Fused CSG: the expression builder's operations as types (see EBGeometry_Fused.hpp). More...

Namespaces
namespace	Detail
	Implementation details of the fused operations.

Classes
struct	AffineOp
	An affine map (translation, rotation, scaling, reflection, or a composition of them): the operand's value at the mapped point, times a value scale. More...

struct	BlurOp
	Blur: a weighted average of the operand's values at 27 points (CSGOps::blur()). More...

struct	CombineOp
	Union or intersection: the minimum or the maximum of the operands' values, in order. More...

struct	ComplementOp
	Complement: -v, inside and outside swapped. More...

struct	ElongateOp
	Elongation: the operand's value at p - clamp(p, -h, h). More...

struct	MollifyOp
	Mollification: the operand convolved with a bump kernel sampled on a grid (CSGOps::mollify()). More...

class	Node
	A fused composition: an operation applied to its operands, itself a shape (isShape). More...

struct	OperandList
	A list of operands, for the n-ary smooth operations (whose smoothing parameters follow the operands): Fused::SmoothUnion(Fused::operands(a, b, c), s). More...

struct	RepetitionOp
	Finite repetition: the minimum of the operand's value over all its copies (CSGOps::repetition()). More...

struct	ShiftOp
	Offset (v - r) or annulus (\|v\| - delta). More...

struct	SmoothCombineOp
	Smooth union or intersection: a smooth minimum (maximum) of the two smallest (largest) values. More...

Typedefs
using	UnionOp = CombineOp< true >
	A union: the minimum of the operands' values.

using	IntersectionOp = CombineOp< false >
	An intersection: the maximum of the operands' values.

template<class Op , class... Cs>
using	NodeOf = Node< Op, Cs... >
	The shape type a Fused:: function returns for an operation and its operands.

Functions
template<class... Cs>
OperandList< Cs... >	operands (const Cs &... a_operands)
	A list of operands for an n-ary smooth operation.

template<class C , class... Cs>
auto	Union (const C &a_first, const Cs &... a_others)
	Union of shapes: the minimum of their values. One shape is returned as is.

template<class C , class... Cs>
auto	Intersection (const C &a_first, const Cs &... a_others)
	Intersection of shapes: the maximum of their values. One shape is returned as is.

template<class A , class B , class... Bs>
auto	Difference (const A &a_first, const B &a_second, const Bs &... a_others)
	Difference A \ (B1 u B2 u ...): max(A, -min_i Bi).

template<class C >
Node< ComplementOp, C >	Complement (const C &a_operand)
	Complement: inside and outside swapped, -v.

template<class A , class B >
Node< SmoothCombineOp< ShapePrecision< A >, true >, A, B >	SmoothUnion (const A &a_first, const B &a_second, const ShapePrecision< A > a_smooth, const BlendKind a_blend=BlendKind::Polynomial)
	Smooth union of two shapes: a smooth minimum of their values.

template<class... Cs>
auto	SmoothUnion (const OperandList< Cs... > &a_operands, const ShapePrecision< typename Detail::TypeAt< 0, Cs... >::type > a_smooth, const BlendKind a_blend=BlendKind::Polynomial)
	Smooth union of any number of shapes: a smooth minimum of the two smallest values (see EBGeometry::SmoothUnion()).

template<class A , class B >
Node< SmoothCombineOp< ShapePrecision< A >, false >, A, B >	SmoothIntersection (const A &a_first, const B &a_second, const ShapePrecision< A > a_smooth, const BlendKind a_blend=BlendKind::Polynomial)
	Smooth intersection of two shapes: a smooth maximum of their values.

template<class... Cs>
auto	SmoothIntersection (const OperandList< Cs... > &a_operands, const ShapePrecision< typename Detail::TypeAt< 0, Cs... >::type > a_smooth, const BlendKind a_blend=BlendKind::Polynomial)
	Smooth intersection of any number of shapes: a smooth maximum of the two largest values.

