model2d

package
v0.2.18 Latest Latest
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 Go to latest Published: Aug 1, 2021 License: BSD-2-Clause Imports: 21 Imported by: 10

Documentation

Overview

Package model2d provides various tools for loading, manipulating, saving, and using 2D shapes. It is also intended to aid in creating 3D models which incorporate 2D shapes in some way.

Index

Constants

View Source 
const (
	DefaultBezierFitterNumIters  = 100
	DefaultBezierFitTolerance    = 1e-8
	DefaultBezierFitDelta        = 1e-5
	DefaultBezierFitMinStepScale = 1e-2
	DefaultBezierFitLineStep     = 2.0
	DefaultBezierFitLineGSS      = 8
)
View Source 
const (
	DefaultMedialAxisIters = 32
	DefaultMedialAxisEps   = 1e-8
)
View Source 
const (
	RasterizerDefaultSubsamples = 8
	RasterizerDefaultLineWidth  = 1.0
)
View Source 
const DefaultBezierMaxSplits = 16

DefaultBezierMaxSplits determines the maximum number of subdivisions when computing Bezier arc lengths.

Variables

This section is empty.

Functions

func BoundsValid added in v0.2.9 

func BoundsValid(b Bounder) bool

BoundsValid checks for numerical issues with the bounds.

func CacheScalarFunc added in v0.2.13 

func CacheScalarFunc(f func(float64) float64) func(float64) float64

CacheScalarFunc creates a scalar function that is equivalent to a deterministic function f, but caches results across calls in a concurrency-safe manner.

func ColliderContains 

func ColliderContains(c Collider, coord Coord, margin float64) bool

ColliderContains checks if a point is within a Collider and at least margin away from the border.

If the margin is negative, points are also conatined if the point is less than -margin away from the surface.

func Colorize added in v0.2.13 

func Colorize(g *image.Gray, co color.Color) *image.RGBA

Colorize turns a grayscale image into a color image with an alpha channel.

It is assumed that black (0) is "positive" while white (0xff) is negative.

func ColorizeOverlay added in v0.2.13 

func ColorizeOverlay(gs []*image.Gray, cs []color.Color) *image.RGBA

ColorizeOverlay turns a series of grayscale images into corresponding colors and then overlays them, each on top of the last.

All images must have the same bounds.

func CurveEvalX added in v0.2.6 

func CurveEvalX(c Curve, x float64) float64

CurveEvalX finds the y value that occurs at the given x value, assuming that the curve is monotonic in x.

If the y value cannot be found, NaN is returned.

func CurveInverseX added in v0.2.6 

func CurveInverseX(c Curve, x float64) float64

CurveInverseX gets the t value between 0 and 1 where the x value is equal to some x, assuming the curve is monotonic in x.

If the t cannot be found, NaN is returned.

func EncodeCSV added in v0.2.13 

func EncodeCSV(m *Mesh) []byte

EncodeCSV encodes the mesh as a CSV file.

func EncodeCustomSVG added in v0.2.11 

func EncodeCustomSVG(meshes []*Mesh, colors []string, thicknesses []float64, bounds Bounder) []byte

EncodeCustomSVG encodes multiple meshes, each with a different color and line thickness.

If bounds is not nil, it is used to determine the resulting bounds of the SVG. Otherwise, the union of all meshes is used.

func EncodeSVG 

func EncodeSVG(m *Mesh) []byte

EncodeSVG encodes the mesh as an SVG file.

func GroupBounders added in v0.2.11 

func GroupBounders(objects []Bounder)

GroupBounders sorts a slice of objects into a balanced bounding box hierarchy.

The sorted slice can be recursively cut in half, and each half will be spatially separated as well as possible along some axis. To cut a slice in half, divide the length by two, round down, and use the result as the start index for the second half.

func GroupSegments 

func GroupSegments(faces []*Segment)

GroupSegments is like GroupBounders, but for segments in particular.

This can be used to prepare models for being turned into a collider efficiently, or for storing meshes in an order well-suited for file compression.

The resulting hierarchy can be passed directly to GroupedSegmentsToCollider().

func InBounds 

func InBounds(b Bounder, c Coord) bool

InBounds returns true if c is contained within the bounding box of b.

func MarchingSquaresASCII added in v0.2.8 

func MarchingSquaresASCII(s Solid, delta float64) string

MarchingSquaresASCII turns a Solid into an ASCII-art line-drawing using a 2D version of marching cubes.

The delta is used as the horizontal spacing, and an aspect ratio of 2.0 (height/width) is assumed.

func Rasterize added in v0.2.6 

func Rasterize(path string, obj interface{}, scale float64) error

Rasterize renders a Solid, Collider, or Mesh to an image file.

The bounds of the object being rendered are scaled by the provided scale factor to convert to pixel coordinates.

This uses the default rasterization settings, such as the default line width and anti-aliasing settings. To change this, use a Rasterizer object directly.

func RasterizeColor added in v0.2.13 

func RasterizeColor(path string, objs []interface{}, colors []color.Color, scale float64) error

RasterizeColor is like Rasterize, but it renders multiple objects in different colors.

func SaveImage added in v0.2.7 

func SaveImage(path string, img image.Image) error

SaveImage saves a rasterized image to a file, inferring the file type from the extension.

func Triangulate 

func Triangulate(polygon []Coord) [][3]Coord

Triangulate turns any simple polygon into a set of equivalent triangles.

The polygon is passed as a series of points, in order. The first point is re-used as the ending point, so no ending should be explicitly specified.

Unlike TriangulateMesh, the order of the coordinates needn't be clockwise, and the orientation of the resulting triangles is undefined.

This should only be used for polygons with several vertices. For more complex shapes, use TriangulateMesh.

func TriangulateMesh added in v0.2.10 

func TriangulateMesh(m *Mesh) [][3]Coord

TriangulateMesh creates a minimal collection of triangles that cover the enclosed region of a mesh.

The mesh must be manifold, non-intersecting, and have the correct orientation (i.e. correct normals). The mesh may have holes, and is assumed to obey the even-odd rule for containment. If the mesh does not meet the expected criteria, the behavior of TriangulateMesh is undefined and may result in a panic.

The vertices of the resulting triangles are ordered clockwise (assuming a y-axis that points upward). This way, each triangle can itself be considered a minimal, correctly-oriented mesh.

Types

type BVH added in v0.2.11 

type BVH struct {
	// Leaf, if non-nil, is the sole object in this node.
	Leaf *Segment

	// Branch, if Leaf is nil, points to two children.
	Branch []*BVH
}

BVH represents a (possibly unbalanced) axis-aligned bounding box hierarchy of segments.

A BVH can be used to accelerate collision detection. See BVHToCollider() for more details.

A BVH node is either a leaf (a single segment), or a branch with two or more children.

For a more generic BVH that supports any object rather than just segments, see GeneralBVH.

func NewBVHAreaDensity added in v0.2.11 

func NewBVHAreaDensity(objs []*Segment) *BVH

NewBVHAreaDensity is like NewGeneralBVHAreaDensity but for segments.

type BezierCurve 

type BezierCurve []Coord

BezierCurve implements an arbitrarily high-dimensional Bezier curve.

func (BezierCurve) CachedEvalX added in v0.2.13 

func (b BezierCurve) CachedEvalX(x float64) func(float64) float64

CachedEvalX returns a function like EvalX that is cached between calls in a concurrency-safe manner.

func (BezierCurve) Eval 

func (b BezierCurve) Eval(t float64) Coord

Eval evaluates the curve at time t, where 0 <= t <= 1.

func (BezierCurve) EvalX 

func (b BezierCurve) EvalX(x float64) float64

EvalX finds the y value that occurs at the given x value, assuming that the curve is monotonic in x.

If the y value cannot be found, NaN is returned.

func (BezierCurve) InverseX 

func (b BezierCurve) InverseX(x float64) float64

InverseX gets the t value between 0 and 1 where the x value is equal to some x, assuming the curve is monotonic in x.

If the t cannot be found, NaN is returned.

func (BezierCurve) Length added in v0.2.22 

func (b BezierCurve) Length(tol float64, maxSplits int) float64

Length approximates the arclength of the curve within the given margin of error.

