//pronalazenje Y za dato X i odredjen set tacaka
public static double LinearInterpolationYGraph(double X, PointD[] points)
{
int first = 0;
double Y;
LinearFunctionD interpolate;
//pronalazenje izmedju kojih tacaka se nalazi odabrano X
for (int i = 0; i < points.Length - 1; i++)
{
if (X <= points[i].X)
{
first = i; break;
}
}
interpolate = new LinearFunctionD(points[first], points[first + 1]);
Y = GetY(X, interpolate);
return(Y);
}
/* Simulacija koristeci Eulerov metod*/
public void simulationEuler()
{
/* FUNKCIONALNE PROMENLJIVE */
int i = 0; //brojac iteracija
bool simulationRunning = true; // promenljiva za pokretanje/prekidanje simulacije
/* Stil za oznacavanje zapisa */
DataGridViewCellStyle boja = new DataGridViewCellStyle();
boja.ForeColor = Color.DarkOrange;
boja.Font = new Font(Tabela.Font, FontStyle.Bold);
double axPrim;
double ayPrim;
double axSec;
double aySec;
PointD[] points =
{ new PointD(865, 0.296221041243509),
new PointD(815, 0.362064203509306),
new PointD(776, 0.371578055743002),
new PointD(737, 0.382525045298620),
new PointD(700, 0.382835165547702),
new PointD(664, 0.384235165547702),
new PointD(629, 0.385786703294031), };
try
{
while (simulationRunning)
{
/* Upis podataka u datagridview */
string[] row = new string[] {
posX.ToString(), posY.ToString(),
V.ToString(), Vx.ToString(),
Vy.ToString(), ax.ToString(),
ay.ToString(), Fd.ToString(),
Cd.ToString(), (currAngle * 180 / Math.PI).ToString()
};
Tabela.Rows.Add(row);
Tabela.Rows[Tabela.Rows.Count - 2].DefaultCellStyle = boja;
/* Upis u grafik */
Grafik.Series[3].Points.AddXY(posX, posY); // crtanje pozicije na grafiku
Grafik1.Series[3].Points.AddXY(posX, V); // crtanje pozicije na grafiku
/* Ugao vektora brzine i apscise */
angleA = g / V * Math.Cos(currAngle);
angleSpeed = angleSpeed + angleA * interval;
currAngle = Math.Atan(Vy / Vx) - angleSpeed * interval;
/* Racunanje vremena leta */
t += interval;
/* pomeranje projektila */
posX = posX + Vx * interval - 0.5 * Math.Pow(interval, 2) * ax; // pomeranje po X osi
posY = posY + Vy * interval - 0.5 * Math.Pow(interval, 2) * ay; // pomeranje po Y osi
/* Trenutna brzina */
V = Math.Sqrt(Math.Pow(Vx, 2) + Math.Pow(Vy, 2)); //racunanje efektivne vrednosti vektora brzine
/* otpor vazduha IMPLEMENTIRATI INTERPOLACIJU ZA Cx */
Cd = LinearFunctionD.LinearInterpolationY(V, points);
Fd = Cd * airDensity * S * Math.Pow(Vx, 2) * 0.5; //racunanje sile otpora vazduha
/* Racunanje ubraznja */
axPrim = airDensity * S * Cd * Vx * ax;
ayPrim = airDensity * S * Cd * Vy * ay;
axSec = airDensity * S * Cd * axPrim;
aySec = airDensity * S * Cd * ayPrim;
ax = Fd * Math.Cos(currAngle) / m + axPrim * interval + 0.5 * Math.Pow(interval, 2) * axSec;
ay = g + Fd * Math.Sin(currAngle) / m + ayPrim * interval + 0.5 * Math.Pow(interval, 2) * aySec;
/* promena brzine u intervalu vremena */
