Trace
iOS Graphing App
App Concept
Trace is a work-in-progress mathematical graphing app that I have been working on this year. The app allows users to plot graphs of a wide array of curves and functions with a wealth of styling and display options.
A Beautiful Graphing Experience
My goal with this app is to create a fully-featured graphing app that was native to iOS. Whilst there are many powerful graphing apps available, none feels truly at home in iOS, with many of the most popular apps not even adapting correctly to the available screen size on iPhones. Later down the line, I have plans to add many more original features such as support for complex (imaginary) numbers and recursively defined functions.
Graphing View
Styled Curves
Custom Keyboard
Curve Style
Inline Menus
How the App Works
I built Trace from scratch using purely Swift and SwiftUI, without relying on any existing graphing software. This involved quite a number of challenges. The first of these involved converting textual descriptions of functions from the user (such as '-xsinx' or '-x(x-1)' into a structured, mathematical object. A sample of code illustrating some of this structure is shown below.
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import Foundation
protocol Expression {
var value: (Assignment) -> Double? { get }
var debugDescription: String { get }
}
protocol Symbol {
var validator: (String) -> Bool { get }
var description: String { get }
}
protocol Operator {
var priority: Int { get }
}
struct UnaryOperator: Symbol, Operator {
var priority: Int
var description: String
var validator: (String) -> Bool
var closure: (Double?) -> (Double?)
}
// ...
The biggest challenge of all was to actually plot the functions in an efficient but elegant manner. This involved a lot of head-scratching and the implementation of a great deal of algorithms, for example to handle asymptotes and to highlight turning points.
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