formula

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 Go to latest Published: Feb 13, 2022 License: MIT Imports: 8 Imported by: 0

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Index

Constants

This section is empty.

Variables

This section is empty.

Functions

func CalculateCoordinateUsingWavePackets 

func CalculateCoordinateUsingWavePackets(coordinate complex128, latticeVectors []complex128, wavePackets []WavePacket) complex128

CalculateCoordinateUsingWavePackets transforms the coordinate using the lattice and its wave packets.

func CalculateEulerTerm 

func CalculateEulerTerm(z complex128, power1, power2 int, scale complex128, ignoreComplexConjugate bool) complex128

CalculateEulerTerm calculates e^(i*n*z) * e^(-i*m*zConj)

func CalculateExponentTerm 

func CalculateExponentTerm(coordinate complex128, power1, power2 int, scale complex128, ignoreComplexConjugate bool) complex128

CalculateExponentTerm calculates (z^power * zConj^conjugatePower) 

where z is a complex number, zConj is the complex conjugate
and power and conjugatePower are integers.

func CanWavePacketsBeGroupedAmongCoefficientRelationships 

func CanWavePacketsBeGroupedAmongCoefficientRelationships(wavePackets []WavePacket, desiredRelationships []coefficient.Relationship) bool

CanWavePacketsBeGroupedAmongCoefficientRelationships returns true if the WavePackets involved satisfy the relationships.

func ContainsRelationship 

func ContainsRelationship(relationships []coefficient.Relationship, target coefficient.Relationship) bool

ContainsRelationship returns true if the target relationship is in the list of relationships.

func ConvertToLatticeCoordinates 

func ConvertToLatticeCoordinates(cartesianPoint complex128, latticeVectors []complex128) complex128

ConvertToLatticeCoordinates changes the coordinate to match the axes defined by the latticeVectors.

func GetAllPossibleTermRelationships3 

func GetAllPossibleTermRelationships3(
	term1, term2 Term,
	term1Multiplier complex128,
	term2Multiplier complex128,
) []coefficient.Relationship

GetAllPossibleTermRelationships3 returns a list of relationships that all terms conform to.

func GetWavePacketRelationship 

func GetWavePacketRelationship(wavePacket1, wavePacket2 WavePacket) []coefficient.Relationship

GetWavePacketRelationship returns a list of relationships that all of the wave packets conform to.

func HasSymmetry 

func HasSymmetry(wavePackets []WavePacket, desiredSymmetry Symmetry, desiredSymmetryToCoefficients map[Symmetry][]coefficient.Relationship) bool

HasSymmetry returns true if the WavePackets involved form the desired symmetry.

func SatisfiesRelationship 

func SatisfiesRelationship(term1, term2 Term, term1Multiplier, term2Multiplier complex128, relationship coefficient.Relationship) bool

SatisfiesRelationship sees if the all terms match the coefficient relationship.

func ValidateLatticeVectors 

func ValidateLatticeVectors(latticeVectors []complex128) error

ValidateLatticeVectors returns an error if the lattice vectors are invalid.

Types

type Arbitrary 

type Arbitrary interface {
	Calculate(coordinate complex128) complex128
	FormulaLevelTerms() []Term
	WavePackets() []WavePacket
	LatticeVectors() []complex128
	SymmetriesFound() []Symmetry
}

Arbitrary formulas have all of these methods.

type Builder 

type Builder struct {
	// contains filtered or unexported fields
}

Builder is used to create formula objects.

func NewBuilder 

func NewBuilder() *Builder

NewBuilder returns a new object used to Build Formula objects.

func (*Builder) AddTerm 

func (b *Builder) AddTerm(term *Term) *Builder

AddTerm adds a term to the formula.

func (*Builder) AddWavePacket 

func (b *Builder) AddWavePacket(packet *WavePacket) *Builder

AddWavePacket adds a wave packet to the formula.

func (*Builder) Build 

func (b *Builder) Build() (Arbitrary, error)

Build creates a new Formula object.

func (*Builder) DesiredSymmetry 

func (b *Builder) DesiredSymmetry(symmetry Symmetry) *Builder

DesiredSymmetry sets the desired symmetry

func (*Builder) Frieze 

func (b *Builder) Frieze() *Builder

Frieze sets the formula as a frieze formula.

func (*Builder) Generic 

func (b *Builder) Generic() *Builder

Generic sets the formula as a generic formula.