Vx = Vx - ax * interval - 0.5 * Math.Pow(interval, 2) * axPrim;
Vy = Vy - ay * interval - 0.5 * Math.Pow(interval, 2) * axPrim;
/* USLOV ZA PREKIDANJE SIMULACIJE */
if (posY < -1)
{
simulationRunning = false;
//MessageBox.Show("Vreme leta:" + t + "s");
}
i++;
}
}
catch (Exception ex) { MessageBox.Show(ex.ToString()); }
}
/* Simulacija sa otporom vazduha - prediktor-korektor */
public void simulationAdams()
{
/* FUNKCIONALNE PROMENLJIVE */
bool simulationRunning = true; // promenljiva za pokretanje/prekidanje simulacije
/* Stil za oznacavanje zapisa */
DataGridViewCellStyle boja = new DataGridViewCellStyle();
boja.ForeColor = Color.DarkCyan;
boja.Font = new Font(Tabela.Font, FontStyle.Bold);
//promenljive za poziciju, brzinu i ubrzanje - nizovi zbog koraka prediktor-korektor metode
double[] posXPC = new double[3];
double[] posYPC = new double[3];
double[] VxPC = new double[3];
double[] VyPC = new double[3];
double[] axPC = new double[3];
double[] ayPC = new double[3];
double[] currAnglePC = new double[3];
double[] angleSpeedPC = new double[3];
double[] angleAPC = new double[3];
//promenljive za poziciju, brzinu i ubrzanje - nizovi zbog koraka adamsovog metod
double[] posXStep = new double[5];
double[] posYStep = new double[5];
double[] VxStep = new double[5];
double[] VyStep = new double[5];
double[] axStep = new double[5];
double[] ayStep = new double[5];
double[] currAngleStep = new double[5];
double[] angleSpeedStep = new double[5];
double[] angleAStep = new double[5];
PointD[] points =
{ new PointD(865, 0.296221041243509),
new PointD(815, 0.362064203509306),
new PointD(776, 0.371578055743002),
new PointD(737, 0.382525045298620),
new PointD(700, 0.382835165547702),
new PointD(664, 0.384235165547702),
new PointD(629, 0.385786703294031), };
try
{
/* FOR petlja za popunjavanje cetiri koraka metode*/
for (int i = 0; i < 5; i++)
{
/* Upis podataka u datagridview */
string[] row = new string[]
{
posX.ToString(), posY.ToString(),
V.ToString(), Vx.ToString(),
Vy.ToString(), ax.ToString(),
ay.ToString(), Fd.ToString(),
Cd.ToString(), (currAngle * 180 / Math.PI).ToString()
};
Tabela.Rows.Add(row);
Tabela.Rows[Tabela.Rows.Count - 2].DefaultCellStyle = boja;
/* Upis u grafik */
Grafik.Series[4].Points.AddXY(posX, posY); // crtanje pozicije na grafiku
Grafik1.Series[4].Points.AddXY(posX, V); // crtanje pozicije na grafiku
/* PREDIKTOR start */
/* Ugao vektora brzine i apscise */
angleAPC[0] = g / V * Math.Cos(currAngle);
angleSpeedPC[0] = angleSpeedPC[0] + angleAPC[0] * interval;
currAnglePC[0] = Math.Atan(Vy / Vx) - angleSpeedPC[0] * interval;
/* Racunanje vremena leta */
t += interval;
/* pomeranje projektila */
posXPC[0] = posX + Vx * interval; // pomeranje po X osi
posYPC[0] = posY + Vy * interval; // pomeranje po Y osi
/* Trenutna brzina */
V = Math.Sqrt(Math.Pow(Vx, 2) + Math.Pow(Vy, 2)); //racunanje efektivne vrednosti vektora brzine
