Lateen
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A lateen or latin-rig is a triangular sail set on a long yard mounted at an angle on the mast, and running in a fore-and-aft direction. The settee can be considered to be an associated type of the same overall category of sail.
Byzantine ship rigged with settee sail (miniature from c. 880)
Dhow with lateen sail in "bad tack" with the sail pressing against the mast, in Mozambique.
A large dhow with two settee sail rigs and a headsail.
The Bracera: a traditional lateen-rigged sailboat of the Mediterranean.
Crab claw sail
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The crab claw sail is a fore-and-aft triangular sail with spars along upper and lower edges. The crab claw sail was first developed by the Austronesian peoples by at least 2000 BCE. It is used in many traditional Austronesian cultures in Island Southeast Asia, Micronesia, Island Melanesia, Polynesia, and Madagascar. It is sometimes known as the Oceanic lateen or the Oceanic sprit, even though it is not restricted to Oceania, is neither a lateen sail nor a spritsail, and has an independent older origin.
1846 illustration of a Fijian camakau, a single-outrigger canoe with a canted mast "crane sprit"-type crab claw sail
Hokule'a in 2009, with crab claw sails where the upper spars also function as fixed masts
Crab claw sail being constructed for Hot Buoys trimaran. Notice pocket in right hand edge of sail to hold spar. Second spar in this particular configuration is not required since a bolt-rope holds the sail's upper edge and the mast is located in the back of the sailboat. Note lack of shaping.
"Crane sprit" type crab claw rig of the Philippines with a fixed mast