Wumpus.Drawing.Paths.Base

Absolute path type - this should be more amenable for building complex drawings than the PrimPath type in Wumpus-Core.

Note - there is no concatenation (i.e. no Monoid instance), this is because concatenating ** absolute ** paths has no obvious interpretation - draw a join between the paths, move the second path to start where the first ends...

Use CatTrail from Wumpus-Basic if you need a relative-path like object that supports concatenation, then convert it in a final step to an AbsPath.

Absolute path type

data AbsPath u

Absolute path data type.

Instances

Functor AbsPath

(Ord u, Tolerance u) => Eq (AbsPath u)

Show u => Show (AbsPath u)

(Real u, Floating u, Ord u, Tolerance u) => Rotate (AbsPath u)

This is expensive on paths - needs a traversal.

(Real u, Floating u, Ord u, Tolerance u) => RotateAbout (AbsPath u)

This is expensive on paths - needs a traversal.

(Floating u, Ord u, Tolerance u) => Scale (AbsPath u)

This is expensive on paths - needs a traversal.

Num u => Translate (AbsPath u)

Translate is cheap on AbsPath it just moves the start and end points. The path itself is otherwise built from vectors so it doesn't respond to translation (translate == id).

type DAbsPath = AbsPath Double

Construction

emptyPath :: Floating u => Point2 u -> AbsPath u

Create the empty path.

Note - an absolute path needs locating and cannot be built without a start point. Figuratively, the empty path is a path from the start point to the end point.

Thus AbsPath operates as a semigroup but not a monoid.

line1 :: Floating u => Point2 u -> Point2 u -> AbsPath u

Create an absolute path as a straight line between the supplied points.

curve1 :: (Floating u, Ord u, Tolerance u) => Point2 u -> Point2 u -> Point2 u -> Point2 u -> AbsPath u

Create an absolute path from a single cubic Bezier curve.

vertexPath :: (Floating u, Ord u, Tolerance u) => [Point2 u] -> AbsPath u

vertexPath throws a runtime error if the supplied list is empty.

curvePath :: (Floating u, Ord u, Tolerance u) => [Point2 u] -> AbsPath u

curvePath consumes 4 points from the list on the intial step (start, control1, control2, end) then steps through the list taking 3 points at a time thereafter (control1,control2, end). Leftover points are discarded.

curvePath throws a runtime error if the supplied list is has less than 4 elements (start, control1, control2, end).

controlCurve :: (Floating u, Ord u, Tolerance u) => Point2 u -> Radian -> Radian -> Point2 u -> AbsPath u

This is not an arc...

vectorPath :: (Floating u, Ord u, Tolerance u) => [Vec2 u] -> Point2 u -> AbsPath u

vectorPathTheta :: (Real u, Floating u, Tolerance u) => [Vec2 u] -> Radian -> Point2 u -> AbsPath u

anaTrailPath :: (Floating u, Ord u, Tolerance u) => Point2 u -> AnaTrail u -> AbsPath u

catTrailPath :: (Floating u, Ord u, Tolerance u) => Point2 u -> CatTrail u -> AbsPath u

Queries

null :: AbsPath u -> Bool

Is the path empty?

length :: Num u => AbsPath u -> u

Length of the Path.

Length is the length of the path as it is drawn, it is not a count of the number or path segments.

Length is cached so this operation is cheap - though this puts a tax on the build operations.

Concat and extension

snocLine :: Floating u => AbsPath u -> Vec2 u -> AbsPath u

Extend the path with a straight line segment from the end-point defined by the supplied vector.

 infixl 5 `snocLine`

snocLineTo :: Floating u => AbsPath u -> Point2 u -> AbsPath u

Extend the path with a straight line segment from the end-point to the supplied point.

 infixl 5 `snocLineTo`

snocCurve :: (Floating u, Ord u, Tolerance u) => AbsPath u -> (Vec2 u, Vec2 u, Vec2 u) -> AbsPath u

Extend the path from the end-point with a Bezier curve segment formed by the supplied points.

 infixl 5 `snocCurve`

snocCurveTo :: (Floating u, Ord u, Tolerance u) => AbsPath u -> (Point2 u, Point2 u, Point2 u) -> AbsPath u

Extend the path from the end-point with a Bezier curve segment formed by the supplied points.

 infixl 5 `snocCurveTo`

Conversion

toPrimPath :: InterpretUnit u => AbsPath u -> Query u PrimPath

Turn a Path into an ordinary PrimPath.