If maxSplits is specified, it determines the maximum number of sub-divisions to perform. Otherwise, DefaultBezierMaxSplits is used.

func (BezierCurve) Split added in v0.2.22 

func (b BezierCurve) Split(t float64) (BezierCurve, BezierCurve)

Split creates two Bezier curves from b, where the first curve represents b in the range [0, t] and the second in the range [t, 1].

func (BezierCurve) Transpose 

func (b BezierCurve) Transpose() BezierCurve

Transpose generates a BezierCurve where x and y are swapped.

type BezierFitter added in v0.2.15 

type BezierFitter struct {
	// NumIters is the number of gradient steps to use to
	// fit each Bezier curve.
	// If 0, DefaultBezierFitterNumIters is used.
	NumIters int

	// Tolerance is the maximum mean-squared error for a
	// curve when fitting a chain of connected points.
	// It is relative to the area of the bounding box of
	// the points in the chain.
	//
	// If 0, DefaultBezierFitTolerance is used.
	Tolerance float64

	// Delta, if specified, controls the step size used
	// for finite differences, relative to the size of the
	// entire Bezier curve.
	// If 0, DefaultBezierFitDelta is used.
	Delta float64

	// L2Penalty, if specified, is a loss penalty imposed
	// on the squared distance between the control points
	// and their corresponding endpoints, scaled relative
	// to the distance between the endpoints.
	L2Penalty float64

	// MinStepScale, if specified, is a scalar multiplied
	// by the finite-differences delta to decide the first
	// (and smallest) step to try for line search.
	// If 0, DefaultBezierFitMinStepScale is used.
	MinStepScale float64

	// LineStep, if specified, is the rate of increase for
	// each step of line search. Larger values make line
	// search faster, but can miss local minima.
	// If 0, DefaultBezierFitLineStep is used.
	LineStep float64

	// LineGSS, if specified, is the number of steps used
	// for golden section search at the end of line
	// search. Higher values yield more precise steps.
	// If 0, DefaultBezierFitLineGSS is used.
	LineGSS int

	// Momentum, if specified, is the momentum coefficient.
	// If 0, regular gradient descent is used.
	Momentum float64

	// AllowIntersections can be set to true to allow
	// Bezier curves to cross themselves.
	AllowIntersections bool

	// NoFirstGuess disables FirstGuess() approximations
	// during Fit() and FitChain() calls.
	NoFirstGuess bool
}

A BezierFitter fits Bezier curves to points.

func (*BezierFitter) FirstGuess added in v0.2.15 

func (b *BezierFitter) FirstGuess(points []Coord) BezierCurve

FirstGuess attempts to quickly approximate some subset of the specified points with a cubic Bezier curve, allowing for potentially faster convergence when fitting all of the points.

This method assumes that all of the points are sorted along the curve from a start point to an end point, and no two points are exactly equal. This is a stronger assumption than FitCubic() makes.

func (*BezierFitter) FirstGuessConstrained added in v0.2.22 

func (b *BezierFitter) FirstGuessConstrained(points []Coord, t1, t2 *Coord) BezierCurve

FirstGuessConstrained is like FirstGuess, but the control points are optionally constrained to given tangent directions.

func (*BezierFitter) Fit added in v0.2.15 

func (b *BezierFitter) Fit(m *Mesh) []BezierCurve

Fit fits a collection of cubic Bezier curves to a manifold mesh.

func (*BezierFitter) FitChain added in v0.2.15 

func (b *BezierFitter) FitChain(points []Coord, closed bool) []BezierCurve

FitChain fits a sequence of points along some curve using one or more cubic Bezier curves.

The closed argument indicates if the final point should be smoothly reconnected to the first point.

The points should be ordered along the desired curve, and no two points should be exactly equal.

func (*BezierFitter) FitCubic added in v0.2.15 

func (b *BezierFitter) FitCubic(points []Coord, start BezierCurve) BezierCurve

FitCubic finds the cubic Bezier curve of best fit for the points.

The first and last points are used as start and end points, and all the other points may be in any order.

func (*BezierFitter) FitCubicConstrained added in v0.2.15 

func (b *BezierFitter) FitCubicConstrained(points []Coord, t1, t2 *Coord,
	start BezierCurve) BezierCurve

FitCubicConstrained is like FitCubic, but constrains the tangent vectors at either the start or end point, or both.

If non-nil, t1 is the direction for the first control point from the first point, and t2 is the direction of the second control point from the last point.

func (*BezierFitter) MSE added in v0.2.15 

func (b *BezierFitter) MSE(points []Coord, curve BezierCurve) float64

MSE computes the MSE of a cubic Bezier fit.

type Bitmap 

type Bitmap struct {
	Data   []bool
	Width  int
	Height int
}

A Bitmap is a two-dimensional image with boolean values. The data is stored in row-major order.

func MustReadBitmap 

func MustReadBitmap(path string, c ColorBitFunc) *Bitmap

MustReadBitmap is like ReadBitmap, except that it panics if the bitmap cannot be read.

func NewBitmap 

func NewBitmap(width, height int) *Bitmap

NewBitmap creates an empty bitmap.

func NewBitmapImage 

func NewBitmapImage(img image.Image, c ColorBitFunc) *Bitmap

NewBitmapImage creates a Bitmap from an image, by calling c for each pixel and using the result as the bit.

If c is nil, then the mean RGBA is computed, and pixels are considered true if they are closer to the mean in L2 distance than they are to the top-left pixel. For images with two dominant colors, this is equivalent to making the background false, and the foreground true, assuming that the first pixel is background.

func ReadBitmap 

func ReadBitmap(path string, c ColorBitFunc) (*Bitmap, error)

ReadBitmap is like NewBitmapImage, except that it reads the image from a file.

func (*Bitmap) FlipX 

func (b *Bitmap) FlipX() *Bitmap

FlipX reverses the x-axis.

func (*Bitmap) FlipY 

func (b *Bitmap) FlipY() *Bitmap

FlipY reverses the y-axis.

func (*Bitmap) Get 

func (b *Bitmap) Get(x, y int) bool

Get gets the bit at the coordinate.

If the coordinate is out of bounds, false is returned.

func (*Bitmap) Invert 

func (b *Bitmap) Invert() *Bitmap

Invert creates a new bitmap with the opposite values.

func (*Bitmap) Mesh 

func (b *Bitmap) Mesh() *Mesh

Mesh converts the bitmap to a mesh by creating boxes around every true pixel and deleting duplicate segments.

func (*Bitmap) Set 

func (b *Bitmap) Set(x, y int, v bool)

Set sets the bit at the coordinate.

The coordinate must be in bounds.

type Bounder 

type Bounder interface {
	// Get the corners of a bounding box.
	//
	// A point p satisfies p >= Min and p <= Max if it is
	// within the bounds.
	Min() Coord
	Max() Coord
}

A Bounder is an object contained in an axis-aligned bounding box.

type Circle added in v0.2.3 

type Circle struct {
	Center Coord
	Radius float64
}

A Circle is a 2D perfect circle.

func (*Circle) Contains added in v0.2.3 

func (c *Circle) Contains(coord Coord) bool

func (*Circle) Max added in v0.2.3 

func (c *Circle) Max() Coord

func (*Circle) Min added in v0.2.3 

func (c *Circle) Min() Coord

type Collider 

type Collider interface {
	Bounder

	// RayCollisions enumerates the collisions with a ray.
	// It returns the total number of collisions.
	//
	// f may be nil, in which case this is simply used for
	// counting.
	RayCollisions(r *Ray, f func(RayCollision)) int

	// FirstRayCollision gets the ray collision with the
	// lowest scale.
	//
	// The second return value is false if no collisions
	// were found.
	FirstRayCollision(r *Ray) (collision RayCollision, collides bool)

	// CircleCollision checks if the collider touches a
	// circle with origin c and radius r.
	CircleCollision(c Coord, r float64) bool
}

A Collider is the outline of a 2-dimensional shape. It can count its intersections with a ray, and check if any part of the outline is inside a circle.

All methods of a Collider are safe for concurrency.

func TransformCollider added in v0.2.11 

func TransformCollider(t DistTransform, c Collider) Collider

TransformCollider applies t to the Collider c to produce a new, transformed Collider.

type ColliderSolid 

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

A ColliderSolid is a Solid that uses a Collider to check if points are in the solid.

There are two modes for a ColliderSolid. In the first, points are inside the solid if a ray passes through the surface of the Collider an odd number of times. In the second, points are inside the solid if a sphere of a pre-determined radius touches the surface of the Collider from the point. The second modality is equivalent to creating a thick but hollow solid.

func NewColliderSolid 

func NewColliderSolid(c Collider) *ColliderSolid

NewColliderSolid creates a basic ColliderSolid.

func NewColliderSolidHollow 

func NewColliderSolidHollow(c Collider, r float64) *ColliderSolid

NewColliderSolidHollow creates a ColliderSolid that only reports containment around the edges.

func NewColliderSolidInset 

func NewColliderSolidInset(c Collider, inset float64) *ColliderSolid

NewColliderSolidInset creates a ColliderSolid that only reports containment at some distance from the surface.

If inset is negative, then the solid is outset from the collider.

func (*ColliderSolid) Contains 

func (c *ColliderSolid) Contains(coord Coord) bool

Contains checks if coord is in the solid.

func (*ColliderSolid) Max 

func (c *ColliderSolid) Max() Coord

Max gets the maximum of the bounding box.

func (*ColliderSolid) Min 

func (c *ColliderSolid) Min() Coord

Min gets the minimum of the bounding box.

type ColorBitFunc 

type ColorBitFunc func(c color.Color) bool

ColorBitFunc turns colors into single bits.

type ConvexPolytope added in v0.2.11 

type ConvexPolytope []*LinearConstraint

A ConvexPolytope is the intersection of some linear constraints.

func NewConvexPolytopeRect added in v0.2.11 

func NewConvexPolytopeRect(min, max Coord) ConvexPolytope

NewConvexPolytopeRect creates a rectangular convex polytope.

func (ConvexPolytope) Contains added in v0.2.11 

func (c ConvexPolytope) Contains(coord Coord) bool

Contains checks that c satisfies the constraints.

func (ConvexPolytope) Mesh added in v0.2.11 

func (c ConvexPolytope) Mesh() *Mesh

Mesh creates a mesh containing all of the finite faces of the polytope.

For complicated polytopes, this may take a long time to run, since it is O(n^2) in the constraints.

func (ConvexPolytope) Solid added in v0.2.11 

func (c ConvexPolytope) Solid() Solid

Solid creates a solid out of the polytope.

