add quat Lua library

doc/en/scripting/builtins/libmat4.md

@@ -4,19 +4,6 @@
 
 Most functions have several options for argument lists (overloads).
 
-## Data types
-
-Type conventions will be used on this page.
-- vector - an array of three or four numbers
-- vec3 - array of three numbers
-- vec4 - array of four numbers
-- quat - array of four numbers - quaternion
-- matrix - array of 16 numbers - matrix
-
-> [!WARNING]
->
-> Type annotations are part of the documentation and are not present in Lua.
-
 ## Identity matrix - *mat4.idt(...)*
 
 ```lua

doc/en/scripting/builtins/libquat.md

@@ -0,0 +1,34 @@
+# *quat* library
+
+Quaternions manipulation library.
+
+## Quaternion from matrix - *mat4.from_quat(...)*
+
+```lua
+-- creates a quaternion based on the rotation matrix
+quat.from_mat4(m: matrix)
+
+-- writes a quaternion from the rotation matrix to dst
+quat.from_mat4(m: matrix, dst: quat)
+```
+
+## Spherical linear interpolation - *quat.slerp(...)*
+
+The interpolation always take the short path and the rotation is performed at constant speed.
+
+```lua
+-- creates a quaternion as an interpolation between a and b,
+-- where t is interpolation factor
+quat.slerp(a: quat, b: quat, t: number)
+
+-- writes a quaternion as an interpolation between a and b to dst,
+-- where t is interpolation factor
+quat.slerp(a: quat, b: quat, t: number, dst: quat)
+```
+
+## Casting to string - *quat.tostring(...)*
+
+```lua
+-- returns a string representing the contents of the quaternion
+quat.tostring(q: quat)
+```