Freedom-of-Form-Foundation / anatomy3d

A CAD tool for humanoid anatomy alterations. See the anatomy3d-blender repository for more recent work.
https://freedomofform.org/1856/3d-anatomy-project-scope-phase-1-focus-on-a-limb-joint/
GNU General Public License v2.0
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Use a two-term expansion for small-perturbation quartic equations #29

Closed Lathreas closed 2 years ago

Lathreas commented 3 years ago

Currently the engine resolves numerical instability (precision errors due to dividing by a very small number) by disregarding the term in the equation that gives problems: the perturbation term. This is essentially a one-term perturbative expansion of the quartic equation. Although it resolves the numeric issues, it is not the most accurate approximation. For a better result, we should opt for using a two-term perturbative expansion, so that the perturbation term is included again (but this time without numeric instability).

See https://en.wikipedia.org/wiki/Perturbation_theory for more info.