I'm trying to create a game using Apple's SpriteKit game engine.
While implementing some physics-based calculations in the game, I noticed that the calculated results differ from what effectively then happens to objects.
Example: calculating a body's trajectory through projectile motion's equations causes the body to actually fall down much sooner/quicker than what calculated.
How can I make the physics engine match the real-world physics laws when calculating something gravity-related?
I think I know what's going on with the sample code you have supplied on GitHub, which I'll reproduce here as questions on SO should contain the code:
//
// GameScene.swift
// SpriteKitGravitySample
//
// Created by Emilio Schepis on 17/01/2020.
// Copyright © 2020 Emilio Schepis. All rights reserved.
//
import SpriteKit
import GameplayKit
class GameScene: SKScene {
private var subject: SKNode!
override func didMove(to view: SKView) {
super.didMove(to: view)
// World setup (no friction, default gravity)
// Note that this would work with any gravity set to the scene.
physicsBody = SKPhysicsBody(edgeLoopFrom: frame)
physicsBody?.friction = 0
subject = SKShapeNode(circleOfRadius: 10)
subject.position = CGPoint(x: frame.midX, y: 30)
subject.physicsBody = SKPhysicsBody(circleOfRadius: 10)
subject.physicsBody?.allowsRotation = false
// Free falling body (no damping)
subject.physicsBody?.linearDamping = 0
subject.physicsBody?.angularDamping = 0
addChild(subject)
// Set an arbitrary velocity to the body
subject.physicsBody?.velocity = CGVector(dx: 30, dy: 700)
// Inaccurate prediction of position over time
for time in stride(from: CGFloat(0), to: 1, by: 0.01) {
let inaccuratePosition = SKShapeNode(circleOfRadius: 2)
inaccuratePosition.strokeColor = .red
// These lines use the projectile motion equations as-is.
// https://en.wikipedia.org/wiki/Projectile_motion#Displacement
let v = subject.physicsBody?.velocity ?? .zero
let x = v.dx * time
let y = v.dy * time + 0.5 * physicsWorld.gravity.dy * pow(time, 2)
inaccuratePosition.position = CGPoint(x: x + subject.position.x,
y: y + subject.position.y)
addChild(inaccuratePosition)
}
// Actual prediction of position over time
for time in stride(from: CGFloat(0), to: 1, by: 0.01) {
let accuratePosition = SKShapeNode(circleOfRadius: 2)
accuratePosition.strokeColor = .green
// These lines use the projectile motion equations
// as if the gravity was 150 times stronger.
// The subject follows this curve perfectly.
let v = subject.physicsBody?.velocity ?? .zero
let x = v.dx * time
let y = v.dy * time + 0.5 * physicsWorld.gravity.dy * 150 * pow(time, 2)
accuratePosition.position = CGPoint(x: x + subject.position.x,
y: y + subject.position.y)
addChild(accuratePosition)
}
}
}
What you've done is to:
subject with a physicsBody and placed it
on screen with a initial velocity.inaccuratePosition node, using Newton's laws of
motion (v = ut + 1/2at²)accuratePosition node, using Newton's laws of
motionAll this is is didMoveTo. When the simulation runs, the path of the node subject follows the accuratePosition path accurately.
I think what's happening is that you are calculating the predicted position using subject's physicsBody's velocity, which is in m/s, but the position is in points, so what you should do is convert m/s into point/s first.
So what's the scale factor? Well from Apple's documentation here; it's.... 150 which is too much of a coincidence 😀, so I think that's the problem.
Bear in mind that you set the vertical velocity of your object to 700m/s - that's 1500mph or 105000 SK point/s. You'd expect it to simply disappear out through the top of the screen at high speed, as predicted by your red path. The screen is somewhere between 1,000 and 2,000 points.