gaul

package module
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 Go to latest Published: Jun 21, 2026 License: Apache-2.0 Imports: 18 Imported by: 19

README

Generative Art Utility Library (gaul)

Gaul is a generative art library. It was originally part of Sketchy, but I separated the non-gui parts and put them in gaul. The main reason for this is to make it easy to containerize generative art applications.

Documentation

Index

Constants

View Source 
const (
	BackgroundColorType = iota
	OutlineColorType
	TextColorType
	FillColorType
)
View Source 
const (
	LUTSize   = 1 << 16
	LUTMask   = LUTSize - 1
	LUTFactor = LUTSize / Tau
)
View Source 
const (
	Pi    = math.Pi
	Tau   = 2 * math.Pi
	Sqrt2 = math.Sqrt2
	Sqrt3 = 1.7320508075688772
	// Smol is a small value used for floating point comparisons
	Smol = 1e-5 // Increased from 1e-6 to handle geometric calculations better
	Phi  = 1.618033988749895
)

Variables

View Source 
var (
	ErrInvalidSides = errors.New("invalid number of sides")
)

Functions

func Clamp 

func Clamp(a float64, b float64, c float64) float64

Clamp restricts a value to a given range

func Deg2Rad 

func Deg2Rad(f float64) float64

Deg2Rad converts from degrees to radians

func Distance 

func Distance(p Point, q Point) float64

Distance between two points

func Equalf 

func Equalf(a, b float64) bool

func FloatString 

func FloatString(f float64, prec int) string

func Gcd 

func Gcd(a int, b int) int

Gcd calculates the greatest common divisor

func GetTimestampString 

func GetTimestampString() string

GetTimestampString creates a string based on the current time for use in filenames

func Lerp 

func Lerp(a float64, b float64, i float64) float64

Lerp calculates the linear interpolation between two values

func Linspace 

func Linspace(i float64, j float64, n int, b bool) []float64

Linspace creates a slice of linearly distributed values in a range

func Map 

func Map(a float64, b float64, c float64, d float64, i float64) float64

Map calculates the linear interpolation from one range to another

func NamedColor 

func NamedColor(name string) color.Color

func NoTinyVals 

func NoTinyVals(a float64) float64

NoTinyVals sets values very close to zero to zero

func Rad2Deg 

func Rad2Deg(f float64) float64

Rad2Deg converts from radians to degrees

func Shuffle 

func Shuffle(p *[]Point)

Shuffle a slice of points

func Smoothstep 

func Smoothstep(t float64) float64

func SquaredDistance 

func SquaredDistance(p Point, q Point) float64

SquaredDistance is the square of the distance between two points

func StringToColor 

func StringToColor(colorString string) color.Color

Types

type Affine2D 

type Affine2D struct {
	// contains filtered or unexported fields
}

Affine2D is a type for dealing with affine transformations in 2D using homogeneous coordinates

func Add 

func Add(p, q *Affine2D) *Affine2D

Add calculates the new Affine2D corresponding to adding p and q

func Mult 

func Mult(p, q *Affine2D) *Affine2D

Mult calculates the new Affine2D corresponding to multiplying p and q

func NewAffine2D 

func NewAffine2D() *Affine2D

NewAffine2D returns an identity affine transformation (no rotation, scaling, shearing, or translation)

func NewAffine2DWithRotation 

func NewAffine2DWithRotation(angle float64) *Affine2D

NewAffine2DWithRotation returns an affine transformation with rotation configured

func NewAffine2DWithScale 

func NewAffine2DWithScale(sx, sy float64) *Affine2D

NewAffine2DWithScale returns an affine transformation with scaling configured

func NewAffine2DWithShear 

func NewAffine2DWithShear(sx, sy float64) *Affine2D

NewAffine2DWithShear returns an affine transformation with shearing configured

func NewAffine2DWithTranslation 

func NewAffine2DWithTranslation(tx, ty float64) *Affine2D

NewAffine2DWithTranslation returns an affine transformation with translation configured

func (*Affine2D) MultVec 

func (a *Affine2D) MultVec(v Vec2) Vec2

MultVec returns a new vector which is the result of applying the affine transformation

func (*Affine2D) RotateAboutPoint 

func (a *Affine2D) RotateAboutPoint(vec Vec2, angle float64, point Point) Vec2

RotateAboutPoint rotates a vector around a point instead of the origin

func (*Affine2D) RotateCurveAboutPoint 

func (a *Affine2D) RotateCurveAboutPoint(curve Curve, angle float64, rotationPoint Point) Curve

RotateCurveAboutPoint rotates a curve around a point instead of the origin

func (*Affine2D) RotateLineAboutPoint 

func (a *Affine2D) RotateLineAboutPoint(line Line, angle float64, rotationPoint Point) Line

RotateLineAboutPoint rotates a line around a point instead of the origin

func (*Affine2D) RotatePointAboutPoint 

func (a *Affine2D) RotatePointAboutPoint(point Point, angle float64, rotationPoint Point) Point

RotatePointAboutPoint rotates a point around a point instead of the origin

func (*Affine2D) SetRotation 

func (a *Affine2D) SetRotation(angle float64)

SetRotation sets the rotation for the transformation

func (*Affine2D) SetRotationDegrees 

func (a *Affine2D) SetRotationDegrees(angle float64)

SetRotationDegrees sets the rotation of the transformation

func (*Affine2D) SetScale 

func (a *Affine2D) SetScale(sx, sy float64)

SetScale sets the scale factor for the x and y directions

func (*Affine2D) SetShearAngle 

func (a *Affine2D) SetShearAngle(ax, ay float64)

SetShearAngle sets the shear factor in the x and y directions

func (*Affine2D) SetShearAngleDegrees 

func (a *Affine2D) SetShearAngleDegrees(ax, ay float64)

