Okay, here goes. I've collected together the basic functionality that
would probably make a good starting point. As I've mentioned my code is
very messy and has bits missing (e.g. I never had a use for the cross
product but it's pretty important in general). I guess a good way to
begin would be to write the pubic interfaces then start on the
implementation.
Cubic Solvers:
General complex cubic solver with two algorithms (one requiring a
complex cosine and and arcosine one using only +-*/ and roots). A
special case cubic solver for the reduced cubic x^^3 + px - q = 0.
Quaternions:
opAdd, opSub, opMult(quaternion), opMult(vector), opDiv, Normalise,
Normalized, conjugate, conjugated, toEulerAngles*, fromEulerAngles,
this(real,i,j,k), this(angle,axis), getAngle(), getAxis()
*Currently I've only got a quaternion->euler angles routine that works
in the ZYZ convention but I have read a paper that generalises my method
to all valid axis conventions. Will probably impliment as something like:
toEulerAngles(string convention="XYZ")()
Vectors:
opAdd, opSub, opMult(scalar), opMult(vector)*, cross**, Normalise,
Normalized, Length
* dot product. Would this be better named as dot()?
** 3D vectors only. Perhaps defining a cross product on the
Matrices:
opAdd, opSub, opMult(scalar), opMult(vector), opMult(matrix)**, Invert,
Inverted, Orthogonalize, Orthogonalized, Reorthogonalize***,
Reorthogonalized***, Det, Transpose, Transposed, Dagger*, Daggered*,
Eigenvalues****, Eigenvectors****
*The hermitian conjugate/conjugate transpose. Reduces to the transpose
for a real matrix
** Matrix-matrix multiplication doesn't commute. Could this be a problem
when using operator notation?
*** Othogonalize assuming the matrix is nearly orthogonal already
(possibly using some quick, approximate method such as a Taylor series)
**** I have a eigenvalue/vector solver for 3x3 matrices which seems
reasonably stable but needs more testing.
Free functions:
MatrixToQuaternion
QuaternionToMatrix
+ code to allow easy printing to stdout/streams and such.
Andrei Alexandrescu wrote:
On 04/15/2010 01:49 PM, Gareth Charnock wrote:
As a side effect of my PhD project I've got a collection of mathematical
classes. I'd be happy to collect them together, tidy them up and donate
them to phobos the authors are interested in including them. Matrices
and vectors in particular get reinvented all the time so I'm sure users
of D will appreciate them being there. Quaternions are probably somewhat
more specialised; they are most often used for representing rotations
(they have different advantages and disadvantages to rotation matrices).
I've also written a solver for cubic equations.
The matrix and vector classes are of the sort where the dimension is
known at compile time and will probably be most useful for modelling
geometry. High dimensional matrices and vectors are probably better left
to a scientific library (I remember there was talk that one might be
being proposed).
Would this sort of functionality be useful for phobos? At the moment, I
can't promise anything, I'm just trying to judge the interest should I
find time to look into it.
Gareth Charnock
I think it would. Could you please post a brief list of features so
people can take a look?
Andrei