This runs in O(n^2) in the constraints, so it may be unacceptable for large polytopes.

type Coord 

type Coord struct {
	X float64
	Y float64
}

A Coord is a coordinate in 2-D Euclidean space.

func NewCoordArray 

func NewCoordArray(a [2]float64) Coord

NewCoordArray creates a Coord from an array of x and y.

func NewCoordPolar added in v0.2.9 

func NewCoordPolar(theta, radius float64) Coord

NewCoordPolar converts polar coordinates to a Coord.

func NewCoordRandBounds added in v0.2.8 

func NewCoordRandBounds(min, max Coord) Coord

NewCoordRandBounds creates a random Coord uniformly inside the given rectangular boundary.

func NewCoordRandNorm 

func NewCoordRandNorm() Coord

NewCoordRandNorm creates a random Coord with normally distributed components.

func NewCoordRandUniform added in v0.2.4 

func NewCoordRandUniform() Coord

NewCoordRandUniform creates a random Coord with uniformly random coordinates in [0, 1).

func NewCoordRandUnit 

func NewCoordRandUnit() Coord

NewCoordRandUnit creates a random Coord with magnitude 1.

func Ones added in v0.2.6 

func Ones(a float64) Coord

Ones creates the unit vector scaled by a constant.

func ProjectMedialAxis added in v0.2.8 

func ProjectMedialAxis(p PointSDF, c Coord, iters int, eps float64) Coord

ProjectMedialAxis projects the point c onto the medial axis of the shape defined by SDF p.

The iters argument specifies the number of search steps to perform to narrow down the medial axis. If 0, DefaultMedialAxisIters is used.

The eps argument specifies how close two points on the surface of p must be to be considered the same point. If 0, DefaultMedialAxisEps is used.

The bounds of p are used to aid computation. Thus, it is important to get tight bounds on the SDF for maximally accurate results.

func X added in v0.2.4 

func X(x float64) Coord

X gets a coordinate in the X direction.

func XY added in v0.2.6 

func XY(x, y float64) Coord

XY constructs a coordinate.

func Y added in v0.2.4 

func Y(y float64) Coord

Y gets a coordinate in the Y direction.

func (Coord) Add 

func (c Coord) Add(c1 Coord) Coord

Add computes the sum of c and c1.

func (Coord) AddScalar added in v0.2.6 

func (c Coord) AddScalar(s float64) Coord

AddScalar adds s to all of the coordinates and returns the new coordinate.

func (Coord) Array 

func (c Coord) Array() [2]float64

Array gets an array of x and y.

func (Coord) Dist 

func (c Coord) Dist(c1 Coord) float64

Dist computes the Euclidean distance to c1.

func (Coord) Div added in v0.2.2 

func (c Coord) Div(c1 Coord) Coord

Div computes the element-wise quotient of c / c1.

func (Coord) Dot 

func (c Coord) Dot(c1 Coord) float64

Dot computes the dot product of c and c1.

func (Coord) L1Dist added in v0.2.13 

func (c Coord) L1Dist(c1 Coord) float64

L1Dist computes the L1 distance to c1.

func (Coord) Max 

func (c Coord) Max(c1 Coord) Coord

Max gets the element-wise maximum of c and c1.

func (Coord) Mid 

func (c Coord) Mid(c1 Coord) Coord

Mid computes the midpoint between c and c1.

func (Coord) Min 

func (c Coord) Min(c1 Coord) Coord

Min gets the element-wise minimum of c and c1.

func (Coord) Mul 

func (c Coord) Mul(c1 Coord) Coord

Mul computes the element-wise product of c and c1.

func (Coord) Norm 

func (c Coord) Norm() float64

Norm computes the vector L2 norm.

func (Coord) Normalize 

func (c Coord) Normalize() Coord

Normalize gets a unit vector from c.

func (Coord) ProjectOut 

func (c Coord) ProjectOut(c1 Coord) Coord

ProjectOut projects the c1 direction out of c.

func (Coord) Recip added in v0.2.9 

func (c Coord) Recip() Coord

Recip gets a coordinate as 1 / c.

func (Coord) Reflect 

func (c Coord) Reflect(c1 Coord) Coord

Reflect reflects c1 around c.

func (Coord) Scale 

func (c Coord) Scale(s float64) Coord

Scale scales all the coordinates by s and returns the new coordinate.

func (Coord) SquaredDist added in v0.2.13 

func (c Coord) SquaredDist(c1 Coord) float64

SquaredDist gets the squared Euclidean distance to c1.

func (Coord) Sub 

func (c Coord) Sub(c1 Coord) Coord

Sub computes c - c1.

func (Coord) Sum 

func (c Coord) Sum() float64

Sum sums the elements of c.

type CoordMap added in v0.2.14 

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

CoordMap implements a map-like interface for mapping Coord to interface{}.

This can be more efficient than using a map directly, since it uses a special hash function for coordinates. The speed-up is variable, but was ~2x as of mid-2021.

func NewCoordMap added in v0.2.14 

func NewCoordMap() *CoordMap

NewCoordMap creates an empty map.

func (*CoordMap) Delete added in v0.2.14 

func (m *CoordMap) Delete(key Coord)

Delete removes the key from the map if it exists, and does nothing otherwise.

func (*CoordMap) KeyRange added in v0.2.14 

func (m *CoordMap) KeyRange(f func(key Coord) bool)

KeyRange is like Range, but only iterates over keys, not values.

func (*CoordMap) Len added in v0.2.14 

func (m *CoordMap) Len() int

Len gets the number of elements in the map.

func (*CoordMap) Load added in v0.2.14 

func (m *CoordMap) Load(key Coord) (interface{}, bool)

Load gets the value for the given key.

If no value is present, the first return argument is a zero value, and the second is false. Otherwise, the second return value is true.

func (*CoordMap) Range added in v0.2.14 

func (m *CoordMap) Range(f func(key Coord, value interface{}) bool)

Range iterates over the map, calling f successively for each value until it returns false, or all entries are enumerated.

It is not safe to modify the map with Store or Delete during enumeration.

func (*CoordMap) Store added in v0.2.14 

func (m *CoordMap) Store(key Coord, value interface{})

Store assigns the value to the given key, overwriting the previous value for the key if necessary.

func (*CoordMap) Value added in v0.2.14 

func (m *CoordMap) Value(key Coord) interface{}

Value is like Load(), but without a second return value.

func (*CoordMap) ValueRange added in v0.2.14 

func (m *CoordMap) ValueRange(f func(value interface{}) bool)

ValueRange is like Range, but only iterates over values only.

type CoordToCoord added in v0.2.14 

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

CoordToCoord implements a map-like interface for mapping Coord to Coord.

This can be more efficient than using a map directly, since it uses a special hash function for coordinates. The speed-up is variable, but was ~2x as of mid-2021.

func NewCoordToCoord added in v0.2.14 

func NewCoordToCoord() *CoordToCoord

NewCoordToCoord creates an empty map.

func (*CoordToCoord) Delete added in v0.2.14 

func (m *CoordToCoord) Delete(key Coord)

Delete removes the key from the map if it exists, and does nothing otherwise.

func (*CoordToCoord) KeyRange added in v0.2.14 

func (m *CoordToCoord) KeyRange(f func(key Coord) bool)

KeyRange is like Range, but only iterates over keys, not values.

func (*CoordToCoord) Len added in v0.2.14 

func (m *CoordToCoord) Len() int

Len gets the number of elements in the map.

func (*CoordToCoord) Load added in v0.2.14 

func (m *CoordToCoord) Load(key Coord) (Coord, bool)

Load gets the value for the given key.

If no value is present, the first return argument is a zero value, and the second is false. Otherwise, the second return value is true.

func (*CoordToCoord) Range added in v0.2.14 

func (m *CoordToCoord) Range(f func(key Coord, value Coord) bool)

Range iterates over the map, calling f successively for each value until it returns false, or all entries are enumerated.

It is not safe to modify the map with Store or Delete during enumeration.

func (*CoordToCoord) Store added in v0.2.14 

func (m *CoordToCoord) Store(key Coord, value Coord)

Store assigns the value to the given key, overwriting the previous value for the key if necessary.

func (*CoordToCoord) Value added in v0.2.14 

func (m *CoordToCoord) Value(key Coord) Coord

Value is like Load(), but without a second return value.

func (*CoordToCoord) ValueRange added in v0.2.14 

func (m *CoordToCoord) ValueRange(f func(value Coord) bool)

ValueRange is like Range, but only iterates over values only.

type CoordToFaces added in v0.2.14 

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

CoordToFaces implements a map-like interface for mapping Coord to []*Segment.

This can be more efficient than using a map directly, since it uses a special hash function for coordinates. The speed-up is variable, but was ~2x as of mid-2021.

func NewCoordToFaces added in v0.2.14 

func NewCoordToFaces() *CoordToFaces

NewCoordToFaces creates an empty map.

func (*CoordToFaces) Append added in v0.2.14 

func (m *CoordToFaces) Append(key Coord, x *Segment) []*Segment

Append appends x to the value stored for the given key and returns the new value.

func (*CoordToFaces) Delete added in v0.2.14 

func (m *CoordToFaces) Delete(key Coord)

Delete removes the key from the map if it exists, and does nothing otherwise.

func (*CoordToFaces) KeyRange added in v0.2.14 

func (m *CoordToFaces) KeyRange(f func(key Coord) bool)

KeyRange is like Range, but only iterates over keys, not values.

func (*CoordToFaces) Len added in v0.2.14 

func (m *CoordToFaces) Len() int

Len gets the number of elements in the map.

func (*CoordToFaces) Load added in v0.2.14 

func (m *CoordToFaces) Load(key Coord) ([]*Segment, bool)

Load gets the value for the given key.