SetShearAngleDegrees sets the shear factor in the x and y directions

func (*Affine2D) SetShearFactor 

func (a *Affine2D) SetShearFactor(sx, sy float64)

SetShearFactor sets the shear factor in the x and y directions

func (*Affine2D) SetTranslation 

func (a *Affine2D) SetTranslation(tx, ty float64)

SetTranslation sets the translation for the x and y directions

func (*Affine2D) Transform 

func (a *Affine2D) Transform(v Vec2) Vec2

Transform applies the affine transformation to a vector

func (*Affine2D) TransformCurve 

func (a *Affine2D) TransformCurve(c Curve) Curve

TransformCurve applies the affine transformation to a curve

func (*Affine2D) TransformLine 

func (a *Affine2D) TransformLine(l Line) Line

TransformLine applies the affine transformation to a line

func (*Affine2D) TransformPoint 

func (a *Affine2D) TransformPoint(p Point) Point

TransformPoint applies the affine transformation to a point

type BBox 

type BBox struct {
	Xl, Xr, Yt, Yb float64
}

Bounding Box

func NewBBox 

func NewBBox(xl, xr, yt, yb float64) BBox

Create new Bounding Box

type Beachsection 

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

type BeachsectionPtrs 

type BeachsectionPtrs []*Beachsection

type Cell 

type Cell struct {
	// Site of the cell
	Site Point
	// Array of halfedges sorted counterclockwise
	Halfedges []*Halfedge
}

Cell of voronoi diagram

type Circle 

type Circle struct {
	Center Point
	Radius float64
}

A Circle represented by a center point and radius

func (Circle) Boundary 

func (c Circle) Boundary() Rect

Boundary returns the smallest rect that contains all points on the circle

func (Circle) ContainsPoint 

func (c Circle) ContainsPoint(p Point) bool

ContainsPoint determines if a point lies inside the circle, including the boundary

func (Circle) Copy 

func (c Circle) Copy() Circle

Copy returns a new circle with the same center and radius

func (Circle) Draw 

func (c Circle) Draw(ctx *canvas.Context)

Draw draws the circle given a canvas context

func (Circle) PointOnEdge 

func (c Circle) PointOnEdge(p Point) bool

PointOnEdge determines if a point lies on the boundary of a circle

func (Circle) ToCurve 

func (c Circle) ToCurve(resolution int) Curve

ToCurve calculates a curve that approximates the circle with a given resolution (number of sides)

type ColorConfig 

type ColorConfig struct {
	Background color.Color
	Outline    color.Color
	Text       color.Color
	Fill       color.Color
	Gradient   SimpleGradient
}

func (*ColorConfig) Set 

func (cc *ColorConfig) Set(hexString string, colorType ColorType, defaultString string)

type ColorSpace 

type ColorSpace int
const (
	ColorSpaceRGB ColorSpace = iota
	ColorSpaceHSV
)

type ColorType 

type ColorType int

type CubicSpline 

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

CubicSpline represents a cubic spline

func NewCubicSpline 

func NewCubicSpline(points []Point) CubicSpline

NewCubicSpline creates a cubic spline from a set of points

func NewCubicSplineWithResolution 

func NewCubicSplineWithResolution(points []Point, res int) CubicSpline

NewCubicSplineWithResolution creates a cubic spline from a set of points with a specific resolution

func NewRegularCubicSpline 

func NewRegularCubicSpline(points []Point) CubicSpline

func (CubicSpline) At 

func (cs CubicSpline) At(x float64) float64

At evaluates the spline at a given x value

func (CubicSpline) ToCurve 

func (cs CubicSpline) ToCurve() Curve

ToCurve converts the spline to a curve

type Curve 

type Curve struct {
	Points []Point
	Closed bool
}

Curve A curve is a list of points, may be closed

func Chaikin 

func Chaikin(c Curve, q float64, n int) Curve

Chaikin senerates a Chaikin curve given a set of control points, a cutoff ratio, and the number of steps to use in the calculation.

func CubicBezier 

func CubicBezier(p, q, c1, c2 Point) Curve

CubicBezier generates a cubic Bézier curve between two points given two control points

func CubicBezierWithResolution 

func CubicBezierWithResolution(p, q, c1, c2 Point, resolution int) Curve

CubicBezierWithResolution generates a cubic Bézier curve with a specific resolution

func GenLissajous 

func GenLissajous(l Lissajous, n int, offset Point, s float64) Curve

GenLissajous generates a Lissajous curve given parameters, a number of points to use (i.e. resolution), and an offset and scale (typically to convert to screen coordinates)

func PulsarPlot 

func PulsarPlot(curves []Curve) []Curve

PulsarPlot transforms a slice of curves into a slice of curves representing the segments that make up a pulsar plot

func QuadBezier 

func QuadBezier(p, q, c Point) Curve

QuadBezier generates a quadratic Bézier curve between two points given a control point

func QuadBezierWithResolution 

func QuadBezierWithResolution(p, q, c Point, resolution int) Curve

QuadBezierWithResolution generates a quadratic Bézier curve with a specific resolution

func QuarticBezier 

func QuarticBezier(p, q, c1, c2, c3 Point) Curve

QuarticBezier generates a quartic Bézier curve between two points given three control points

func QuarticBezierWithResolution 

func QuarticBezierWithResolution(p, q, c1, c2, c3 Point, resolution int) Curve

QuarticBezierWithResolution generates a quartic Bézier curve with a specific resolution

func QuarticBezierWithTriangleControl 

func QuarticBezierWithTriangleControl(p, q Point, tri Triangle) Curve

func VoronoiWithCurve 

func VoronoiWithCurve(boundary Curve, sites []Point) ([]Curve, error)

