User:Dsekercioglu/MEA
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After doing some tests with the code below I have found out that every MEA theory I have written was wrong.
Code
package dsekercioglu.mega.mea;
import java.awt.geom.Point2D;
import java.util.ArrayList;
public class Test {
static MEAFormula[] formulas = new MEAFormula[4];
static final double SIM_SENSITIVITY = 50000;
static final double DISTANCE = 500;
static final boolean LINEAR_MOVE = false;
public static void main(String[] args) {
formulas[0] = new TraditionalMEA();
formulas[1] = new TraditionalMEAPlusSomeNumber(0);
formulas[2] = new DsekerciogluOldMEA();
formulas[3] = new DsekerciogluTestMEA(0.01);
for (int f = 0; f < formulas.length; f++) {
System.out.println("=================================" + formulas[f].getName() + "=================================");
int counter = 0;
double averageMEA = 0;
for (int i = 110; i <= 197; i++) {
double bulletSpeed = i * 0.1;
Bot b = new Bot(formulas[f].getRetreatAngle(bulletSpeed), formulas[f].getTurnPerTick(DISTANCE));
Wave w = new Wave(bulletSpeed);
Point2D.Double intersection;
if (!LINEAR_MOVE) {
while (w.source.distance(b.location) > w.distanceTraveled) {
w.update();
b.update();
}
intersection = b.location;
} else {
intersection = b.interceptWave(w);
}
averageMEA += (absoluteBearing(w.source, intersection) - averageMEA) / (++counter);
System.out.println("Bullet Speed: " + bulletSpeed + ":");
System.out.println("Escape Angle: " + absoluteBearing(w.source, intersection));
System.out.println("Prediction: " + formulas[f].getMEA(bulletSpeed));
System.out.println("");
}
System.out.println("Average MEA:" + averageMEA);
}
}
public static class Wave {
Point2D.Double source = new Point2D.Double(0, 0);//starting from the origin
final double VELOCITY;
double distanceTraveled;
public Wave(double velocity) {
this.VELOCITY = velocity;//We don't set distanceTraveled to velocity since the MEA calculations doesn't take that into account.
}
public void update() {
distanceTraveled += VELOCITY / SIM_SENSITIVITY;
}
}
public static class Bot {
Point2D.Double location = new Point2D.Double(0, DISTANCE);
final double VELOCITY = 8;
final double TURN;
double angle;
public Bot(double retreatAngle, double turnPerTick) {
angle = retreatAngle;
TURN = turnPerTick;
}
public void update() {
location = project(location, angle, VELOCITY / SIM_SENSITIVITY);
angle += TURN / SIM_SENSITIVITY;
}
public Point2D.Double interceptWave(Wave w) {
return intercept(w.source, w.VELOCITY, location, angle, VELOCITY);
}
}
//CREDIT: Chase-san
public static Point2D.Double intercept(Point2D pos, double vel, Point2D tPos, double tHeading, double tVel) {
double tVelX = Math.sin(tHeading) * tVel;
double tVelY = Math.cos(tHeading) * tVel;
double relX = tPos.getX() - pos.getX();
double relY = tPos.getY() - pos.getY();
double b = relX * tVelX + relY * tVelY;
double a = vel * vel - tVel * tVel;
b = (b + Math.sqrt(b * b + a * (relX * relX + relY * relY))) / a;
return new Point2D.Double(tVelX * b + tPos.getX(), tVelY * b + tPos.getY());
}
public static abstract class MEAFormula {
public abstract double getMEA(double bulletSpeed);
public abstract double getRetreatAngle(double bulletSpeed);
public abstract double getTurnPerTick(double distance);
public abstract String getName();
}
public static class DsekerciogluOldMEA extends MEAFormula {
@Override
public double getMEA(double bulletSpeed) {
double x = bulletSpeed;
double xx = x * x;
double xxx = xx * x;
double a = 4.626248824E-7;
double b = -4.203721619E-5;
double c = 1.571662957E-3;
double d = -3.085855208E-2;
double e = 3.337262571E-1;
double f = -2.893934846E-1;
double angle = a * xxx * xx + b * xx * xx + c * xxx + d * xx + e * x + f;
return Math.asin(Math.sin(angle) / (bulletSpeed / 8 - Math.cos(angle) / 2));
