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orientlib (version 0.7.2)

nearest: Find nearest SO(3) or orthogonal matrix.

Description

Converts arbitrary 3 x 3 matrices into the nearest SO(3) or orthogonal matrix.

Usage

nearest.SO3(x)
nearest.orthog(x)

Arguments

x
3 x 3 matrices stored in a 3 x 3 x n array)

Value

  • nearest.SO3 produces an orientation-class object holding the closest orientations.

    nearest.orthog produces a 3 x 3 x n array of orthogonal matrices.

Details

Uses Stephens' (1979) algorithm to find the nearest (in entry-wise Euclidean sense) SO(3) or orthogonal matrix to a given matrix.

References

Stephens (1979). Vector correlation. {Biometrika 66, 41-48.} [object Object]

orientation-class x <- matrix(rnorm(9), 3,3) nearest.orthog(x) nearest.SO3(x) x <- -x nearest.orthog(x) nearest.SO3(x) arrayalgebra