model2d

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 Go to latest Published: Apr 24, 2020 License: BSD-2-Clause Imports: 15 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

This section is empty.

Variables

This section is empty.

Functions

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 EncodeSVG 

func EncodeSVG(m *Mesh) []byte

func GroupSegments 

func GroupSegments(segs []*Segment)

GroupSegments sorts the segments recursively by their x and y values. This can be used to prepare segments for GroupedSegmentsToCollider.

func InBounds 

func InBounds(b Bounder, c Coord) bool

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

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.

Types

type BezierCurve 

type BezierCurve []Coord

BezierCurve implements an arbitrarily high-dimensional Bezier curve.

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) Transpose 

func (b BezierCurve) Transpose() BezierCurve

Transpose generates a BezierCurve where x and y are swapped.

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 rectangle.
	//
	// 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 a rectangle.

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 GroupedSegmentsToCollider 

func GroupedSegmentsToCollider(segs []*Segment) Collider

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

func MeshToCollider 

func MeshToCollider(m *Mesh) Collider

MeshToCollider converts a mesh to an efficient Collider.

type ColliderSolid 

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

ColliderSolid is a Solid which uses the even-odd test for a Collider.

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 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 NewCoordRandNorm 

func NewCoordRandNorm() Coord

NewCoordRandNorm creates a random Coord with normally distributed components.

func NewCoordRandUnit 

func NewCoordRandUnit() Coord

NewCoordRandUnit creates a random Coord with magnitude 1.

func (Coord) Add 

func (c Coord) Add(c1 Coord) Coord

Add computes the sum of c and c1.

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) Dot 

func (c Coord) Dot(c1 Coord) float64

Dot computes the dot product of c and 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) 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) 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 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 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 JoinedSolid 

type JoinedSolid []Solid

JoinedSolid combines one or more other solids into a single union.

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

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) Det 

func (m *Matrix2) Det() float64

Det computes the determinant of the matrix.

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) 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) 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 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 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 NewMeshSegments 

func NewMeshSegments(segs []*Segment) *Mesh

NewMeshSegments creates a mesh with the given collection of Segments.

func (*Mesh) Add 

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

Add adds the Segment s 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(s *Segment) bool

Contains checks if s has been added to the mesh.

func (*Mesh) Find 

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

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

This is only useful with one or two coordinates.

func (*Mesh) Iterate 

func (m *Mesh) Iterate(f func(s *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(s *Segment), cmp func(s1, s2 *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(s *Segment) []*Segment

Neighbors gets all the Segments with a vertex touching a given Segment s.

The Segment s itself is not included in the results.

The Segment s 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(s *Segment)

Remove removes the Segment t from the mesh.

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

func (*Mesh) SaveSVG 

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

func (*Mesh) SegmentsSlice 

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

SegmentsSlice 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) 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) 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 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
}

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

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 down), then the normals face outwards from the polygon.

func (*Segment) CircleCollision 

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

CircleCollision checks if the circle intersects the segment s.

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).

type Solid 

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

	Contains(c Coord) bool
}

A Solid defines a two-dimensional shape.

For any given coordinate, the solid can check if the shape contains that coordinate.

All methods of a Solid are safe for concurrency.

func BitmapToSolid 

func BitmapToSolid(b *Bitmap) Solid

BitmapToSolid creates a Solid which is true at pixels where the bitmap is true, and false elsewhere.

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.

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