tMatrixDC_SM <- function(a, b=NULL){
# Direction cosines method
# a is global coordinate system unit vectors, b is local coordinate system unit vectors
# The transformation matrix returned will transform points in the b coordinate system to the a coordinate system
# IF B IS NULL USE IDENTITY MATRIX AS LOCAL COORDINATE SYSTEM
if(is.null(b)) b <- diag(nrow(a))
r <- matrix(NA, 3, 3)
r[1, ] <- c(sum(a[1,]*b[1,]), sum(a[2,]*b[1,]), sum(a[3,]*b[1,]))
r[2, ] <- c(sum(a[1,]*b[2,]), sum(a[2,]*b[2,]), sum(a[3,]*b[2,]))
r[3, ] <- c(sum(a[1,]*b[3,]), sum(a[2,]*b[3,]), sum(a[3,]*b[3,]))
return(r)
}
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