[OpenSCAD] Matrix inversion
Lucas Vinicius Hartmann
lucas.hartmann at gmail.com
Sat Jun 11 17:33:15 EDT 2016
(Sorry if this is a double post, I sent this message the first time before
completing registration on the mailing list.)
Sometime ago I wrote a small set of functions for construction and use
transformation matrices, including matrix inversion. Here is the code:
https://github.com/lhartmann/openscad_m4lib/blob/master/m4.scad
Matrix inversion code works most of the time, except I just detected a bug
I can not solve. A simple dual rotation matrix, 90º around Y then 90º
around Z, is yielding nan+inf on all elements of the inverse. Works nicely
for other angles, though...
M = m4rz(90) * m4ry(90); // Rotates around Y first, then Z
Minv = m4inv(M); // Fails
I managed to narrow it down to m4inv_solve(...) which does diagonal zero
detection. This is the testing code I used to isolate the error:
M = m4rz(90)*m4ry(90); // Test matrix
echo( // Failing
m4inv_solve(0, // Solve row 0: Detect diagonal zero, swap rows, calls
solve2(...).
m4inv_mx(M) // Expand to Row-Reduced Echelon Format
)
);
echo( // Working by bypassing m4inv_solve(...)
m4inv_solve2(0, // Solve row 0 (normalize, scale and subtract from all
other rows)
m4inv_rowswap(0,2, // Swap rows 0 and 2 by hand
m4inv_mx(M) // Expand to Row-Reduced Echelon Format
)
)
);
This is the code for the misbehaving function, it should check move zeroes
away from the diagonal of row i:
// Solve one step, ensure nonzero at diagonal element.
function m4inv_zero(x) = abs(x) < 1e-5;
function m4inv_solve(i,mx) =
!m4inv_zero(mx[i][i ]) ?
m4inv_solve2(i, mx ) :
i+1<4 && !m4inv_zero(mx[i][i+1]) ? m4inv_solve2(i,
m4inv_rowswap(i,i+1,mx)) :
i+2<4 && !m4inv_zero(mx[i][i+2]) ? m4inv_solve2(i,
m4inv_rowswap(i,i+2,mx)) :
i+3<4 && !m4inv_zero(mx[i][i+3]) ? m4inv_solve2(i,
m4inv_rowswap(i,i+3,mx)) :
m4identity(); // Singular matrix, reset to identity
I looked at the code for m4inv_solve(...) above for a while, but don't get
why it is failing... Any ideas?
--
Lucas Vinicius Hartmann
Dizem que se você rodar o CD do Windows ao contrário ele mostra uma
mensagem demoníaca... Mas isso nem é o pior, se você rodar ele normal ele
instala o Windows!
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