I wouldn't say that Eastern timber framing in general uses housings in the same way that western square rule does. Many times there seems to be an emphasis on stock preparation making reduction housings unnecessary. Anderson's Sumitsuke 1 seems to also refer to some use of mapping as well "While marking these, memos can be noted on the ezuita regarding irregularities in dimension, height variation, local adjustments, etc." What I don't know is how this changes over the various forms (Minka vs. temple carpentry for instance in Japan). I would love to hear from some people that specialize in Eastern practice such as Chris Hall or Jay on the usage or lack of usage of reduction housings in traditional Japanese framing.