func (*Builder) Hexagonal 

func (b *Builder) Hexagonal() *Builder

Hexagonal sets the formula as a hexagonal formula.

func (*Builder) LatticeHeight 

func (b *Builder) LatticeHeight(latticeHeight float64) *Builder

LatticeHeight sets the lattice height for wallpaper based patterns.

func (*Builder) LatticeWidth 

func (b *Builder) LatticeWidth(latticeWidth float64) *Builder

LatticeWidth sets the lattice width for wallpaper based patterns.

func (*Builder) Rectangular 

func (b *Builder) Rectangular() *Builder

Rectangular sets the formula as a rectangular formula.

func (*Builder) Rhombic 

func (b *Builder) Rhombic() *Builder

Rhombic sets the formula as a rhombic formula.

func (*Builder) Rosette 

func (b *Builder) Rosette() *Builder

Rosette sets the formula as a rosette formula.

func (*Builder) Square 

func (b *Builder) Square() *Builder

Square sets the formula as a square formula.

func (*Builder) UsingJSONData 

func (b *Builder) UsingJSONData(data []byte) *Builder

UsingJSONData updates the builder, given data

func (*Builder) UsingYAMLData 

func (b *Builder) UsingYAMLData(data []byte) *Builder

UsingYAMLData updates the builder, given data

func (*Builder) WithMarshalOptions 

func (b *Builder) WithMarshalOptions(marshaledOptions BuilderOptionMarshal) *Builder

WithMarshalOptions uses the options to populate the builder.

type BuilderOptionMarshal 

type BuilderOptionMarshal struct {
	Type            string              `json:"type" yaml:"type"`
	Terms           []TermMarshal       `json:"terms" yaml:"terms"`
	LatticeWidth    float64             `json:"lattice_width" yaml:"lattice_width"`
	LatticeHeight   float64             `json:"lattice_height" yaml:"lattice_height"`
	WavePackets     []WavePacketMarshal `json:"wave_packets" yaml:"wave_packets"`
	DesiredSymmetry Symmetry            `json:"desired_symmetry" yaml:"desired_symmetry"`
}

BuilderOptionMarshal is a flattened representation of all Builder options.

type Frieze 

type Frieze struct {
	// contains filtered or unexported fields
}

Frieze formulas transform points into a horizontal repeating strip, like the frieze patterns on ceilings and columns.

func NewFriezeFormula 

func NewFriezeFormula(formulaLevelTerms []Term) (*Frieze, error)

NewFriezeFormula returns a new formula

func (*Frieze) Calculate 

func (f *Frieze) Calculate(coordinate complex128) complex128

Calculate applies the Frieze formula to the complex number z.

func (*Frieze) FormulaLevelTerms 

func (f *Frieze) FormulaLevelTerms() []Term

FormulaLevelTerms returns the terms this formula will use.

func (*Frieze) LatticeVectors 

func (f *Frieze) LatticeVectors() []complex128

LatticeVectors returns an empty list, this formula does not use them

func (*Frieze) SymmetriesFound 

func (f *Frieze) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Frieze) WavePackets 

func (f *Frieze) WavePackets() []WavePacket

WavePackets returns an empty array, this type of formula does not use WavePackets.

type Generic 

type Generic struct {
	// contains filtered or unexported fields
}

Generic formulas will transform points by returning the same coordinates.

func NewGenericFormula 

func NewGenericFormula(packets []WavePacket, latticeWidth, latticeHeight float64, desiredSymmetry Symmetry) (*Generic, error)

NewGenericFormula returns a new formula object.

func (*Generic) Calculate 

func (r *Generic) Calculate(coordinate complex128) complex128

Calculate transforms the coordinate using the Generic lattice's wave packets.

func (*Generic) FormulaLevelTerms 

func (r *Generic) FormulaLevelTerms() []Term

FormulaLevelTerms returns an empty list, Generic formulas do not have base-level terms.

func (*Generic) LatticeVectors 

func (r *Generic) LatticeVectors() []complex128

LatticeVectors returns the lattice vectors used to create the rectangle.

func (*Generic) SymmetriesFound 

func (r *Generic) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Generic) WavePackets 

func (r *Generic) WavePackets() []WavePacket

WavePackets returns the wave packets used.

type Hexagonal 

type Hexagonal struct {
	// contains filtered or unexported fields
}

Hexagonal formulas will transform points by returning the same coordinates.