VoronoiWithCurve computes the Euclidean Voronoi diagram for sites clipped to a convex polygonal boundary using Fortune's algorithm on the boundary's axis-aligned bounding box, followed by Sutherland–Hodgman clipping of each cell to boundary. Each returned Curve is closed and corresponds to the cell of sites[i] intersected with boundary. Vertices are counterclockwise for positive signed area in a Y-up coordinate system.

boundary must be Curve.Closed with at least three vertices, define a strictly positive area, and form a simple convex polygon (for example a Rect from Rect.ToCurve, a triangle, or another Voronoi cell). Non-convex boundaries are not supported because clipping is O(segments) per cell via convex half-plane cuts. Duplicate site coordinates yield identical curves. Sites must lie inside or on the boundary polygon.

func VoronoiWithRect 

func VoronoiWithRect(bounds Rect, sites []Point) ([]Curve, error)

VoronoiWithRect computes the Euclidean Voronoi diagram for sites clipped to bounds using Fortune's sweep line algorithm (O(n log n)). Each returned Curve is closed and corresponds to the Voronoi cell of sites[i] intersected with bounds (a polygon, not a triangle mesh). Vertices are ordered counterclockwise for positive signed area in a Y-up coordinate system. Duplicate input coordinates yield identical curves. Sites must lie strictly inside or on bounds (see Rect.ContainsPoint).

func (*Curve) AddPoint 

func (c *Curve) AddPoint(x, y float64)

AddPoint appends a point to the curve

func (*Curve) Area 

func (c *Curve) Area() float64

func (*Curve) Boundary 

func (c *Curve) Boundary() Rect

Boundary returns the smallest rect that contains all the points in the curve

func (*Curve) Centroid 

func (c *Curve) Centroid() Point

Centroid returns the centroid for the curve

func (*Curve) Copy 

func (c *Curve) Copy() Curve

Copy returns a new line with the same points and closed property

func (*Curve) Draw 

func (c *Curve) Draw(ctx *canvas.Context)

Draw draws the curve given a canvas context

func (*Curve) Last 

func (c *Curve) Last() Point

Last returns the last point in a curve

func (*Curve) LastLine 

func (c *Curve) LastLine() Line

LastLine returns the last line in a curve

func (*Curve) Length 

func (c *Curve) Length() float64

Length Calculates the length of the line segments of a curve

func (*Curve) Lerp 

func (c *Curve) Lerp(percentage float64) Point

Lerp calculates a point a given percentage along a curve

func (*Curve) LineAt 

func (c *Curve) LineAt(percentage float64) (Line, float64)

LineAt returns the line segment in a curve that is closest to the given percentage along the curve's length

func (*Curve) PerpendicularAt 

func (c *Curve) PerpendicularAt(percentage float64, length float64) Line

PerpendicularAt calculates a line that is perpendicular to the curve at a given percentage along the curve's length

func (*Curve) Reverse 

func (c *Curve) Reverse()

func (*Curve) Rotate 

func (c *Curve) Rotate(a float64)

Rotate calculates a new curve for which each point is rotated by the given angle

func (*Curve) Scale 

func (c *Curve) Scale(x, y float64)

Scale calculates a new curve for which each point is scaled by the give amount

func (*Curve) Shear 

func (c *Curve) Shear(x, y float64)

Shear calculates a new curve for which each point is sheared by the given amount

func (*Curve) Stitch 

func (c *Curve) Stitch(d *Curve)

func (*Curve) Translate 

func (c *Curve) Translate(x, y float64)

Translate calculates a new curve for which each point is translated by the given amount

type Edge 

type Edge struct {
	// Cell on the left
	LeftCell *Cell
	// Cell on the right
	RightCell *Cell
	// Start Point
	Va EdgeVertex
	// End Point
	Vb EdgeVertex
}

Edge structure

func (*Edge) GetOtherCell 

func (e *Edge) GetOtherCell(cell *Cell) *Cell

func (*Edge) GetOtherEdgeVertex 

func (e *Edge) GetOtherEdgeVertex(v Point) EdgeVertex

type EdgeVertex 

type EdgeVertex struct {
	Point
	Edges []*Edge
}

type Gradient 

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

func NewGradientFromColors 

func NewGradientFromColors(colors []color.Color) Gradient

NewGradientFromColors creates a Gradient directly from color.Color values. Used when reconstructing a gradient from the palette database.

func NewGradientFromNamed 

func NewGradientFromNamed(names []string) Gradient

func (*Gradient) AddStop 

func (g *Gradient) AddStop(colorString string)

func (*Gradient) Color 

func (g *Gradient) Color(percentage float64) color.Color

func (*Gradient) ColorAt 

func (g *Gradient) ColorAt(t float64) color.Color

ColorAt satisfies the Palette interface for Gradient.

func (*Gradient) ColorAtStop 

func (g *Gradient) ColorAtStop(i, n int) color.Color

ColorAtStop satisfies the Palette interface for Gradient.

