/// <summary>
/// Shoot a missile from the source.
/// For players.
/// </summary>
public void SpawnPlayerMissile(Mobj source, MobjType type)
{
var hs = this.world.Hitscan;
// See which target is to be aimed at.
var angle = source.Angle;
var slope = hs.AimLineAttack(source, angle, Fixed.FromInt(16 * 64));
if (hs.LineTarget == null)
{
angle += new Angle(1 << 26);
slope = hs.AimLineAttack(source, angle, Fixed.FromInt(16 * 64));
if (hs.LineTarget == null)
{
angle -= new Angle(2 << 26);
slope = hs.AimLineAttack(source, angle, Fixed.FromInt(16 * 64));
}
if (hs.LineTarget == null)
{
angle = source.Angle;
slope = Fixed.Zero;
}
}
var x = source.X;
var y = source.Y;
var z = source.Z + Fixed.FromInt(32);
var missile = this.SpawnMobj(x, y, z, type);
if (missile.Info.SeeSound != 0)
{
this.world.StartSound(missile, missile.Info.SeeSound, SfxType.Misc);
}
missile.Target = source;
missile.Angle = angle;
missile.MomX = new Fixed(missile.Info.Speed) * Trig.Cos(angle);
missile.MomY = new Fixed(missile.Info.Speed) * Trig.Sin(angle);
missile.MomZ = new Fixed(missile.Info.Speed) * slope;
this.CheckMissileSpawn(missile);
}
/// <summary>
/// Shoot a missile from the source to the destination.
/// For monsters.
/// </summary>
public Mobj SpawnMissile(Mobj source, Mobj dest, MobjType type)
{
var missile = this.SpawnMobj(source.X, source.Y, source.Z + Fixed.FromInt(32), type);
if (missile.Info.SeeSound != 0)
{
this.world.StartSound(missile, missile.Info.SeeSound, SfxType.Misc);
}
// Where it came from?
missile.Target = source;
var angle = Geometry.PointToAngle(source.X, source.Y, dest.X, dest.Y);
// Fuzzy player.
if ((dest.Flags & MobjFlags.Shadow) != 0)
{
var random = this.world.Random;
angle += new Angle((random.Next() - random.Next()) << 20);
}
var speed = this.GetMissileSpeed(missile.Type);
missile.Angle = angle;
missile.MomX = new Fixed(speed) * Trig.Cos(angle);
missile.MomY = new Fixed(speed) * Trig.Sin(angle);
var dist = Geometry.AproxDistance(dest.X - source.X, dest.Y - source.Y);
var num = (dest.Z - source.Z).Data;
var den = (dist / speed).Data;
if (den < 1)
{
den = 1;
}
missile.MomZ = new Fixed(num / den);
this.CheckMissileSpawn(missile);
return(missile);
}
/// <summary>
/// Fire a hitscan bullet.
/// If damage == 0, it is just a test trace that will leave linetarget set.
/// </summary>
public void LineAttack(Mobj shooter, Angle angle, Fixed range, Fixed slope, int damage)
{
this.currentShooter = shooter;
this.currentShooterZ = shooter.Z + (shooter.Height >> 1) + Fixed.FromInt(8);
this.currentRange = range;
this.currentAimSlope = slope;
this.currentDamage = damage;
var targetX = shooter.X + range.ToIntFloor() * Trig.Cos(angle);
var targetY = shooter.Y + range.ToIntFloor() * Trig.Sin(angle);
this.world.PathTraversal.PathTraverse(
shooter.X,
shooter.Y,
targetX,
targetY,
PathTraverseFlags.AddLines | PathTraverseFlags.AddThings,
this.shootTraverseFunc
);
}
public void Cos()
{
for (var deg = -720; deg <= 720; deg++)
{
var angle = Angle.FromDegree(deg);
var fineAngle = (int)(angle.Data >> Trig.AngleToFineShift);
var radian = 2 * Math.PI * deg / 360;
var expected = Math.Cos(radian);
{
var actual = Trig.Cos(angle).ToDouble();
Assert.AreEqual(expected, actual, 1.0E-3);
}
{
var actual = Trig.Cos(fineAngle).ToDouble();
Assert.AreEqual(expected, actual, 1.0E-3);
}
}
}
/// <summary>
/// Adjusts the x and y movement so that the next move will
/// slide along the wall.
