Diagrams.CubicSpline

A cubic spline is a smooth, connected sequence of cubic curves. This module provides two methods for constructing splines.

The cubicSpline method can be used to create closed or open cubic splines from a list of points. The resulting splines pass through all the control points, but depend on the control points in a "global" way (that is, changing one control point may alter the entire curve). For access to the internals of the spline generation algorithm, see Diagrams.CubicSpline.Internal.

bspline creates a cubic B-spline, which starts and ends at the first and last control points, but does not necessarily pass through any of the other control points. It depends on the control points in a "local" way, that is, changing one control point will only affect a local portion of the curve near that control point.

Constructing paths from cubic splines

cubicSpline :: (V t ~ v, N t ~ n, TrailLike t, Fractional (v n)) => Bool -> [Point v n] -> t

Construct a spline path-like thing of cubic segments from a list of vertices, with the first vertex as the starting point. The first argument specifies whether the path should be closed.

pts = map p2 [(0,0), (2,3), (5,-2), (-4,1), (0,3)]
spot = circle 0.2 # fc blue # lw none
mkPath closed = position (zip pts (repeat spot))
             <> cubicSpline closed pts
cubicSplineEx = (mkPath False ||| strutX 2 ||| mkPath True)
              # centerXY # pad 1.1

For more information, see http://mathworld.wolfram.com/CubicSpline.html.

type BSpline v n = [Point v n]

bspline :: (TrailLike t, V t ~ v, N t ~ n) => BSpline v n -> t

Generate a uniform cubic B-spline from the given control points. The spline starts and ends at the first and last control points, and is tangent to the line to the second(-to-last) control point. It does not necessarily pass through any of the other control points.

pts = map p2 [(0,0), (2,3), (5,-2), (-4,1), (0,3)]
spot = circle 0.2 # fc blue # lw none
bsplineEx = mconcat
  [ position (zip pts (repeat spot))
  , bspline pts
  ]
  # frame 0.5