Runge Kutta 2nd order movement test

rungekutta2nd.swift

//: Playground - noun: a place where people can play

import UIKit
import PlaygroundSupport

// Helper functions
func * (point: CGPoint, scalar: CGFloat) -> CGPoint {
    return CGPoint(x: point.x * scalar, y: point.y * scalar)
}
func + (left: CGPoint, right: CGPoint) -> CGPoint {
    return CGPoint(x: left.x + right.x, y: left.y + right.y)
}
func / (point: CGPoint, scalar: CGFloat) -> CGPoint {
    return CGPoint(x: point.x / scalar, y: point.y / scalar)
}

// Variables
var timerCount = 0
let maxTimeCount = 10
let framerate = 1.0
var position = CGPoint(x: 0, y: 0)
var velocity = CGPoint(x: 0, y: 0)
var acceleration = CGPoint(x: 10, y: 0)
let mass = 1

func force(position: CGPoint, velocity: CGPoint, time: CGFloat = 0) -> CGPoint {
    return acceleration
}

// Update function
func update(deltaTime: Double) {
    let acceleration1 = force(position: position, velocity: velocity)
    let position2 = position + velocity * CGFloat(deltaTime)
    let velocity2 = velocity + acceleration1 * CGFloat(deltaTime)
    
    let acceleration2 = force(position: position2, velocity: velocity2)
    position = position + (velocity + velocity2) / 2 * CGFloat(deltaTime)
    velocity = velocity + (acceleration1 + acceleration2) / 2 * CGFloat(deltaTime)
}

// Run update function
while (timerCount < maxTimeCount) {
    timerCount += 1
    update(deltaTime: 1.0.divided(by: framerate))
}