/// </summary>
private void HitSlideLine(LineDef line)
{
if (line.SlopeType == SlopeType.Horizontal)
{
this.slideMoveY = Fixed.Zero;
return;
}
if (line.SlopeType == SlopeType.Vertical)
{
this.slideMoveX = Fixed.Zero;
return;
}
var side = Geometry.PointOnLineSide(this.slideThing.X, this.slideThing.Y, line);
var lineAngle = Geometry.PointToAngle(Fixed.Zero, Fixed.Zero, line.Dx, line.Dy);
if (side == 1)
{
lineAngle += Angle.Ang180;
}
var moveAngle = Geometry.PointToAngle(Fixed.Zero, Fixed.Zero, this.slideMoveX, this.slideMoveY);
var deltaAngle = moveAngle - lineAngle;
if (deltaAngle > Angle.Ang180)
{
deltaAngle += Angle.Ang180;
}
var moveDist = Geometry.AproxDistance(this.slideMoveX, this.slideMoveY);
var newDist = moveDist * Trig.Cos(deltaAngle);
this.slideMoveX = newDist * Trig.Cos(lineAngle);
this.slideMoveY = newDist * Trig.Sin(lineAngle);
}
Vector3F rotatePointAroundPivot(Vector3F point, Vector3F angles)
{
Fix32 x = point.x;
Fix32 y = point.y;
Fix32 z = point.z;
Fix32 a = angles.z * Fix32.Deg2Rad;
Fix32 b = angles.y * Fix32.Deg2Rad;
Fix32 c = angles.x * Fix32.Deg2Rad;
Fix32 x1 = x * Trig.Cos(a) - y * Trig.Sin(a);
Fix32 y1 = x * Trig.Sin(a) + y * Trig.Cos(a);
Fix32 x2 = x * Trig.Cos(b) - z * Trig.Sin(b);
Fix32 z2 = x * Trig.Sin(b) + z * Trig.Cos(b);
Fix32 y3 = y * Trig.Cos(c) - z * Trig.Sin(c);
Fix32 z3 = y * Trig.Sin(c) + z * Trig.Cos(c);
var ret = new Vector3F(x2, y3, z3);
return(ret);
}
private void Func()
{
DataContext = null;
int N = Convert.ToInt32(Ntext.Text);
double ax = -1, bx = 1;
double h = (bx - ax) / (N);
double[] x = new double[N + 1];
List <double> y = new List <double>();
double[,] ACB = new double[N, N];
double[] F = new double[N];
double a = Convert.ToDouble(Atext.Text);
double YAnalytic(double x) => (Trig.Cos(Math.PI * x) + x + ((x * SpecialFunctions.Erf(x / Math.Sqrt(2 * a)) + Math.Sqrt((2 * a) / Math.PI) * Math.Exp(-(x * x) / (2 * a))) / (SpecialFunctions.Erf(1 / Math.Sqrt(2 * a)) + Math.Sqrt(2 * a / Math.PI) * Math.Exp(-1 / (2 * a)))));
for (int i = 0; i <= N; i++)
{
x[i] = ax + i * h;
}
for (int i = 0; i <= N; i++)
{
y.Add(YAnalytic(x[i]));
}
var ACBmatrix = MathNet.Numerics.LinearAlgebra.Matrix <double> .Build.DenseOfArray(new double[, ]
{
{ a *Math.PI *Math.PI + 1, Math.PI },
{ a *Math.PI *Math.PI + Math.PI / 4 - 1, (-8 * a *Math.PI *Math.PI) / Math.Sqrt(2) - 1 }
});
var Fvector = MathNet.Numerics.LinearAlgebra.Vector <double> .Build.DenseOfArray(new double[]
{
-Math.PI / 2,
// -Math.PI/2+((a*Math.PI*Math.PI/8)*Math.Sin(Math.PI/8))+(Math.PI/4)*Math.Cos(Math.PI/8)-1+2*Math.Sin(Math.PI/8),
-(1 + a *Math.PI *Math.PI) - Math.PI / 4
// -(1+a*Math.PI*Math.PI)-Math.PI/4+Math.Sqrt(2)*(((a*Math.PI*Math.PI)/8)*Math.Sin(5*Math.PI/16)-(Math.PI/8)*Math.Cos(5*Math.PI/16)-1+2*Math.Sin(5*Math.PI/16))
});
var Cvector = ACBmatrix.Solve(Fvector);
double c1 = Cvector[0];
double c2 = Cvector[1];
List <double> yres = new List <double>();
for (int i = 0; i <= N; i++)
{
yres.Add(x[i] + c1 * (1 - Math.Pow(x[i], 2)) + c2 * (1 + x[i] - Math.Pow(x[i], 2) - Math.Pow(x[i], 3)));
}
SeriesCollection = new SeriesCollection
{
new LineSeries
{
Title = "Analytic Y",
Values = new ChartValues <double>(y.ToList <double>())
},
new LineSeries
{
Title = "Gilerkin",
Values = new ChartValues <double>(yres)
}
};
Labels = x.Select(x => x.ToString("F2")).ToArray();
YFormatter = value => value.ToString("F2");
DataContext = this;
List <MyTable> result = new List <MyTable>();
for (int i = 0; i <= N; i++)
{
result.Add(new MyTable(x[i], y[i], yres[i]));
}
grid.ItemsSource = result;
}
static void Main(string[] args)
{
// A simple accelerometer is constructed by suspending a
// mass m from a string of length L that is tied to the top
// of a cart. As the cart is accelerated the string-mass
// system makes a constant angle th with the vertical.