func (*Gradient) LinearPalette 

func (g *Gradient) LinearPalette(num int) []color.Color

func (*Gradient) LinearPaletteStrings 

func (g *Gradient) LinearPaletteStrings(num int) []string

func (*Gradient) NumStops 

func (g *Gradient) NumStops() int

type Halfedge 

type Halfedge struct {
	Cell  *Cell
	Edge  *Edge
	Angle float64
}

Halfedge (directed edge)

func (*Halfedge) GetEndpoint 

func (h *Halfedge) GetEndpoint() Point

func (*Halfedge) GetStartpoint 

func (h *Halfedge) GetStartpoint() Point

type Halfedges 

type Halfedges []*Halfedge

Sort interface for halfedges

func (Halfedges) Len 

func (s Halfedges) Len() int

func (Halfedges) Swap 

func (s Halfedges) Swap(i, j int)

type IndexPoint 

type IndexPoint struct {
	Index int
	Point
}

An IndexPoint is a wrapper around a point with an extra int identifier, useful when used with trees and heaps

func (IndexPoint) ToPoint 

func (p IndexPoint) ToPoint() Point

type InteriorAngle 

type InteriorAngle int
const (
	CAB InteriorAngle = iota
	ABC
	BCA
)

type KDTree 

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

func NewKDTree 

func NewKDTree(r Rect) *KDTree

func NewKDTreeWithPoint 

func NewKDTreeWithPoint(p IndexPoint, r Rect) *KDTree

func (*KDTree) Clear 

func (k *KDTree) Clear()

func (*KDTree) Draw 

func (k *KDTree) Draw(ctx *canvas.Context)

func (*KDTree) DrawWithPoints 

func (k *KDTree) DrawWithPoints(s float64, ctx *canvas.Context)

func (*KDTree) Insert 

func (k *KDTree) Insert(p IndexPoint)

func (*KDTree) IsLeaf 

func (k *KDTree) IsLeaf() bool

func (*KDTree) NearestNeighbors 

func (k *KDTree) NearestNeighbors(point IndexPoint, s int) []IndexPoint

func (*KDTree) Query 

func (k *KDTree) Query(r Rect) []Point

func (*KDTree) Search 

func (k *KDTree) Search(p IndexPoint) *IndexPoint

func (*KDTree) Size 

func (k *KDTree) Size() int

func (*KDTree) UpdateIndex 

func (k *KDTree) UpdateIndex(p IndexPoint, index int) *IndexPoint

type LFSRLarge 

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

LFSRLarge is a 64-bit Xorshift PRNG Benchmarks show this is faster than LFSRMedium and LFSRSmall, so you might as well use this one. Benchmarks also show this is 6-7x faster than the standard math/rand PRNG

func NewLFSRLarge 

func NewLFSRLarge() LFSRLarge

func NewLFSRLargeWithSeed 

func NewLFSRLargeWithSeed(seed uint64) LFSRLarge

func (*LFSRLarge) Float64 

func (l *LFSRLarge) Float64() float64

func (*LFSRLarge) Next 

func (l *LFSRLarge) Next() uint64

func (*LFSRLarge) Uint64 

func (l *LFSRLarge) Uint64() uint64

func (*LFSRLarge) Uint64n 

func (l *LFSRLarge) Uint64n(n uint64) uint64

type LFSRMedium 

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

func NewLFSRMedium 

func NewLFSRMedium() LFSRMedium

func NewLFSRMediumWithSeed 

func NewLFSRMediumWithSeed(seed uint32) LFSRMedium

func (*LFSRMedium) Next 

func (l *LFSRMedium) Next() uint32

type LFSRSmall 

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

func NewLFSRSmall 

func NewLFSRSmall() LFSRSmall

func NewLFSRSmallWithSeed 

func NewLFSRSmallWithSeed(seed uint16) LFSRSmall

func (*LFSRSmall) Next 

func (l *LFSRSmall) Next() uint16

type Line 

type Line struct {
	P Point
	Q Point
}

Line is two points that form a line

func (Line) Angle 

func (l Line) Angle() float64

Angle calculates the angle between the line and the x-axis

func (Line) Boundary 

func (l Line) Boundary() Rect

Boundary returns the smallest rect that contains both points in the line

func (Line) ClosestPoint 

func (l Line) ClosestPoint(p Point) Point

ClosestPoint returns the closest point on the line segment to the given point

func (Line) Copy 

func (l Line) Copy() Line

Copy returns a new line with the same points P and Q

func (Line) Draw 

func (l Line) Draw(ctx *canvas.Context)

Draw draws the line given a canvas context

func (Line) Intersects 

func (l Line) Intersects(k Line) bool

Intersects determines if two lines intersect each other

func (Line) InvertedSlope 

func (l Line) InvertedSlope() float64

InvertedSlope calculates one over the slope of the line

func (Line) IsEqual 

func (l Line) IsEqual(k Line) bool

IsEqual determines if two lines are equal to each other

func (Line) Length 

func (l Line) Length() float64

Length Calculates the length of a line

func (Line) Lerp 

func (l Line) Lerp(i float64) Point

Lerp is an interpolation between the two points of a line

func (Line) Midpoint 

func (l Line) Midpoint() Point

Midpoint Calculates the midpoint of a line

func (Line) ParallelTo 

func (l Line) ParallelTo(k Line) bool

ParallelTo determines if two lines are parallel

func (Line) PerpendicularAt 

func (l Line) PerpendicularAt(percentage float64, length float64) Line

PerpendicularAt calculates a line at a given percentage along the line with a given length that is perpendicular to the original line

func (Line) PerpendicularBisector 

func (l Line) PerpendicularBisector(length float64) Line

PerpendicularBisector calculates a line with a given length at the midpoint of the original line that is also perpendicular to the line

func (Line) Rotate 

func (l Line) Rotate(a float64) Line

Rotate calculates a new line for which both points are rotated by the given angle

func (Line) SDF 

func (l Line) SDF(p Point) float64

SDF calculates the signed distance from a point to a line segment

func (Line) Scale 

func (l Line) Scale(x, y float64) Line

Scale calculates a new line for which both points are scaled by the given amount

func (Line) Shear 

func (l Line) Shear(x, y float64) Line

Shear calculates a new line for which both points are sheared by the given amount

func (Line) Slope 

func (l Line) Slope() float64

Slope computes the slope of the line

func (Line) String 

func (l Line) String() string

Line functions String representation of a line, useful for debugging

func (Line) Translate 

func (l Line) Translate(x, y float64) Line

Translate calculates a new line for which both points are translated by the given amount

type Lissajous 

type Lissajous struct {
	Nx int
	Ny int
	Px float64
	Py float64
}

Lissajous represents the core parameters for a 2D Lissajous curve

type MetricPoint 

type MetricPoint struct {
	Metric float64
	Index  int
	Point
}

A MetricPoint is a wrapper around a point with to extra identifiers, useful when used with trees and heaps

func (MetricPoint) ToIndexPoint 

func (p MetricPoint) ToIndexPoint() IndexPoint

func (MetricPoint) ToPoint 

func (p MetricPoint) ToPoint() Point

type Palette 

type Palette interface {
	ColorAt(t float64) color.Color
	ColorAtStop(i, n int) color.Color
}

