This is the complete list of Lua APIs for Corona. If you're looking to extend Corona beyond the functionality provided by these Lua APIs, please see the Corona Native documentation.
If you're new, download Corona and proceed to the Getting Started series. There are also numerous guides on specific topics.
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display.safeActualContentHeight
display.safeActualContentWidth
physics.getAverageCollisionPositions()
physics.getDebugErrorsEnabled()
physics.getReportCollisionsInContentCoordinates()
physics.setAverageCollisionPositions()
physics.setDebugErrorsEnabled()
physics.setPositionIterations()
physics.setReportCollisionsInContentCoordinates()