Made sure files in core/ and tools/ have a proper Godot license header
when written by us. Also renamed aabb.{cpp,h} and object_type_db.{cpp,h}
to rect3.{cpp,h} and class_db.{cpp,h} respectively.
Also added a proper header to core/io/base64.{c,h} after clarifying
the licensing with the original author (public domain).
This is the follow up for the 2D changes mentioned in PR #6865. It fixes various mistakes regarding the order of matrix indices, order of transformation operations, usage of atan2 function and ensures that the sense of rotation is compatible with a left-handed coordinate system with Y-axis pointing down (which flips the sense of rotations along the z-axis). Also replaced float with real_t, and tried to make use of Matrix32 methods rather than accessing its elements directly.
Affected code in the Godot code base is also fixed in this commit.
The user code using functions involving angles such as atan2, angle_to, get_rotation, set_rotation will need to be updated to conform with the new behavior. Furthermore, the sign of the rotation angles in existing 2D scene files need to be flipped as well.
This is a part of the breaking changes proposed in PR #6865, solving the issue regarding the order of affine transformations described in #2565. This PR also fixes the affected code within Godot codebase. Includes improvements to documentation too.
Another change is, Matrix3::get_scale() will now return negative scaling when the determinant of the matrix is negative. The rationale behind this is simple: when performing a polar decomposition on a basis matrix M = R.S, we have to ensure that the determinant of R is +1, such that it is a proper rotation matrix (with no reflections) which can be represented by Euler angles or a quaternion.
Also replaced the few instances of float with real_t in Matrix3 and Transform.
Furthermore, this PR fixes an issue introduced due to the API breakage in #6865. Namely Matrix3::get_euler() now only works with proper rotation matrices. As a result, the code that wants to get the rotation portion of a transform needs to use Matrix3::get_rotation() introduced in this commit, which complements Matrix3::get_scaled(), providing both parts of the polar decomposition.
Finally, it is now possible to construct a rotation matrix from Euler angles using the new constructor Matrix3::Matrix3(const Vector3 &p_euler).
Furthermore, functions which expect a rotation matrix will now give an error simply, rather than trying to orthonormalize such matrices. The documentation for such functions has be updated accordingly.
This commit breaks code using 3D rotations, and is a part of the breaking changes in 2.1 -> 3.0 transition. The code affected within Godot code base is fixed in this commit.
That year should bring the long-awaited OpenGL ES 3.0 compatible renderer
with state-of-the-art rendering techniques tuned to work as low as middle
end handheld devices - without compromising with the possibilities given
for higher end desktop games of course. Great times ahead for the Godot
community and the gamers that will play our games!