Palette is the common interface for all gaul palette types. ColorAt accepts a normalized position t ∈ [0,1]. ColorAtStop returns the color at discrete stop i of n (t = i/(n-1)).

type Point 

type Point struct {
	X float64
	Y float64
}

Point is a simple point in 2D space

func Midpoint 

func Midpoint(p Point, q Point) Point

Midpoint Calculates the midpoint between two points

func PaduaPoints 

func PaduaPoints(n int) []Point

PaduaPoints calculates Padua points for a certain class of Lissajous curves, where Nx = Ny +/- 1. The correspond to intersection points and some of the outside points on the curve See https://en.wikipedia.org/wiki/Padua_points for more details.

func (Point) Copy 

func (p Point) Copy() Point

Copy returns a new point with the same x and y coordinates

func (Point) Draw 

func (p Point) Draw(s float64, ctx *canvas.Context)

Draw draws the point as a circle with a given radius using a canvas context

func (Point) IsEqual 

func (p Point) IsEqual(q Point) bool

IsEqual determines if two points are equal

func (Point) Lerp 

func (p Point) Lerp(a Point, i float64) Point

Lerp is a linear interpolation between two points

func (Point) Reflect 

func (p Point) Reflect() Point

Reflect calculates a new point that is reflected about both the x and y axes

func (Point) ReflectX 

func (p Point) ReflectX() Point

ReflectX calculates a new point that is reflected about the x-axis

func (Point) ReflectY 

func (p Point) ReflectY() Point

ReflectY calculates a new point that is reflected about the y-axis

func (Point) Rotate 

func (p Point) Rotate(a float64) Point

Rotate calculates a new point rotated around the origin by a given angle

func (Point) Scale 

func (p Point) Scale(x, y float64) Point

Scale multiplies point coordinates by a fixed value

func (Point) ScaleX 

func (p Point) ScaleX(x float64) Point

ScaleX scales the x value of a point

func (Point) ScaleY 

func (p Point) ScaleY(y float64) Point

ScaleY scales the y value of a point

func (Point) Shear 

func (p Point) Shear(x, y float64) Point

Shear calculates a new point sheared given angles for the x and y directions

func (Point) ShearX 

func (p Point) ShearX(a float64) Point

ShearX calculates a new point sheared in the x direction by a given angle

func (Point) ShearY 

func (p Point) ShearY(a float64) Point

ShearY calculates a new point sheared in the x direction by a given angle

func (Point) String 

func (p Point) String() string

Tuple representation of a point, useful for debugging

func (Point) ToIndexPoint 

func (p Point) ToIndexPoint(index int) IndexPoint

func (Point) ToMetricPoint 

func (p Point) ToMetricPoint(index int, metric float64) MetricPoint

func (Point) ToVec2 

func (p Point) ToVec2() Vec2

ToVec2 translates the point to a Vec2 struct

func (Point) Translate 

func (p Point) Translate(x, y float64) Point

Translate calculates a new point with coordinates translated by the given amounts

func (Point) TranslateX 

func (p Point) TranslateX(x float64) Point

TranslateX calculates a new point with the x coordinated translated by the given amount

func (Point) TranslateY 

func (p Point) TranslateY(y float64) Point

TranslateY calculates a new point with the y coordinated translated by the given amount

type PointHeap 

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

PointHeap is a min/max heap for Points using inter-point distance as the metric

func NewMaxPointHeap 

func NewMaxPointHeap() *PointHeap

func NewMinPointHeap 

func NewMinPointHeap() *PointHeap

func (*PointHeap) Len 

func (m *PointHeap) Len() int

func (*PointHeap) Peek 

func (m *PointHeap) Peek() MetricPoint

func (*PointHeap) Pop 

func (m *PointHeap) Pop() MetricPoint

func (*PointHeap) Push 

func (m *PointHeap) Push(p MetricPoint)

func (*PointHeap) Report 

func (m *PointHeap) Report() []MetricPoint

func (*PointHeap) ReportReversed 

func (m *PointHeap) ReportReversed() []MetricPoint

type Polygon 

type Polygon []Point

func (Polygon) Area 

func (p Polygon) Area() float64

func (Polygon) Centroid 

func (p Polygon) Centroid() Point

func (Polygon) Perimeter 

func (p Polygon) Perimeter() float64

type QuadTree 

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

func NewQuadTree 

func NewQuadTree(r Rect) *QuadTree

func NewQuadTreeWithCapacity 

func NewQuadTreeWithCapacity(r Rect, c int) *QuadTree

func (*QuadTree) Clear 

func (q *QuadTree) Clear()

func (*QuadTree) Draw 

func (q *QuadTree) Draw(ctx *canvas.Context)

func (*QuadTree) DrawWithPoints 

func (q *QuadTree) DrawWithPoints(s float64, ctx *canvas.Context)

