Hierarchy of ellipses

Characters in Ecstatica are described as a hierarchy of "parts" (that's what they are called in Ecstatica). Just like a skeleton in more recent titles. For the matter of simplicity, let's assume at this point that every part corresponds to an ellipse. The size and location of these ellipses are described by a couple of properties (which every part possesses):

  1. A local coordinate system for the part, described by 3 euler angles and an origin vector (given in the coordinate system of the part's parent).
  2. The centre of the ellipse as well as the 3 halfaxes of the ellipse, both given in the part's local coordinate system
  3. The origin of a part's local coordinate system is not specified directly but it is given relative to the centre of the part's ellipse. In Figure 1 this vector is called "offset".
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