template<class A , class B >
auto	SmoothDifference (const A &a_first, const B &a_second, const ShapePrecision< A > a_smooth, const BlendKind a_blend=BlendKind::Polynomial)
	Smooth difference A \ B: the smooth intersection of A and the complement of B.

template<class A , class... Bs>
auto	SmoothDifference (const A &a_first, const OperandList< Bs... > &a_others, const ShapePrecision< A > a_smooth, const BlendKind a_blend=BlendKind::Polynomial)
	Smooth difference A \ (B1, B2, ...): the smooth intersection of A and the complement of each Bi.

template<class C >
auto	Translate (const C &a_operand, const Vec3T< ShapePrecision< C > > &a_shift)
	Translate a shape by a shift.

template<class C >
auto	Rotate (const C &a_operand, const ShapePrecision< C > a_degrees, const size_t a_axis)
	Rotate a shape about a coordinate axis through the origin.

template<class C >
auto	Rotate (const C &a_operand, const ShapePrecision< C > a_degrees, const Vec3T< ShapePrecision< C > > &a_axis)
	Rotate a shape about an arbitrary axis through the origin.

template<class C >
auto	Scale (const C &a_operand, const ShapePrecision< C > a_factor)
	Scale a shape uniformly about the origin: \|s\| times its value at p / s.

template<class C >
auto	Reflect (const C &a_operand, const size_t a_axis)
	Reflect a shape in a coordinate plane through the origin.

template<class C >
Node< ShiftOp< ShapePrecision< C >, false >, C >	Offset (const C &a_operand, const ShapePrecision< C > a_offset)
	Offset a shape's surface outward by a distance, v - r.

template<class C >
Node< ShiftOp< ShapePrecision< C >, true >, C >	Annular (const C &a_operand, const ShapePrecision< C > a_delta)
	A shell around a shape's surface, \|v\| - delta.

template<class C >
Node< ElongateOp< ShapePrecision< C > >, C >	Elongate (const C &a_operand, const Vec3T< ShapePrecision< C > > &a_elongation)
	Elongate a shape: stretch it by inserting a box of half-lengths h at the origin.

template<class C >
Node< RepetitionOp< ShapePrecision< C > >, C >	FiniteRepetition (const C &a_operand, const Vec3T< ShapePrecision< C > > &a_period, const Vec3T< ShapePrecision< C > > &a_repeatLo, const Vec3T< ShapePrecision< C > > &a_repeatHi)
	Finite repetition: copies of a shape on a grid of tiles, the minimum over all of them (see EBGeometry::FiniteRepetition()).

template<class C >
Node< BlurOp< ShapePrecision< C > >, C >	Blur (const C &a_operand, const ShapePrecision< C > a_blur, const ShapePrecision< C > a_alpha=ShapePrecision< C >(0.5))
	Blur a shape: a weighted average of its values at the 27 points p + d (i, j, k), i, j, k in {-1, 0, 1} (see EBGeometry::Blur()).

template<class C >
Node< MollifyOp< ShapePrecision< C > >, C >	Mollify (const C &a_operand, const ShapePrecision< C > a_dist, const size_t a_samples)
	Mollify a shape: convolve it with a smooth bump kernel sampled on an n x n x n grid over [-r, r]^3 (see EBGeometry::Mollify()).

Detailed Description

Fused CSG: the expression builder's operations as types (see EBGeometry_Fused.hpp).

Typedef Documentation

◆ NodeOf

template<class Op , class... Cs>

using EBGeometry::Fused::NodeOf = typedef Node<Op, Cs...>

The shape type a Fused:: function returns for an operation and its operands.

Template Parameters

Op	Operation.
Cs	Operand types.

Function Documentation

◆ Annular()

template<class C >

Node< ShiftOp< ShapePrecision< C >, true >, C > EBGeometry::Fused::Annular	(	const C &	a_operand,
		const ShapePrecision< C >	a_delta
	)

inline

A shell around a shape's surface, |v| - delta.

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_delta	Shell half-thickness (finite).

Returns: The shell.