func (*QuadTree) Insert 

func (q *QuadTree) Insert(p IndexPoint) bool

func (*QuadTree) NearestNeighbors 

func (q *QuadTree) NearestNeighbors(point IndexPoint, k int) []IndexPoint

func (*QuadTree) Query 

func (q *QuadTree) Query(r Rect) []Point

func (*QuadTree) QueryCircle 

func (q *QuadTree) QueryCircle(center Point, radius float64) []Point

func (*QuadTree) QueryCircleExcludeIndex 

func (q *QuadTree) QueryCircleExcludeIndex(center Point, radius float64, index int) []Point

func (*QuadTree) QueryExcludeIndex 

func (q *QuadTree) QueryExcludeIndex(r Rect, index int) []Point

func (*QuadTree) Search 

func (q *QuadTree) Search(p IndexPoint) *IndexPoint

func (*QuadTree) Size 

func (q *QuadTree) Size() int

func (*QuadTree) UpdateIndex 

func (q *QuadTree) UpdateIndex(p IndexPoint, index int) *IndexPoint

type Rect 

type Rect struct {
	X float64
	Y float64
	W float64
	H float64
}

Rect is a simple rectangle

func (Rect) Center 

func (r Rect) Center() Point

Center returns a point at the center of the rectangle

func (Rect) Contains 

func (r Rect) Contains(rect Rect) bool

Contains determines if the rectangle contains a given rectangle

func (Rect) ContainsPoint 

func (r Rect) ContainsPoint(p Point) bool

ContainsPoint determines if a point lies within a rectangle

func (Rect) Copy 

func (r Rect) Copy() Rect

Copy returns a new rectangle with the same corner, width, and height

func (Rect) Draw 

func (r Rect) Draw(ctx *canvas.Context)

Draw draws the rectangle given a canvas context

func (Rect) GoldenSubdivision 

func (r Rect) GoldenSubdivision() (Rect, Rect)

GoldenSubdivision returns two rectangles using the golden ratio to calculate where to split the rectangle

func (Rect) Intersects 

func (r Rect) Intersects(rect Rect) bool

Intersects determines if the rectangle intersects the given rectangle

func (Rect) IsDisjoint 

func (r Rect) IsDisjoint(rect Rect) bool

IsDisjoint determines if the rectangle is disjoint (no overlap) from a given rectangle

func (Rect) Overlaps 

func (r Rect) Overlaps(rect Rect) bool

Overlaps determines if the rectangle overlaps the given rectangle

func (Rect) Subdivide 

func (r Rect) Subdivide(perc float64) (Rect, Rect)

func (Rect) ToCurve 

func (r Rect) ToCurve() Curve

ToCurve calculates a closed curve with points corresponding to the vertices of the rectangle

type RegularPolygon 

type RegularPolygon struct {
	Sides    int
	Radius   float64
	Rotation float64 // in radians
	Center   Point
}

func NewRegularPolygon 

func NewRegularPolygon(sides int, radius float64, center Point) (RegularPolygon, error)

func NewRegularPolygonWithSideLength 

func NewRegularPolygonWithSideLength(sides int, sideLength float64, center Point) (RegularPolygon, error)

func (RegularPolygon) Apothem 

func (p RegularPolygon) Apothem() float64

func (RegularPolygon) Area 

func (p RegularPolygon) Area() float64

func (RegularPolygon) Draw 

func (p RegularPolygon) Draw(ctx *canvas.Context)

func (RegularPolygon) Edges 

func (p RegularPolygon) Edges() []Line

func (RegularPolygon) Lerp 

func (p RegularPolygon) Lerp(t float64) Point

func (RegularPolygon) Perimeter 

func (p RegularPolygon) Perimeter() float64

func (RegularPolygon) Points 

func (p RegularPolygon) Points() []Point

func (RegularPolygon) SideLength 

func (p RegularPolygon) SideLength() float64

func (RegularPolygon) ToCurve 

func (p RegularPolygon) ToCurve() Curve

type Rng 

type Rng struct {
	Prng    LFSRLarge
	Simplex *gfx.SimplexNoise
	// contains filtered or unexported fields
}

Rng is a random number generator with a system PRNG and simplex noise

func NewRng 

func NewRng(i int64) Rng

NewRng returns a PRNG with a system and Noise generator

func (*Rng) Gaussian 

func (r *Rng) Gaussian(mean float64, stdev float64) float64

func (*Rng) Noise1D 

func (r *Rng) Noise1D(x float64) float64

Noise1D 1D Noise values in the range of [-1, 1]

func (*Rng) Noise2D 

func (r *Rng) Noise2D(x float64, y float64) float64

Noise2D generates 2D Noise values in the range of [-1, 1]

func (*Rng) Noise3D 

func (r *Rng) Noise3D(x float64, y float64, z float64) float64

Noise3D generates 3D Noise values in the range of [0, 1]

func (*Rng) Noise4D 

func (r *Rng) Noise4D(x float64, y float64, z float64, w float64) float64

Noise4D generates 4D Noise values in the range of [-1, 1]

func (*Rng) NoisyRandomPoints 

func (r *Rng) NoisyRandomPoints(num int, threshold float64, rect Rect) []Point

func (*Rng) SetNoiseLacunarity 

func (r *Rng) SetNoiseLacunarity(l float64)

SetNoiseLacunarity sets how frequency scales with octaves

func (*Rng) SetNoiseOctaves 

func (r *Rng) SetNoiseOctaves(i int)

SetNoiseOctaves sets the number of steps when calculating fractal Noise

func (*Rng) SetNoiseOffsetX 

func (r *Rng) SetNoiseOffsetX(offset float64)

SetNoiseOffsetX offsets the x position in Noise calculations

func (*Rng) SetNoiseOffsetY 

func (r *Rng) SetNoiseOffsetY(offset float64)

SetNoiseOffsetY offsets the y position in Noise calculations

func (*Rng) SetNoiseOffsetZ 

func (r *Rng) SetNoiseOffsetZ(offset float64)

