DA40 pilot reported a NMAC on short final after miscalculating headings for pattern entry and landing runway and then attempting to land in opposite direction of departing aircraft.

Narrative

How the problem arose; was discovered: Intending to land on Runway 08 via and extended base entry into the pattern; I instead made the wrong approach turn into the extended base so that when I turned into a short final I was heading the opposite way for a landing on Runway 26.At this point I was 300 to 400 feet AGL; half a mile from touch down; and could see no aircraft on the runway; so decided to continue with the landing. Shortly thereafter I looked up and saw an aircraft about 400 feet above me; at about a 45 degree slant. Then the pilot of the aircraft radioed if I had seen him to which I answered yes.How the problem could have been avoided in the first place: more careful planning and checking of headings leading to entry into the pattern.Corrective actions that should have been taken: As soon as the problem was discovered (when seeing the runway markings); I should have aborted the landing and gone into a climbing turn 90 degrees to the right to join the Runway 08 left downwind.