If no value is present, the first return argument is a zero value, and the second is false. Otherwise, the second return value is true.

func (*CoordToFaces) Range added in v0.2.14 

func (m *CoordToFaces) Range(f func(key Coord, value []*Segment) bool)

Range iterates over the map, calling f successively for each value until it returns false, or all entries are enumerated.

It is not safe to modify the map with Store or Delete during enumeration.

func (*CoordToFaces) Store added in v0.2.14 

func (m *CoordToFaces) Store(key Coord, value []*Segment)

Store assigns the value to the given key, overwriting the previous value for the key if necessary.

func (*CoordToFaces) Value added in v0.2.14 

func (m *CoordToFaces) Value(key Coord) []*Segment

Value is like Load(), but without a second return value.

func (*CoordToFaces) ValueRange added in v0.2.14 

func (m *CoordToFaces) ValueRange(f func(value []*Segment) bool)

ValueRange is like Range, but only iterates over values only.

type CoordToInt added in v0.2.14 

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

CoordToInt implements a map-like interface for mapping Coord to int.

This can be more efficient than using a map directly, since it uses a special hash function for coordinates. The speed-up is variable, but was ~2x as of mid-2021.

func NewCoordToInt added in v0.2.14 

func NewCoordToInt() *CoordToInt

NewCoordToInt creates an empty map.

func (*CoordToInt) Add added in v0.2.14 

func (m *CoordToInt) Add(key Coord, x int) int

Add adds x to the value stored for the given key and returns the new value.

func (*CoordToInt) Delete added in v0.2.14 

func (m *CoordToInt) Delete(key Coord)

Delete removes the key from the map if it exists, and does nothing otherwise.

func (*CoordToInt) KeyRange added in v0.2.14 

func (m *CoordToInt) KeyRange(f func(key Coord) bool)

KeyRange is like Range, but only iterates over keys, not values.

func (*CoordToInt) Len added in v0.2.14 

func (m *CoordToInt) Len() int

Len gets the number of elements in the map.

func (*CoordToInt) Load added in v0.2.14 

func (m *CoordToInt) Load(key Coord) (int, bool)

Load gets the value for the given key.

If no value is present, the first return argument is a zero value, and the second is false. Otherwise, the second return value is true.

func (*CoordToInt) Range added in v0.2.14 

func (m *CoordToInt) Range(f func(key Coord, value int) bool)

Range iterates over the map, calling f successively for each value until it returns false, or all entries are enumerated.

It is not safe to modify the map with Store or Delete during enumeration.

func (*CoordToInt) Store added in v0.2.14 

func (m *CoordToInt) Store(key Coord, value int)

Store assigns the value to the given key, overwriting the previous value for the key if necessary.

func (*CoordToInt) Value added in v0.2.14 

func (m *CoordToInt) Value(key Coord) int

Value is like Load(), but without a second return value.

func (*CoordToInt) ValueRange added in v0.2.14 

func (m *CoordToInt) ValueRange(f func(value int) bool)

ValueRange is like Range, but only iterates over values only.

type CoordTree added in v0.2.13 

type CoordTree struct {
	Coord Coord

	// SplitAxis is the dimension to split on for branches.
	SplitAxis int

	// At least one of these is non-nil for branches.
	LessThan     *CoordTree
	GreaterEqual *CoordTree
}

A CoordTree is a k-d tree over Coords.

A nil *CoordTree represents an empty tree.

func NewCoordTree added in v0.2.13 

func NewCoordTree(points []Coord) *CoordTree

func (*CoordTree) Contains added in v0.2.13 

func (c *CoordTree) Contains(p Coord) bool

Contains checks if any point in the tree is exactly equal to p.

func (*CoordTree) Dist added in v0.2.14 

func (c *CoordTree) Dist(p Coord) float64

Dist gets the distance from a point p to its nearest neighbor in c.

func (*CoordTree) Empty added in v0.2.13 

func (c *CoordTree) Empty() bool

Empty returns true if c contains no points.

func (*CoordTree) KNN added in v0.2.13 

func (c *CoordTree) KNN(k int, p Coord) []Coord

KNN gets the closest K coordinates to p in the tree. The results are sorted by ascending distance.

If there are fewer than K coordinates in the tree, then fewer than K coordinates are returned.

func (*CoordTree) Leaf added in v0.2.13 

func (c *CoordTree) Leaf() bool

Leaf returns true if this tree contains 1 or fewer points.

func (*CoordTree) NearestNeighbor added in v0.2.13 

func (c *CoordTree) NearestNeighbor(p Coord) Coord

NearestNeighbor gets the closest coordinate to p in the tree.

This will panic() if c is empty.

func (*CoordTree) Slice added in v0.2.13 

func (c *CoordTree) Slice() []Coord

Slice combines the points back into a slice.

The order will be from the first (less than) leaf to the final (greater than) leaf, with intermediate nodes interspersed throughout the middle.

func (*CoordTree) SphereCollision added in v0.2.13 

func (c *CoordTree) SphereCollision(p Coord, r float64) bool

SphereCollision checks if the sphere centered at point p with radius r contains any points in the tree.

type Curve added in v0.2.6 

type Curve interface {
	Eval(t float64) Coord
}

A Curve is a parametric curve that returns points for values of t in the range [0, 1].

func CurveTranspose added in v0.2.6 

func CurveTranspose(c Curve) Curve

CurveTranspose generates a Curve where x and y are swapped from the original c.

type DistTransform added in v0.2.11 

type DistTransform interface {
	Transform

	// ApplyDistance computes the distance between
	// t.Apply(c1) and t.Apply(c2) given the distance
	// between c1 and c2, where c1 and c2 are arbitrary
	// points.
	ApplyDistance(d float64) float64
}

DistTransform is a Transform that changes Euclidean distances in a coordinate-independent fashion.

The inverse of a DistTransform should also be a DistTransform.

func Rotation added in v0.2.11 

func Rotation(theta float64) DistTransform

Rotation creates a rotation transformation using an angle in radians.

type EdgeMap added in v0.2.14 

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

EdgeMap implements a map-like interface for mapping [2]Coord to interface{}.

This can be more efficient than using a map directly, since it uses a special hash function for coordinates. The speed-up is variable, but was ~2x as of mid-2021.

func NewEdgeMap added in v0.2.14 

func NewEdgeMap() *EdgeMap

NewEdgeMap creates an empty map.

func (*EdgeMap) Delete added in v0.2.14 

func (m *EdgeMap) Delete(key [2]Coord)

Delete removes the key from the map if it exists, and does nothing otherwise.

func (*EdgeMap) KeyRange added in v0.2.14 

func (m *EdgeMap) KeyRange(f func(key [2]Coord) bool)

KeyRange is like Range, but only iterates over keys, not values.

func (*EdgeMap) Len added in v0.2.14 

func (m *EdgeMap) Len() int

Len gets the number of elements in the map.

func (*EdgeMap) Load added in v0.2.14 

func (m *EdgeMap) Load(key [2]Coord) (interface{}, bool)

Load gets the value for the given key.

If no value is present, the first return argument is a zero value, and the second is false. Otherwise, the second return value is true.

func (*EdgeMap) Range added in v0.2.14 

func (m *EdgeMap) Range(f func(key [2]Coord, value interface{}) bool)

Range iterates over the map, calling f successively for each value until it returns false, or all entries are enumerated.

It is not safe to modify the map with Store or Delete during enumeration.

func (*EdgeMap) Store added in v0.2.14 

func (m *EdgeMap) Store(key [2]Coord, value interface{})

Store assigns the value to the given key, overwriting the previous value for the key if necessary.

func (*EdgeMap) Value added in v0.2.14 

func (m *EdgeMap) Value(key [2]Coord) interface{}

Value is like Load(), but without a second return value.

func (*EdgeMap) ValueRange added in v0.2.14 

func (m *EdgeMap) ValueRange(f func(value interface{}) bool)

ValueRange is like Range, but only iterates over values only.

type EdgeToBool added in v0.2.14 

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

EdgeToBool implements a map-like interface for mapping [2]Coord to bool.

This can be more efficient than using a map directly, since it uses a special hash function for coordinates. The speed-up is variable, but was ~2x as of mid-2021.

func NewEdgeToBool added in v0.2.14 

func NewEdgeToBool() *EdgeToBool

NewEdgeToBool creates an empty map.

func (*EdgeToBool) Delete added in v0.2.14 

func (m *EdgeToBool) Delete(key [2]Coord)

Delete removes the key from the map if it exists, and does nothing otherwise.

func (*EdgeToBool) KeyRange added in v0.2.14 

func (m *EdgeToBool) KeyRange(f func(key [2]Coord) bool)

KeyRange is like Range, but only iterates over keys, not values.

func (*EdgeToBool) Len added in v0.2.14 

func (m *EdgeToBool) Len() int

Len gets the number of elements in the map.

func (*EdgeToBool) Load added in v0.2.14 

func (m *EdgeToBool) Load(key [2]Coord) (bool, bool)

Load gets the value for the given key.

