Does Trinisphere affect spells that have been reduced to zero mana by other effects?

Trinisphere's ability reads: 'As long as Trinisphere is untapped, each spell that would cost less than three mana to cast costs three mana to cast.' This is a cost-setting effect that establishes a minimum total cost of three generic mana for any spell, regardless of other reductions.

The order of cost modifications matters here. Under CR 601.2f and CR 601.2e, you first apply cost increases, then apply cost reductions, and then apply Trinisphere's floor effect. So even after all discounts are applied, if the resulting total is less than three mana, Trinisphere raises it back up to exactly three generic mana (CR 601.2f).

This means effects like Affinity, Convoke, Delve, or other cost-reduction abilities cannot bring a spell below three total mana while Trinisphere is untapped. The same applies to spells with a natural cost of zero, such as Ornithopter or Mox Opal — they still cost three mana to cast.

Example: You control Trinisphere and cast Ornithopter, which normally costs {0}. After applying all reductions (none in this case), the cost is {0} — less than three — so Trinisphere's effect raises the cost to {3}. You must pay three generic mana to cast Ornithopter.

Note that Trinisphere only sets a floor on the mana cost portion; additional costs like targeting or sacrifice requirements are unaffected. Also, if Trinisphere is tapped, its ability does not apply.