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| %=======================================================================% | ||
| % [Euler] intrinsic (relative) transformation (z-y'-z") | ||
| %=======================================================================% | ||
| \newcommand{\tdsetzyzrel}{ | ||
| \renewcommand{\tdplotcalctransformrotmain}{ | ||
| %-----------------------------------------------------------------------% | ||
| % calculate sin and cos from all angles | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotsinandcos{\sa}{\ca}{\tdplotalpha} | ||
| \tdplotsinandcos{\sb}{\cb}{\tdplotbeta} | ||
| \tdplotsinandcos{\sg}{\cg}{\tdplotgamma} | ||
| %-----------------------------------------------------------------------% | ||
| % calculate all possible multiplications of sin/cos in a,b,g | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sasb}{\sa}{\sb} | ||
| \tdplotmult{\sacb}{\sa}{\cb} | ||
| \tdplotmult{\casb}{\ca}{\sb} | ||
| \tdplotmult{\cacb}{\ca}{\cb} | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sasg}{\sa}{\sg} | ||
| \tdplotmult{\sacg}{\sa}{\cg} | ||
| \tdplotmult{\casg}{\ca}{\sg} | ||
| \tdplotmult{\cacg}{\ca}{\cg} | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sbsg}{\sb}{\sg} | ||
| \tdplotmult{\sbcg}{\sb}{\cg} | ||
| \tdplotmult{\cbsg}{\cb}{\sg} | ||
| \tdplotmult{\cbcg}{\cb}{\cg} | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sasbsg}{\sasb}{\sg} | ||
| \tdplotmult{\sasbcg}{\sasb}{\cg} | ||
| \tdplotmult{\sacbsg}{\sacb}{\sg} | ||
| \tdplotmult{\sacbcg}{\sacb}{\cg} | ||
| \tdplotmult{\casbsg}{\casb}{\sg} | ||
| \tdplotmult{\casbcg}{\casb}{\cg} | ||
| \tdplotmult{\cacbsg}{\cacb}{\sg} | ||
| \tdplotmult{\cacbcg}{\cacb}{\cg} | ||
| %-----------------------------------------------------------------------% | ||
| % define rotation matrix according to z-y'-z"-convention | ||
| % source: https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix | ||
| %-----------------------------------------------------------------------% | ||
| \pgfmathsetmacro{\raaeul}{\cacbcg - \sasg} | ||
| \pgfmathsetmacro{\rabeul}{-\sacg - \cacbsg} | ||
| \pgfmathsetmacro{\raceul}{\casb} | ||
| \pgfmathsetmacro{\rbaeul}{\casg + \sacbcg} | ||
| \pgfmathsetmacro{\rbbeul}{\cacg - \sacbsg} | ||
| \pgfmathsetmacro{\rbceul}{\sasb} | ||
| \pgfmathsetmacro{\rcaeul}{-\sbcg} | ||
| \pgfmathsetmacro{\rcbeul}{\sbsg} | ||
| \pgfmathsetmacro{\rcceul}{\cb} | ||
| %-----------------------------------------------------------------------% | ||
| }} | ||
|
|
||
| %=======================================================================% | ||
| % [Euler] extrinsic (absolute) transformation (z-y-z) | ||
| %=======================================================================% | ||
| \newcommand{\tdsetzyzabs}{ | ||
| \renewcommand{\tdplotcalctransformrotmain}{ | ||
| %-----------------------------------------------------------------------% | ||
| % calculate sin and cos from all angles | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotsinandcos{\sa}{\ca}{\tdplotalpha} | ||
| \tdplotsinandcos{\sb}{\cb}{\tdplotbeta} | ||
| \tdplotsinandcos{\sg}{\cg}{\tdplotgamma} | ||
| %-----------------------------------------------------------------------% | ||
| % calculate all possible multiplications of sin/cos in a,b,g | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sasb}{\sa}{\sb} | ||
| \tdplotmult{\sacb}{\sa}{\cb} | ||
| \tdplotmult{\casb}{\ca}{\sb} | ||
| \tdplotmult{\cacb}{\ca}{\cb} | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sasg}{\sa}{\sg} | ||
| \tdplotmult{\sacg}{\sa}{\cg} | ||
| \tdplotmult{\casg}{\ca}{\sg} | ||
| \tdplotmult{\cacg}{\ca}{\cg} | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sbsg}{\sb}{\sg} | ||
| \tdplotmult{\sbcg}{\sb}{\cg} | ||
| \tdplotmult{\cbsg}{\cb}{\sg} | ||
| \tdplotmult{\cbcg}{\cb}{\cg} | ||
| %-----------------------------------------------------------------------% | ||
| \tdplotmult{\sasbsg}{\sasb}{\sg} | ||
| \tdplotmult{\sasbcg}{\sasb}{\cg} | ||
| \tdplotmult{\sacbsg}{\sacb}{\sg} | ||
| \tdplotmult{\sacbcg}{\sacb}{\cg} | ||
| \tdplotmult{\casbsg}{\casb}{\sg} | ||
| \tdplotmult{\casbcg}{\casb}{\cg} | ||
| \tdplotmult{\cacbsg}{\cacb}{\sg} | ||
| \tdplotmult{\cacbcg}{\cacb}{\cg} | ||
| %-----------------------------------------------------------------------% | ||
| % define rotation matrix according to z-y-z-convention | ||
| % extrinsic matrix = intrinsic matrix transposed and with negative angles | ||
| %-----------------------------------------------------------------------% | ||
| \pgfmathsetmacro{\raaeul}{\cacbcg - \sasg} | ||
| \pgfmathsetmacro{\rabeul}{-\casg - \sacbcg} | ||
| \pgfmathsetmacro{\raceul}{\sbcg} | ||
| \pgfmathsetmacro{\rbaeul}{\sacg + \cacbsg} | ||
| \pgfmathsetmacro{\rbbeul}{\cacg - \sacbsg} | ||
| \pgfmathsetmacro{\rbceul}{\sbsg} | ||
| \pgfmathsetmacro{\rcaeul}{-\casb} | ||
| \pgfmathsetmacro{\rcbeul}{\sasb} | ||
| \pgfmathsetmacro{\rcceul}{\cb} | ||
| %-----------------------------------------------------------------------% | ||
| }} |