If no value is present, the first return argument is a zero value, and the second is false. Otherwise, the second return value is true.

func (*EdgeToBool) Range added in v0.2.14 

func (m *EdgeToBool) Range(f func(key [2]Coord, value bool) bool)

Range iterates over the map, calling f successively for each value until it returns false, or all entries are enumerated.

It is not safe to modify the map with Store or Delete during enumeration.

func (*EdgeToBool) Store added in v0.2.14 

func (m *EdgeToBool) Store(key [2]Coord, value bool)

Store assigns the value to the given key, overwriting the previous value for the key if necessary.

func (*EdgeToBool) Value added in v0.2.14 

func (m *EdgeToBool) Value(key [2]Coord) bool

Value is like Load(), but without a second return value.

func (*EdgeToBool) ValueRange added in v0.2.14 

func (m *EdgeToBool) ValueRange(f func(value bool) bool)

ValueRange is like Range, but only iterates over values only.

type EdgeToInt added in v0.2.14 

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

EdgeToInt implements a map-like interface for mapping [2]Coord to int.

This can be more efficient than using a map directly, since it uses a special hash function for coordinates. The speed-up is variable, but was ~2x as of mid-2021.

func NewEdgeToInt added in v0.2.14 

func NewEdgeToInt() *EdgeToInt

NewEdgeToInt creates an empty map.

func (*EdgeToInt) Add added in v0.2.14 

func (m *EdgeToInt) Add(key [2]Coord, x int) int

Add adds x to the value stored for the given key and returns the new value.

func (*EdgeToInt) Delete added in v0.2.14 

func (m *EdgeToInt) Delete(key [2]Coord)

Delete removes the key from the map if it exists, and does nothing otherwise.

func (*EdgeToInt) KeyRange added in v0.2.14 

func (m *EdgeToInt) KeyRange(f func(key [2]Coord) bool)

KeyRange is like Range, but only iterates over keys, not values.

func (*EdgeToInt) Len added in v0.2.14 

func (m *EdgeToInt) Len() int

Len gets the number of elements in the map.

func (*EdgeToInt) Load added in v0.2.14 

func (m *EdgeToInt) Load(key [2]Coord) (int, bool)

Load gets the value for the given key.

If no value is present, the first return argument is a zero value, and the second is false. Otherwise, the second return value is true.

func (*EdgeToInt) Range added in v0.2.14 

func (m *EdgeToInt) Range(f func(key [2]Coord, value int) bool)

Range iterates over the map, calling f successively for each value until it returns false, or all entries are enumerated.

It is not safe to modify the map with Store or Delete during enumeration.

func (*EdgeToInt) Store added in v0.2.14 

func (m *EdgeToInt) Store(key [2]Coord, value int)

Store assigns the value to the given key, overwriting the previous value for the key if necessary.

func (*EdgeToInt) Value added in v0.2.14 

func (m *EdgeToInt) Value(key [2]Coord) int

Value is like Load(), but without a second return value.

func (*EdgeToInt) ValueRange added in v0.2.14 

func (m *EdgeToInt) ValueRange(f func(value int) bool)

ValueRange is like Range, but only iterates over values only.

type FaceSDF added in v0.2.14 

type FaceSDF interface {
	PointSDF

	// FaceSDF gets the SDF at c and also returns the
	// nearest point and face to c on the surface.
	FaceSDF(c Coord) (*Segment, Coord, float64)
}

A FaceSDF is a PointSDF that can additionally get the segment containing the closest point.

func GroupedSegmentsToSDF added in v0.2.3 

func GroupedSegmentsToSDF(faces []*Segment) FaceSDF

GroupedSegmentsToSDF creates a FaceSDF from a slice of segments. If the segments are not grouped by GroupSegments(), the resulting PointSDF is inefficient.

func MeshToSDF added in v0.2.3 

func MeshToSDF(m *Mesh) FaceSDF

MeshToSDF turns a mesh into a FaceSDF.

type GeneralBVH added in v0.2.11 

type GeneralBVH struct {
	// Leaf, if non-nil, is the final bounder.
	Leaf Bounder

	// Branch, if Leaf is nil, points to two children.
	Branch []*GeneralBVH
}

GeneralBVH represents a (possibly unbalanced) axis-aligned bounding box hierarchy.

A GeneralBVH can store arbitrary Bounders. For a mesh-specific version, see BVH.

func NewGeneralBVHAreaDensity added in v0.2.11 

func NewGeneralBVHAreaDensity(objects []Bounder) *GeneralBVH

NewGeneralBVHAreaDensity creates a GeneralBVH by minimizing the product of each bounding box's perimeter with the number of objects contained in the bounding box at each branch.

This is good for efficient ray collision detection.

type InterpBitmap 

type InterpBitmap struct {
	Data   []color.RGBA
	Width  int
	Height int
	Model  color.Model
	F      ColorBitFunc

	// Interp is the interpolation function.
	// A zero value is Bicubic.
	Interp Interpolator
}

An InterpBitmap is a dynamic Bitmap backed by an image with a color interpolation scheme.

func MustReadInterpBitmap 

func MustReadInterpBitmap(path string, c ColorBitFunc) *InterpBitmap

MustReadInterpBitmap is like ReadInterpBitmap, except that it panics if the InterpBitmap cannot be read.

func NewInterpBitmap 

func NewInterpBitmap(img image.Image, c ColorBitFunc) *InterpBitmap

NewInterpBitmap creates a InterpBitmap from an image.

If c is nil, then the mean RGBA is computed, and pixels are considered true if they are closer to the mean in L2 distance than they are to the top-left pixel. For images with two dominant colors, this is equivalent to making the background false, and the foreground true, assuming that the first pixel is background.

func ReadInterpBitmap 

func ReadInterpBitmap(path string, c ColorBitFunc) (*InterpBitmap, error)

ReadInterpBitmap is like NewInterpBitmap, except that it reads the image from a file.

func (*InterpBitmap) Bitmap 

func (b *InterpBitmap) Bitmap() *Bitmap

Bitmap gets an uninterpolated bitmap from b.

func (*InterpBitmap) Contains 

func (b *InterpBitmap) Contains(c Coord) bool

Contains gets the bit at the interpolated coordinate.

If the coordinate is out of bounds, false is returned.

func (*InterpBitmap) FlipX 

func (b *InterpBitmap) FlipX() *InterpBitmap

FlipX reverses the x-axis.

func (*InterpBitmap) FlipY 

func (b *InterpBitmap) FlipY() *InterpBitmap

FlipY reverses the y-axis.

func (*InterpBitmap) Get 

func (b *InterpBitmap) Get(x, y int) color.RGBA

Get gets the color at the coordinate.

If the coordinate is out of bounds, a the edge of the image is extended.

func (*InterpBitmap) Invert 

func (b *InterpBitmap) Invert() *InterpBitmap

Invert creates a new InterpBitmap with the opposite color bitmap values.

func (*InterpBitmap) Max 

func (b *InterpBitmap) Max() Coord

Max gets the maximum of the pixel bounding box.

func (*InterpBitmap) Min 

func (b *InterpBitmap) Min() Coord

Min gets the minimum of the pixel bounding box.

type Interpolator 

type Interpolator int

Interpolator is a 1-dimensional interpolation kernel. 

const (
	Bicubic Interpolator = iota
	Bilinear
)

func (Interpolator) Kernel 

func (i Interpolator) Kernel(t float64) []float64

type IntersectedSolid added in v0.2.3 

type IntersectedSolid []Solid

IntersectedSolid is a Solid containing the intersection of one or more Solids.

func (IntersectedSolid) Contains added in v0.2.3 

func (i IntersectedSolid) Contains(c Coord) bool

func (IntersectedSolid) Max added in v0.2.3 

func (i IntersectedSolid) Max() Coord

func (IntersectedSolid) Min added in v0.2.3 

func (i IntersectedSolid) Min() Coord

type JoinedCollider 

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

A JoinedCollider wraps multiple other Colliders and only passes along rays and circles that enter their combined bounding box.

func NewJoinedCollider 

func NewJoinedCollider(other []Collider) *JoinedCollider

NewJoinedCollider creates a JoinedCollider which combines zero or more other colliders.

func (*JoinedCollider) CircleCollision 

func (j *JoinedCollider) CircleCollision(center Coord, r float64) bool

func (*JoinedCollider) FirstRayCollision 

func (j *JoinedCollider) FirstRayCollision(r *Ray) (RayCollision, bool)

func (*JoinedCollider) Max 

func (j *JoinedCollider) Max() Coord

func (*JoinedCollider) Min 

func (j *JoinedCollider) Min() Coord

func (*JoinedCollider) RayCollisions 

func (j *JoinedCollider) RayCollisions(r *Ray, f func(RayCollision)) int

type JoinedCurve added in v0.2.6 

type JoinedCurve []Curve

A JoinedCurve combines Curves into a single curve. Each curve should end where the next curve begins.

func SmoothBezier added in v0.2.6 

func SmoothBezier(start1, c1, c2, end1 Coord, ctrlEnds ...Coord) JoinedCurve

SmoothBezier creates a joined cubic bezier curve where control points are reflected around end-points. The first four points define the first bezier curve. After that, each group of two points defines a control point and an endpoint.

func (JoinedCurve) Eval added in v0.2.6 

func (j JoinedCurve) Eval(t float64) Coord

Eval evaluates the joint curve.

