2 I suspect that the name bind pose arises because designers attach or bind the

# 2 i suspect that the name bind pose arises because

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2 I suspect that the name “bind pose” arises because designers attach or “bind” the skin to the model relative to this initial pose. Lecture 9 2 Spring 2018 CMSC 425 Dave Mount & Roger Eastman 30 (a) (c) j 0 j 2 j 3 j 4 j 5 j 1 j 0 j 2 j 3 j 4 j 1 j 5 j 0 j 1 j 2 j 3 j 4 j 5 (b)Fig. 2: (a) Skeletal model, (b) inverted tree structure, and (c) rotating a frame propagates to thedescendants.coordinate frames,FandG(see Fig. 3). LetF.o,F.x, andF.ydenoteF’s origin point, andits two basis vectors. DefineG.o,G.xandG.ysimilarly. Lecture 9 3 Spring 2018 CMSC 425 Dave Mount & Roger Eastman G.x [ F ] , G.y [ F ] , and G.o [ F ] : T [ F G ] = 2 - 1 4 1 2 2 0 0 1 . Conversely, to convert the other direction, define T G F to be the transformation that maps a point given in F ’s coordinate system to its representation in G ’s coordinate system. This transformation can be represented as a matrix whose columns are F.x [ G ] , F.y [ G ] , and F.o [ G ] : T [ G F ] = 2 / 5 1 / 5 - 2 - 1 / 5 2 / 5 0 0 0 1 . (See any standard reference on linear algebra for a proof.) Change-of-Coordinates Example: To test this, let’s consider the point p and vector ~v in Fig. 4. G F o x y o x y G F o x y o x y p [ F ] = (1 , 3 , 1) ~v [ F ] = (3 , - 1 , 0) p p ~v ~v p [ G ] = ( - 1 , 1 , 1) ~v [ G ] = (1 , - 1 , 0) Fig. 4: Example of applying the change-of-coordinates transformation. Clearly, p [ F ] = (1 , 3 , 1) and p [ G ] = ( - 1 , 1 , 1). Applying the above transformations, we obtain the expected results T [ F G ] · p [ G ] = 2 - 1 4 1 2 2 0 0 1 - 1 1 1 = 1 3 1 = p [ F ] , and T [ G F ] · p [ F ] = 2 / 5 1 / 5 - 2 - 1 / 5 2 / 5 0 0 0 1 1 3 1 = - 1 1 1 = p [ G ] , Next, consider ~v . We have ~v [ F ] = (3 , - 1 , 0) and ~v [ G ] = (1 , - 1 , 0). Again, applying the above transformations, we have T [ F G ] · ~v [ G ] = 2 - 1 4 1 2 2 0 0 1 1 - 1 0 = 3 - 1 0 = ~v [ F ] , and T [ G F ] · ~v [ F ] = 2 / 5 1 / 5 - 2 - 1 / 5 2 / 5 0 0 0 1 3 - 1 0 = 1 - 1 0 = ~v [ G ] .  • • • 