func NewHexagonalFormula 

func NewHexagonalFormula(packets []WavePacket, desiredSymmetry Symmetry) (*Hexagonal, error)

NewHexagonalFormula returns a new formula object.

func (*Hexagonal) Calculate 

func (r *Hexagonal) Calculate(coordinate complex128) complex128

Calculate transforms the coordinate using the Hexagonal lattice's wave packets.

func (*Hexagonal) FormulaLevelTerms 

func (r *Hexagonal) FormulaLevelTerms() []Term

FormulaLevelTerms returns an empty list, Hexagonal formulas do not have base-level terms.

func (*Hexagonal) LatticeVectors 

func (r *Hexagonal) LatticeVectors() []complex128

LatticeVectors returns the lattice vectors used to create the rectangle.

func (*Hexagonal) SymmetriesFound 

func (r *Hexagonal) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Hexagonal) WavePackets 

func (r *Hexagonal) WavePackets() []WavePacket

WavePackets returns the wave packets used.

type Identity 

type Identity struct{}

Identity formulas will transform points by returning the same coordinates.

func (*Identity) Calculate 

func (i *Identity) Calculate(coordinate complex128) complex128

Calculate returns the coordinate, the Identity formula returns the given input.

func (*Identity) FormulaLevelTerms 

func (i *Identity) FormulaLevelTerms() []Term

FormulaLevelTerms returns an empty list, Identity formulas do not have terms.

func (*Identity) LatticeVectors 

func (i *Identity) LatticeVectors() []complex128

LatticeVectors returns an empty list, this formula does not use them

func (*Identity) SymmetriesFound 

func (i *Identity) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Identity) WavePackets 

func (i *Identity) WavePackets() []WavePacket

WavePackets returns an empty array, this type of formula does not use WavePackets.

type Rectangular 

type Rectangular struct {
	// contains filtered or unexported fields
}

Rectangular formulas will transform points by returning the same coordinates.

func NewRectangularFormula 

func NewRectangularFormula(packets []WavePacket, latticeHeight float64, desiredSymmetry Symmetry) (*Rectangular, error)

NewRectangularFormula returns a new formula object.

func (*Rectangular) Calculate 

func (r *Rectangular) Calculate(coordinate complex128) complex128

Calculate transforms the coordinate using the Rectangular lattice's wave packets.

func (*Rectangular) FormulaLevelTerms 

func (r *Rectangular) FormulaLevelTerms() []Term

FormulaLevelTerms returns an empty list, Rectangular formulas do not have base-level terms.

func (*Rectangular) LatticeVectors 

func (r *Rectangular) LatticeVectors() []complex128

LatticeVectors returns the lattice vectors used to create the rectangle.

func (*Rectangular) SymmetriesFound 

func (r *Rectangular) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Rectangular) WavePackets 

func (r *Rectangular) WavePackets() []WavePacket

WavePackets returns the wave packets used.

type Rhombic 

type Rhombic struct {
	// contains filtered or unexported fields
}

Rhombic formulas will transform points by returning the same coordinates.

func NewRhombicFormula 

func NewRhombicFormula(packets []WavePacket, latticeHeight float64, desiredSymmetry Symmetry) (*Rhombic, error)

NewRhombicFormula returns a new formula object.

func (*Rhombic) Calculate 

func (r *Rhombic) Calculate(coordinate complex128) complex128

Calculate transforms the coordinate using the Rhombic lattice's wave packets.

func (*Rhombic) FormulaLevelTerms 

func (r *Rhombic) FormulaLevelTerms() []Term

FormulaLevelTerms returns an empty list, Rhombic formulas do not have base-level terms.

func (*Rhombic) LatticeVectors 

func (r *Rhombic) LatticeVectors() []complex128

LatticeVectors returns the lattice vectors used to create the rectangle.

func (*Rhombic) SymmetriesFound 

func (r *Rhombic) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Rhombic) WavePackets 

func (r *Rhombic) WavePackets() []WavePacket

WavePackets returns the wave packets used.

type Rosette 

type Rosette struct {
	// contains filtered or unexported fields
}

Rosette formulas transform points around a central origin, similar to a rosette surrounding a center.

func NewRosetteFormula 

func NewRosetteFormula(formulaLevelTerms []Term) (*Rosette, error)

