SwiftSplines

I need a function that connects f(0)=0.1, f(1)=1.5 and f(2)=1 with a smooth line.

With SwiftSplines you can easily create smooth functions that interpolate control points.

Simple function (1D):

2D Curve:

Features

• Interpolate points with a piecewise cubic spline
• Written for generic image space, called DataPoint, which can be float, double, CGPoint or vectors of arbitrary dimension
• Matrix calculation to get the derivatives at the control points uses Accelerate's sparse matrix solvers, so built for speed on all platforms that support Accelerate
• Offers smooth, fixed ends or circular boundary conditions
• use Double/Float accelerate functions depending on intput data. So far scalars are converted to Double,
• offer polynomials of different degrees, not just Cubic Splines

Requirements

• iOS 11.0+ / macOS 10.13+ / tvOS 11.0+ / watchOS 4.0+
• Xcode 11+
• Swift 5.1+

Dependencies

• Accelerate framework

Based on

The math for the splines is detailed on wolfram alpha and this source book.

Installation

Swift Package Manager

The Swift Package Manager is a tool for automating the distribution of Swift code and is now available for all Apple platforms.

Just open Add package dependency in Xcode:

and enter the following url

https://github.com/Bersaelor/SwiftSplines.git

You can also manually edit the SPM Package.swift and add SwiftSplines as dependencies value of your Package.swift.

dependencies: [
    .package(url: "https://github.com/Bersaelor/SwiftSplines.git", .upToNextMajor(from: "0.1.0"))
]

Carthage/Cocoapods etc

Since the swift package manager is now mature, older package managers are no longer supported.

Usage

Import the package in your *.swift file:

import SwiftSplines

Example A : Dampening a signal

If you want a function that dampens a signal in the range of [0,3], like

f(0.1) = 0.3,
f(0.4) = 0.6,
f(1) = 1,
f(2) = 1.6
f(2.5) = 2
f'(0.1) = 0
f'(2.5) = 0

you could define:

// private let dampingFunction: (Double) -> Double
private let dampingFunction = Spline(
    arguments: [0.1, 0.4, 1, 2,   2.5],
    values:    [0.3, 0.6, 1, 1.6, 2],
    boundaryCondition: .fixedTangentials(dAtStart: 0, dAtEnd: 0.0)
).f

Example B: Connect custom vector data

Make sure your data values conform to

public protocol DataPoint {
    associatedtype Scalar: FloatingPoint & DoubleConvertable
    
    static var scalarCount: Int { get }
    subscript(index: Int) -> Scalar { get set }
    
    static func * (left: Scalar, right: Self) -> Self
    static func + (left: Self, right: Self) -> Self
}

extension MyVector: DataPoint { ... }

(Float, CGFloat, Double, CGPoint conform to DataPoint as part of the package)

Then you can create your spline functions by:

let values: [MyVector] = ...

let spline = Spline(values: values)

func calculate(t: Double) -> MyVector {
    return spline.f(t: t)
}

Applications

• calculate some moving object's positions between fixed control points
• interpolate given values smoothly
• originally created because we needed a function that starts at a constant value above 0, then approaches y(x) = x around 1 and then peters out towards 2. In that case the application was an ARKit app where we wanted to smoothly filter the incoming light estimation

License

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