Diagrams.TwoD.Arc

Two-dimensional arcs, approximated by cubic bezier curves.

Documentation

arc :: (InSpace V2 n t, OrderedField n, TrailLike t) => Direction V2 n -> Angle n -> t

Given a start direction d and a sweep angle s, arc d s is the path of a radius one arc starting at d and sweeping out the angle s counterclockwise (for positive s). The resulting Trail is allowed to wrap around and overlap itself.

arc' :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t

Given a radus r, a start direction d and an angle s, arc' r d s is the path of a radius (abs r) arc starting at d and sweeping out the angle s counterclockwise (for positive s). The origin of the arc is its center.

arc'Ex = mconcat [ arc' r xDir (1/4 @@ turn) | r <- [0.5,-1,1.5] ]
       # centerXY # pad 1.1

arcT :: OrderedField n => Direction V2 n -> Angle n -> Trail V2 n

Given a start direction d and a sweep angle s, arcT d s is the Trail of a radius one arc starting at d and sweeping out the angle s counterclockwise (for positive s). The resulting Trail is allowed to wrap around and overlap itself.

arcCCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t

Given a start direction s and end direction e, arcCCW s e is the path of a radius one arc counterclockwise between the two directions. The origin of the arc is its center.

arcCW :: (InSpace V2 n t, RealFloat n, TrailLike t) => Direction V2 n -> Direction V2 n -> t

Like arcAngleCCW but clockwise.

bezierFromSweep :: OrderedField n => Angle n -> [Segment Closed V2 n]

bezierFromSweep s constructs a series of Cubic segments that start in the positive y direction and sweep counter clockwise through the angle s. If s is negative, it will start in the negative y direction and sweep clockwise. When s is less than 0.0001 the empty list results. If the sweep is greater than fullTurn later segments will overlap earlier segments.

wedge :: (InSpace V2 n t, OrderedField n, TrailLike t) => n -> Direction V2 n -> Angle n -> t

Create a circular wedge of the given radius, beginning at the given direction and extending through the given angle.

wedgeEx = hcat' (with & sep .~ 0.5)
  [ wedge 1 xDir (1/4 @@ turn)
  , wedge 1 (rotate (7/30 @@ turn) xDir) (4/30 @@ turn)
  , wedge 1 (rotate (1/8 @@ turn) xDir) (3/4 @@ turn)
  ]
  # fc blue
  # centerXY # pad 1.1

arcBetween :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) => Point V2 n -> Point V2 n -> n -> t

arcBetween p q height creates an arc beginning at p and ending at q, with its midpoint at a distance of abs height away from the straight line from p to q. A positive value of height results in an arc to the left of the line from p to q; a negative value yields one to the right.

arcBetweenEx = mconcat
  [ arcBetween origin (p2 (2,1)) ht | ht <- [-0.2, -0.1 .. 0.2] ]
  # centerXY # pad 1.1

annularWedge :: (TrailLike t, V t ~ V2, N t ~ n, RealFloat n) => n -> n -> Direction V2 n -> Angle n -> t

Create an annular wedge of the given radii, beginning at the first direction and extending through the given sweep angle. The radius of the outer circle is given first.

annularWedgeEx = hsep 0.50
  [ annularWedge 1 0.5 xDir (1/4 @@ turn)
  , annularWedge 1 0.3 (rotate (7/30 @@ turn) xDir) (4/30 @@ turn)
  , annularWedge 1 0.7 (rotate (1/8 @@ turn) xDir) (3/4 @@ turn)
  ]
  # fc blue
  # centerXY # pad 1.1