Each sub-curve consumes an equal fraction of t. For t outside of [0, 1], the first or last curve is used.

type JoinedSolid 

type JoinedSolid []Solid

A JoinedSolid is a Solid composed of other solids.

func (JoinedSolid) Contains 

func (j JoinedSolid) Contains(c Coord) bool

func (JoinedSolid) Max 

func (j JoinedSolid) Max() Coord

func (JoinedSolid) Min 

func (j JoinedSolid) Min() Coord

func (JoinedSolid) Optimize added in v0.2.11 

func (j JoinedSolid) Optimize() Solid

Optimize creates a version of the solid that is faster when joining a large number of smaller solids.

type JoinedTransform added in v0.2.8 

type JoinedTransform []Transform

A JoinedTransform composes transformations from left to right.

func (JoinedTransform) Apply added in v0.2.8 

func (j JoinedTransform) Apply(c Coord) Coord

func (JoinedTransform) ApplyBounds added in v0.2.8 

func (j JoinedTransform) ApplyBounds(min Coord, max Coord) (Coord, Coord)

func (JoinedTransform) ApplyDistance added in v0.2.11 

func (j JoinedTransform) ApplyDistance(d float64) float64

ApplyDistance transforms a distance.

It panic()s if any transforms don't implement DistTransform.

func (JoinedTransform) Inverse added in v0.2.8 

func (j JoinedTransform) Inverse() Transform

type LinearConstraint added in v0.2.11 

type LinearConstraint struct {
	Normal Coord
	Max    float64
}

A LinearConstraint defines a half-space of all points c such that c.Dot(Normal) <= Max.

func (*LinearConstraint) Contains added in v0.2.11 

func (l *LinearConstraint) Contains(c Coord) bool

Contains checks if the half-space contains c.

type Matrix2 

type Matrix2 [4]float64

Matrix2 is a 2x2 matrix, stored in row-major order.

func NewMatrix2Columns 

func NewMatrix2Columns(c1, c2 Coord) *Matrix2

NewMatrix2Columns creates a Matrix2 with the given coordinates as column entries.

func NewMatrix2Rotation 

func NewMatrix2Rotation(theta float64) *Matrix2

NewMatrix2Rotation creates a rotation matrix that rotates column vectors by theta.

func (*Matrix2) Add added in v0.2.2 

func (m *Matrix2) Add(m1 *Matrix2) *Matrix2

Add computes m+m1 and returns the sum.

func (*Matrix2) Det 

func (m *Matrix2) Det() float64

Det computes the determinant of the matrix.

func (*Matrix2) Eigenvalues added in v0.2.2 

func (m *Matrix2) Eigenvalues() [2]complex128

Eigenvalues computes the eigenvalues of the matrix.

There may be a repeated eigenvalue, but for numerical reasons two are always returned.

func (*Matrix2) Inverse 

func (m *Matrix2) Inverse() *Matrix2

Inverse computes the inverse matrix.

func (*Matrix2) InvertInPlace 

func (m *Matrix2) InvertInPlace()

InvertInPlace moves the inverse of m into m without causing any new allocations.

func (*Matrix2) InvertInPlaceDet added in v0.2.14 

func (m *Matrix2) InvertInPlaceDet(det float64)

InvertInPlaceDet is an optimization for InvertInPlace when the determinant has been pre-computed.

func (*Matrix2) Mul 

func (m *Matrix2) Mul(m1 *Matrix2) *Matrix2

Mul computes m*m1 and returns the product.

func (*Matrix2) MulColumn 

func (m *Matrix2) MulColumn(c Coord) Coord

MulColumn multiplies the matrix m by a column vector represented by c.

func (*Matrix2) MulColumnInv added in v0.2.14 

func (m *Matrix2) MulColumnInv(c Coord, det float64) Coord

MulColumnInv multiplies the inverse of m by the column c, given the determinant of m.

func (*Matrix2) SVD added in v0.2.2 

func (m *Matrix2) SVD(u, s, v *Matrix2)

SVD computes the singular value decomposition of the matrix.

It populates matrices u, s, and v, such that 

m = u*s*v.Transpose()

The singular values in s are sorted largest to smallest.

func (*Matrix2) Scale 

func (m *Matrix2) Scale(s float64)

Scale scales m by a factor s.

func (*Matrix2) Transpose 

func (m *Matrix2) Transpose() *Matrix2

Transpose computes the matrix transpose.

type Matrix2Transform added in v0.2.8 

type Matrix2Transform struct {
	Matrix *Matrix2
}

Matrix2Transform is a Transform that applies a matrix to coordinates.

func (*Matrix2Transform) Apply added in v0.2.8 

func (m *Matrix2Transform) Apply(c Coord) Coord

func (*Matrix2Transform) ApplyBounds added in v0.2.8 

func (m *Matrix2Transform) ApplyBounds(min, max Coord) (Coord, Coord)

func (*Matrix2Transform) Inverse added in v0.2.8 

func (m *Matrix2Transform) Inverse() Transform

type Mesh 

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

A Mesh is a collection of segments.

The segments are uniquely identified as pointers, not as values. This is important for methods which reference existing segments, such as Remove and Neighbors.

Segments in a mesh are "connected" when they contain exactly identical points. Thus, small rounding errors can cause segments to incorrectly be disassociated with each other.

A Mesh can be read safely from concurrent Goroutines, but modifications must not be performed concurrently with any mesh operations.

func MarchingSquares 

func MarchingSquares(s Solid, delta float64) *Mesh

MarchingSquares turns a Solid into a mesh using a 2D version of the marching cubes algorithm.

func MarchingSquaresConj added in v0.2.9 

func MarchingSquaresConj(s Solid, delta float64, iters int, xforms ...Transform) *Mesh

MarchingSquaresConj is like MarchingSquaresSearch, but in a transformed space. In particular, it applies a series of transformations to the Solid, and then applies the inverse to the resulting mesh.

func MarchingSquaresSearch 

func MarchingSquaresSearch(s Solid, delta float64, iters int) *Mesh

MarchingSquaresSearch is like MarchingSquares, but applies an additional search step to move the vertices along the edges of each square.

The tightness of the triangulation will double for every iteration.

func NewMesh 

func NewMesh() *Mesh

NewMesh creates an empty mesh.

func NewMeshPolar added in v0.2.9 

func NewMeshPolar(radius func(theta float64) float64, stops int) *Mesh

NewMeshPolar creates a closed polar mesh.

The mesh will have correct normals if the radius function returns positive values when theta is in the range [0, 2*pi].

Even if the polar function does not reach its original value at 2*pi radians, the mesh will be closed by connecting the first point to the last.

func NewMeshRect added in v0.2.13 

func NewMeshRect(min, max Coord) *Mesh

NewMeshRect creates a rectangle mesh.

func NewMeshSegments 

func NewMeshSegments(faces []*Segment) *Mesh

NewMeshSegments creates a mesh with the given collection of segments.

func (*Mesh) Add 

func (m *Mesh) Add(f *Segment)

Add adds the segment f to the mesh.

func (*Mesh) AddMesh 

func (m *Mesh) AddMesh(m1 *Mesh)

AddMesh adds all the segments from m1 to m.

func (*Mesh) Blur 

func (m *Mesh) Blur(rate float64) *Mesh

Blur moves each vertex closer to the average of its neighbors.

The rate argument controls how much the vertices move. If it is 1, then the vertices become the average of their neighbors. If it is 0, then the vertices remain where they are.

func (*Mesh) Contains 

func (m *Mesh) Contains(f *Segment) bool

Contains checks if f has been added to the mesh.

func (*Mesh) Decimate added in v0.2.6 

func (m *Mesh) Decimate(maxVertices int) *Mesh

Decimate repeatedly removes vertices from a mesh until it contains maxVertices or fewer vertices with two neighbors.

For manifold meshes, maxVertices is a hard-limit on the number of resulting vertices. For non-manifold meshes, more than maxVertices vertices will be retained if all of the remaining vertices are not part of exactly two segments.

func (*Mesh) EliminateColinear added in v0.2.13 

func (m *Mesh) EliminateColinear(epsilon float64) *Mesh

EliminateColinear eliminates vertices that connect nearly co-linear edges.

The epsilon argument should be a small positive value that is used to approximate co-linearity. A good value for very precise results is 1e-8.

func (*Mesh) Find 

func (m *Mesh) Find(ps ...Coord) []*Segment

Find gets all the segments that contain all of the passed points.

For example, to find all segments containing a line from from p1 to p2, you could do m.Find(p1, p2).

func (*Mesh) Invert added in v0.2.11 

func (m *Mesh) Invert() *Mesh

Invert flips every segment in the mesh, effectively inverting all the normals.

func (*Mesh) Iterate 

func (m *Mesh) Iterate(f func(*Segment))

Iterate calls f for every segment in m in an arbitrary order.

If f adds or removes segments, they will not be visited.

func (*Mesh) IterateSorted 

func (m *Mesh) IterateSorted(f func(*Segment), cmp func(f1, f2 *Segment) bool)

IterateSorted is like Iterate, but it first sorts all the segments according to a less than function, cmp.

func (*Mesh) IterateVertices added in v0.1.1 

func (m *Mesh) IterateVertices(f func(c Coord))

IterateVertices calls f for every vertex in m in an arbitrary order.