// (a) Assuming that the string mass is negligible compared
// with m, derive an expression for the cart’s acceleration
// in terms of and show that it is independent of
// the mass mand the length L.
// (b) Determine the acceleration of the cart when th = 23.0°.
var F1 = new Symbol("F1"); // force of string
var F2 = new Symbol("F2"); // force of gravity
var th1 = new Symbol("th1");
var th2 = new Symbol("th2");;
var _F1 = new Point()
{
angle = th1
};
var _F2 = new Point()
{
angle = th2, magnitude = F2
};
var m = new Symbol("m");
var g = new Symbol("g");
var obj = new Obj()
{
mass = m
};
obj.acceleration.y = 0;
obj.forces.Add(_F1);
obj.forces.Add(_F2);
_F1.magnitude = obj.ForceMagnitude(_F1);
("Derive an expression for the cart’s acceleration in terms " +
"of and show that it is independent of the mass mand the length L:").Disp();
"".Disp();
obj.AccelerationX()
.Substitute(F2, m * g)
.Substitute(Trig.Cos(th2), 0)
.Substitute(Trig.Sin(th2), -1)
.Disp();
"".Disp();
"Determine the acceleration of the cart when th = 23.0°".Disp(); "".Disp();
obj.AccelerationX()
.Substitute(F2, m * g)
.Substitute(Trig.Cos(th2), 0)
.Substitute(Trig.Sin(th2), -1)
.Substitute(th1, (90 - 23).ToRadians())
.Substitute(Trig.Pi, Math.PI)
.Substitute(g, 9.8)
.Disp();
Console.ReadLine();
}
/// <summary>
/// Creating the multiplier for each x,y,z movement by the amplitude , aimuth , elevtion and tilt.
/// </summary>
/// <param name="amplitude">Amplitude (degree).</param>
/// <param name="azimuth">Azimuth (degree).</param>
/// <param name="elevation">Elevation (degree).</param>
/// <param name="tilt">Tilt (degree).</param>
/// <returns></returns>
public Tuple <double, double, double> CreateMultiplyTuple(double amplitude, double azimuth, double elevation, double tilt)
{
//converting the angles to radian.
amplitude = amplitude * Math.PI / 180;
azimuth = azimuth * Math.PI / 180;
elevation = elevation * Math.PI / 180;
tilt = tilt * Math.PI / 180;
//making the multipliers vector.
double xM = -Trig.Sin(amplitude) * Trig.Sin(azimuth) * Trig.Cos(tilt) +
Trig.Cos(amplitude) *
(Trig.Cos(azimuth) * Trig.Cos(elevation) + Trig.Sin(azimuth) * Trig.Sin(tilt) * Trig.Sin(elevation));
double yM = Trig.Sin(amplitude) * Trig.Cos(azimuth) * Trig.Cos(tilt) +
Trig.Cos(amplitude) *
(Trig.Sin(azimuth) * Trig.Cos(elevation) +
-Trig.Cos(azimuth) * Trig.Sin(tilt) * Trig.Sin(elevation));
//the axis for y and z are opposite in the Moog.
yM = -yM;
double zM = -Trig.Sin(amplitude) * Trig.Sin(tilt) - Trig.Cos(amplitude) * Trig.Sin(elevation) * Trig.Cos(tilt);
//the axis for y and z are opposite in the Moog.
zM = -zM;
//return the requested vector.
return(new Tuple <double, double, double>(xM, yM, zM));
}
/// <summary>
/// Moves the given origin along a given angle.
/// </summary>
public void Thrust(Player player, Angle angle, Fixed move)
{
player.Mobj.MomX += move * Trig.Cos(angle);
player.Mobj.MomY += move * Trig.Sin(angle);
}
/// <summary>
/// Returns the cosine of an <paramref name="angle" /> in radians.