◆ Blur()

template<class C >

Node< BlurOp< ShapePrecision< C > >, C > EBGeometry::Fused::Blur	(	const C &	a_operand,
		const ShapePrecision< C >	a_blur,
		const ShapePrecision< C >	a_alpha = `ShapePrecision< C >(0.5)`
	)

inline

Blur a shape: a weighted average of its values at the 27 points p + d (i, j, k), i, j, k in {-1, 0, 1} (see EBGeometry::Blur()).

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_blur	Blur distance d (finite, >= 0).
[in]	a_alpha	Center weight factor in [0, 1]; 1 = no blur.

Returns: The blurred shape.

◆ Complement()

template<class C >

Node< ComplementOp, C > EBGeometry::Fused::Complement ( const C & a_operand )

inline

Complement: inside and outside swapped, -v.

Template Parameters

C	Operand type.

Parameters

[in] a_operand Operand.

Returns: The complement.

◆ Difference()

template<class A , class B , class... Bs>

auto EBGeometry::Fused::Difference	(	const A &	a_first,
		const B &	a_second,
		const Bs &...	a_others
	)

inline

Difference A \ (B1 u B2 u ...): max(A, -min_i Bi).

Template Parameters

A	Operand to subtract from.
B	First operand to subtract.
Bs	The others.

Parameters

[in]	a_first	Operand to subtract from.
[in]	a_second	First operand to subtract.
[in]	a_others	The others.

Returns: The difference.

◆ Elongate()

template<class C >

Node< ElongateOp< ShapePrecision< C > >, C > EBGeometry::Fused::Elongate	(	const C &	a_operand,
		const Vec3T< ShapePrecision< C > > &	a_elongation
	)

inline

Elongate a shape: stretch it by inserting a box of half-lengths h at the origin.

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_elongation	Half-lengths h (finite, >= 0).

Returns: The elongated shape.

◆ FiniteRepetition()

template<class C >

Node< RepetitionOp< ShapePrecision< C > >, C > EBGeometry::Fused::FiniteRepetition	(	const C &	a_operand,
		const Vec3T< ShapePrecision< C > > &	a_period,
		const Vec3T< ShapePrecision< C > > &	a_repeatLo,
		const Vec3T< ShapePrecision< C > > &	a_repeatHi
	)

inline

Finite repetition: copies of a shape on a grid of tiles, the minimum over all of them (see EBGeometry::FiniteRepetition()).

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Shape to repeat; its home copy sits in the tile around the origin.
[in]	a_period	Tile period along each axis (> 0).
[in]	a_repeatLo	Tiles in the decreasing direction of each axis (>= 0; rounded to whole tiles).
[in]	a_repeatHi	Tiles in the increasing direction of each axis (>= 0; rounded to whole tiles).

Returns: The repetition.

◆ Intersection()

template<class C , class... Cs>

auto EBGeometry::Fused::Intersection	(	const C &	a_first,
		const Cs &...	a_others
	)

inline

Intersection of shapes: the maximum of their values. One shape is returned as is.

Template Parameters

C	First operand type.
Cs	The others.

Parameters

[in]	a_first	First operand.
[in]	a_others	The others.

Returns: The intersection.

◆ Mollify()

template<class C >

Node< MollifyOp< ShapePrecision< C > >, C > EBGeometry::Fused::Mollify	(	const C &	a_operand,
		const ShapePrecision< C >	a_dist,
		const size_t	a_samples
	)

inline

Mollify a shape: convolve it with a smooth bump kernel sampled on an n x n x n grid over [-r, r]^3 (see EBGeometry::Mollify()).

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_dist	Mollification distance r: the half-width of the sampling cube (finite).
[in]	a_samples	Samples per axis n (between 1 and 64).

Returns: The mollified shape.

◆ Offset()

template<class C >

Node< ShiftOp< ShapePrecision< C >, false >, C > EBGeometry::Fused::Offset	(	const C &	a_operand,
		const ShapePrecision< C >	a_offset
	)

inline

Offset a shape's surface outward by a distance, v - r.

