A C172 PLT HAS A CONFLICT WITH A LOW WINGED LIGHT ACFT IN THE TFC PATTERN AT 38Z; HI.

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I DEPARTED HNL ON WESTLOCH 3 DEP. SVCS WITH HNL DEP CTL WERE TERMINATED 3-4 MI SE OF THE WAIPATU SUGAR MILL. I SQUAWKED 1200 AND SWITCHED TO NPS FREQ 122.80. I ANNOUNCED INBOUND FOR LNDG APPROX 1-2 MI S OF THE WAIPATU SUGAR MILL; 1500 FT MSL; AS REQUIRED; BY STATE PUBLISHED 'HAWAII ARPTS AND FLYING SAFETY MANUAL;' WHEN INBOUND FOR RWY 22. NPS UNICOM TOLD ME TO 'RPT THE SUGAR MILL; ENTER R DOWNWIND FOR RWY 22; ONE IN THE PATTERN.' I RPTED PASSING OVER THE WAIPATU SUGAR MILL AT 1000 FT MSL AND SAID; 'CONFIRM ARE IN THE PATTERN?' NPS REPLIED; 'AFFIRMATIVE.' AS I GOT CLOSER; I INQUIRED ABOUT THE LOCATION OF THE OTHER AIRPLANE. NPS UNICOM SAID; 'THEY'RE ON A XWIND NOW.' I SCANNED FOR TFC OFF TO MY 12-1 O'CLOCK POS AND RPTED; 'I HAVE THE TFC.' IT WAS MY THOUGHT PROCESS AT THE TIME THAT I SHOULD MAKE A L 360 DEG TURN FOR SEPARATION. I WANTED TO GIVE THE OTHER AIRPLANE TIME TO TURN DOWNWIND AND PASS ME SO I COULD BE BEHIND; #2; AND KEEP THE TFC IN SIGHT. THEREFORE; I RPTED; 'I'M GOING TO MAKE A L 360 DEG TURN NOW FOR SEPARATION.' DURING MY TURN I DSNDED FROM 1000 FT MSL TO 800 FT MSL BECAUSE THE PATTERN ALT AT NPS IS 600 FT MSL AND I DIDN'T WANT TO HAVE TO DIVE DOWN ON THE DOWNWIND. AS I TURNED BACK TOWARDS NPS; I SAW AN AIRPLANE TO MY 3-4 O'CLOCK POS; SLIGHTLY LOWER; AND AT ABOUT 1/2 - 1 MI AWAY HEADED TOWARDS RWY 4. I HAD NO IDEA IT WAS THE SAME AIRPLANE I SAW ON A XWIND EARLIER. I ASSUMED THE AIRPLANE WAS GOING TO TURN FROM XWIND TO DOWNWIND BTWN THE NPS RWY AND THE PEARL CITY PENINSULA AS PUBLISHED IN THE 'MANUAL.' THE AIRPLANE STARTED A R 360 DEG TURN OF ITS OWN; AND I IMMEDIATELY TURNED L AND ENTERED A DOWNWIND FOR RWY 22. THE AIRPLANE ASKED NPS UNICOM; 'WHAT'S THAT CESSNA DOING?' I REPLIED 'I DID A L 360 DEG TURN FOR SEPARATION; AND I THOUGHT YOU WERE GOING TO KEEP YOUR PATTERN IN TIGHTER ON THE DOWNWIND.' THE AIRPLANE REPLIED; 'YOU ALMOST HIT US WHEN YOU TURNED BACK TOWARDS NPS.' IN RETHINKING THIS OCCURRENCE OVER AN HR; I REALIZED THAT I SHOULD'VE ASKED THE TYPE OF ACFT AND HORSEPWR OR SPD. I COULD'VE HAD BETTER JUDGEMENT ON WHETHER OR NOT I SHOULD'VE ENTERED THE DOWNWIND EARLIER. ALSO; BECAUSE MANY PLTS DON'T KEEP THE PROPER PATTERN; I SHOULDN'T HAVE ASSUMED OTHER AIRPLANES ARE WHERE THEY'RE SUPPOSED TO BE OR GO. IN ADDITION TO THE ABOVE; THE OTHER AIRPLANE DIDN'T MAKE DOWNWIND OR BASE LEG ANNOUNCEMENTS. SUGGESTIONS: 1) MAKE RPTS IN PATTERN. 2) LISTEN TO OTHERS MAKING RPTS; IE; L 360 DEGS FOR SEPARATION. 3) FLY THE PROPER PATTERN PLEASE.