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Added matrix inversion

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Chris Palmer
2020-06-20 15:01:01 +01:00
parent 9cfde7f524
commit bf5b6d7c30
2 changed files with 37 additions and 0 deletions
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31
utils/maths.scad
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@@ -90,3 +90,34 @@ function euler(R) = let(ay = asin(-R[2][0]), cy = cos(ay)) //! Convert a rotatio
cy ? [ atan2(R[2][1] / cy, R[2][2] / cy), ay, atan2(R[1][0] / cy, R[0][0] / cy) ]
: R[2][0] < 0 ? [atan2( R[0][1], R[0][2]), 180, 0]
: [atan2(-R[0][1], -R[0][2]), -180, 0];
// Matrix inversion: https://www.mathsisfun.com/algebra/matrix-inverse-row-operations-gauss-jordan.html
function augment(m) = let(l = len(m), n = identity(l)) [ //! Augment a matrix by adding an identity matrix to the right
for(i = [0 : l - 1])
concat(m[i], n[i])
];
function rowswap(m, i, j) = [ //! Swap two rows of a matrix
for(k = [0 : len(m) - 1])
k == i ? m[j] : k == j ? m[i] : m[k]
];
function solve_row(m, i) = let(diag = m[i][i]) [ //! Make diagonal one by dividing the row by it and subtract from other rows to make column zero
for(j = [0 : len(m) - 1])
i == j ? m[j] / diag : m[j] - m[i] * m[j][i] / diag
];
function nearly_zero(x) = abs(x) < 1e-5; //! True if x is close to zero
function solve(m, i = 0, j = 0) = //! Solve each row ensuring diagonal is not zero
i < len(m) ?
assert(i + j < len(m), "matrix is singular")
solve(!nearly_zero(m[i + j][i]) ? solve_row(j ? rowswap(m, i, i + j) : m, i) : solve(m, i, j + 1), i + 1)
: m;
function invert(m) = let(n =len(m), m = solve(augment(m))) [ //! Invert a matrix
for(i = [0 : n - 1]) [
for(j = [n : 2 * n - 1])
each m[i][j]
]
];