public void UpdateCurve(PVector3 velocity, int cElementCount = PSettings.CurveElementCount)
{
var ElInfo = GetEllipseInfo(Body.LocalPosition, velocity, Body.Mass, Body.GravityBody.Mass);
Curve = MakeCurve(ElInfo.a, ElInfo.b, Body.LocalPosition, velocity, Body.GravityBody.Position, Body.GravityBody.Mass, cElementCount);
//Debug.Log("e: "+ Curve.e + " p: "+Curve.p + " iA: "+Curve.PositionAngle);
}
double GetAlphaDt(double dt)
{
PCurve curve = Trajectory.Curve;
double a = curve.a; // большая полуось
double n = Math.Sqrt(PWorld.G * GravityBody.Mass / (a * a * a)); //среднее движение
double M = n * dt; // средняя аномалия
var func = curve.KeplerFunc;
var Dfunc = curve.KeplerDFunc;
double M0 = curve.e < 1 ? M : -M;
int t;
//double tEx = NumericalMethods.NewtonForKepler(curve.KeplerFunc, curve.KeplerDFunc, M0, M, out t);
double tEx = NumericalMethods.StaticPointKepler(curve.e, M0, out t);
double alpha = curve.AlphaFromEAnomaly(tEx);
if (t > 100)
{
Console.Write("angle:" + alpha + " M:" + M + " E:" + tEx + " func:" + func(tEx, M) + " t:" + t);
}
//UnityEngine.Debug.Log("e: " + curve.e+ " sqrt((e+1)/(e-1)):" + Math.Sqrt((curve.e + 1) / (curve.e - 1)) + " tanh(H/2)" + Math.Tanh(Ex/2));
//UnityEngine.Debug.Log("dt " + dt + " Ex " + Ex + " alpha "+alpha + " M: " + M + " func "+ func(Ex,M));
return(alpha);
}
public override void Draw(List <PVector> data)
{
var crv = new PCurve(data, CurveType.Normal);
_renderer.DrawCurve(crv);
//if (data.Count > 1 && lastAddedIndex > -1)
//{
// PVector p1, p2, p3;
// if (data.Count > lastAddedIndex + 2)
// {
// if (lastAddedIndex == 0)
// {
// p1 = data[0];
// }
// else
// {
// var vec = PVector.Sub(data[lastAddedIndex + 1], data[lastAddedIndex]);
// vec.Mult(0.5);
// vec.Add(data[lastAddedIndex]);
// p1 = vec;
// }
// p2 = data[lastAddedIndex + 1];
// if (data.Count == lastAddedIndex + 3) { p3 = data[lastAddedIndex + 2]; }
// else
// {
// PVector vec = PVector.Sub(data[lastAddedIndex + 2], data[lastAddedIndex + 1]);
// vec.Mult(0.5); vec.Add(data[lastAddedIndex + 1]);
// p3 = vec;
// }
// }
// else
// {
// p1 = data[lastAddedIndex];
// p3 = data[lastAddedIndex+1];
// var vec = PVector.Sub(p3, p1);
// vec.Mult(0.5);
// vec.Add(p1);
// p2 = vec;
// }
// var list = new List<PVector>() { p1, p2, p3 };
// var curve = new PCurve(list, CurveType.Loose);
//}
}
public void DrawCurve(PCurve curve, SKCanvas canv) {
int drawnPoints = 0;
var step = _BrushInfoService.XSpacing;
var div = curve.DivideLength(step);
float len = 0;
for(int i = 0;i< div.Count - 1; i++)
{
DrawPoint(div[i], div[i + 1], canv, drawnPoints, CurvePositionKoeficient(len, curve.Length));
drawnPoints++;
len += PVector.DistanceBetween(div[i], div[i + 1]).ToFloat();
}
PVector vec = PVector.Sub(div.Last(), div.Count>1?div[div.Count - 2]:PVector.Add(div.Last(), new PVector(0,1)));
vec.Add(div.Last());
DrawPoint(div.Last(), vec, canv, drawnPoints, CurvePositionKoeficient(curve.Length, curve.Length));
drawnPoints++;
}
private void SKCanvasView_PaintSurface(object sender, SKPaintSurfaceEventArgs e)
{
var canv = e.Surface.Canvas;
var info = e.Info;
canv.DrawPaint(BgPaint);
//canv.DrawCircle(info.Width / 2, info.Height / 2, Math.Min(info.Height, info.Width) * 0.8F, Service.GetBrush(new PVector(info.Width / 2, info.Height / 2)));
var p = new List <PVector>
{
new PVector(info.Width * 0.2, info.Height * 0.2),
new PVector(info.Width * 0.33, info.Height * 1),
new PVector(info.Width / 3 * 2, info.Height * 0.2),
new PVector(info.Width * 0.8, info.Height * 0.8)
};
var cdata = new PCurve(p, Geometry.GeometryShapes.CurveType.Normal);
_renderer.DrawCurve(cdata, canv);
}
public void DrawCurve(PCurve curve) {
DrawCurve(curve, ActiveCanvas);
}
public PCurve MakeCurve(double e, double p, PVector3 pos, PVector3 velocity, PVector3 GBodyPosition, double GBodyMass, int StepCount, bool TransitionCurve = false)
{
#region Начальный угол, построение кривой, апоцентр\перицентр
var crv = new PCurve
{
e = e,
p = p,
Curve = new List <Pair <PVector3, double> >(),
Lv = PVector3.Cross(pos, velocity)
};