NewRosetteFormula returns a new formula

func (*Rosette) Calculate 

func (r *Rosette) Calculate(coordinate complex128) complex128

Calculate applies the Rosette formula to the complex number z.

func (*Rosette) FormulaLevelTerms 

func (r *Rosette) FormulaLevelTerms() []Term

FormulaLevelTerms returns the terms this formula will use.

func (*Rosette) LatticeVectors 

func (r *Rosette) LatticeVectors() []complex128

LatticeVectors returns an empty list, this formula does not use them

func (*Rosette) SymmetriesFound 

func (r *Rosette) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Rosette) WavePackets 

func (r *Rosette) WavePackets() []WavePacket

WavePackets returns an empty array, this type of formula does not use WavePackets.

type Square 

type Square struct {
	// contains filtered or unexported fields
}

Square formulas will transform points by returning the same coordinates.

func NewSquareFormula 

func NewSquareFormula(packets []WavePacket, desiredSymmetry Symmetry) (*Square, error)

NewSquareFormula returns a new formula object.

func (*Square) Calculate 

func (r *Square) Calculate(coordinate complex128) complex128

Calculate transforms the coordinate using the Square lattice's wave packets.

func (*Square) FormulaLevelTerms 

func (r *Square) FormulaLevelTerms() []Term

FormulaLevelTerms returns an empty list, Square formulas do not have base-level terms.

func (*Square) LatticeVectors 

func (r *Square) LatticeVectors() []complex128

LatticeVectors returns the lattice vectors used to create the rectangle.

func (*Square) SymmetriesFound 

func (r *Square) SymmetriesFound() []Symmetry

SymmetriesFound returns all symmetries found in this pattern.

func (*Square) WavePackets 

func (r *Square) WavePackets() []WavePacket

WavePackets returns the wave packets used.

type Symmetry 

type Symmetry string

Symmetry encodes all possible symmetries for wallpaper patterns. 

const (
	P1   Symmetry = "p1"
	P2   Symmetry = "p2"
	P3   Symmetry = "p3"
	P3m1 Symmetry = "p3m1"
	P31m Symmetry = "p31m"
	P6   Symmetry = "p6"
	P6m  Symmetry = "p6m"
	P4   Symmetry = "p4"
	P4m  Symmetry = "p4m"
	P4g  Symmetry = "p4g"
	Cm   Symmetry = "cm"
	Cmm  Symmetry = "cmm"
	Pm   Symmetry = "pm"
	Pg   Symmetry = "pg"
	Pgg  Symmetry = "pgg"
	Pmm  Symmetry = "pmm"
	Pmg  Symmetry = "pmg"
)

All possible symmetries for wallpaper patterns, based on crystallography.

type Term 

type Term struct {
	Multiplier               complex128
	PowerN                   int
	PowerM                   int
	IgnoreComplexConjugate   bool
	CoefficientRelationships []coefficient.Relationship
}

Term objects help shape the calculation of every formula.

func NewTerm 

func NewTerm(multiplier complex128, powerN, powerM int, ignoreComplexConjugate bool, coefficientRelationships []coefficient.Relationship) *Term

NewTerm returns a new Term object.

func NewTermWithMultiplierAndPowers 

func NewTermWithMultiplierAndPowers(multiplier complex128, powerN, powerM int) *Term

NewTermWithMultiplierAndPowers returns a new Term object using just the multiplier, PowerN and PowerM.

func (Term) CalculateInLatticeCoordinates 

func (term Term) CalculateInLatticeCoordinates(zInLatticeCoordinates complex128) complex128

CalculateInLatticeCoordinates (z) = e ^ (2 PI i * (nX + mY)) 

where n amd m are PowerN and PowerM,
and TransformedX and TransformedY are the real and imag parts of (zInLatticeCoordinates)

func (Term) PowerSumIsEven 

func (term Term) PowerSumIsEven() bool

PowerSumIsEven returns true if the sum of the term powers is divisible by 2.

type TermBuilder 

type TermBuilder struct {
	// contains filtered or unexported fields
}

TermBuilder is used to create formula objects.

func NewTermBuilder 

func NewTermBuilder() *TermBuilder

NewTermBuilder returns a new object used to build Term objects.

func (*TermBuilder) AddCoefficientRelationship 

func (t *TermBuilder) AddCoefficientRelationship(coefficient coefficient.Relationship) *TermBuilder