/// </summary>
/// <param name="absoluteValue">Return absolute values? (default: false).</param>
public static double Cos(this double angle, bool absoluteValue = false) =>
absoluteValue
? Trig.Cos(angle).CoerceZero(1E-6).Abs()
: Trig.Cos(angle).CoerceZero(1E-6);
private void Func()
{
DataContext = null;
int N = Convert.ToInt32(Ntext.Text);
double ax = -1, bx = 1;
double h = (bx - ax) / (N);
double[] x = new double[N + 1];
List <double> y = new List <double>();
double[,] ACB = new double[N, N];
double[] F = new double[N];
double a = Convert.ToDouble(Atext.Text);
double YAnalytic(double x) => (Trig.Cos(Math.PI * x) + x + ((x * SpecialFunctions.Erf(x / Math.Sqrt(2 * a)) + Math.Sqrt((2 * a) / Math.PI) * Math.Exp(-(x * x) / (2 * a))) / (SpecialFunctions.Erf(1 / Math.Sqrt(2 * a)) + Math.Sqrt(2 * a / Math.PI) * Math.Exp(-1 / (2 * a)))));
for (int i = 0; i <= N; i++)
{
x[i] = ax + i * h;
}
for (int i = 0; i <= N; i++)
{
y.Add(YAnalytic(x[i]));
}
ACB[0, 0] = -a + ((x[0] * h) / 2);
ACB[0, 1] = 2 * a - ((-1) * h * h);
F[0] = -(1 + a * Math.Pow(Math.PI, 2)) * Math.Cos(Math.PI * x[0]) - Math.PI * x[0] * Math.Sin(Math.PI * x[0]) + (((-a + ((x[0] * h) / 2)) * (-1)) / (h * h));
for (int i = 1; i < N - 1; i++)
{
ACB[i, i - 1] = -a + ((x[i] * h) / 2);
ACB[i, i] = 2 * a - ((-1) * h * h);
ACB[i, i + 1] = -a - ((x[i] * h) / 2);
F[i] = -(1 + a * Math.Pow(Math.PI, 2)) * Math.Cos(Math.PI * x[i]) - Math.PI * x[i] * Math.Sin(Math.PI * x[i]);
}
ACB[N - 1, N - 2] = 2 * a - ((-1) * h * h);
ACB[N - 1, N - 1] = -a - ((x[N - 1] * h) / 2);
F[N - 1] = -(1 + a * Math.Pow(Math.PI, 2)) * Math.Cos(Math.PI * x[N - 1]) - Math.PI * x[N - 1] * Math.Sin(Math.PI * x[N - 1]) + (((-a - ((x[N - 1] * h) / 2)) * (1)) / (h * h));
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
Console.Write(ACB[i, j].ToString("f3") + " ");
}
Console.WriteLine(" = " + F[i]);
}
var ACBmatrix = MathNet.Numerics.LinearAlgebra.Matrix <double> .Build.DenseOfArray(ACB);
var Fvector = MathNet.Numerics.LinearAlgebra.Vector <double> .Build.DenseOfArray(F);
Fvector = Fvector * -Math.Pow(h, 2);
var Yvector = ACBmatrix.Solve(Fvector);
List <double> yres = new List <double>();
for (int i = 0; i < N; i++)
{
yres.Add(Yvector[i]);
}
yres.Insert(0, -1);
yres[N] = 1;
SeriesCollection = new SeriesCollection
{
new LineSeries
{
Title = "Analytic Y",
Values = new ChartValues <double>(y.ToList <double>())
},
new LineSeries
{
Title = "Y method",
Values = new ChartValues <double>(yres)
}
};
Labels = x.Select(x => x.ToString("F2")).ToArray();
YFormatter = value => value.ToString("F2");
DataContext = this;
List <MyTable> result = new List <MyTable>();
result.Add(new MyTable(x[0], y[0], -1));
for (int i = 1; i < N; i++)
{
result.Add(new MyTable(x[i], y[i], yres[i]));
}
result.Add(new MyTable(x[N], y[N], 1));
grid.ItemsSource = result;
}
static void Main(string[] args)
{
// Two people pull as hard as they can on ropes attached
// to a boat that has a mass of 200 kg. If they pull in the
// same direction, the boat has an acceleration of
// 1.52 m/s^2 to the right. If they pull in opposite directions,
// the boat has an acceleration of 0.518 m/s^2
// to the left. What is the force exerted by each person on the
// boat? (Disregard any other forces on the boat.)
