You can ovulate without seeing a positive result (positive meaning two lines of equal color). The reason is that urine ovulation tests are usually used with the 2nd morning urine. However many women actually surge in the afternoon.

Follow this:

Day 1 am: Take the ovulation test and you see a light result line.
Day 2 am: Take the ovulation test and you see a light result line.

If you surged in the afternoon...you missed seeing a dark line.

Often, when women are being closely monitored for an IUI or other procedure they will be told to take 2 tests a day. One around 10 am and the other around 4pm. That is so they do not miss that afternoon surge result.

So yes, it is possible to ovulate and not see a positive result. It more than likely means you surged somewhere inbetween the 24 hour space of testing.