Assumes path is properly formed - i.e. end point of one segment is the same point as the start point of the next segment.

renderPath :: InterpretUnit u => PathMode -> AbsPath u -> Image u (AbsPath u)

renderPath_ :: InterpretUnit u => PathMode -> AbsPath u -> Graphic u

Shortening

shortenPath :: (Real u, Floating u) => u -> u -> AbsPath u -> AbsPath u

sortenPath : left_dist * right_dist * path -> Path

shortenL :: (Real u, Floating u) => u -> AbsPath u -> AbsPath u

Note - shortening a line from the left by greater-than-or-equal its length is operationally equivalent to making a zero-length line at the end point.

shortenR :: (Real u, Floating u) => u -> AbsPath u -> AbsPath u

Note - shortening a line from the right by greater-than-or-equal its length is operationally equivalent to making a zero-length line at the start point.

Tips and inclination

tipL :: AbsPath u -> Point2 u

tipR :: AbsPath u -> Point2 u

inclinationL :: (Real u, Floating u) => AbsPath u -> Radian

Direction of empty path is considered to be 0.

inclinationR :: (Real u, Floating u) => AbsPath u -> Radian

Direction of empty path is considered to be 0.

isBezierL :: AbsPath u -> Bool

Is the left tip a Bezier curve?

isBezierR :: AbsPath u -> Bool

Is the right tip a Bezier curve?

Path anchors

midway :: (Real u, Floating u) => AbsPath u -> (Point2 u, Radian)

midway_ :: (Real u, Floating u) => AbsPath u -> Point2 u

atstart :: (Real u, Floating u) => AbsPath u -> (Point2 u, Radian)

atstart_ :: AbsPath u -> Point2 u

atend :: (Real u, Floating u) => AbsPath u -> (Point2 u, Radian)

atend_ :: AbsPath u -> Point2 u

Views

data PathViewL u

Constructors

EmptyPathL

(PathSegment u) :<< (AbsPath u)

Instances

Functor PathViewL

(Ord u, Tolerance u) => Eq (PathViewL u)

Show u => Show (PathViewL u)

type DPathViewL = PathViewL Double

data PathViewR u

Constructors

EmptyPathR

(AbsPath u) :>> (PathSegment u)

Instances

Functor PathViewR

(Ord u, Tolerance u) => Eq (PathViewR u)

Show u => Show (PathViewR u)

type DPathViewR = PathViewR Double

data PathSegment u

PathSegments are annotated with length.

Constructors

LineSeg u (Point2 u) (Point2 u)

CurveSeg u (Point2 u) (Point2 u) (Point2 u) (Point2 u)

Instances

Functor PathSegment

(Ord u, Tolerance u) => Eq (PathSegment u)

Show u => Show (PathSegment u)

type DPathSegment = PathSegment Double

pathViewL :: Num u => AbsPath u -> PathViewL u

pathViewR :: Num u => AbsPath u -> PathViewR u

optimizeLines :: (Real u, Floating u, Ord u, Tolerance u) => AbsPath u -> AbsPath u

roundExterior :: (Real u, Floating u, Tolerance u) => u -> AbsPath u -> AbsPath u

Round a "closed" path.

Caution - all path sgements are expected to be longer than 2x the round corner length, though this is not checked..

roundInterior :: (Real u, Floating u, Tolerance u) => u -> AbsPath u -> AbsPath u

Round interior corners of a Path.

The path is treated as open - the start of the initial and end of the final segments are not rounded. Only straight line to straight line joins are rounded, joins to or from Bezier curves are not rounded.

Caution - all path segments are expected to be longer than 2x the round corner length, though this is not checked..

deBezier :: Floating u => AbsPath u -> AbsPath u

Redraw an AbsPath replacing the Bezier curves with three lines along the control vectors.

pathMajorPoints :: Num u => AbsPath u -> [Point2 u]

This does not extract the control points of Bezier curves.

pathAllPoints :: Num u => AbsPath u -> [Point2 u]

This extracts the control points of Bezier curves.

Path division

pathdiv :: (Real u, Floating u) => u -> u -> u -> AbsPath u -> [(Point2 u, Radian)]

Divide a path returning intermediate points and direction

Args are initial-prefix, division size, trailing size.

Generation is stopped if the remainder of the path is shorter than the trailing size.