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MrPedanticI would call "based on" a dangler, here:Is that dangling modification considered as natural, as 'speaking of X' or 'considering X'? Or do you think it should be consiered as grammatically undesirable, or even wrong?
Grammar GeekTo avoid the ambuiguity, rephrase slightly and get rid of "based on": Using the picture as a guide, they rebuilt ...GG, how would you rephrase the passive version 'The temple was rebuilt' with the phrase 'the picture as a guide'?