Round corners with an adaptive version of Chaikin's Corner Cutting algorithm

Corners can be rounded in many ways. One approach is to recursively cut away a part of the corner, introducing a new edge into the line/polygon. Chaikin's algorithm defines the cut to be placed 1/4th into the edges on either side of the corner. As the recursion progresses the result approaches the bspline defined by the points. Chaikins algorithm works best on rather coarse polygons as the edge length defines the extent of the cutting. Subdividing all edges into two will thus alter the result of the algorithm, just like adding more control points would alter a b spline. The corner cutting provided here is based on the idea of chaikin but is adaptive so that it can ignore vertices with very obtuse angles, as well as set an upper bound on how big the cut can be, meaning that the distance between corner points have less effect on the rounding.

Usage

corner_clip(poly, max_angle = Inf, max_cut = Inf, n_cuts = 4L)

Arguments

poly: A polyclid_polygon or polyclid_polyline vector
max_angle: The maximum inner angle at a vertex for it to be considered a corner
max_cut: The maximum distance from the corner vertex the rounding may influence the polygon. Take note that this is not a measure of the radius of the rounding as this depends on the angle of the corner
n_cuts: The number of iterations to perform of the cutting. Be aware that the number of additional edges increases exponentially with the number of cuts so increase this only in small steps.

Value

A vector of the same type as poly. Be aware that corner cutting may render a polygon invalid as the rounding may cause edges to cross.

Examples

poly <- polyclid::polygon(
  c(391, 240, 252, 374, 289, 134, 68, 154, 161, 435, 208, 295, 421, 441),
  c(374, 431, 340, 320, 214, 390, 186, 259, 107, 108, 148, 160, 212, 303)
)
plot(poly)


# Default values provide non-adaptive behaviour
plot(corner_clip(poly))

# As can be seen, this behaviour is sensitive to the density of the polygon
euclid_plot(corner_clip(densify_poly(poly, n_splits = 2)), lty = 2)


# Use max_cut to have more local rounding
plot(corner_clip(poly, max_cut = 25))


# Use max_angle to leave out very obtuse angled vertices
plot(corner_clip(poly, max_cut = 25, max_angle = pi * 0.8))


# The corner cutting also works for polylines
poly <- polyclid::polyline(
  c(391, 240, 252, 374, 289, 134, 68, 154, 161, 435),
  c(374, 431, 340, 320, 214, 390, 186, 259, 107, 108)
)
plot(poly)
euclid_plot(corner_clip(poly, max_cut = 25), lty = 2, col = "red")