/* otpor vazduha*/
Cd = LinearFunctionD.LinearInterpolationY(V, points);
Fd = Cd * airDensity * S * Math.Pow(Vx, 2) * 0.5; //racunanje sile otpora vazduha
/* Racunanje ubraznja */
axPC[0] = Fd * Math.Cos(currAngle) / m;
ayPC[0] = g + Fd * Math.Sin(currAngle) / m;
/* promena brzine u intervalu vremena */
VxPC[0] = Vx - ax * interval;
VyPC[0] = Vy - ay * interval;
/* Ugao vektora brzine i apscise */
angleAPC[1] = g / V * Math.Cos(currAnglePC[0]);
angleSpeedPC[1] = angleSpeedPC[0] + angleAPC[1] * interval;
currAnglePC[1] = Math.Atan(VyPC[0] / VxPC[0]) - angleSpeedPC[1] * interval;
/* Racunanje vremena leta */
t += interval;
/* pomeranje projektila */
posXPC[1] = posXPC[0] + VxPC[0] * interval; // pomeranje po X osi
posYPC[1] = posYPC[0] + VyPC[0] * interval; // pomeranje po Y osi
/* Trenutna brzina */
V = Math.Sqrt(Math.Pow(Vx, 2) + Math.Pow(Vy, 2)); //racunanje efektivne vrednosti vektora brzine
/* otpor vazduha IMPLEMENTIRATI INTERPOLACIJU ZA Cx */
Cd = LinearFunctionD.LinearInterpolationY(V, points);
Fd = Cd * airDensity * S * Math.Pow(VxPC[0], 2) * 0.5; //racunanje sile otpora vazduha
/* Racunanje ubrzanja */
axPC[1] = Fd * Math.Cos(currAngle) / m;
ayPC[1] = g + Fd * Math.Sin(currAngle) / m;
/* promena brzine u intervalu vremena */
VxPC[1] = VxPC[0] - axPC[0] * interval;
VyPC[1] = VyPC[0] - ayPC[0] * interval;
/* PREDIKTOR end*/
/* KOREKTOR start */
axPC[2] = (axPC[0] + axPC[1]) / 2.0;
ayPC[2] = (ayPC[0] + ayPC[1]) / 2.0;
VxPC[2] = (VxPC[0] + VxPC[1]) / 2.0;
VyPC[2] = (VyPC[0] + VyPC[1]) / 2.0;
posXPC[2] = (posXPC[0] + posXPC[1]) / 2.0;
posYPC[2] = (posYPC[0] + posYPC[1]) / 2.0;
angleAPC[2] = (angleAPC[0] + angleAPC[1]) / 2.0;
angleSpeedPC[2] = (angleSpeedPC[0] + angleSpeedPC[1]) / 2.0;
currAnglePC[2] = (currAnglePC[0] + currAnglePC[1]) / 2.0;
ax = axPC[2];
ay = ayPC[2];
Vx = VxPC[2];
Vy = VyPC[2];
posX = posXPC[2];
posY = posYPC[2];
angleA = angleAPC[2];
angleSpeed = angleSpeedPC[2];
currAngle = currAnglePC[2];
V = Math.Sqrt(Math.Pow(Vx, 2) + Math.Pow(Vy, 2));
/*KOREKTOR end */
/* Promenljive za 4 koraka adams metode start */
axStep[i] = ax;
ayStep[i] = ay;
VxStep[i] = Vx;
VyStep[i] = Vy;
posXStep[i] = posX;
posYStep[i] = posY;
angleAStep[i] = angleA;
angleSpeedStep[i] = angleSpeed;
currAngleStep[i] = currAngle;
/* Promenljive za 4 koraka adams metode end */
/* USLOV ZA PREKIDANJE SIMULACIJE */
if (posY < -1)
{
simulationRunning = false;
//MessageBox.Show("Vreme leta:" + t + "s");
}
}
while (simulationRunning)
{
/* Upis podataka u datagridview */
string[] row = new string[]
{
posX.ToString(), posY.ToString(),
V.ToString(), Vx.ToString(),
Vy.ToString(), ax.ToString(),
ay.ToString(), Fd.ToString(),
Cd.ToString(), (currAngle * 180 / Math.PI).ToString()
};
Tabela.Rows.Add(row);
Tabela.Rows[Tabela.Rows.Count - 2].DefaultCellStyle = boja;
/* Upis u grafik */