A bound (an offset of an exact distance by r >= 0 is exact, but the type cannot tell the sign of r).

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_offset	Offset distance r (finite); negative erodes.

Returns: The offset shape.

◆ operands()

template<class... Cs>

OperandList< Cs... > EBGeometry::Fused::operands ( const Cs &... a_operands )

inline

A list of operands for an n-ary smooth operation.

Template Parameters

Cs	Operand types (shapes).

Parameters

[in] a_operands Operands.

Returns: The list.

◆ Reflect()

template<class C >

auto EBGeometry::Fused::Reflect	(	const C &	a_operand,
		const size_t	a_axis
	)

inline

Reflect a shape in a coordinate plane through the origin.

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_axis	Axis normal to the plane (0, 1 or 2).

Returns: The reflected shape.

◆ Rotate() [1/2]

template<class C >

auto EBGeometry::Fused::Rotate	(	const C &	a_operand,
		const ShapePrecision< C >	a_degrees,
		const size_t	a_axis
	)

inline

Rotate a shape about a coordinate axis through the origin.

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_degrees	Angle in degrees, counterclockwise seen from the positive end of the axis (finite).
[in]	a_axis	Coordinate axis (0, 1 or 2).

Returns: The rotated shape.

◆ Rotate() [2/2]

template<class C >

auto EBGeometry::Fused::Rotate	(	const C &	a_operand,
		const ShapePrecision< C >	a_degrees,
		const Vec3T< ShapePrecision< C > > &	a_axis
	)

inline

Rotate a shape about an arbitrary axis through the origin.

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_degrees	Angle in degrees, counterclockwise seen from the positive end of the axis (finite).
[in]	a_axis	Axis direction (finite, non-zero; need not be normalized).

Returns: The rotated shape.

◆ Scale()

template<class C >

auto EBGeometry::Fused::Scale	(	const C &	a_operand,
		const ShapePrecision< C >	a_factor
	)

inline

Scale a shape uniformly about the origin: |s| times its value at p / s.

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_factor	Scale factor s (finite, non-zero; a negative factor also reflects through the origin).

Returns: The scaled shape.

◆ SmoothDifference() [1/2]

template<class A , class B >

auto EBGeometry::Fused::SmoothDifference	(	const A &	a_first,
		const B &	a_second,
		const ShapePrecision< A >	a_smooth,
		const BlendKind	a_blend = `BlendKind::Polynomial`
	)

inline

Smooth difference A \ B: the smooth intersection of A and the complement of B.

Template Parameters

A	Operand to subtract from.
B	Operand to subtract.

Parameters

[in]	a_first	Operand to subtract from.
[in]	a_second	Operand to subtract.
[in]	a_smooth	Smoothing length (> 0).
[in]	a_blend	Blend kind.

Returns: The smooth difference.

◆ SmoothDifference() [2/2]

template<class A , class... Bs>

auto EBGeometry::Fused::SmoothDifference	(	const A &	a_first,
		const OperandList< Bs... > &	a_others,
		const ShapePrecision< A >	a_smooth,
		const BlendKind	a_blend = `BlendKind::Polynomial`
	)

inline

Smooth difference A \ (B1, B2, ...): the smooth intersection of A and the complement of each Bi.

Template Parameters

A	Operand to subtract from.
Bs	Operands to subtract.

Parameters

[in]	a_first	Operand to subtract from.
[in]	a_others	Operands to subtract (Fused::operands(b1, b2, ...)).
[in]	a_smooth	Smoothing length (> 0).
[in]	a_blend	Blend kind.

Returns: The smooth difference.

◆ SmoothIntersection() [1/2]

template<class A , class B >

Node< SmoothCombineOp< ShapePrecision< A >, false >, A, B > EBGeometry::Fused::SmoothIntersection	(	const A &	a_first,
		const B &	a_second,
		const ShapePrecision< A >	a_smooth,
		const BlendKind	a_blend = `BlendKind::Polynomial`
	)

inline

Smooth intersection of two shapes: a smooth maximum of their values.

