Swiftpack.co - Package - hfutrell/BezierKit


Build Status License: MIT codecov CocoaPods Compatible

BezierKit is a comprehensive Bezier Path library written in Swift.

Warning! Prerelease software!

Please note that BezierKit is currently pre-release software. Its releases follow semantic versioning which means that until it reaches 1.0 status the API may not be stable or backwards compatible.


  • ☑ Constructs linear (line segment), quadratic, and cubic Bézier curves
  • ☑ Draws curves via CoreGraphics
  • ☑ Determines positions, derivatives, and normals along curves
  • ☑ Lengths of curves via Legendre-Gauss quadrature
  • ☑ Intersects curves and computes cubic curve self-intersection to any degree of accuracy
  • ☑ Determines bounding boxes, extrema,
  • ☑ Locates nearest on-curve location to point
  • ☑ to any degree of accuracy
  • ☑ Splits curves into subcurves
  • ☑ Offsets and outlines curves
  • ☐ Comprehensive Unit and Integration Test Coverage
  • ☐ Complete Documentation



CocoaPods is a dependency manager for Cocoa projects. You can install it with the following command:

$ gem install cocoapods

To integrate BezierKit into your Xcode project using CocoaPods, add it to your target in your Podfile:

target '<Your Target Name>' do
    pod 'BezierKit', '>= 0.8.0'

Then, run the following command:

$ pod install

Swift Package Manager

The Swift Package Manager is a tool for automating the distribution of Swift code and is integrated into the swift compiler. Once you have your Swift package set up, adding BezierKit as a dependency is as easy as adding it to the dependencies value of your Package.swift.

// swift-tools-version:5.0
import PackageDescription

let package = Package(
    name: "<Your Target Name>",
    dependencies: [
        .package(url: "https://github.com/hfutrell/BezierKit.git", from: "0.8.0"),


Constructing & Drawing Curves

BezierKit supports cubic Bezier curves (CubicCurve) and quadratic Bezier curves (QuadraticCurve) as well as line segments (LineSegment) each of which adopts the BezierCurve protocol that encompasses most API functionality.

import BezierKit

let curve = CubicCurve(
    p0: CGPoint(x: 100, y: 25),
    p1: CGPoint(x: 10, y: 90),
    p2: CGPoint(x: 110, y: 100),
    p3: CGPoint(x: 150, y: 195)
 let context: CGContext = ...       // your graphics context here
 Draw.drawSkeleton(context, curve)  // draws visual representation of curve control points
 Draw.drawCurve(context, curve)     // draws the curve itself

Intersecting Curves

The intersections(with curve: BezierCurve) -> [Intersection] method determines each intersection between self and curve as an array of Intersection objects. Each intersection has two fields: t1 represents the t-value for self at the intersection while t2 represents the t-value for curve at the intersection. You can use the ponit(at:) method on either of the curves to calculate the coordinates of the intersection by passing in the corresponding t-value for the curve.

Cubic curves may self-intersect which can be determined by calling the selfIntersections() method.

let intersections: [Intersection] = curve1.intersections(with: curve2)
let points: [CGPoint] = intersections.map { curve1.point(at: $0.t1) }

Draw.drawCurve(context, curve: curve1)
Draw.drawCurve(context, curve: curve2)
for p in points {
    Draw.drawPoint(context, origin: p)

Splitting Curves

The split(from:, to:) method produces a subcurve over a given range of t-values. The split(at:) method can be used to produce a left subcurve and right subcurve created by splitting across a single t-value.

Draw.setColor(context, color: Draw.lightGrey)
Draw.drawSkeleton(context, curve: curve)
Draw.drawCurve(context, curve: curve)
let subcurve = curve.split(from: 0.25, to: 0.75) // or try (leftCurve, rightCurve) = curve.split(at:)
Draw.setColor(context, color: Draw.red)
Draw.drawCurve(context, curve: subcurve)
Draw.drawCircle(context, center: curve.point(at: 0.25), radius: 3)
Draw.drawCircle(context, center: curve.point(at: 0.75), radius: 3)

Determining Bounding Boxes

let boundingBox = curve.boundingBox
Draw.drawSkeleton(context, curve: curve)
Draw.drawCurve(context, curve: curve)
Draw.setColor(context, color: Draw.pinkish)
Draw.drawBoundingBox(context, boundingBox: curve.boundingBox)


BezierKit is a powerful library with a lot of functionality. For the time being the best way to see what it offers is to build the MacDemos target and check out each of the provided demos.


BezierKit is released under the MIT license. See LICENSE for details.


Stars: 93


Used By

Total: 0



  • speeds up implementation of CubicCurve.project(_:) by a factor of 2
  • provides implementation of Path.project(_:) and PathComponent.project(_:) to help common task of finding closest point on path
  • additional performance tests


Makes PathComponentRange properties mutable and exposes constructor publicly


  • adds support for installation via Swift Package Manager (SPM)
  • adds support for NSSecureCoding in Path
  • adds support for Linux (excluding interoperability with unavailable CoreGraphics APIs such as CGPath)


  • reverts a change from v0.6.6 that was causing issues


  • improves performance of cubic curve self-intersection routine selfIntersects
  • minor bug fixes


Fixes an issue where curve.project(_:) could return incorrect results because the closest solution could be missed.