}
@Override
public double getRetreatAngle(double bulletSpeed) {
double x = bulletSpeed;
double xx = x * x;
double xxx = xx * x;
double a = 4.626248824E-7;
double b = -4.203721619E-5;
double c = 1.571662957E-3;
double d = -3.085855208E-2;
double e = 3.337262571E-1;
double f = -2.893934846E-1;
return a * xxx * xx + b * xx * xx + c * xxx + d * xx + e * x + f;
}
@Override
public double getTurnPerTick(double distance) {
return 0;
}
@Override
public String getName() {
return "Dsekercioglu's Old MEA";
}
}
public static class TraditionalMEA extends MEAFormula {
@Override
public double getMEA(double bulletSpeed) {
return Math.asin(8 / bulletSpeed);
}
@Override
public double getRetreatAngle(double bulletSpeed) {
return Math.PI / 2;
}
@Override
public double getTurnPerTick(double distance) {
return 0;
}
@Override
public String getName() {
return "Traditional MEA";
}
}
public static class TraditionalMEAPlusSomeNumber extends MEAFormula {
private final double EXTRA;
public TraditionalMEAPlusSomeNumber(double extra) {
EXTRA = extra;
}
@Override
public double getMEA(double bulletSpeed) {
return Math.asin(8 / bulletSpeed);
}
@Override
public double getRetreatAngle(double bulletSpeed) {
return Math.PI / 2 + EXTRA;
}
@Override
public double getTurnPerTick(double distance) {
return 0;
}
@Override
public String getName() {
return "Traditional MEA Plus " + EXTRA;
}
}
public static class DsekerciogluTestMEA extends MEAFormula {
private final double RETREAT_FACTOR;
public DsekerciogluTestMEA(double retreatFactor) {
RETREAT_FACTOR = retreatFactor;
}
@Override
public double getMEA(double bulletSpeed) {
return 0;
}
@Override
public double getRetreatAngle(double bulletSpeed) {
return Math.PI / 2;
}
@Override
public double getTurnPerTick(double distance) {
return RETREAT_FACTOR / distance;
}
@Override
public String getName() {
return "Dsekercioglu Test MEA";
}
}
public static Point2D.Double project(Point2D.Double source, double angle, double distance) {
return new Point2D.Double(source.x + Math.sin(angle) * distance, source.y + Math.cos(angle) * distance);
}
public static double absoluteBearing(Point2D.Double p1, Point2D.Double p2) {
return Math.atan2(p2.x - p1.x, p2.y - p1.y);
}
}
Test Results
- My Old MEA
Bullet Speed: 11.0: Escape Angle: 0.7443390319356681 Prediction: 0.8958173020565081 Bullet Speed: 11.100000000000001: Escape Angle: 0.7373080257129179 Prediction: 0.8829756036277365 Bullet Speed: 11.200000000000001: Escape Angle: 0.7304125890046199 Prediction: 0.8706053037227797 Bullet Speed: 11.3: Escape Angle: 0.7236486178072312 Prediction: 0.8586747798058824 Bullet Speed: 11.4: Escape Angle: 0.7170121910884176 Prediction: 0.8471556332457875 Bullet Speed: 11.5: Escape Angle: 0.7104995591301005 Prediction: 0.8360222462765713 Bullet Speed: 11.600000000000001: Escape Angle: 0.7041071328615146 Prediction: 0.8252514148545027 Bullet Speed: 11.700000000000001: Escape Angle: 0.6978314740784414 Prediction: 0.8148220420131798 Bullet Speed: 11.8: Escape Angle: 0.6916692864575538 Prediction: 0.8047148798932051 Bullet Speed: 11.9: Escape Angle: 0.685617407285771 Prediction: 0.7949123112702848 Bullet Speed: 12.0: Escape Angle: 0.6796727998340208 Prediction: 0.7853981633902923 Bullet Speed: 12.100000000000001: Escape Angle: 0.6738325463130002 Prediction: 0.7761575484239104 Bullet Speed: 12.200000000000001: Escape Angle: 0.668093841355649 Prediction: 0.7671767260049279 Bullet Speed: 12.3: Escape Angle: 0.6624539859772478 Prediction: 0.7584429842061166 Bullet Speed: 12.4: Escape Angle: 0.6569103819694577 Prediction: 0.7499445360003807 Bullet Speed: 12.5: Escape Angle: 0.6514605266893417 Prediction: 0.74167042880019 Bullet Speed: 12.600000000000001: Escape Angle: 0.646102008208559 Prediction: 0.7336104651002772 