peclet::core::geom::body_detail Namespace Reference

Functions
template<class Real , class Phi >
void	interiorMoments (const Phi &phi, Vec3< Real > p0, Vec3< Real > d, int nseg, Real &m0, Real &m1, Real &m2)
	Moments of the NEGATIVE set {phi < 0} along p0 + s*d, s in [0,1], in the PARAMETER s: m0 = ∫ 1 ds, m1 = ∫ s ds, m2 = ∫ s² ds over the interior runs.
template<class Real >
void	eigSym3 (const Real A[3][3], Real w[3], Real V[3][3])
	Jacobi eigensolver for a symmetric 3x3: A = V diag(w) V^T, V orthonormal columns.
template<class Real >
void	resolveDegenerateFrame (Real w[3], Real V[3][3], Real relTol=Real(1e-2))
	Within each cluster of (near-)equal eigenvalues, rotate the eigenbasis onto the input axes with the largest projection into that subspace (orthogonal Procrustes on the k x k projection).
template<class Real >
Quat< Real >	quatFromRotation (const Real R[3][3])
	Rotation matrix (columns orthonormal, det +1) -> quaternion (x, y, z, w), Shepperd's method.

Function Documentation

interiorMoments()

template<class Real , class Phi >

void peclet::core::geom::body_detail::interiorMoments	(	const Phi &	phi,
		Vec3< Real >	p0,
		Vec3< Real >	d,
		int	nseg,
		Real &	m0,
		Real &	m1,
		Real &	m2
	)

Moments of the NEGATIVE set {phi < 0} along p0 + s*d, s in [0,1], in the PARAMETER s: m0 = ∫ 1 ds, m1 = ∫ s ds, m2 = ∫ s² ds over the interior runs.

Same bracketed bisection as quadrature.hpp's positiveLength (an initial nseg subdivision brackets, 40 bisections refine to ~1 ulp of the parameter); the per-run integrals are analytic. NOTE the sign convention: bodies are the interior (phi < 0), where the aperture code measured the fluid (phi > 0).

Definition at line 66 of file body_properties.hpp.

eigSym3()

template<class Real >

void peclet::core::geom::body_detail::eigSym3	(	const Real	A[3][3],
		Real	w[3],
		Real	V[3][3]
	)

Jacobi eigensolver for a symmetric 3x3: A = V diag(w) V^T, V orthonormal columns.

Small, exact enough (50 sweeps to machine precision), no dependencies.

Definition at line 113 of file body_properties.hpp.

Referenced by resolveDegenerateFrame().

resolveDegenerateFrame()

template<class Real >

void peclet::core::geom::body_detail::resolveDegenerateFrame	(	Real	w[3],
		Real	V[3][3],
		Real	relTol = Real(1e-2)
	)

Within each cluster of (near-)equal eigenvalues, rotate the eigenbasis onto the input axes with the largest projection into that subspace (orthogonal Procrustes on the k x k projection).

See the header comment; a fully degenerate tensor yields exactly the identity.

Definition at line 165 of file body_properties.hpp.

References eigSym3(), and peclet::core::scale().

quatFromRotation()

template<class Real >

Quat< Real > peclet::core::geom::body_detail::quatFromRotation

(

const Real

R[3][3]

)

Rotation matrix (columns orthonormal, det +1) -> quaternion (x, y, z, w), Shepperd's method.

Definition at line 240 of file body_properties.hpp.