// Trig.Cos(new DoubleFloat(Math.PI)).Disp();
var m = new Symbol("m");
var aAx = new Symbol("aAx");
var aBx = new Symbol("aBx");
var objA = new Obj()
{
mass = m
};
objA.acceleration.x = aAx;
var _F1A = new Point()
{
angle = 0
};
var _F2A = new Point()
{
angle = 0
};
objA.forces.Add(_F1A);
objA.forces.Add(_F2A);
var objB = new Obj()
{
mass = m
};
objB.acceleration.x = aBx;
var _F1B = new Point()
{
angle = 0
};
var _F2B = new Point()
{
angle = new DoubleFloat(Math.PI)
};
objB.forces.Add(_F1B);
objB.forces.Add(_F2B);
"force 1 magnitude (symbolic):".Disp(); "".Disp();
Calc.ForceMagnitude(objA, objB, _F1A, _F1B)
.Substitute(Trig.Cos(0), 1)
.Disp();
"force 1 magnitude (numeric):".Disp(); "".Disp();
Calc.ForceMagnitude(objA, objB, _F1A, _F1B)
.Substitute(Trig.Cos(0), 1)
.Substitute(m, 200)
.Substitute(aAx, 1.52)
.Substitute(aBx, -0.518)
.Disp();
"".Disp();
"force 2 magnitude (symbolic):".Disp(); "".Disp();
Calc.ForceMagnitude(objA, objB, _F2A, _F2B)
.Substitute(Trig.Cos(0), 1)
.Disp();
"force 2 magnitude (numeric):".Disp(); "".Disp();
Calc.ForceMagnitude(objA, objB, _F2A, _F2B)
.Substitute(Trig.Cos(0), 1)
.Substitute(m, 200)
.Substitute(aAx, 1.52)
.Substitute(aBx, -0.518)
.Disp();
"".Disp();
Console.ReadLine();
}
/// <summary>
/// Returns false if the player cannot be respawned at the given
/// mapthing spot because something is occupying it.
/// </summary>
public bool CheckSpot(int playernum, MapThing mthing)
{
var players = this.world.Options.Players;
if (players[playernum].Mobj == null)
{
// First spawn of level, before corpses.
for (var i = 0; i < playernum; i++)
{
if (players[i].Mobj.X == mthing.X && players[i].Mobj.Y == mthing.Y)
{
return(false);
}
}
return(true);
}
var x = mthing.X;
var y = mthing.Y;
if (!this.world.ThingMovement.CheckPosition(players[playernum].Mobj, x, y))
{
return(false);
}
// Flush an old corpse if needed.
if (this.bodyQueSlot >= ThingAllocation.bodyQueSize)
{
this.RemoveMobj(this.bodyQue[this.bodyQueSlot % ThingAllocation.bodyQueSize]);
}
this.bodyQue[this.bodyQueSlot % ThingAllocation.bodyQueSize] = players[playernum].Mobj;
this.bodyQueSlot++;
// Spawn a teleport fog.
var subsector = Geometry.PointInSubsector(x, y, this.world.Map);
var angle = (Angle.Ang45.Data >> Trig.AngleToFineShift) * ((int)Math.Round(mthing.Angle.ToDegree()) / 45);
//
// The code below to reproduce respawn fog bug in deathmath
// is based on Chocolate Doom's implementation.
//
Fixed xa;
Fixed ya;
switch (angle)
{
case 4096: // -4096:
xa = Trig.Tan(2048); // finecosine[-4096]
ya = Trig.Tan(0); // finesine[-4096]
break;
case 5120: // -3072:
xa = Trig.Tan(3072); // finecosine[-3072]
ya = Trig.Tan(1024); // finesine[-3072]
break;
case 6144: // -2048:
xa = Trig.Sin(0); // finecosine[-2048]
ya = Trig.Tan(2048); // finesine[-2048]
break;
case 7168: // -1024:
xa = Trig.Sin(1024); // finecosine[-1024]
ya = Trig.Tan(3072); // finesine[-1024]
break;
case 0:
case 1024:
case 2048:
case 3072:
xa = Trig.Cos((int)angle);
ya = Trig.Sin((int)angle);
break;
default:
throw new Exception("Unexpected angle: " + angle);
}
var mo = this.SpawnMobj(x + 20 * xa, y + 20 * ya, subsector.Sector.FloorHeight, MobjType.Tfog);
if (!this.world.FirstTicIsNotYetDone)
{
// Don't start sound on first frame.
this.world.StartSound(mo, Sfx.TELEPT, SfxType.Misc);
}
return(true);
}
public void CanComputeCosine(double value, double expected)
{
var actual = Trig.Cos(value);
AssertHelpers.AlmostEqual(expected, actual, 14);
}
/// <summary>
/// Damages both enemies and players.
/// "inflictor" is the thing that caused the damage creature
/// or missile, can be null (slime, etc).
/// "source" is the thing to target after taking damage creature
/// or null.
/// Source and inflictor are the same for melee attacks.
/// Source can be null for slime, barrel explosions and other
/// environmental stuff.