AddCoefficientRelationship adds the coefficient.

func (*TermBuilder) Build 

func (t *TermBuilder) Build() *Term

Build creates a new Term object.

func (*TermBuilder) IgnoreComplexConjugate 

func (t *TermBuilder) IgnoreComplexConjugate() *TermBuilder

IgnoreComplexConjugate sets the field.

func (*TermBuilder) Multiplier 

func (t *TermBuilder) Multiplier(multiplier complex128) *TermBuilder

Multiplier sets the field.

func (*TermBuilder) PowerM 

func (t *TermBuilder) PowerM(coefficient int) *TermBuilder

PowerM sets the field.

func (*TermBuilder) PowerN 

func (t *TermBuilder) PowerN(coefficient int) *TermBuilder

PowerN sets the field.

func (*TermBuilder) UsingJSONData 

func (t *TermBuilder) UsingJSONData(data []byte) *TermBuilder

UsingJSONData updates the term, given data

func (*TermBuilder) UsingYAMLData 

func (t *TermBuilder) UsingYAMLData(data []byte) *TermBuilder

UsingYAMLData updates the term, given data

func (*TermBuilder) WithMarshalOptions 

func (t *TermBuilder) WithMarshalOptions(marshaledOptions TermMarshal) *TermBuilder

WithMarshalOptions updates the term builder using the options.

type TermMarshal 

type TermMarshal struct {
	Multiplier               *utility.ComplexNumberForMarshal `json:"multiplier" yaml:"multiplier"`
	PowerN                   int                              `json:"power_n" yaml:"power_n"`
	PowerM                   int                              `json:"power_m" yaml:"power_m"`
	CoefficientRelationships []coefficient.Relationship       `json:"coefficient_relationships" yaml:"coefficient_relationships"`
	IgnoreComplexConjugate   bool                             `json:"ignore_complex_conjugate" yaml:"ignore_complex_conjugate"`
}

TermMarshal is a representation of a term object

type WavePacket 

type WavePacket struct {
	// contains filtered or unexported fields
}

WavePacket for Waves mathematically creates repeating, cyclical mathematical patterns 

in 2D space, similar to waves on the ocean.

func (WavePacket) Calculate 

func (wavePacket WavePacket) Calculate(zInLatticeCoordinates complex128) complex128

Calculate takes the complex number zInLatticeCoordinates and processes it using the mathematical terms.

func (WavePacket) Multiplier 

func (wavePacket WavePacket) Multiplier() complex128

Multiplier is a getter.

func (WavePacket) Terms 

func (wavePacket WavePacket) Terms() []Term

Terms is a getter.

type WavePacketBuilder 

type WavePacketBuilder struct {
	// contains filtered or unexported fields
}

WavePacketBuilder is used to create new WavePackets.

func NewWavePacketBuilder 

func NewWavePacketBuilder() *WavePacketBuilder

NewWavePacketBuilder returns a blank WavePacketBuilder.

func (*WavePacketBuilder) AddTerm 

func (w *WavePacketBuilder) AddTerm(term *Term) *WavePacketBuilder

AddTerm adds a term to the formula.

func (*WavePacketBuilder) Build 

func (w *WavePacketBuilder) Build() *WavePacket

Build returns a new WavePacket.

func (*WavePacketBuilder) Multiplier 

func (w *WavePacketBuilder) Multiplier(multiplier complex128) *WavePacketBuilder

Multiplier sets the wave packet's multiplier.

func (*WavePacketBuilder) UsingJSONData 

func (w *WavePacketBuilder) UsingJSONData(data []byte) *WavePacketBuilder

UsingJSONData updates the term, given data

func (*WavePacketBuilder) UsingYAMLData 

func (w *WavePacketBuilder) UsingYAMLData(data []byte) *WavePacketBuilder

UsingYAMLData updates the term, given data

func (*WavePacketBuilder) WithMarshalOptions 

func (w *WavePacketBuilder) WithMarshalOptions(marshaledOptions WavePacketMarshal) *WavePacketBuilder

WithMarshalOptions updates the builder with options read from the options object.

type WavePacketMarshal 

type WavePacketMarshal struct {
	Multiplier *utility.ComplexNumberForMarshal `json:"multiplier" yaml:"multiplier"`
	Terms      []TermMarshal                    `json:"terms" yaml:"terms"`
}

WavePacketMarshal is a representation of a term object

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