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Fitting Hastie's principal surfaces in R

What are the operational requirements for satisfaction with this assignment? I wonder if a regression "surface" of some other sort would be sufficient?  Assuming the three dimensions are X,Y, Z, then a loess (or locfit) "surface" or a regression estimate that used a spline surface for  Z ~ X+Y would not be a principal surface, but should satisfy some of your other requirements. This question would become clearer if you would offer data for analysis (the lack of which is one reason that duplicates of this question were closed as off-topic at both CrossValidated.com and StackOverflow.)
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David Winsemius
Alameda, CA, USA