Grafik.Series[4].Points.AddXY(posX, posY); // crtanje pozicije na grafiku
Grafik1.Series[4].Points.AddXY(posX, V); // crtanje pozicije na grafiku
/* PREDIKTOR start */
/* Ugao vektora brzine i apscise */
angleA = g / V * Math.Cos(currAngle);
angleSpeed = angleSpeed + angleA * interval;
currAngle = Math.Atan(Vy / Vx) - angleSpeed * interval;
/* Racunanje vremena leta */
t += interval;
/* pomeranje projektila */
// pomeranje po X osi
posX = posX + interval / 24 * (55 * VxStep[3] - 59 * VxStep[2] + 37 * VxStep[1] - 9 * VxStep[0]);
// pomeranje po Y osi
posY = posY + interval / 24 * (55 * VyStep[3] - 59 * VyStep[2] + 37 * VyStep[1] - 9 * VyStep[0]);;
/* Trenutna brzina */
V = Math.Sqrt(Math.Pow(Vx, 2) + Math.Pow(Vy, 2)); //racunanje efektivne vrednosti vektora brzine
/* otpor vazduha*/
Cd = LinearFunctionD.LinearInterpolationY(V, points);
Fd = Cd * airDensity * S * Math.Pow(Vx, 2) * 0.5; //racunanje sile otpora vazduha
/* Racunanje ubraznja */
ax = Fd * Math.Cos(currAngle) / m;
ay = g + Fd * Math.Sin(currAngle) / m;
/* promena brzine u intervalu vremena */
Vx = Vx - interval / 24 * (55 * axStep[3] - 59 * axStep[2] + 37 * axStep[1] - 9 * axStep[0]);
Vy = Vy - interval / 24 * (55 * ayStep[3] - 59 * ayStep[2] + 37 * ayStep[1] - 9 * ayStep[0]);;
for (int i = 0; i < 3; i++)
{
VxStep[i] = VxStep[i + 1];
VyStep[i] = VyStep[i + 1];
axStep[i] = axStep[i + 1];
ayStep[i] = ayStep[i + 1];
}
VxStep[3] = Vx;
VyStep[3] = Vy;
axStep[3] = ax;
ayStep[3] = ay;
/* USLOV ZA PREKIDANJE SIMULACIJE */
if (posY < -1)
{
simulationRunning = false;
//MessageBox.Show("Vreme leta:" + t + "s");
}
}
}
catch (Exception ex) { MessageBox.Show(ex.ToString()); }
}
//Funkcija za dobijanje vredenosti X za dati Y u odredjenoj funkciji
private static double GetX(double Y, LinearFunctionD A)
{
double X = (Y - A.n) / A.k;
return(X);
}
//Funkcija za dobijanje vredenosti Y za dati X u odredjenoj funkciji
private static double GetY(double X, LinearFunctionD A)
{
double Y = A.k * X + A.n;
return(Y);
}
//Konstruktor kopije
public LinearFunctionD(LinearFunctionD A)
{
k = A.k;
n = A.n;
}
/* Popunjavanje druge tabele */
public void MiniTablePopulate()
{
if (vakuum)
{
PointD[] points = new PointD[Grafik.Series[2].Points.Count];
PointD[] points1 = new PointD[Grafik1.Series[2].Points.Count];
for (int i = 0; i < Grafik.Series[2].Points.Count - 1; i++)
{
points[i] = new PointD(Grafik.Series[2].Points[i]);
points1[i] = new PointD(Grafik1.Series[2].Points[i]);
}
/* Stil za oznacavanje zapisa */
DataGridViewCellStyle boja = new DataGridViewCellStyle();
boja.ForeColor = Color.ForestGreen;
boja.Font = new Font(Tabela.Font, FontStyle.Bold);
for (int i = 0; i < 350; i += 50)
{
Tabela1.Rows.Add(i, LinearFunctionD.LinearInterpolationYGraph(i, points), LinearFunctionD.LinearInterpolationYGraph(i, points1));
Tabela1.Rows[Tabela1.Rows.Count - 2].DefaultCellStyle = boja;
}
}
if (vazduh)
{
