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## Computing Euler angles from a rotation matrix on SO(3) ##
rot2eul <- function(X) {
v1 <- numeric(3)
v2 <- numeric(3)
x1.13 <- asin( X[3, 1] )
x2.13 <- pi - x1.13
x1.23 <- atan2( X[3, 2] / cos(x1.13), X[3, 3] / cos(x1.13) )
x2.23 <- atan2( X[3, 2] / cos(x2.13), X[3, 3] / cos(x2.13) )
x1.12 <- atan2( X[2, 1] / cos(x1.13), X[1, 1] / cos(x1.13) )
x2.12 <- atan2( X[2, 1] / cos(x2.13), X[1, 1] / cos(x2.13) )
v1 <- c( x1.13, x1.23, x1.12 )
v2 <- c( x2.13, x2.23, x2.12 )
list( v1 = v1, v2 = v2 )
}
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