Solves #1013.
Previously, when screw-linearly interpolating two unit dual quaternions
that had an identical orientation, `try_sclerp` would return `None`, as
the operation would introduce a division-by-zero.
This PR splits out the cases where two unit dual quaternions have an
identical orientation from the cases where they have opposite
orientations. In the case where they have identical orientations, the
operation is well-defined, but the exponential parameterization could
not handle it without introducing NaNs. Therefore, the function detects
this case and simply defaults to linearly interpolating the
translational components and using one of the two inputs' rotation
components.
The case where the inputs have opposite rotations is now detected
separately using the dot product of the real (rotation) parts, which was
already being computed anyway.
Also introduces proptests for these specific scenarios, to avoid any
regression.
Replace the verbose derived (or nearly equivalent) Debug impls for
several newtypes with explicit impls that forward to the inner type,
making readable diagnostics logging much easier.
There is a custom compiler error, hinting that the "debug", "compare"
and "rand" feature are required for compiling and running the tests.
However, this error was not displayed when running `cargo test` due to
other compilation errors taking precedence.
This is now avoided by just not compiling the integration tests when the
necessary features are not enabled.
The previous implementation was correct only for real elements. The
Cholesky decomposition is `L L^H`, so the determinant is `det(L) *
det(L^H)`. Since `L` is a triangular matrix, `det(L)` is the product
of the diagonal elements of `L`. Since `L^H` is triangular and its
diagonal elements are the conjugates of the diagonal elements of `L`,
`det(L^H)` is the conjugate of `det(L)`. So, the overall determinant
is the product of the diagonal elements of `L` times its conjugate.
Terence
Sébastien Crozet
Mateusz Kowalczyk
Benjamin Saunders
Violeta Hernández
nathan.eckert
Violeta Hernández
Andreas Longva
Vinzent Steinberg
Jim Turner
Christopher Rabotin
Remco Bloemen
russellb23