peclet::core::geom::prim::Superquadric< Real > Struct Template Reference

Solid superquadric with semi-axes (rx, ry, rz) and exponent e: the implicit |x/rx|^e + |y/ry|^e + |z/rz|^e = 1. More...

#include <primitives.hpp>

Public Types
using	value_type = Real

Public Member Functions
PECLET_HD Real	eval (Vec3< Real > p) const
PECLET_HD Vec3< Real >	grad (Vec3< Real > p) const
	Finite differences over this leaf's own eval (the Taubin estimate has no gradient worth hand-deriving at this rung).

Public Attributes
Real	rx = Real(1)
Real	ry = Real(1)
Real	rz = Real(1)
Real	e = Real(2)

Static Public Attributes
static constexpr bool	exact_distance = false
static constexpr bool	analytic_gradient = false

Detailed Description

template<class Real>
struct peclet::core::geom::prim::Superquadric< Real >

Solid superquadric with semi-axes (rx, ry, rz) and exponent e: the implicit |x/rx|^e + |y/ry|^e + |z/rz|^e = 1.

e = 2 is an ellipsoid, large e approaches a box, e < 2 gives the pinched/octahedral family. The DEM literature's workhorse non-spherical grain.

NOT an exact distance: the implicit is normalised by its own gradient (the Taubin estimate), which is first-order correct near the surface and degrades away from it. Bound direction is MEASURED by the rung-2 gate, not assumed.

Definition at line 370 of file primitives.hpp.

Member Typedef Documentation

value_type

template<class Real >

using peclet::core::geom::prim::Superquadric< Real >::value_type = Real

Definition at line 371 of file primitives.hpp.

Member Function Documentation

eval()

template<class Real >

PECLET_HD Real peclet::core::geom::prim::Superquadric< Real >::eval ( Vec3< Real >  p ) const

inline

Definition at line 376 of file primitives.hpp.

References peclet::core::geom::prim::Superquadric< Real >::e, peclet::core::detail::hdAbs(), peclet::core::detail::hdMax(), peclet::core::detail::hdMin(), peclet::core::detail::hdPow(), peclet::core::detail::hdSqrt(), peclet::core::geom::prim::Superquadric< Real >::rx, peclet::core::geom::prim::Superquadric< Real >::ry, peclet::core::geom::prim::Superquadric< Real >::rz, peclet::core::Vec3< Real >::x, peclet::core::Vec3< Real >::y, and peclet::core::Vec3< Real >::z.

grad()

template<class Real >

PECLET_HD Vec3< Real > peclet::core::geom::prim::Superquadric< Real >::grad ( Vec3< Real >  p ) const

inline

Finite differences over this leaf's own eval (the Taubin estimate has no gradient worth hand-deriving at this rung).

h is dem's 1e-4 probe convention.

Definition at line 398 of file primitives.hpp.

References peclet::core::geom::prim::Superquadric< Real >::e, and peclet::core::geom::prim::gradient().

Member Data Documentation

rx

template<class Real >

Real peclet::core::geom::prim::Superquadric< Real >::rx = Real(1)

Definition at line 372 of file primitives.hpp.

Referenced by peclet::core::geom::prim::Superquadric< Real >::eval().

ry

template<class Real >

Real peclet::core::geom::prim::Superquadric< Real >::ry = Real(1)

Definition at line 372 of file primitives.hpp.

Referenced by peclet::core::geom::prim::Superquadric< Real >::eval().

rz

template<class Real >

Real peclet::core::geom::prim::Superquadric< Real >::rz = Real(1)

Definition at line 372 of file primitives.hpp.

Referenced by peclet::core::geom::prim::Superquadric< Real >::eval().

e

template<class Real >

Real peclet::core::geom::prim::Superquadric< Real >::e = Real(2)

Definition at line 372 of file primitives.hpp.

Referenced by peclet::core::geom::prim::Superquadric< Real >::eval(), and peclet::core::geom::prim::Superquadric< Real >::grad().

exact_distance

template<class Real >

constexpr bool peclet::core::geom::prim::Superquadric< Real >::exact_distance = false

staticconstexpr

Definition at line 373 of file primitives.hpp.

analytic_gradient

template<class Real >

constexpr bool peclet::core::geom::prim::Superquadric< Real >::analytic_gradient = false

staticconstexpr

Definition at line 374 of file primitives.hpp.

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

• primitives.hpp