Positions were originally done using Point2D/3D to simplify their
transformation using matrices and to some extent simplify their usage in
shaders. But now the disadvantages exceeded the advantages:
* They take 50% more for 2D positions and 33% more for 3D positions, as
last coordinate is always equal to 1, on the other hand when last
coordinate is errorneously not equal to 1 they have crazy behavior.
* Normalizing them or transforming them with anything else than with
matrices is PITA, as we need to strip the last component, do the
transformation, and then add the component back.
* All transformation handling classes (Complex, DualComplex,
Quaternion, DualQuaternion, Matrix3, Matrix4) now have convenience
functions for transforming points specified directly as
Vector2/Vector3 (and also for transforming vectors).
* When someone wants to use homogeneous coordinates with crazy last
component values, they can do so with plain Vector3 for 2D and
Vector4 for 3D and it will be less confusing than using Point2D/3D
which no important detail hidden.
Remaining unspecified components are set to 0, 0, 1, according to spec.
Also cleaned up and simplified the internals, added debug output
operators for attribute component count and types and tested the whole
thing.
The text will be rendered without all the nifty features like kerning
and it will most probably fail on everything non-latin, but HarfBuzz is
currently PITA on some systems.
HarfBuzz usage can be configured using USE_HARFBUZZ CMake option.
Next few commits will add requirement for "strongly typed" angles in all
function parameters, e.g.:
Matrix3::rotation(24.0_degf);
Math::sin(1.047_radf);
The purpose is to make angle entering less error-prone, e.g. not passing
degrees when radians should be etc.
Hopefully this is properly implemented and properly named. On the other
hand, having length everywhere (vectors, quaternions, complex numbers)
and norm only at one place is inconsistent.
It's now possible to conveniently transform 2D vectors and points with
3x3 matrices and 3D vectors/points with 4x4 matrices. Previous most
low-level solution:
Matrix4 m;
Vector3 v;
Vector3 a = (m*Vector4(v, 1.0f)).xyz();
Vector4 b = (m*Vector4(v, 0.0f)).xyz();
Another, more generalized solution for points was with Point2D/Point3D,
adding a lot of confusion (what is that class and what does .vector()?):
Vector3 a = (m*Point3D(v)).vector();
And the worst solution was with generic 2D/3D code (WTF!):
auto a = (m*typename DimensionTraits::PointType(v)).vector();
Now it is just this, similar for both dimensions:
Vector3 a = m.transformPoint(v);
Vector3 b = m.transformVector(v);
Note that transformation three-component vectors with 3x3 matrices or
four-component vectors with 4x4 matrices is easy enough so it doesn't
need any special convenience functions whatsoever:
Vector3 c = m.rotation()*v;