If f adds or removes vertices, they will not be visited.

func (*Mesh) Manifold 

func (m *Mesh) Manifold() bool

Manifold checks if the mesh is manifold, i.e. if every vertex has two segments.

func (*Mesh) MapCoords 

func (m *Mesh) MapCoords(f func(Coord) Coord) *Mesh

MapCoords creates a new mesh by transforming all of the coordinates according to the function f.

func (*Mesh) Max 

func (m *Mesh) Max() Coord

Max gets the component-wise maximum across all the vertices in the mesh.

func (*Mesh) Min 

func (m *Mesh) Min() Coord

Min gets the component-wise minimum across all the vertices in the mesh.

func (*Mesh) Neighbors 

func (m *Mesh) Neighbors(f *Segment) []*Segment

Neighbors gets all the segments with a side touching a given segment f.

The segment f itself is not included in the results.

The segment f needn't be in the mesh. However, if it is not in the mesh, but an equivalent segment is, then said equivalent segment will be in the results.

func (*Mesh) Remove 

func (m *Mesh) Remove(f *Segment)

Remove removes the segment f from the mesh.

It looks at f as a pointer, so the pointer must be exactly the same as one passed to Add.

func (*Mesh) Repair added in v0.2.6 

func (m *Mesh) Repair(epsilon float64) *Mesh

Repair finds vertices that are close together and combines them into one.

The epsilon argument controls how close points have to be. In particular, it sets the approximate maximum distance across all dimensions.

func (*Mesh) RepairNormals added in v0.2.4 

func (m *Mesh) RepairNormals(epsilon float64) (*Mesh, int)

RepairNormals flips normals when they point within the shape defined by the mesh, as determined by the even-odd rule.

The repaired mesh is returned, along with the number of modified segments.

The check is performed by adding the normal, scaled by epsilon, to the center of the segment, and then counting the number of ray collisions from this point in the direction of the normal.

func (*Mesh) Rotate added in v0.2.15 

func (m *Mesh) Rotate(angle float64) *Mesh

Rotate returns a mesh with all coordinates rotated around the origin by a given angle (in radians).

func (*Mesh) SaveSVG 

func (m *Mesh) SaveSVG(path string) error

SaveSVG encodes the mesh to an SVG file.

func (*Mesh) Scale added in v0.2.2 

func (m *Mesh) Scale(s float64) *Mesh

Scale creates a new mesh by scaling the coordinates by a factor s.

func (*Mesh) SegmentSlice added in v0.2.11 

func (m *Mesh) SegmentSlice() []*Segment

SegmentSlice gets a snapshot of all the segments currently in the mesh. The resulting slice is a copy, and will not change as the mesh is updated.

func (*Mesh) SegmentsSlice 

func (m *Mesh) SegmentsSlice() []*Segment

SegmentsSlice is exactly like SegmentSlice(), and is only implemented for backwards-compatibility.

func (*Mesh) Smooth 

func (m *Mesh) Smooth(iters int) *Mesh

Smooth is similar to Blur, but it is less sensitive to differences in segment length.

func (*Mesh) SmoothSq 

func (m *Mesh) SmoothSq(iters int) *Mesh

SmoothSq is like Smooth, but it minimizes the sum of squared segment lengths rather than the sum of lengths directly. Thus, SmoothSq produces more even segments than Smooth.

func (*Mesh) Subdivide 

func (m *Mesh) Subdivide(iters int) *Mesh

Subdivide uses Chaikin subdivision to add segments between every vertex.

This can only be applied to manifold meshes. This can be checked with m.Manifold().

func (*Mesh) Transform added in v0.2.9 

func (m *Mesh) Transform(t Transform) *Mesh

Transform applies t to the coordinates.

func (*Mesh) Translate added in v0.2.13 

func (m *Mesh) Translate(v Coord) *Mesh

Translate returns a mesh with all coordinates added to a given vector.

func (*Mesh) VertexSlice added in v0.1.1 

func (m *Mesh) VertexSlice() []Coord

VertexSlice gets a snapshot of all the vertices currently in the mesh.

The result is a copy and is in no way connected to the mesh in memory.

type MeshHierarchy added in v0.2.10 

type MeshHierarchy struct {
	// Mesh is the root shape of this (sub-)hierarchy.
	Mesh *Mesh

	// MeshSolid is a solid indicating which points are
	// contained in the mesh.
	MeshSolid Solid

	Children []*MeshHierarchy
}

A MeshHierarchy is a tree structure where each node is a closed, simple polygon, and children are contained inside their parents.

Only manifold meshes with no self-intersections can be converted into a MeshHierarchy.

func MeshToHierarchy added in v0.2.10 

func MeshToHierarchy(m *Mesh) []*MeshHierarchy

MeshToHierarchy creates a MeshHierarchy for each exterior mesh contained in m.

The mesh m must be manifold and have no self-intersections.

func (*MeshHierarchy) Contains added in v0.2.10 

func (m *MeshHierarchy) Contains(c Coord) bool

Contains checks if c is inside the hierarchy using the even-odd rule.

func (*MeshHierarchy) FullMesh added in v0.2.10 

func (m *MeshHierarchy) FullMesh() *Mesh

FullMesh re-combines the root mesh with all of its children.

func (*MeshHierarchy) MapCoords added in v0.2.10 

func (m *MeshHierarchy) MapCoords(f func(Coord) Coord) *MeshHierarchy

MapCoords creates a new MeshHierarchy by applying f to every coordinate in every mesh.

func (*MeshHierarchy) Max added in v0.2.10 

func (m *MeshHierarchy) Max() Coord

Max gets the maximum point of the outer mesh's bounding box.

func (*MeshHierarchy) Min added in v0.2.10 

func (m *MeshHierarchy) Min() Coord

Min gets the minimum point of the outer mesh's bounding box.

type MultiCollider added in v0.2.6 

type MultiCollider interface {
	Collider
	SegmentCollider
	RectCollider
}

func GroupedSegmentsToCollider 

func GroupedSegmentsToCollider(segs []*Segment) MultiCollider

GroupedSegmentsToCollider converts pre-grouped segments into an efficient MultiCollider. If the segments were not grouped with GroupSegments, then the resulting collider may be highly inefficient.

func MeshToCollider 

func MeshToCollider(m *Mesh) MultiCollider

MeshToCollider converts a mesh to an efficient MultiCollider.

type PointSDF added in v0.2.3 

type PointSDF interface {
	SDF

	// PointSDF gets the SDF at c and also returns the
	// nearest point to c on the surface.
	PointSDF(c Coord) (Coord, float64)
}

A PointSDF is an SDF that can additionally get the nearest point on a surface.

func FuncPointSDF added in v0.2.13 

func FuncPointSDF(min, max Coord, f func(Coord) (Coord, float64)) PointSDF

FuncPointSDF creates a PointSDF from a function.

If the bounds are invalid, FuncPointSDF() will panic(). In particular, max must be no less than min, and all floating-point values must be finite numbers.

type Rasterizer added in v0.2.6 

type Rasterizer struct {
	// Scale determines how many pixels comprise a unit
	// distance in the model being rasterized.
	//
	// This determines how large output images are, given
	// the bounds of the model being rasterized.
	//
	// A value of 0 defaults to a value of 1.
	Scale float64

	// Subsamples indicates how many sub-samples to test
	// for each axis in each pixel.
	// A value of 1 means one sample is taken per pixel,
	// and values higher than one cause anti-aliasing.
	// If 0, RasterizerDefaultSubsamples is used.
	Subsamples int

	// LineWidth is the thickness of lines (in pixels)
	// when rendering a mesh or collider.
	//
	// If 0, RasterizerDefaultLineWidth is used.
	LineWidth float64

	// Bounds, if non-nil, is used to override the bounds
	// of any rasterized object.
	// This can be used to add padding, or have a
	// consistent canvas when drawing a moving scene.
	Bounds Bounder
}

A Rasterizer converts 2D models into raster images.

func (*Rasterizer) Rasterize added in v0.2.6 

func (r *Rasterizer) Rasterize(obj interface{}) *image.Gray

Rasterize rasterizes a Solid, Mesh, or Collider.

func (*Rasterizer) RasterizeCollider added in v0.2.6 

func (r *Rasterizer) RasterizeCollider(c Collider) *image.Gray

RasterizeCollider rasterizes the collider as a line drawing.

func (*Rasterizer) RasterizeColliderSolid added in v0.2.7 

func (r *Rasterizer) RasterizeColliderSolid(c Collider) *image.Gray

RasterizeColliderSolid rasterizes the collider as a filled in Solid using the even-odd test.

func (*Rasterizer) RasterizeSolid added in v0.2.6 

func (r *Rasterizer) RasterizeSolid(s Solid) *image.Gray

RasterizeSolid rasterizes a Solid into an image.

func (*Rasterizer) RasterizeSolidFilter added in v0.2.6 

func (r *Rasterizer) RasterizeSolidFilter(s Solid, f func(r *Rect) bool) *image.Gray

RasterizeSolidFilter rasterizes a Solid using a heuristic filter than can eliminate the need to render blank regions of the image.

