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Like it's predecessor, CPA, Jade uses a C-like proprietary scripting language for implementing game, object and world specific behaviours.
This language appears to be only typically used for development purposes, and instead as when a title is shipped, the scripting language will usually be converted into C/C++ and compiled natively for the target platform for better performance.
A basic guide on getting started with scripting in Jade is available here.
 TODO: List all the functions of the language
With some of these, if you have an object variable, you can preface the function with @objectVariable to specify what the function is for.
OBJ_Me() : A reference to the object the script is attached to.
OBJ_PosGet() : Returns a vector of the position of an object
OBJ_PosSet(VECTOR) : Sets object position to vector
OBJ_RotateLocalZ(FLOAT): Rotates an object locally around the z axis
OBJ_RotateLocalX(FLOAT): Rotates an object locally around the x axis
OBJ_RotateLocalY(FLOAT): Rotates an object locally around the y axis
OBJ_FlagInvisibleSet(INT): Disables the AI of an object with hiding it
OBJ_FlagInactiveSet(INT): Disables the AI of an object without hiding it
OBJ_FlagsIdentityTest(INT) : returns int
OBJ_SightGet(): Returns vector of forward vector of the object
OBJ_Duplicate(VECTOR) : Duplicates current object to location (?)
OBJ_Rotate_FromTo(VECTOR, VECTOR) : Rotates an object from one rotation to another.
OBJ_Destroy(): Destroys object
OBJ_MorphProgSet(INT, FLOAT) : Determines the current frame of a shapekey/morph animation
OBJ_SqrDist(OBJECT) : returns float, also gets the distance between objects?
 TODO: List all the functions of the language
 TODO: Explain the basic concepts of the language
 TODO: Explain the syntax of the language
 TODO: List all the keywords of the language
 TODO: List all the conditions of the language