Both sublime words, not used nearly enough.
Supplant comes from the Latin "sub" for "under" and "planta" for "the sole of the foot". Therefore, literally it means "under foot", but poetically, as we have seen from other Latin derivations, the preposition comes after the verb, so it means to put one's foot under another, and thereby thrown that person down by tripping them. I suppose you would only want to trip someone who was under foot. From "tripping" someone, it is only a moderate stretch through "to displace or substitute" to "to take by force". After all, as we remember from grade school, when we "trip" someone, it is usually intentionally.
My cat regularly supplants my need for sleep with her need for affection. Someday alternative energy will supplant our reliance on fossil fuels. Plaintiff's counsel's client's whining supplanted his good sense not to take the case. Since supplant involves an issue of perception about the tripping or substitution, it works with tangibles and intangibles.
Now, the real fun is how it differs from usurp. Usurp comes from the Latin "usus" for "a use" and "rapere" for "to seize", and therefore means "seize for use". Usurp, by the etymology of "to seize", is more violent than supplant which was just tripping, and therefore, usurp has the connotation of being "without right" while supplant is just accidental or negligent. So, the uncle usurped the throne from his brother. Standard usage. Or building the fence 1" onto his neighbor's property, which position was not noticed for 20 years, allowed him to usurp the land through adverse possession. Perhaps a little less standard, but still correct. Having swapped urine samples, he usurped his competitor's place on the team. Ok, enough of standard usage. If we talk business, the release of the new Microsoft OS was intended to usurp Apple's dominance in the market. While not technically an issue of "without right", it gives the spectre of being underhanded or dirty as if it were "without right" from not being fair. The water cooler gossip of her affair which led to her promotion usurped her authority. Eh. Perhaps undermined would be better here, but it is possible that the gossip did replace her authority, and not merely countermand it. The water cooler gossip of her affair usurped the good reputation she had developed for her charitable work. Better, but still not quite right. It is violent enough in that the gossip is invidious, but the element being taken still doesn't appear to lend itself to such seizure. Plaintiff's counsel's client's whining usurped his good sense not to take the case. Hmmm. If he were weak-willed that his client could seize control of his good sense, maybe. Ok, well, basically, taking usurp to an expanded usage, it needs to have the appearance of being "without right" or raised to the level of appearing to be "without right" and the element being taken needs to be susceptible to being taken. She would never usurp someone else's idea or work and pass it off as her own, although she was often jokingly accused of having read everyone's mind.
We endeavor not to supplant our own word meanings, and thereby, not to usurp correct usage.