Chaikin corner-cutting subdivision for polygon smoothing. More...

#include <geom_algorithms.H>

Public Member Functions
Array< Point >	operator() (const Array< Point > &polyline, size_t iterations, const Geom_Number &ratio=Geom_Number(1, 4)) const
	Smooth an open polyline.

Array< Point >	operator() (const DynList< Point > &polyline, size_t iterations, const Geom_Number &ratio=Geom_Number(1, 4)) const
	Overload accepting DynList.

Static Public Member Functions
static Polygon	smooth_polygon (const Polygon &poly, size_t iterations, const Geom_Number &ratio=Geom_Number(1, 4))
	Smooth a closed polygon.

Static Private Member Functions
static Array< Point >	smooth_open_once (const Array< Point > &pts, const Geom_Number &r)

static Array< Point >	smooth_closed_once (const Array< Point > &pts, const Geom_Number &r)

Detailed Description

Chaikin corner-cutting subdivision for polygon smoothing.

Each iteration replaces every edge (P_i, P_{i+1}) with two new points at fractions ratio and 1 - ratio along the edge. After k iterations the result converges toward a quadratic B-spline curve.

Closed polygon with n vertices -> n * 2^k vertices after k iterations.
Open polyline preserves first and last vertices.

Complexity: O(n * 2^k) where n = input size, k = iterations.

Definition at line 12805 of file geom_algorithms.H.

Member Function Documentation

◆ operator()() [1/2]

Array< Point > Aleph::ChaikinSmoothing::operator()	(	const Array< Point > &	polyline,
		size_t	iterations,
		const Geom_Number &	ratio = `Geom_Number(1, 4)`
	)		const

inline

Smooth an open polyline.

First and last vertices are preserved.

Parameters

polyline	Ordered sequence of vertices.
iterations	Number of subdivision iterations (>= 1).
ratio	Cutting fraction in (0, 0.5). Default 1/4.

Returns: Smoothed vertex array.

Definition at line 12857 of file geom_algorithms.H.

References ah_domain_error_if, Aleph::divide_and_conquer_partition_dp(), k, and smooth_open_once().

◆ operator()() [2/2]

Array< Point > Aleph::ChaikinSmoothing::operator()	(	const DynList< Point > &	polyline,
		size_t	iterations,
		const Geom_Number &	ratio = `Geom_Number(1, 4)`
	)		const