SetNoiseOffsetZ offsets the z position in Noise calculations

func (*Rng) SetNoisePersistence 

func (r *Rng) SetNoisePersistence(p float64)

SetNoisePersistence sets how amplitude scales with octaves

func (*Rng) SetNoiseScaleX 

func (r *Rng) SetNoiseScaleX(scale float64)

SetNoiseScaleX scales the x position in Noise calculations

func (*Rng) SetNoiseScaleY 

func (r *Rng) SetNoiseScaleY(scale float64)

SetNoiseScaleY scales the y position in Noise calculations

func (*Rng) SetNoiseScaleZ 

func (r *Rng) SetNoiseScaleZ(scale float64)

SetNoiseScaleZ scales the z position in Noise calculations

func (*Rng) SetSeed 

func (r *Rng) SetSeed(seed int64)

func (*Rng) UniformRandomPoints 

func (r *Rng) UniformRandomPoints(num int, rect Rect) []Point

UniformRandomPoints generates a list of points whose coordinates follow a uniform random distribution within a rectangle

type SimpleGradient 

type SimpleGradient struct {
	StartColor color.Color
	EndColor   color.Color
}

func NewSimpleGradient 

func NewSimpleGradient(c1, c2 string) SimpleGradient

func (*SimpleGradient) Color 

func (sg *SimpleGradient) Color(percentage float64) color.Color

func (*SimpleGradient) ColorAt 

func (sg *SimpleGradient) ColorAt(t float64) color.Color

ColorAt satisfies the Palette interface for SimpleGradient.

func (*SimpleGradient) ColorAtStop 

func (sg *SimpleGradient) ColorAtStop(i, n int) color.Color

ColorAtStop satisfies the Palette interface for SimpleGradient.

type SinePalette 

type SinePalette struct {
	A, B, C, D Vec3
	Alpha      float64
	Space      ColorSpace
}

func NewSinePalette 

func NewSinePalette(c, d Vec3) SinePalette

func (*SinePalette) ColorAt 

func (sp *SinePalette) ColorAt(t float64) color.Color

func (*SinePalette) ColorAtStop 

func (sp *SinePalette) ColorAtStop(i, n int) color.Color

func (*SinePalette) Palette 

func (sp *SinePalette) Palette(num int) []color.Color

func (*SinePalette) ToGridPng 

func (sp *SinePalette) ToGridPng() (string, error)

func (*SinePalette) ToPng 

func (sp *SinePalette) ToPng() (string, error)

type Triangle 

type Triangle struct {
	A Point
	B Point
	C Point
}

A Triangle specified by vertices as points

func DelaunayTriangles 

func DelaunayTriangles(sites []Point) []Triangle

DelaunayTriangles returns the Delaunay triangulation of the unique sites (duplicate coordinates are merged). Each output Triangle is oriented counterclockwise. The result is nil if there are fewer than three unique sites, or if no triangles remain after removing the artificial super-triangle (e.g. all sites collinear).

Implementation: Bowyer–Watson with a bounding super-triangle. The straightforward formulation scans all triangles for each insertion, which is O(n²) in the worst case. Divide-and-conquer or sweepline Delaunay constructions achieve O(n log n) time but are more intricate to implement and maintain. CCW winding is not a property of any particular asymptotic class: it is applied when building each triangle, and any correct Delaunay routine can enforce the same convention.

func (Triangle) AB 

func (t Triangle) AB() float64

AB returns the length of the side defined by vertices A and B also known as side "c" in typical notation

func (Triangle) AC 

func (t Triangle) AC() float64

AC returns the length of the side defined by vertices A and C also known as side "b" in typical notation

func (Triangle) Angles 

func (t Triangle) Angles() (alpha, beta, gamma float64)

Angles calculates the interior angles of the triangle

func (Triangle) Area 

func (t Triangle) Area() float64

Area calculates the area of the triangle

func (Triangle) BC 

func (t Triangle) BC() float64

BC returns the length of the side defined by vertices B and C also known as side "a" in typical notation

func (Triangle) BarycentricSubdivision 

func (t Triangle) BarycentricSubdivision() []Triangle

BarycentricSubdivision returns a slice of triangles that are the result of subdividing the triangle into three smaller triangles using the centroid and each vertex as the new vertices

func (Triangle) BisectSubdivision 

func (t Triangle) BisectSubdivision(angle InteriorAngle, percent float64) []Triangle

BisectSubdivision returns a slice of triangles that are the result of subdividing the triangle into two smaller triangles by bisecting one angle with a variable percent offset along the opposite side

func (Triangle) Boundary 

func (t Triangle) Boundary() Rect

Boundary returns the smallest rect that contains all three vertices

func (Triangle) Centroid 

func (t Triangle) Centroid() Point

Centroid calculates the centroid of the triangle

func (Triangle) Circumcenter 

func (t Triangle) Circumcenter() Point

Circumcenter calculates the circumcenter of the triangle

func (Triangle) CircumcenterSubdivision 

func (t Triangle) CircumcenterSubdivision() []Triangle

CircumcenterSubdivision returns a slice of triangles that are the result of subdividing the triangle into three smaller triangles using the circumcenter and each vertex as the new vertices

func (Triangle) Circumcircle 

func (t Triangle) Circumcircle() Circle

Circumcircle returns the circumcircle of the triangle

func (Triangle) CircumcircleRadius 

func (t Triangle) CircumcircleRadius() float64

CircumcircleRadius calculates the radius of the circumcircle

func (Triangle) ClosestPoint 

func (t Triangle) ClosestPoint(p Point) Point

ClosestPoint returns the closest point on the triangle to the given point

func (Triangle) ContainsPoint 

func (t Triangle) ContainsPoint(p Point) bool

func (Triangle) Copy 

func (t Triangle) Copy() Triangle

Copy returns a new triangle with the same vertices

func (Triangle) Draw 

func (t Triangle) Draw(ctx *canvas.Context)

