Some vector functions useful for working with rotations (#9572)

* added vector.rotate

* added vector.forward_from_rotation and vector.up_from_rotation

* added vector.forward_up_to_rotatiton

* fixed some bugs and formatting with vector functions

* shortened name of some new vector functions and added documentation

* made vector.rotate not require a unit vector as axis

* fixed crash with vector.forward_up_to_rot

* renamed new vector functions, made vector.rotate apply a rotation matrix, old vector.rotate is now called vector.rotate_around_axis

* documented vector function changes

* removed some whitespace to appease luacheck

* implemented and fixed optimization of vector.rotate_around_axis by SmallJoker

* added some unit tests for rotation vector functions

* clarified that rotation vectors are in radians and according to the left hand rule

* hopefully appeased luacheck

* renamed rotation_to_horizontal to forward_at_rotation, rotation_to_vertical to up_at_rotation

* handled cases where sin or cos are 0 in rotation vector functions

* added more comments

* clarified documentation of rotation vector functions

* added more unit tests

* changed way in which vector.rotate_around_axis is adjusted for left handed coordinate systems

* made vector.rotate_around_axis actually left handed

* unrolled matrix multiplication

* removed vector.forward_at_rotation and vector.up_at_rotation

* prettified vector.rotate_around_axis, made previous commits not break anything

* removed references to removed vector.forward_at_rotation and vector.up_at_rotation

* removed documentation of removed vector functions

* clarified documentation and fixed styling of rotation vector functions

* restyled comments minorly

* spelling fixes and some hopefully better comments

* allowed 'up' to be missing from vector.directions_to_rotation and removed requirement for unit vectors as arguments

* made vector.rotate_around_axis() right handed again for consistency

* documented previous changes

* made matrix multiplication actually multiply

* renamed vector.directions_to_rotation() to vector.dir_to_rotation()

* optimized a distance comparison

* Fixed potential false positive in unit tests.

Co-authored-by: NetherEran <nethereran@hotmail.com>

1 files changed, 18 insertions, 0 deletions

diff --git a/doc/lua_api.txt b/doc/lua_api.txt
index 898531880..ed060c4ad 100644
--- a/doc/lua_api.txt
+++ b/doc/lua_api.txt
@@ -3007,6 +3007,24 @@ For the following functions `x` can be either a vector or a number:
 * `vector.divide(v, x)`:
     * Returns a scaled vector or Schur quotient.
 
+For the following functions `a` is an angle in radians and `r` is a rotation
+vector ({x = <pitch>, y = <yaw>, z = <roll>}) where pitch, yaw and roll are
+angles in radians.
+
+* `vector.rotate(v, r)`:
+    * Applies the rotation `r` to `v` and returns the result.
+    * `vector.rotate({x = 0, y = 0, z = 1}, r)` and
+      `vector.rotate({x = 0, y = 1, z = 0}, r)` return vectors pointing
+      forward and up relative to an entity's rotation `r`.
+* `vector.rotate_around_axis(v1, v2, a)`:
+    * Returns `v1` rotated around axis `v2` by `a` radians according to
+      the right hand rule.
+* `vector.dir_to_rotation(direction[, up])`:
+    * Returns a rotation vector for `direction` pointing forward using `up`
+      as the up vector.
+    * If `up` is omitted, the roll of the returned vector defaults to zero.
+    * Otherwise `direction` and `up` need to be vectors in a 90 degree angle to each other.
+