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- THE PROBLEM OF THE TANGENT OF THE BLINES UNDER BONE INFLUENCE
- =============================================================
- Tangents are relative to vertices in any of its definitions (radius, angle)
- or (x,y). As the transformation performed by bones is prepaed to work on
- global coordinates vertices, the tangent transformation can not be directly
- transformed by bones in that way.
- There are some solutions to solve that:
- 1) The solution that Anime Studio gives to the tangents: It doesn't
- have real tangents but calculated ones based on the neighbour vertices
- position and a parameter called 'curvature'.
- 2) As well the tangents are relative to the vertex it belongs to, we
- need to convert the tangent to global coordinates, transform it by the
- bone(s) influence and then convert it to local coordinates again.
- 1) PROPOSAL FOR TANGENTS 'CALCULATED' BASED ON NEIGBOUR VERTICES
- ================================================================
- param convert type value type
- ----- ------------ ----------
- Tangent AverageTangent Vector
- Current BoneInfluence Vector
- Next BoneInfluence Vector
- Previous BoneInfluence Vector
- Link Vector Vector
- 'Current' is the current vertex in the bline (where the tangent lies) it is not a parameter
- 'Next' is the next vertex in the bline relative to Current
- 'Previous' it is the previous vertex in the bline relative to Current.
- Resulting Tangent (radius, angle) is defined by:
- Let's call: V=Current-(Next+Previous)*0.5
- Let's call: V0=Current.Link-(Next.Link+Previous.Link)*0.5
- Radius:
- radius = Link.radius
- Angle:
- angle=atan2(V.x,V.y) - (atan2(V0.x,V0.y)-Link.angle)
- When the user manipulates the tangent duck it modifies Link as an offset.
- Problems:
- -Insert a vertex
- -Vertex "on", "off"
- 2) PROPOSAL FOR TANGENTS IN GLOBAL COORDINATES
- ==============================================
- Given a vertex V and a tangent T and a transformed position of the vertex
- after bone influence V', calculate the transformed position of the tangent.
- global position of the tangent:
- TG=V+T
- TG'=V'+T'
- T'=TG'-V' = (V+T)' -V' where ' means tranformed by bones.
- param convert type value type
- ----- ------------ ----------
- Tangent BoneTangent Vector
- Bone Weight List List Static List
- Link (T) Vector
- Vertex (V) Vector
- It is reasonable that the Bone Weight List is the same for both parameters.
- When user manipulates the tangent duck it modifies the parameter T.
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