peclet::voro::Power Struct Reference

#include <plane_policy.hpp>

Static Public Member Functions
template<class Real >
static KOKKOS_INLINE_FUNCTION Real	offsetFromRel (const Real r[3], Real wSelf, Real wNbr)
template<class Real >
static KOKKOS_INLINE_FUNCTION Real	blockReachSq (Real rSqMax, Real wSelf, Real wMaxAll)
template<class Real >
static KOKKOS_INLINE_FUNCTION void	planeFromNeighbour (const Real pSelf[3], const Real pNbr[3], Real wSelf, Real wNbr, Real L, Real pdir[3], Real &off)
template<class Real >
static KOKKOS_INLINE_FUNCTION void	buildNormal (const Real pSelf[3], const Real pNbr[3], Real wSelf, Real wNbr, Real L, Real nOut[3])
	Foot-point normal n = (off/|pdir|²) pdir = α r.
template<class Real >
static KOKKOS_INLINE_FUNCTION void	chain (const Real g[3], const Real r[3], Real rho, Real c, Real fSelf[3], Real fNbr[3], Real &fwSelf, Real &fwNbr)

Static Public Attributes
static constexpr bool	kHasWeightDof = true

Detailed Description

Power / Laguerre plane policy: the radical plane between weighted seeds. With r = p_j − p_i, ρ = |r|², c = w_i − w_j, α = (ρ+c)/(2ρ), the foot-point normal is n = α r and the half-space offset is d = ½(ρ+c). Unlike the bisector, d can be negative (the seed can lie OUTSIDE its own cell) — the generic ConvexCell::clip already tolerates that. Both positions and weights are DOFs.

Member Function Documentation

blockReachSq()

template<class Real >

static KOKKOS_INLINE_FUNCTION Real peclet::voro::Power::blockReachSq ( Real  rSqMax, Real  wSelf, Real  wMaxAll  )

inlinestatic

Squared reachability radius for the sorted-worklist early-out (weight-aware). A radical plane to a neighbour with weight w_nbr ≤ W_max cuts iff some vertex v has r·v > d = ½(|r|²+w_self− w_nbr) ≥ ½(|r|²+w_self−W_max). With |r|·√rSqMax ≥ r·v the worst (heaviest) neighbour can cut only while |r| < √rSqMax + √(rSqMax + max(0, W_max−w_self)); beyond that block, break. Reduces to 4·rSqMax when weights are equal (W_max = w_self), matching the Voronoi bound.

buildNormal()

template<class Real >

static KOKKOS_INLINE_FUNCTION void peclet::voro::Power::buildNormal ( const Real  pSelf[3], const Real  pNbr[3], Real  wSelf, Real  wNbr, Real  L, Real  nOut[3]  )

inlinestatic

Foot-point normal n = (off/|pdir|²) pdir = α r.

chain()

template<class Real >

static KOKKOS_INLINE_FUNCTION void peclet::voro::Power::chain ( const Real  g[3], const Real  r[3], Real  rho, Real  c, Real  fSelf[3], Real  fNbr[3], Real &  fwSelf, Real &  fwNbr  )

inlinestatic

Chain g = dGeom/dn_k to the seed DOFs. n = α r, α = ½ + c/(2ρ), c = w_self − w_nbr. Position: J = ∂n/∂r = α I − (c/ρ²) r rᵀ, ∂r/∂p_nbr = +I ⇒ dGeom/dp_nbr = α g − (c/ρ²)(r·g) r , dGeom/dp_self = −(that). Weight: ∂n/∂w_self = r/(2ρ), ∂n/∂w_nbr = −r/(2ρ) ⇒ dGeom/dw_self = (g·r)/(2ρ) , dGeom/dw_nbr = −(that). c = 0 recovers the Voronoi split (∓½ g, zero weight force).

offsetFromRel()

template<class Real >

static KOKKOS_INLINE_FUNCTION Real peclet::voro::Power::offsetFromRel ( const Real  r[3], Real  wSelf, Real  wNbr  )

inlinestatic

Half-space offset for the forward clip {x : r·x ≤ off} given the min-image relative vector r = p_j − p_i (pdir == r). Power: off = d = ½(|r|² + w_self − w_nbr), which can be negative.

planeFromNeighbour()

template<class Real >

static KOKKOS_INLINE_FUNCTION void peclet::voro::Power::planeFromNeighbour ( const Real  pSelf[3], const Real  pNbr[3], Real  wSelf, Real  wNbr, Real  L, Real  pdir[3], Real &  off  )

inlinestatic

FORWARD clip: pdir = r (min-image), off = d = ½(|r|² + w_self − w_nbr). ConvexCell::clip then stores n = (off/|pdir|²) pdir = α r.

Member Data Documentation

kHasWeightDof

constexpr bool peclet::voro::Power::kHasWeightDof = true

staticconstexpr

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The documentation for this struct was generated from the following file:

• include/peclet/voro/plane_policy.hpp