Bullet Speed: 12.700000000000001: Escape Angle: 0.6408325007915578 Prediction: 0.7257551325932152 Bullet Speed: 12.8: Escape Angle: 0.6356497606747965 Prediction: 0.7180955424043315 Bullet Speed: 12.9: Escape Angle: 0.6305516221218561 Prediction: 0.7106233743162302 Bullet Speed: 13.0: Escape Angle: 0.6255359937317999 Prediction: 0.7033308280352042 Bullet Speed: 13.100000000000001: Escape Angle: 0.620600854980369 Prediction: 0.6962105797007199 Bullet Speed: 13.200000000000001: Escape Angle: 0.6157442529755357 Prediction: 0.6892557429615973 Bullet Speed: 13.3: Escape Angle: 0.6109642994107284 Prediction: 0.682459834043714 Bullet Speed: 13.4: Escape Angle: 0.6062591677005588 Prediction: 0.6758167403181464 Bullet Speed: 13.5: Escape Angle: 0.601627090285309 Prediction: 0.669320691948796 Bullet Speed: 13.600000000000001: Escape Angle: 0.5970663560916503 Prediction: 0.6629662362573612 Bullet Speed: 13.700000000000001: Escape Angle: 0.5925753081382007 Prediction: 0.6567482144929919 Bullet Speed: 13.8: Escape Angle: 0.5881523412755126 Prediction: 0.6506617407357893 Bullet Speed: 13.9: Escape Angle: 0.5837959000509967 Prediction: 0.6447021826987749 Bullet Speed: 14.0: Escape Angle: 0.5795044766900752 Prediction: 0.638865144223163 Bullet Speed: 14.100000000000001: Escape Angle: 0.575276609185606 Prediction: 0.6331464492875558 Bullet Speed: 14.200000000000001: Escape Angle: 0.5711108794882658 Prediction: 0.6275421273738028 Bullet Speed: 14.3: Escape Angle: 0.5670059117911797 Prediction: 0.6220484000512764 Bullet Speed: 14.4: Escape Angle: 0.562960370902617 Prediction: 0.6166616686577209 Bullet Speed: 14.5: Escape Angle: 0.5589729607010712 Prediction: 0.6113785029690175 Bullet Speed: 14.600000000000001: Escape Angle: 0.5550424226674765 Prediction: 0.6061956307625184 Bullet Speed: 14.700000000000001: Escape Angle: 0.5511675344897213 Prediction: 0.6011099281893126 Bullet Speed: 14.8: Escape Angle: 0.5473471087349788 Prediction: 0.5961184108801252 Bullet Speed: 14.9: Escape Angle: 0.5435799915857266 Prediction: 0.5912182257177159 Bullet Speed: 15.0: Escape Angle: 0.5398650616356022 Prediction: 0.5864066432158043 Bullet Speed: 15.100000000000001: Escape Angle: 0.5362012287415584 Prediction: 0.5816810504508354 Bullet Speed: 15.200000000000001: Escape Angle: 0.532587432929 Prediction: 0.5770389444984385 Bullet Speed: 15.3: Escape Angle: 0.5290226433468467 Prediction: 0.5724779263313178 Bullet Speed: 15.4: Escape Angle: 0.5255058572696637 Prediction: 0.5679956951396367 Bullet Speed: 15.5: Escape Angle: 0.5220360991442051 Prediction: 0.5635900430387886 Bullet Speed: 15.600000000000001: Escape Angle: 0.5186124196778965 Prediction: 0.559258850132841 Bullet Speed: 15.700000000000001: Escape Angle: 0.5152338949669462 Prediction: 0.555000079904977 Bullet Speed: 15.8: Escape Angle: 0.511899625661932 Prediction: 0.5508117749089398 Bullet Speed: 15.9: Escape Angle: 0.5086087361688503 Prediction: 0.5466920527379062 Bullet Speed: 16.0: Escape Angle: 0.5053603738837394 Prediction: 0.5426391022493595 Bullet Speed: 16.1: Escape Angle: 0.5021537084591243 Prediction: 0.5386511800264655 Bullet Speed: 16.2: Escape Angle: 0.4989879311006239 Prediction: 0.5347266070581833 Bullet Speed: 16.3: Escape Angle: 0.4958622538921788 Prediction: 0.5308637656219011 Bullet Speed: 16.400000000000002: Escape Angle: 0.49277590914844127 Prediction: 0.5270610963537865 Bullet Speed: 16.5: Escape Angle: 0.48972814879298004 Prediction: 0.5233170954933015 Bullet Speed: 16.6: Escape Angle: 0.4867182437609991 Prediction: 0.519630312289474 Bullet Speed: 16.7: Escape Angle: 0.48374548342538626 Prediction: 0.5159993465575505 Bullet Speed: 16.8: Escape Angle: 0.48080917504494824 Prediction: 0.5124228463755808 Bullet Speed: 16.900000000000002: Escape Angle: 