1RTCQuaternionDecompositionE(m3b)ree Ray Tracing KernelRsTC3QuaternionDecomposition(3)
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5   NAME
6              RTCQuaternionDecomposition - structure that represents a quaternion
7                decomposition of an affine transformation
8
9   SYNOPSIS
10              struct RTCQuaternionDecomposition
11              {
12                float scale_x, scale_y, scale_z;
13                float skew_xy, skew_xz, skew_yz;
14                float shift_x, shift_y, shift_z;
15                float quaternion_r, quaternion_i, quaternion_j, quaternion_k;
16                float translation_x, translation_y, translation_z;
17              };
18
19   DESCRIPTION
20       The  struct RTCQuaternionDecomposition represents an affine transforma‐
21       tion  decomposed  into  three  parts.   An   upper   triangular   scal‐
22       ing/skew/shift matrix
23
24              $$   S  =  \left(  \begin{array}{cccc}  scale_x  &  skew_{xy}  &
25              skew_{xz} & shift_x \\ 0 & scale_y & skew_{yz} & shift_y \\ 0  &
26              0  &  scale_z & shift_z \\ 0 & 0 & 0 & 1 \\ \end{array} \right),
27              $$
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29       a translation matrix
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31              $$ T = \left( \begin{array}{cccc} 1 & 0 & 0 & translation_x \\ 0
32              &  1 & 0 & translation_y \\ 0 & 0 & 1 & translation_z \\ 0 & 0 &
33              0 & 1 \\ \end{array} \right), $$
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35       and a rotation matrix R, represented as a quaternion
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37       quaternion~r~ + quaternion~i~ i + quaternion~j~ i + quaternion~k~ k
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39       where i, j k are the imaginary quaternion units.  The passed quaternion
40       will be normalized internally.
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42       The affine transformation matrix corresponding to a RTCQuaternionDecom‐
43       position is TRS and a point p = (p~x~, p~y~, p~z~, 1)^T^ will be trans‐
44       formed as
45              p′ = T R S p.
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47       The  functions  rtcInitQuaternionDecomposition, rtcQuaternionDecomposi‐
48       tionSetQuaternion, rtcQuaternionDecompositionSetScale, rtcQuaternionDe‐
49       compositionSetSkew,  rtcQuaternionDecompositionSetShift, and rtcQuater‐
50       nionDecompositionSetTranslation allow to set the fields of  the  struc‐
51       ture more conveniently.
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53   EXIT STATUS
54       No error code is set by this function.
55
56   SEE ALSO
57       [rtcSetGeometryTransformQuaternion], [rtcInitQuaternionDecomposition]
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61                                                 RTCQuaternionDecomposition(3)