Template Parameters

A	First operand type.
B	Second operand type.

Parameters

[in]	a_first	First operand.
[in]	a_second	Second operand.
[in]	a_smooth	Smoothing length (> 0).
[in]	a_blend	Blend kind.

Returns: The smooth intersection.

◆ SmoothIntersection() [2/2]

template<class... Cs>

auto EBGeometry::Fused::SmoothIntersection	(	const OperandList< Cs... > &	a_operands,
		const ShapePrecision< typename Detail::TypeAt< 0, Cs... >::type >	a_smooth,
		const BlendKind	a_blend = `BlendKind::Polynomial`
	)

inline

Smooth intersection of any number of shapes: a smooth maximum of the two largest values.

Template Parameters

Cs	Operand types.

Parameters

[in]	a_operands	Operands (Fused::operands(a, b, ...)). One is returned as is.
[in]	a_smooth	Smoothing length (> 0).
[in]	a_blend	Blend kind.

Returns: The smooth intersection.

◆ SmoothUnion() [1/2]

template<class A , class B >

Node< SmoothCombineOp< ShapePrecision< A >, true >, A, B > EBGeometry::Fused::SmoothUnion	(	const A &	a_first,
		const B &	a_second,
		const ShapePrecision< A >	a_smooth,
		const BlendKind	a_blend = `BlendKind::Polynomial`
	)

inline

Smooth union of two shapes: a smooth minimum of their values.

Template Parameters

A	First operand type.
B	Second operand type.

Parameters

[in]	a_first	First operand.
[in]	a_second	Second operand.
[in]	a_smooth	Smoothing length (> 0).
[in]	a_blend	Blend kind.

Returns: The smooth union.

◆ SmoothUnion() [2/2]

template<class... Cs>

auto EBGeometry::Fused::SmoothUnion	(	const OperandList< Cs... > &	a_operands,
		const ShapePrecision< typename Detail::TypeAt< 0, Cs... >::type >	a_smooth,
		const BlendKind	a_blend = `BlendKind::Polynomial`
	)

inline

Smooth union of any number of shapes: a smooth minimum of the two smallest values (see EBGeometry::SmoothUnion()).

Template Parameters

Cs	Operand types.

Parameters

[in]	a_operands	Operands (Fused::operands(a, b, ...)). One is returned as is.
[in]	a_smooth	Smoothing length (> 0).
[in]	a_blend	Blend kind.

Returns: The smooth union.

◆ Translate()

template<class C >

auto EBGeometry::Fused::Translate	(	const C &	a_operand,
		const Vec3T< ShapePrecision< C > > &	a_shift
	)

inline

Translate a shape by a shift.

Template Parameters

C	Operand type.

Parameters

[in]	a_operand	Operand.
[in]	a_shift	Shift (finite).

Returns: The translated shape. A map of a map is one map, as in the expression builder.

◆ Union()

template<class C , class... Cs>

auto EBGeometry::Fused::Union	(	const C &	a_first,
		const Cs &...	a_others
	)

inline

Union of shapes: the minimum of their values. One shape is returned as is.

Template Parameters

C	First operand type.
Cs	The others.

Parameters

[in]	a_first	First operand.
[in]	a_others	The others.

Returns: The union.

Namespaces

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ NodeOf

Function Documentation

◆ Annular()

◆ Blur()

◆ Complement()

◆ Difference()

◆ Elongate()

◆ FiniteRepetition()

◆ Intersection()

◆ Mollify()

◆ Offset()

◆ operands()

◆ Reflect()

◆ Rotate() [1/2]

◆ Rotate() [2/2]

◆ Scale()

◆ SmoothDifference() [1/2]

◆ SmoothDifference() [2/2]

◆ SmoothIntersection() [1/2]

◆ SmoothIntersection() [2/2]

◆ SmoothUnion() [1/2]

◆ SmoothUnion() [2/2]

◆ Translate()

◆ Union()