0.477908643233771 Prediction: 0.5088995059113369 Bullet Speed: 17.0: Escape Angle: 0.4750432294507034 Prediction: 0.5054280633707354 Bullet Speed: 17.1: Escape Angle: 0.47221229150801264 Prediction: 0.5020072990596257 Bullet Speed: 17.2: Escape Angle: 0.46941520309832563 Prediction: 0.49863603355144803 Bullet Speed: 17.3: Escape Angle: 0.466651353339011 Prediction: 0.4953131259538367 Bullet Speed: 17.400000000000002: Escape Angle: 0.4639201463332056 Prediction: 0.49203747226777644 Bullet Speed: 17.5: Escape Angle: 0.46122100074673794 Prediction: 0.48880800383339884 Bullet Speed: 17.6: Escape Angle: 0.4585533494002351 Prediction: 0.4856236858569444 Bullet Speed: 17.7: Escape Angle: 0.4559166388757421 Prediction: 0.48248351601382566 Bullet Speed: 17.8: Escape Angle: 0.4533103291372156 Prediction: 0.479386523123083 Bullet Speed: 17.900000000000002: Escape Angle: 0.45073389316429485 Prediction: 0.47633176588887804 Bullet Speed: 18.0: Escape Angle: 0.4481868165987693 Prediction: 0.4733183317049672 Bullet Speed: 18.1: Escape Angle: 0.44566859740320997 Prediction: 0.4703453355183887 Bullet Speed: 18.2: Escape Angle: 0.4431787455312451 Prediction: 0.4674119187488613 Bullet Speed: 18.3: Escape Angle: 0.44071678260898817 Prediction: 0.4645172482606248 Bullet Speed: 18.400000000000002: Escape Angle: 0.43828224162716545 Prediction: 0.46166051538368624 Bullet Speed: 18.5: Escape Angle: 0.4358746666434845 Prediction: 0.4588409349816298 Bullet Speed: 18.6: Escape Angle: 0.4334936124948371 Prediction: 0.45605774456334336 Bullet Speed: 18.7: Escape Angle: 0.43113864451892525 Prediction: 0.45331020343618766 Bullet Speed: 18.8: Escape Angle: 0.4288093382849335 Prediction: 0.4505975918982937 Bullet Speed: 18.900000000000002: Escape Angle: 0.42650527933288 Prediction: 0.4479192104678227 Bullet Speed: 19.0: Escape Angle: 0.4242260629212929 Prediction: 0.44527437914716245 Bullet Speed: 19.1: Escape Angle: 0.42197129378288556 Prediction: 0.44266243672015787 Bullet Speed: 19.200000000000003: Escape Angle: 0.4197405858879035 Prediction: 0.44008274008059534 Bullet Speed: 19.3: Escape Angle: 0.4175335622148354 Prediction: 0.4375346635902649 Bullet Speed: 19.400000000000002: Escape Angle: 0.4153498545281982 Prediction: 0.43501759846502797 Bullet Speed: 19.5: Escape Angle: 0.4131891031631054 Prediction: 0.43253095218741416 Bullet Speed: 19.6: Escape Angle: 0.41105095681634946 Prediction: 0.4300741479443506 Bullet Speed: 19.700000000000003: Escape Angle: 0.40893507234372906 Prediction: 0.4276466240887158 Average MEA:0.5434857572979093
- It is clear that the MEA prediction overshoots the real EA. Additionally, it's average Escape Angle is 0.5434857572979093 while Traditional MEA gets an average of 0.5700086432884667.
- I have also calculated what would happen if I changed the retreat angle a little bit.
RetreatAngle = pi / 4 Escape Angle = 0.3899271370580362 RetreatAngle = 0.1 Escape Angle = 0.5667488043961456 RetreatAngle = 0.001 Escape Angle = 0.5700083166139558 RetreatAngle = -0.001 Escape Angle = 0.5700083166139558 RetreatAngle = -0.1 Escape Angle = 0.5667488043961456 RetreatAngle = -pi / 4 Escape Angle = 0.3899271370580362
- As you can see even a little change in retreat angle can lower MEA. Additionally, since the results are symmetrically separated by PI / 2 which means that PI / 2 is the optimal value for linear movement.
- So I tried a new Retreat Angle formula which increased its retreat angle a bit every tick. Even when I brute-forced to find the best solution Traditional MEA was better so for now, Traditional MEA seems correct except the fact that it doesn't take bot width and bullet start position's into account.
Notes
I am happy that traditional MEA is very likely to be correct since WhiteFang used my incorrect one.