/// </summary>
public void DamageMobj(Mobj target, Mobj inflictor, Mobj source, int damage)
{
if ((target.Flags & MobjFlags.Shootable) == 0)
{
// Shouldn't happen...
return;
}
if (target.Health <= 0)
{
return;
}
if ((target.Flags & MobjFlags.SkullFly) != 0)
{
target.MomX = target.MomY = target.MomZ = Fixed.Zero;
}
var player = target.Player;
if (player != null && this.world.Options.Skill == GameSkill.Baby)
{
// Take half damage in trainer mode.
damage >>= 1;
}
// Some close combat weapons should not inflict thrust and
// push the victim out of reach, thus kick away unless using the chainsaw.
var notChainsawAttack = source == null || source.Player == null || !(source.Player.ReadyWeapon.Info is WeaponChainsaw);
if (inflictor != null && (target.Flags & MobjFlags.NoClip) == 0 && notChainsawAttack)
{
var ang = Geometry.PointToAngle(inflictor.X, inflictor.Y, target.X, target.Y);
var thrust = new Fixed(damage * (Fixed.FracUnit >> 3) * 100 / target.Info.Mass);
// Make fall forwards sometimes.
if (damage < 40 && damage > target.Health && target.Z - inflictor.Z > Fixed.FromInt(64) && (this.world.Random.Next() & 1) != 0)
{
ang += Angle.Ang180;
thrust *= 4;
}
target.MomX += thrust * Trig.Cos(ang);
target.MomY += thrust * Trig.Sin(ang);
}
// Player specific.
if (player != null)
{
// End of game hell hack.
if (target.Subsector.Sector.Special == (SectorSpecial)11 && damage >= target.Health)
{
damage = target.Health - 1;
}
// Below certain threshold, ignore damage in GOD mode, or with INVUL power.
if (damage < 1000 && ((player.Cheats & CheatFlags.GodMode) != 0 || player.Powers[(int)PowerType.Invulnerability] > 0))
{
return;
}
int saved;
if (player.ArmorType != 0)
{
if (player.ArmorType == 1)
{
saved = damage / 3;
}
else
{
saved = damage / 2;
}
if (player.ArmorPoints <= saved)
{
// Armor is used up.
saved = player.ArmorPoints;
player.ArmorType = 0;
}
player.ArmorPoints -= saved;
damage -= saved;
}
// Mirror mobj health here for Dave.
player.Health -= damage;
if (player.Health < 0)
{
player.Health = 0;
}
player.Attacker = source;
// Add damage after armor / invuln.
player.DamageCount += damage;
if (player.DamageCount > 100)
{
// Teleport stomp does 10k points...
player.DamageCount = 100;
}
}
// Do the damage.
target.Health -= damage;
if (target.Health <= 0)
{
this.KillMobj(source, target);
return;
}
if ((this.world.Random.Next() < target.Info.PainChance) && (target.Flags & MobjFlags.SkullFly) == 0)
{
// Fight back!
target.Flags |= MobjFlags.JustHit;
target.SetState(target.Info.PainState);
}
// We're awake now...
target.ReactionTime = 0;
if ((target.Threshold == 0 || target.Type == MobjType.Vile) && source != null && source != target && source.Type != MobjType.Vile)
{
// If not intent on another player, chase after this one.
target.Target = source;
target.Threshold = ThingInteraction.baseThreshold;
if (target.State == DoomInfo.States[(int)target.Info.SpawnState] && target.Info.SeeState != MobjState.Null)
{
target.SetState(target.Info.SeeState);
}
}
}
private static double ObjectiveFunction(double x)
{
return(-x *Trig.Cos(-2 *x) * Math.Exp(-x / 3));
}
/// <summary>
/// Spawns cubes upon an arc of an ellipse.
/// </summary>
/// <param name="n"> The number of cubes. </param>
/// <param name="center"> The center of the ellipse. </param>
/// <param name="sectorChordLength"> The length of the arc's chord. </param>
/// <param name="semiMinorAxisLength"> Half the length of the minor axis. </param>
/// <param name="sectorAngleDeg"> The angular length of the arc in degrees. </param>
/// <param name="cubePrefab"> The template for the cubes. </param>
/// <param name="parent"> The parent of the cubes structure. </param>
/// <returns> Returns the GameObject containing the cubes, whose parent is 'parent'. </returns>
/// <remarks> This function is definitely very time-expensive. Use sparingly. </remarks>
private static GameObject SpawnEllipseCubes(int n, Vector3 center, float sectorChordLength, float semiMinorAxisLength, float sectorAngleDeg, GameObject cubePrefab, Transform parent = null)
{
// TODO: Find constraints for every parameter and variable (minimum and maximum values)
// Problem: for some combination of input parameters, the FindRoots.OfFunction method fails with an exception:
// "ArithmeticException: Function does not accept floating point Not-a-Number values."
