Diagrams.TwoD.Polygons

This module defines a general API for creating various types of polygons.

Polygons

data PolyType

Method used to determine the vertices of a polygon.

Constructors

PolyPolar [Angle] [Double]

A "polar" polygon.

• The first argument is a list of central angles from each vertex to the next.
• The second argument is a list of radii from the origin to each successive vertex.

To construct an n-gon, use a list of n-1 angles and n radii. Extra angles or radii are ignored.

Cyclic polygons (with all vertices lying on a circle) can be constructed using a second argument of (repeat r).

PolySides [Angle] [Double]

A polygon determined by the distance between successive vertices and the angles formed by each three successive vertices. In other words, a polygon specified by "turtle graphics": go straight ahead x1 units; turn by angle a1; go straght ahead x2 units; turn by angle a2; etc. The polygon will be centered at the centroid of its vertices.

• The first argument is a list of vertex angles, giving the angle at each vertex from the previous vertex to the next. The first angle in the list is the angle at the second vertex; the first edge always starts out heading in the positive y direction from the first vertex.
• The second argument is a list of distances between successive vertices.

To construct an n-gon, use a list of n-2 angles and n-1 edge lengths. Extra angles or lengths are ignored.

PolyRegular Int Double

A regular polygon with the given number of sides (first argument) and the given radius (second argument).

data PolyOrientation

Determine how a polygon should be oriented.

Constructors

NoOrient

No special orientation; the first vertex will be at (1,0). This is the default.

OrientH

Orient horizontally, so the bottommost edge is parallel to the x-axis.

OrientV

Orient vertically, so the leftmost edge is parallel to the y-axis.

OrientTo R2

Orient so some edge is facing in the direction of, that is, perpendicular to, the given vector.

Instances

Eq PolyOrientation

Ord PolyOrientation

Read PolyOrientation

Show PolyOrientation

data PolygonOpts

Options for specifying a polygon.

Constructors

PolygonOpts

Fields

_polyType :: PolyType

_polyOrient :: PolyOrientation

_polyCenter :: P2

Instances

Default PolygonOpts

The default polygon is a regular pentagon of radius 1, centered at the origin, aligned to the x-axis.

polyType :: Lens' PolygonOpts PolyType

Specification for the polygon's vertices.

polyOrient :: Lens' PolygonOpts PolyOrientation

Should a rotation be applied to the polygon in order to orient it in a particular way?

polyCenter :: Lens' PolygonOpts P2

Should a translation be applied to the polygon in order to place the center at a particular location?

polygon :: (TrailLike t, V t ~ R2) => PolygonOpts -> t

Generate the polygon described by the given options.

polyTrail :: PolygonOpts -> Located (Trail R2)

Generate a polygon. See PolygonOpts for more information.

Generating polygon vertices

polyPolarTrail :: [Angle] -> [Double] -> Located (Trail R2)

Generate the located trail of a polygon specified by polar data (central angles and radii). See PolyPolar.

polySidesTrail :: [Angle] -> [Double] -> Located (Trail R2)

Generate the vertices of a polygon specified by side length and angles, and a starting point for the trail such that the origin is at the centroid of the vertices. See PolySides.

polyRegularTrail :: Int -> Double -> Located (Trail R2)

Generate the vertices of a regular polygon. See PolyRegular.

orient :: R2 -> Located (Trail R2) -> T2

Generate a transformation to orient a trail. orient v t generates the smallest rotation such that one of the segments adjacent to the vertex furthest in the direction of v is perpendicular to v.

Star polygons

data StarOpts

Options for creating "star" polygons, where the edges connect possibly non-adjacent vertices.

Constructors

StarFun (Int -> Int)

Specify the order in which the vertices should be connected by a function that maps each vertex index to the index of the vertex that should come next. Indexing of vertices begins at 0.

StarSkip Int

Specify a star polygon by a "skip". A skip of 1 indicates a normal polygon, where edges go between successive vertices. A skip of 2 means that edges will connect every second vertex, skipping one in between. Generally, a skip of n means that edges will connect every nth vertex.

star :: StarOpts -> [P2] -> Path R2

Create a generalized star polygon. The StarOpts are used to determine in which order the given vertices should be connected. The intention is that the second argument of type [P2] could be generated by a call to polygon, regPoly, or the like, since a list of vertices is TrailLike. But of course the list can be generated any way you like. A Path R2 is returned (instead of any TrailLike) because the resulting path may have more than one component, for example if the vertices are to be connected in several disjoint cycles.

Function graphs

These functions are used to implement star, but are exported on the offchance that someone else finds them useful.

data GraphPart a

Pieces of a function graph can either be cycles or "hairs".

Constructors

Cycle [a]

Hair [a]

Instances

Functor GraphPart

Show a => Show (GraphPart a)

orbits :: (Int -> Int) -> Int -> [GraphPart Int]

orbits f n computes the graph of f on the integers mod n.

mkGraph :: (Int -> Int) -> [a] -> [GraphPart a]

Generate a function graph from the given function and labels.