A sharp interface model is developed to allow rapid discovery of exactly compatible or averagely compatible laminate twin patterns in a cubic-orthorhombic shape memory alloy system. Given an imposed strain state, the method finds a corresponding exactly compatible twin structure if one exists; otherwise, the method produces an averagely compatible solution. Two cases are considered: The first case allows austenite and martensite phases to be arbitrarily mixed. The second is an essentially fla...