// Sample parameters: (16,, 12.0f, 6.0f, 90°,,)
#region Maths
/*
* C: center of the ellipse
* R: sectorChordLength, the length of the chord
* a: half the length of the major axis of the ellipse
* b: semiMinorAxisLength, half the length of the minor axis of the ellipse
* α: sectorAngleDeg, the sector extension in degrees, from (90° - α/2) to (90° + α/2) counterclock-wise
* n: number of cubes
*
*
* § 1) ELLIPSE'S EQUATIONS
*
* ξ(ϑ): ellipse's parametric equations [-180° ≤ ϑ ≤ 180°]
* where ϑ is the angle of (ξˣ(ϑ), ξʸ(ϑ)) with the major axis of the ellipse itself
* ___________________________
* ξˣ(ϑ) = a b cos(ϑ) √(a² sin²(ϑ) + b² cos²(ϑ))⁻¹
* ___________________________
* ξʸ(ϑ) = a b sin(ϑ) √(a² sin²(ϑ) + b² cos²(ϑ))⁻¹
*
* A = ξ(90° + α/2)
* B = ξ(90° - α/2)
*
* __ _______________________________
* R = AB = 2 a b sin(α/2) √(a² cos²(α/2) + b² sin²(α/2))⁻¹
* _________________________________________ _______________________
* a = √(b² R² tan²(α/2)) / (4 b² tan²(α/2) - R²) = (b R tan(α/2)) √(4 b² tan²(α/2) - R²)⁻¹
*
*
* § 2) CUBES PLACEMENT
* A _____________________
* L = ∫(√D[ξˣ(ϑ)]² + D[ξʸ(ϑ)]²)dϑ: length of arc AB
* B
* l = L/n: distance between each cube's center on the arc
*
* θᵢ: angle of the iᵗʰ arc segment; arc length to the iᵗʰ arc segment = i l
* θᵢ = FindRoot[∫(D[ξˣ(ϑ)]² + D[ξʸ(ϑ)]²)dϑ = i l] 😭
*
* Pᵢ = ξ(θᵢ): position of the iᵗʰ cube
*
*
* § 3) CUBES' SIDE LENGTH
* Let Pᵢ and Pⱼ be the positions of two consecutive cubes (j = i + 1) with angles θᵢ and θⱼ.
* Let Pₖ be a third point placed at the same arc-distance from both Pᵢ and Pⱼ; the angle of Pₖ is θₖ.
*
* rₖ: line from C to Pₖ
* rᵢ: line from C to Pᵢ
* rⱼ: line from C to Pⱼ
*
* M: parametric point on rₖ
* dᵢ: segment MPᵢ
* dⱼ: segment MPⱼ
*
*
* M = (mˣ, mʸ) = (mˣ, mˣ tan(θₖ))
* ____________________________________
* dᵢ = √(x(Pᵢ) - mˣ)² + (y(Pᵢ) - mˣ tan(θₖ))²
* ____________________________________
* dⱼ = √(x(Pⱼ) - mˣ)² + (y(Pⱼ) - mˣ tan(θₖ))²
*
* ASSERTION
* dᵢ = dⱼ = d: dᵢ and dⱼ are the semi-diagonals of the two squares
*
* (x(Pᵢ) - mˣ)² + (y(Pᵢ) - mˣ tan(θₖ))² = (x(Pⱼ) - mˣ)² + (y(Pⱼ) - mˣ tan(θₖ))²
* x(Pᵢ)² + (mˣ)² - 2 x(Pᵢ) mˣ + y(Pᵢ)² + (mˣ tan(θₖ))² - 2 y(Pᵢ) mˣ tan(θₖ) = x(Pⱼ)² + (mˣ)² - 2 x(Pⱼ) mˣ + y(Pⱼ)² + (mˣ tan(θₖ))² - 2 y(Pⱼ) mˣ tan(θₖ)
* x(Pᵢ)² - 2 x(Pᵢ) mˣ + y(Pᵢ)² - 2 y(Pᵢ) mˣ tan(θₖ) = x(Pⱼ)² - 2 x(Pⱼ) mˣ + y(Pⱼ)² - 2 y(Pⱼ) mˣ tan(θₖ)
* 2 x(Pⱼ) mˣ + 2 y(Pⱼ) mˣ tan(θₖ) - 2 x(Pᵢ) mˣ - 2 y(Pᵢ) mˣ tan(θₖ) = x(Pⱼ)² + y(Pⱼ)² - x(Pᵢ)² - y(Pᵢ)²
* 2 mˣ (x(Pⱼ) + y(Pⱼ) tan(θₖ) - x(Pᵢ) - y(Pᵢ) tan(θₖ)) = x(Pⱼ)² + y(Pⱼ)² - x(Pᵢ)² - y(Pᵢ)²
*
* x(Pⱼ)² + y(Pⱼ)² - x(Pᵢ)² - y(Pᵢ)²
* mˣ = ——————————————————————————————————————————————————
* 2 (x(Pⱼ) + y(Pⱼ) tan(θₖ) - x(Pᵢ) - y(Pᵢ) tan(θₖ))
*
* cube's side length = 2 (d/√2)
*
*/
#endregion Maths
double R = sectorChordLength;
double b = semiMinorAxisLength;
#region § 1) ELLIPSE'S EQUATION
double alphaRad = Trig.DegreeToRadian(sectorAngleDeg);
double bTanHalfAlpha = b * Trig.Tan(alphaRad / 2.0);
double a = (R * bTanHalfAlpha) / Math.Sqrt(4 * bTanHalfAlpha * bTanHalfAlpha - R * R);
Func <double, double> EllipseX = t =>
{
double sin = Trig.Sin(t);
double cos = Trig.Cos(t);
double aSin = a * sin;
double bCos = b * cos;
return((a * bCos) / Math.Sqrt(aSin * aSin + bCos * bCos));
};
Func <double, double> EllipseY = t =>
{
double sin = Trig.Sin(t);
double cos = Trig.Cos(t);