Draw draws the triangle given a canvas context

func (Triangle) Incenter 

func (t Triangle) Incenter() Point

Incenter calculates the incenter of the triangle

func (Triangle) IncenterSubdivision 

func (t Triangle) IncenterSubdivision() []Triangle

IncenterSubdivision returns a slice of triangles that are the result of subdividing the triangle into three smaller triangles using the incenter and each vertex as the new vertices

func (Triangle) Incircle 

func (t Triangle) Incircle() Circle

Incircle returns the incircle of the triangle

func (Triangle) IncircleRadius 

func (t Triangle) IncircleRadius() float64

IncircleRadius calculates the radius of the incircle

func (Triangle) IsAcute 

func (t Triangle) IsAcute() bool

IsAcute determines whether the triangle has all angles less than 90 degrees, indicating an acute triangle.

func (Triangle) IsEquilateral 

func (t Triangle) IsEquilateral() bool

IsEquilateral determines whether the triangle has all three sides of equal length, indicating an equilateral triangle.

func (Triangle) IsIsosceles 

func (t Triangle) IsIsosceles() bool

IsIsosceles determines whether the triangle has at least two sides of equal length, indicating an isosceles triangle.

func (Triangle) IsObtuse 

func (t Triangle) IsObtuse() bool

IsObtuse determines whether the triangle has one angle greater than 90 degrees, indicating an obtuse triangle.

func (Triangle) IsRight 

func (t Triangle) IsRight() bool

IsRight determines whether the triangle has one right angle, indicating a right triangle.

func (Triangle) MidAndThirdsSubdivision 

func (t Triangle) MidAndThirdsSubdivision(angle InteriorAngle) []Triangle

func (Triangle) MidpointSubdivision 

func (t Triangle) MidpointSubdivision() []Triangle

MidpointSubdivision returns a slice of triangles that are the result of subdividing the triangle into four smaller triangles using the midpoints of each side as the set of new vertices

func (Triangle) NinePointCenter 

func (t Triangle) NinePointCenter() Point

NinePointCenter calculates the center point of the nine-point circle

func (Triangle) NinePointCircle 

func (t Triangle) NinePointCircle() Circle

NinePointCircle returns the nine-point circle of the triangle

func (Triangle) NinePointRadius 

func (t Triangle) NinePointRadius() float64

NinePointRadius calculates the radius of the nine-point circle

func (Triangle) Orthocenter 

func (t Triangle) Orthocenter() Point

Orthocenter calculates the orthocenter of the triangle

func (Triangle) OrthocenterSubdivision 

func (t Triangle) OrthocenterSubdivision() []Triangle

OrthocenterSubdivision returns a slice of triangles that are the result of subdividing the triangle into three smaller triangles using the orthocenter and each vertex as the new vertices

func (Triangle) Perimeter 

func (t Triangle) Perimeter() float64

Perimeter calculates the perimeter of the triangle

func (Triangle) Reverse 

func (t Triangle) Reverse() Triangle

func (Triangle) SDF 

func (t Triangle) SDF(p Point) float64

func (Triangle) ToCurve 

func (t Triangle) ToCurve() Curve

ToCurve calculates a closed curve with points corresponding to the vertices of the triangle

type TrigLUT 

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

TrigLUT is a lookup table for sine and cosine. In my tests, it is about 9x faster than math.Sin and math.Cos. The margin of error is < 0.005%. This LUT is not suitable for tangents, however.

func NewTrigLUT 

func NewTrigLUT() *TrigLUT

func (*TrigLUT) Cos 

func (lut *TrigLUT) Cos(x float64) float64

func (*TrigLUT) Sin 

func (lut *TrigLUT) Sin(x float64) float64

type Vec2 

type Vec2 struct {
	X float64
	Y float64
}

func Vec2FromLine 

func Vec2FromLine(l Line) Vec2

func Vec2FromPoint 

func Vec2FromPoint(p Point) Vec2

Vec2FromPoint returns a vector from the origin to p

func Vec2FromPoints 

func Vec2FromPoints(p, q Point) Vec2

Vec2FromPoints returns a vector from p to q

func (Vec2) Add 

func (v Vec2) Add(u Vec2) Vec2

func (Vec2) Dot 

func (v Vec2) Dot(u Vec2) float64

func (Vec2) Mag 

func (v Vec2) Mag() float64

func (Vec2) Normalize 

func (v Vec2) Normalize() Vec2

func (Vec2) Scale 

func (v Vec2) Scale(s float64) Vec2

func (Vec2) Sub 

func (v Vec2) Sub(u Vec2) Vec2

func (Vec2) ToPoint 

func (v Vec2) ToPoint() Point

func (Vec2) ToString 

func (v Vec2) ToString(prec int) string

func (Vec2) UnitNormal 

func (v Vec2) UnitNormal() Vec2

type Vec3 

type Vec3 struct {
	X float64
	Y float64
	Z float64
}

func (Vec3) Add 

func (v Vec3) Add(u Vec3) Vec3

func (Vec3) Dot 

func (v Vec3) Dot(u Vec3) float64

func (Vec3) Mag 

func (v Vec3) Mag() float64

func (Vec3) Normalize 

func (v Vec3) Normalize() Vec3

func (Vec3) Scale 

func (v Vec3) Scale(s float64) Vec3

func (Vec3) Sub 

func (v Vec3) Sub(u Vec3) Vec3

func (Vec3) ToString 

func (v Vec3) ToString(prec int) string

type Voronoi 

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

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