Simplified Projectile Physics For Faster Game Calculations
Physics calculations are essential for realistic gameplay mechanics in games, but they can also be computationally expensive. Complex physics equations with many trigonometric functions and floating point operations can lead to poor performance if not optimized properly. By simplifying key physics equations and reducing unnecessary calculations, we can achieve faster and smoother gameplay without sacrificing too much accuracy.
Reducing Floating Point Operations in Motion Calculations
Floating point operations involve numbers with decimals and are more complex for computers to calculate compared to integer operations. Physics equations often require many floating point multiplications, divisions, and trigonometric calculations to determine motion vectors and trajectories.
We can reduce the floating point burden by precomputing constants, using integer math whenever possible, and avoiding unnecessary precision through rounding. For example, precomputing a fixed “gravity” constant as an integer and using whole number changes in position per frame can replace floating point gravity equations.
Precomputing Motion Constants
By precomputing physics constants like gravity, max velocity, acceleration rate, etc. as integer values during initialization, we avoid unnecessary floating point math during each game update loop. This constants can then simply be added or subtracted from positional vectors as fixed integer amounts.
Clamping Positional Changes
Rather than precisely calculate sub-pixel level position changes each frame, we can round changes to whole integer values and clamp them to predefined maximums and minimums. This avoids tiny unnecessary floating point adjustments that are imperceptible visually.
Delta Time Normalization
Basing physics motion on the fixed time interval between frames (delta time) rather than frame rate allows us to use predictable integer changes while ensuring consistent overall speeds. Detecting and clamping exceptionally large delta spikes also prevents instability.
Vector Math Instead of Trigonometry Functions
The motion of game objects often involves calculate trajectories along X, Y axes over time. By representing positions, velocities and accelerations as fixed integer vector quantities instead of trig function coordinates, trajectory math becomes simpler integer addition and subtraction.
Vector Velocities
Instead of calculating precise pixel positions using sine and cosine of angle times speed, simply define horizontal and vertical velocity components directly as X and Y vector quantities instead. Then position can be updated by adding these DeltaX and DeltaY velocity vector values each frame without trig functions at all.
Resultant Vectors
The combination of different velocity vectors, like from player input and gravity, can be precomputed once into a single “resultant” velocity vector on initialization. This resultant vector representing the current net motion is all that needs updating afterwards, avoiding redoing vector math each frame.
Motion Boundaries
Simple comparison of vector positions to predefined integer min/max range boundaries can handle bouncing off surfaces and edges instead of complex collision calculations against polygon geometry. This greatly reduces math needed to constrain motion along intended paths.
Precomputing Values for Repeated Checks
Game logic often requires the same boundary checks and value comparisons to be done each update loop. By precomputing comparisons into simple boolean flags once upfront, we can entirely eliminate raw math from the critical update logic path.
Directional Flags
Boolean flags defining whether velocity on each axis is currently negative or positive can predicate simple minimum maximum clamping without computing precise velocity values each frame.
Proximity Flags
Whether the object is near boundaries, edges, or collision boxes can be cached into flags to skip distance calculations in update loops. Simple “OR” logic on these flags triggers behaviors without raw math.
Behavior Triggers
Game events like enemy spawns, weapon reloads, etc can be precomputed to trigger on specific upcoming frames once initially. Logic simply checks for flagged frame numbers without repeated evaluations.
Example Code for Projectile Physics
Putting these simplification principles into practice, here is example C# code for a simplified projectile trajectory calculation without trig functions or floating point math:
public class Projectile
{
// Velocity vector constants
const int GRAVITY = -20;
const int START_VELOCITY = 60;
// Resultant vector totals
public int XVelocity { get; set; }
public int YVelocity { get; set; }
// Current position
public int XPosition { get; set; }
public int YPosition { get; set; }
// Movement range boundaries
const int MIN_Y = 0;
const int MAX_Y = 1000;
const int MIN_X = 0;
const int MAX_X = 1500;
// Update method handles motion
public void Update()
{
// Apply gravity downward accel
YVelocity += GRAVITY;
// Clamp vertical to terminally velocity
YVelocity = Mathf.Clamp(YVelocity, -500, 200);
// Add resultant velocities
XPosition += XVelocity;
YPosition += YVelocity;
// Constrain motion in bounds
XPosition = Mathf.Clamp(XPosition, MIN_X, MAX_X);
YPosition = Mathf.Clamp(YPosition, MIN_Y, MAX_Y);
}
// Initialize with starting values
public void Launch(int angleDegrees)
{
// Set launch direction
XVelocity = START_VELOCITY * Mathf.Cos(angleDegrees);
YVelocity = START_VELOCITY * Mathf.Sin(angleDegrees);
}
}
Key elements like gravity, maximum ranges, velocities, etc. are predefined as integer constants allowing pure integer math. The launch trajectory trig functions are precomputed once into the initial velocity vectors. No further sine/cosine needed afterward, just simple vector addition and constraint. This runs very fast with no loss of realistic projectile behavior.
Applying Simplifications to Common Game Mechanics
The same concepts of simplifying math and precomputing values can be applied to optimize performance of all sorts of common game mechanics beyond just projectiles.
Jumping
The arc of a player jump can be broken down into integer vertical velocity added and subtracted per frame to trace a believable arc shape with no trigonometry required. Directional booleans track when gravity changes from upward to downward accel over the course of the jump.
Firing Weapons
Complex ballistic trajectories can be faked convincingly by spawning projectiles directly on calculated future positions at predefined times using simplfied velocity and gravity constants. No need to simulate the full arc each frame.
Throwing Grenades
The firing of grenades can utilize the same simplified projectile physics system as other weapons with minor tweaks to max velocity and gravity amounts. No need for custom one-off equations.
Enemy AI
Complex dynamic enemy behavior can be scripted ahead of time by precomputing waypoint paths, spawn sequences, aimed shot locations, melee attack ranges and timing all as fixed integer data. No realtime AI logic needed.
Optimizing Update Loops for Maximum Performance
While individual simplified equations improve performance, more frames with simpler math will still add up without careful management of the game update loop itself:
Reduced Update Frequency
Key simulation systems like projectile motion may only need 30Hz while graphics and input polls can run at 90Hz. Segregating these into nested loops prevents wasting cycles.
Interpolation Over Simulation
Visual smoothness can be maintained at high frame rates through simple positional interpolation instead of actually simulating all intermediate motion, allowing the core game logic to update less frequently.
Asynchronous Updates
Expensive operations like enemy AI planning or physics collisions can be run independently as background tasks while main game state lags slightly behind, preventing spikes from blocking high priority rendering and input handling.
Logic Gates on Updates
Checks whether significant state changes have occurred allow skipping subsets of game logic when not needed. No reason to update motionless projectiles every frame for example.
Finding the Right Balance of Accuracy and Speed
While the techniques outlined about can enable huge performance gains, taken too far games can begin feeling unrealistic, floaty and disconnected. Playtesting is critical to find the right compromises between simplicity and believability for each mechanic to maximize both fun and speed.
Reasonable approximations are okay if they feel good moment to moment. epCompensate where accuracy matters most to the experience like critical jumps or tricky shots. Optimization is an iterative process, but fast fluid play comes first.