If f returns false for a given rectangular region, it means that the solid is definitely uniform within the region (i.e. there is no boundary in the region). The exact pattern with which f is called will depend on the image and rasterization parameters.

type Ray 

type Ray struct {
	Origin    Coord
	Direction Coord
}

A Ray is a line originating at a point and extending infinitely in some (positive) direction.

type RayCollision 

type RayCollision struct {
	// The amount of the ray direction to add to the ray
	// origin to hit the point in question.
	//
	// The scale should be non-negative.
	Scale float64

	// The normal pointing outward from the outline at the
	// point of collision.
	Normal Coord

	// Extra contains additional, implementation-specific
	// information about the collision.
	Extra interface{}
}

RayCollision is a point where a ray intersects a 2-dimensional outline.

type Rect added in v0.2.4 

type Rect struct {
	MinVal Coord
	MaxVal Coord
}

A Rect is a 2D axis-aligned rectangle.

func BoundsRect added in v0.2.13 

func BoundsRect(b Bounder) *Rect

BoundsRect creates a Rect from a Bounder's bounds.

func NewRect added in v0.2.13 

func NewRect(min, max Coord) *Rect

NewRect creates a Rect with a min and a max value.

func (*Rect) Contains added in v0.2.4 

func (r *Rect) Contains(c Coord) bool

func (*Rect) Max added in v0.2.4 

func (r *Rect) Max() Coord

func (*Rect) Min added in v0.2.4 

func (r *Rect) Min() Coord

type RectCollider added in v0.2.6 

type RectCollider interface {
	// RectCollision returns true if any part of the
	// outline is inside the rect.
	RectCollision(r *Rect) bool
}

A RectCollider is a 2-dimensional outline which can detect if a 2D axis-aligned rectangular area collides with the outline.

type SDF added in v0.2.3 

type SDF interface {
	Bounder

	SDF(c Coord) float64
}

An SDF is a signed distance function.

An SDF returns 0 on the boundary of some surface, positive values inside the surface, and negative values outside the surface. The magnitude is the distance to the surface.

All methods of an SDF are safe for concurrency.

func ColliderToSDF added in v0.2.3 

func ColliderToSDF(c Collider, iterations int) SDF

ColliderToSDF generates an SDF that uses bisection search to approximate the SDF for any Collider.

The iterations argument controls the precision. If set to 0, a default of 32 is used.

func FuncSDF added in v0.2.13 

func FuncSDF(min, max Coord, f func(Coord) float64) SDF

FuncSDF creates an SDF from a function.

If the bounds are invalid, FuncSDF() will panic(). In particular, max must be no less than min, and all floating-point values must be finite numbers.

func TransformSDF added in v0.2.11 

func TransformSDF(t DistTransform, s SDF) SDF

TransformSDF applies t to the SDF s to produce a new, transformed SDF.

type Scale added in v0.2.11 

type Scale struct {
	Scale float64
}

Scale is a transform that scales an object.

func (*Scale) Apply added in v0.2.11 

func (s *Scale) Apply(c Coord) Coord

func (*Scale) ApplyBounds added in v0.2.11 

func (s *Scale) ApplyBounds(min Coord, max Coord) (Coord, Coord)

func (*Scale) ApplyDistance added in v0.2.11 

func (s *Scale) ApplyDistance(d float64) float64

func (*Scale) Inverse added in v0.2.11 

func (s *Scale) Inverse() Transform

type Segment 

type Segment [2]Coord

A Segment is a 2-dimensional line segment.

The order determines the normal direction.

In particular, if the segments in a polygon go in the clockwise direction, assuming the y-axis faces up, then the normals face outwards from the polygon.

func DecodeCSV added in v0.2.13 

func DecodeCSV(data []byte) ([]*Segment, error)

DecodeCSV decodes the CSV format from EncodeCSV().

func (*Segment) CircleCollision 

func (s *Segment) CircleCollision(c Coord, r float64) bool

CircleCollision checks if the circle intersects the segment s.

func (Segment) Closest added in v0.2.3 

func (s Segment) Closest(c Coord) Coord

Closest gets the point on the segment closest to c.

func (Segment) Dist added in v0.2.3 

func (s Segment) Dist(c Coord) float64

Dist gets the minimum distance from c to a point on the line segment.

func (*Segment) FirstRayCollision 

func (s *Segment) FirstRayCollision(r *Ray) (RayCollision, bool)

FirstRayCollision gets the ray collision if there is one.

func (Segment) Length 

func (s Segment) Length() float64

Length gets the length of the segment.

func (Segment) Max 

func (s Segment) Max() Coord

Max gets the element-wise maximum of the endpoints.

func (Segment) Mid 

func (s Segment) Mid() Coord

Mid gets the midpoint of the segment.

func (Segment) Min 

func (s Segment) Min() Coord

Min gets the element-wise minimum of the endpoints.

func (*Segment) Normal 

func (s *Segment) Normal() Coord

Normal computes the normal vector to the segment, facing outwards from the surface.

func (*Segment) RayCollisions 

func (s *Segment) RayCollisions(r *Ray, f func(RayCollision)) int

RayCollisions calls f (if non-nil) with a collision (if applicable) and returns the collisions count (0 or 1).

func (*Segment) RectCollision added in v0.2.6 

func (s *Segment) RectCollision(r *Rect) bool

RectCollision returns true if any part of the segment is inside of the rectangle.

func (*Segment) SegmentCollision added in v0.2.6 

func (s *Segment) SegmentCollision(s1 *Segment) bool

SegmentCollision returns true if s intersects s1.

type SegmentCollider added in v0.2.6 

type SegmentCollider interface {
	// SegmentCollision returns true if the segment
	// collides with the outline.
	SegmentCollision(s *Segment) bool
}

A SegmentCollider is a 2-dimensional outline which can detect if a line segment collides with the outline.

type Solid 

type Solid interface {
	// Contains must always return false outside of the
	// boundaries of the solid.
	Bounder

	Contains(p Coord) bool
}

A Solid is a boolean function where a value of true indicates that a point is part of the solid, and false indicates that it is not.

All methods of a Solid are safe for concurrency.

func BitmapToSolid 

func BitmapToSolid(b *Bitmap) Solid

func CacheSolidBounds added in v0.2.11 

func CacheSolidBounds(s Solid) Solid

CacheSolidBounds creates a Solid that has a cached version of the solid's boundary coordinates.

The solid also explicitly checks that points are inside the boundary before passing them off to s.

func CheckedFuncSolid added in v0.2.11 

func CheckedFuncSolid(min, max Coord, f func(Coord) bool) Solid

CheckedFuncSolid is like FuncSolid, but it does an automatic bounds check before calling f.

func ForceSolidBounds added in v0.2.7 

func ForceSolidBounds(s Solid, min, max Coord) Solid

ForceSolidBounds creates a new solid that reports the exact bounds given by min and max.

Points outside of these bounds will be removed from s, but otherwise s is preserved.

func FuncSolid added in v0.2.11 

func FuncSolid(min, max Coord, f func(Coord) bool) Solid

FuncSolid creates a Solid from a function.

If the bounds are invalid, FuncSolid() will panic(). In particular, max must be no less than min, and all floating-point values must be finite numbers.

func RotateSolid added in v0.2.15 

func RotateSolid(solid Solid, axis Coord, angle float64) Solid

RotateSolid creates a new Solid by rotating a Solid by a given angle (in radians).

func ScaleSolid 

func ScaleSolid(solid Solid, s float64) Solid

ScaleSolid creates a new Solid that scales incoming coordinates c by 1/s. Thus, the new solid is s times larger.

func SmoothJoin added in v0.2.11 

func SmoothJoin(radius float64, sdfs ...SDF) Solid

SmoothJoin joins the SDFs into a union Solid and smooths the intersections using a given smoothing radius.

If the radius is 0, it is equivalent to turning the SDFs directly into solids and then joining them.

func TransformSolid added in v0.2.8 

func TransformSolid(t Transform, s Solid) Solid

TransformSolid applies t to the solid s to produce a new, transformed solid.

func TranslateSolid added in v0.2.13 

func TranslateSolid(solid Solid, offset Coord) Solid

TranslateSolid creates a new Solid by translating a Solid by a given offset.

type SubtractedSolid added in v0.2.3 

type SubtractedSolid struct {
	Positive Solid
	Negative Solid
}

SubtractedSolid is a Solid consisting of all the points in Positive which are not in Negative.

func (*SubtractedSolid) Contains added in v0.2.3 

func (s *SubtractedSolid) Contains(c Coord) bool

func (*SubtractedSolid) Max added in v0.2.3 

func (s *SubtractedSolid) Max() Coord

func (*SubtractedSolid) Min added in v0.2.3 

func (s *SubtractedSolid) Min() Coord

type Transform added in v0.2.8 

type Transform interface {
	// Apply applies the transformation to c.
	Apply(c Coord) Coord

	// ApplyBounds gets a new bounding rectangle that is
	// guaranteed to bound the old bounding rectangle when
	// it is transformed.
	ApplyBounds(min, max Coord) (Coord, Coord)

	// Inverse gets an inverse transformation.
	//
	// The inverse may not perfectly invert bounds
	// transformations, since some information may be lost
	// during such a transformation.
	Inverse() Transform
}

Transform is an invertible coordinate transformation.

type Translate added in v0.2.8 

type Translate struct {
	Offset Coord
}

Translate is a Transform that adds an offset to coordinates.

func (*Translate) Apply added in v0.2.8 

func (t *Translate) Apply(c Coord) Coord

func (*Translate) ApplyBounds added in v0.2.8 

func (t *Translate) ApplyBounds(min, max Coord) (Coord, Coord)

func (*Translate) ApplyDistance added in v0.2.11 

func (t *Translate) ApplyDistance(d float64) float64

func (*Translate) Inverse added in v0.2.8 

func (t *Translate) Inverse() Transform

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