double aSin = a * sin;
double bCos = b * cos;
return((b * aSin) / Math.Sqrt(aSin * aSin + bCos * bCos));
};
#endregion § 1) ELLIPSE'S EQUATION
#region § 2) CUBES PLACEMENT
Func <double, double> DEllipseX = Differentiate.FirstDerivativeFunc(EllipseX);
Func <double, double> DEllipseY = Differentiate.FirstDerivativeFunc(EllipseY);
Func <double, double> SqrtOfSumOfSquaredDerivatives = t =>
{
double x = DEllipseX(t);
double y = DEllipseY(t);
return(Math.Sqrt(x * x + y * y));
};
Func <double, double, double> AngleToArcLength = (fromRad, toRad) => Integrate.OnClosedInterval(SqrtOfSumOfSquaredDerivatives, fromRad, toRad);
Func <double, double> ArcLengthToAngle = arcLength => FindRoots.OfFunction(toRad => AngleToArcLength((Math.PI - alphaRad) / 2, toRad) - arcLength, 0, Math.PI);
double L = AngleToArcLength((Math.PI - alphaRad) / 2, (Math.PI + alphaRad) / 2);
double l = L / (n - 1);
Func <int, object[]> CalculateCubePositionAndAngle = i =>
{
double angle = ArcLengthToAngle(i * l);
Vector2 position = new Vector2((float)EllipseX(angle), (float)EllipseY(angle));
return(new object[] { position, angle });
};
#endregion § 2) CUBES PLACEMENT
#region § 3) CUBES' SIDE LENGTH
Vector2[] positions = new Vector2[n];
double[] angles = new double[n];
double[] middleAngles = new double[n - 1];
for (int i = 0; i < n; ++i)
{
object[] res = CalculateCubePositionAndAngle(i);
positions[i] = (Vector2)res[0];
angles[i] = (double)res[1];
if (i > 0)
{
middleAngles[i - 1] = ArcLengthToAngle((2 * i - 1) * l / 2.0);
}
}
double[] sideLengths = new double[n - 1];
Func <int, double> SideLength = j =>
{
double xj = positions[j].x;
double yj = positions[j].y;
double xi = positions[j - 1].x;
double yi = positions[j - 1].y;
double tanK = Trig.Tan(middleAngles[j - 1]);
double mx = (xj * xj + yj * yj - (xi * xi + yi * yi)) / (2.0 * (xj + yj * tanK - (xi + yi * tanK)));
return(Math.Sqrt((xi - mx) * (xi - mx) + (yi - mx * tanK) * (yi - mx * tanK)) * (2.0 / Math.Sqrt(2.0)));
};
for (int i = 1; i < n; ++i)
{
sideLengths[i - 1] = SideLength(i);
}
float squareSide = (float)sideLengths.Min();
#endregion § 3) CUBES' SIDE LENGTH
// Save parent's current local rotation and scale; it will be re-set later
Quaternion parentRotation = parent?.localRotation ?? Quaternion.identity;
Vector3 parentScale = parent?.localScale ?? Vector3.one;
if (parent != null)
{
parent.localRotation = Quaternion.identity;
parent.localScale = Vector3.one;
}
GameObject cubesContainer = parent?.gameObject ?? new GameObject();
cubesContainer.name = $"Ellipse_{n}Cubes";
cubesContainer.transform.localPosition = center;
// Create the cubes
for (int i = 0; i < n; ++i)
{
GameObject cube = Instantiate(cubePrefab);
cube.name = $"Cube{i}";
cube.SetActive(true); // Awake it now, to let it store the prefab's original scale
cube.transform.localScale = new Vector3(squareSide, squareSide, squareSide);
cube.transform.position = cubesContainer.transform.position + new Vector3(positions[i].x, 0.0f, positions[i].y);
cube.transform.localRotation = Quaternion.Euler(0.0f, (float)(90.0 - Trig.RadianToDegree(angles[i])), 0.0f);
cube.transform.parent = cubesContainer.transform;
}
cubesContainer.transform.localRotation = Quaternion.identity;
// Re-set parent's original local rotation
if (parent != null)
{
parent.localRotation = parentRotation;
parent.localScale = parentScale;
}
return(cubesContainer);
}