  • improved algorithm for curve.project(_:) so that accuracy parameter is no longer needed
  • renames curve.compute(_:) to curve.point(at:)
  • renames curve.derivative(_:) to curve.derivative(at:)
  • renames curve.normal(_:) to curve.normal(at:)


  • fixed an issue where importing BezierKit in an app extension would cause a build warning
  • vector boolean operations such as Path.union(_ path: Path) no longer return an optional
  • Path.selfIntersections(accuracy:) once again includes intersections where a single curve element intersects itself


scale() now returns nil when attempting to scale an unscalable curve, such as a point.

PathComponent.offset() now ignores curves that cannot be scaled, and returns nil if none of the component’s curves could be scaled. In previous releases offsetting a circle with zero radius would result in a crash.

Fixes issues with vector boolean operations on paths with coincident edges

Removes cgPath property of PathComponent. If you need this consider constructing a Path with a single component, ie using Path(components: [component]).cgPath

Improves the performance of computing Path.cgPath in the case of multi-component paths. This is especially relevant to dashed paths which can have hundreds of components.


This release patches the old 0.5.13 release so resolve compiler warnings. Most people should use version 0.6+.


This release refactors a number of APIs and improves support for vector boolean operations in cases where edges are coincident.

It also removes some APIs from the core library which were questionably useful, including approximating curves as arcs (ArcApproximateable) and support for variable width outlines.


  • improves the behavior of Path.contains(_:CGPoint) for complex paths
  • new implementation of lock that should appear as OK when thread sanitizer is used
  • fixes behavior of disjointComponents() in certain cases


  • fixes behavior of Path.contains(:_) for some cases of paths where an path element is a cubic curve with multiple extrema


  • improves the reliability of Path.contains


  • fixes bugs in vector boolean operations


  • improves thread safety of Path.cgPath and other lazily computed properties
  • adds swiftlint rules for code quality (though these are not yet enforced)
  • improvements to vector boolean methods
  • improvements to line / curve intersection



  • fixes a minor issue in an edge case of cubic curve normals at cusps regressed in version 0.5.5
  • fixes an edge case issue where calling .reduce() on degenerate curves could result in a very large number of results
  • makes numerous minor improvements to code quality and unit tests


  • improves the behavior of BezierCurve.normal(_:) for t=0 and t=1 in edge cases where derivative may be zero because control points are exactly equal to starting or ending points of the curve.
  • improves behavior of BezierCurve.reduce() when extreme points are very close to each other
  • fixes crash in BezierCurve.scale(distance:)


refines the fix released in version 0.5.3 to address more related crashes


This releases fixes an uncommon crash that could occur vector boolean operations


This release includes several minor bugfixes:

  • ensures that calling BezierCurve.split(from:, to:) on a set of ranges creates a series of curves that are exactly continuous
  • fixes a crash when creating an instance of Path from a cgPath which has a subpath that was started without a move(to:) command
  • fixes behavior of Path.intersections(with:) for with open paths that intersect at end points.


  • added notion of PathComponentRange and PathComponent.split(range:) using it.
  • made it easier for subclassers to support splitting by making it so method to override is guaranteed to be passed a standardized range.



  • upgraded swift version to 5.0
  • renames BezierCurve.project(point: pointToProject, errorThreshold: epsilon) to BezierCurve.project(_:, accuracy:). The method now returns a tuple (point: CGPoint, t: CGFloat) for applications that need the t value of the projection.
  • the errorThreshold parameter of Path.pointIsWithinDistanceOfBoundary has been renamed to accuracy


New features:

  • adds ability to split path components with PathComponent.split(from:, to:)
  • adds utility method for enumerating over points of PathComponent with option to include or exclude control points PathComponent.enumeratePoints(includeControlPoints:, using:)
  • allows subclassing of Path and PathComponent
  • adds Comparable support to IndexedPathLocation and IndexedPathComponentLocation
  • adds distanceSquared function between points


  • fixes a memory leak in vector boolean operations
  • improves support for converting to and from CoreGraphics paths that have single point subpaths


This release refactors several intersection methods and adds new intersects(with:) -> Bool methods for better API usage when the caller only cares if things intersect (without caring about the intersections themselves).

It makes public the Flatness API for determining the maximum distance a Bezier curve strays from the line segment connecting its endpoints.

It renames "threshold" parameters to the more descriptive "accuracy"

It has several other miscellaneous renamings.


greatly improves the accuracy of Path.pointIsWithinDistanceOfBoundary(point:, distance:) and BezierCurve.project(point:). Adds an errorThreshold parameter to these functions and related functions (with a default value) so that the caller can control speed vs accuracy of the result.


This release adds Path.data and Path(data: Data) methods to convert between Path instances and a compact binary representation for serialization / deserialization.

The release also dramatically reduces the memory usage of Path instances.

Path.subpaths has been renamed Path.components

Path.curves may be deprecated in the future. To access elements it's recommended that you use Path.element(at:) instead. It's recommended that you use Path.elementCount instead of Path.curves.count because it's much faster.

Exposed CGPoint.cross(_:) vector cross product method