------------- - `Main Website <http://www.blender.org>`__ - `Reference Manual <https://docs.blender.org/manual/en/latest/index.html>`__ - `User Community <https://www.blender.org/community/>`__ Development ----------- - `Build Instructions <https://wiki.blender.org/wiki/Building_Blender>`__ - `Code Review & Bug Tracker <https://developer.blender.org>`__ - `Developer Forum <https://devtalk.blender.org>`__ - `Developer Documentation <https://wiki.blender.org>`__ License ------- Blender as a whole is licensed under the GNU Public License, Version 3. Individual files may have a different, but compatible license. See `blender.org/about/license <https://www.blender.org/about/license>`__ for details.