PointD[] points = new PointD[Grafik.Series[0].Points.Count];
PointD[] points1 = new PointD[Grafik1.Series[0].Points.Count];
for (int i = 0; i < Grafik.Series[0].Points.Count - 1; i++)
{
points[i] = new PointD(Grafik.Series[0].Points[i]);
points1[i] = new PointD(Grafik1.Series[0].Points[i]);
}
/* Stil za oznacavanje zapisa */
DataGridViewCellStyle boja = new DataGridViewCellStyle();
boja.ForeColor = Color.Crimson;
boja.Font = new Font(Tabela.Font, FontStyle.Bold);
for (int i = 0; i < 350; i += 50)
{
Tabela1.Rows.Add(i, LinearFunctionD.LinearInterpolationYGraph(i, points), LinearFunctionD.LinearInterpolationYGraph(i, points1));
Tabela1.Rows[Tabela1.Rows.Count - 2].DefaultCellStyle = boja;
}
}
if (vazduhPC)
{
PointD[] points = new PointD[Grafik.Series[1].Points.Count];
PointD[] points1 = new PointD[Grafik1.Series[1].Points.Count];
for (int i = 0; i < Grafik.Series[1].Points.Count - 1; i++)
{
points[i] = new PointD(Grafik.Series[1].Points[i]);
points1[i] = new PointD(Grafik1.Series[1].Points[i]);
}
/* Stil za oznacavanje zapisa */
DataGridViewCellStyle boja = new DataGridViewCellStyle();
boja.ForeColor = Color.Purple;
boja.Font = new Font(Tabela.Font, FontStyle.Bold);
for (int i = 0; i < 350; i += 50)
{
Tabela1.Rows.Add(i, LinearFunctionD.LinearInterpolationYGraph(i, points), LinearFunctionD.LinearInterpolationYGraph(i, points1));
Tabela1.Rows[Tabela1.Rows.Count - 2].DefaultCellStyle = boja;
}
}
if (euler)
{
PointD[] points = new PointD[Grafik.Series[3].Points.Count];
PointD[] points1 = new PointD[Grafik1.Series[3].Points.Count];
for (int i = 0; i < Grafik.Series[3].Points.Count - 1; i++)
{
points[i] = new PointD(Grafik.Series[3].Points[i]);
points1[i] = new PointD(Grafik1.Series[3].Points[i]);
}
/* Stil za oznacavanje zapisa */
DataGridViewCellStyle boja = new DataGridViewCellStyle();
boja.ForeColor = Color.DarkOrange;
boja.Font = new Font(Tabela.Font, FontStyle.Bold);
for (int i = 0; i < 350; i += 50)
{
Tabela1.Rows.Add(i, LinearFunctionD.LinearInterpolationYGraph(i, points), LinearFunctionD.LinearInterpolationYGraph(i, points1));
Tabela1.Rows[Tabela1.Rows.Count - 2].DefaultCellStyle = boja;
}
}
if (adams)
{
PointD[] points = new PointD[Grafik.Series[4].Points.Count];
PointD[] points1 = new PointD[Grafik1.Series[4].Points.Count];
for (int i = 0; i < Grafik.Series[4].Points.Count - 1; i++)
{
points[i] = new PointD(Grafik.Series[4].Points[i]);
points1[i] = new PointD(Grafik1.Series[4].Points[i]);
}
/* Stil za oznacavanje zapisa */
DataGridViewCellStyle boja = new DataGridViewCellStyle();
boja.ForeColor = Color.DarkCyan;
boja.Font = new Font(Tabela.Font, FontStyle.Bold);
for (int i = 0; i < 350; i += 50)
{
Tabela1.Rows.Add(i, LinearFunctionD.LinearInterpolationYGraph(i, points), LinearFunctionD.LinearInterpolationYGraph(i, points1));
Tabela1.Rows[Tabela1.Rows.Count - 2].DefaultCellStyle = boja;
}
}
}
