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;
It is now possible to implicitly create one-element Vector and also
explicitly fill more-element Vector with one value without any ambiguous
overload conflicts:
Vector<1, int> a1 = 1; // calls implicit constructor
//Vector<3, int> a3 = 1; // error!
Vector<1, int> b1(1); // still calls the implicit constructor, the
// explicit is disabled for one-element vector
Vector<3, int> b3(1); // calls the explicit "filling" constructor,
// the implicit is disabled for only one argument
The downside of this is that now specifying improper element count in
constructor doesn't lead to static_assert with human readable error, but
rather cryptic "no match" error.
Was causing improper implicit conversions, such as here (example
directly from unit tests, where it was unintentionally used):
Vector3 normal;
Matrix4 transformation;
auto transformedNormal = transformation*normal;
Not only that it was possible to multiply 4x4 matrix with 3-component
vector, but the resulting type was Point3D which was absolutely
confusing. Currently it must be explicitly converted:
transformedNormal = transformation*Point3D(normal);
The comparisons have also SIMD instructions returning bool vector, this
future-proofs them. Also it isn't confusing anymore (a < b is true when
all are less or just one?).
Also updated all dependent classes to follow the change, such as Color
and Rectangle. Backwards compatibility for GCC 4.6 (with lack of support
for delegating constructors) will be done as non-constexpr constructor
using operator=().
Overall architecture is simplififed with this change and also it's not
needed to use reinterpret_cast in matrix internals anymore, thus there
is no need for operator() and [][] works now always as expected without
any risk of GCC misoptimizations.
On the other side, constructing matrix from list of elements is not
possible anymore. You have to specify the elements as list of
column vectors, which might be less convenient to write, but it helps to
distinguish what is column and what is row:
Matrix<2, int> a(1, 2, // before
3, 4);
Matrix<2, int> a(Vector<2, int>(1, 2), // now
Vector<2, int>(3, 4));
For some matrix specializations (i.e. Matrix3 and Matrix4) it is
possible to use list-initialization instead of explicit type
specification:
Matrix<3, int>({1, 2, 3},
{4, 5, 6},
{7, 8, 9});
I didn't yet figure out how to properly implement the general
(constexpr) constructor to also take lists, so it's a bit ugly for now.
Matrix operations are now done column-wise, which should help with
future SIMD implementations, documentation is also updated accordingly.
I also removed forgotten remains of matrix/matrix operator*=(), which
can be confusing, as the multiplication is not commutative. Why it is
not present is explained in d9c900f076.
(De)normalization from/to [0, 1] for unsigned types and from/to [-1, 1]
for signed types. -1.0 is always denormalized to min+1.
Also updated some tests for Color, as they depended on previous
imprecise implementation.
Vladimír Vondruš