var IAngleCosValue = (p - pos.magnitude) / (e * pos.magnitude);
double InitAngle = Math.Acos(IAngleCosValue);
if (double.IsNaN(InitAngle))
{
InitAngle = IAngleCosValue < 0 ? Math.PI : 0;
}
if (PVector3.Dot(pos, velocity) < 0) // проверяем направление движения (см. радиальную компоненту скорости)
{
InitAngle = 2 * Math.PI - InitAngle;
}
var Vz = pos.normalized.RotateAround(crv.Lv, -InitAngle); // выравниваем на перицентр
crv.Periapsis = new Pair <PVector3, double>(Vz * crv.RFuncAlpha(0), 0);
crv.Apoapsis = new Pair <PVector3, double>(crv.RFuncAlphaV3(Math.PI), Math.PI);
for (double x = -Math.PI; x <= Math.PI; x += (2 * Math.PI) / StepCount)
{
var alpha = e < 1 ? crv.AlphaFromEAnomaly(x) : x;
//var alpha = crv.AlphaFromEAnomaly(x);
if (e < 1)
{
crv.Curve.Add(new Pair <PVector3, double>(crv.RFuncAlphaV3(alpha) + GBodyPosition, alpha));
}
else
if (Math.Abs(x) < Math.Acos(-1 / crv.e))
{
crv.Curve.Add(new Pair <PVector3, double>(crv.RFuncAlphaV3(alpha) + GBodyPosition, alpha));
}
}
crv.PositionAngle = InitAngle;
#endregion
#region Начальное время
double t;
if (crv.e < 1)
{
double E = 2 * Math.Atan(Math.Sqrt((1 - e) / (1 + e)) * Math.Tan(InitAngle / 2));
// эксцентрическая аномалия (идем по обратному пути к уравнению кеплера)
double a = crv.a; // большая полуось
t = Math.Sqrt(a * a * a / (PWorld.G * GBodyMass)) * (E - e * Math.Sin(E));
}
else
{
double H = 2 * HyperbolicFuncs.Atanh(Math.Sqrt((e - 1) / (e + 1)) * Math.Tan(InitAngle / 2));
double k = Math.Sqrt(Math.Pow(crv.a, 3) / (PWorld.G * GBodyMass)); // 1/n
t = k * (e * Math.Sinh(H) - H);
}
crv.PositionTime = t; // для уравнения кеплера начальное время - до перицентра
#endregion
#region Наклонение орбиты, AN\DN
double inclination = PVector3.Angle(crv.Lv, PVector3.up) * 180.0 / Math.PI;
crv.inclination = inclination <= 90 ? inclination : 180 - inclination;
if (Math.Abs(crv.inclination) > 0)
{
var DescendingNodeV = PVector3.Cross(crv.Lv, PVector3.up).normalized;
double DNAngle = PVector3.Angle(DescendingNodeV, crv.Periapsis.a);
double DNLength = crv.RFuncAlpha(DNAngle);
double ANAngle = DNAngle - Math.PI;
double ANLength = crv.RFuncAlpha(ANAngle);
crv.DN = new Pair <PVector3, double>(DescendingNodeV * DNLength, DNAngle);
crv.AN = new Pair <PVector3, double>(-DescendingNodeV * ANLength, -DNAngle);
}
#endregion
#region Точка перехода
var TPoint = new Pair <PVector3, double>();
var isTPoint = false;
foreach (var gb in World.Gravitybodies)
{
foreach (var point in crv.Curve)
{
double distSqr1 = (point.a - GBodyPosition).magnitude;
double distSqr2 = (point.a - gb.Position).magnitude;
if (!(distSqr1 * distSqr1 * gb.Mass - distSqr2 * distSqr2 * GBodyMass > 0))
{
// грубый метод поиска точки перехода
continue;
}
isTPoint = true;
crv.PHGBody = gb;
var C = GBodyPosition - gb.Position;
Func <double, double> Falpha =
alpha =>
Math.Pow(crv.RFuncAlpha(alpha), 2) * crv.PHGBody.Mass -
(C + crv.RFuncAlphaV3(alpha)).sqrMagnitude * GBodyMass;
int i = crv.Curve.IndexOf(point);
int it;
double a = /*crv.Curve[i+1 > crv.Curve.Count ? 1 : i+1].b*/ Math.PI;
double b = /*crv.Curve[i - 3 < 0 ? crv.Curve.Count - 3 : i-3].b*/ 0;
double angle = NumericalMethods.Dichotomy(Falpha, a, b, out it);
// уточнение координат точки
TPoint = new Pair <PVector3, double>(crv.RFuncAlphaV3(angle) + GBodyPosition, angle);
if (it > 100)
{
Debug.Write("angle: " + angle * 180 / Math.PI + " iterations:" + it + " a:" +
a * 180 / Math.PI + " b:" + b * 180 / Math.PI);
}
break;
}
if (isTPoint)
{
break;
}
}
if (isTPoint)
{
crv.isTPoint = true;
crv.TransitionPoint = TPoint;
}
else
{
crv.isTPoint = false;
}
#endregion
#region Фантомная траектория перехода
if (Curve == null)
{
return(crv);
}
if (!isTPoint || TransitionCurve)
{
return(crv);
}
PCurve PHCurve;
PVector3 PHVelocity = GetVelocityMagnitude(TPoint.a, TPoint.b);
PVector3 PHPosition = TPoint.a - crv.PHGBody.Position;
var PHCInfo = GetEllipseInfo(PHPosition, PHVelocity, Body.Mass, crv.PHGBody.Mass);
PHCurve = MakeCurve(PHCInfo.a, PHCInfo.b, PHPosition, PHVelocity, crv.PHGBody.Position, crv.PHGBody.Mass, PSettings.CurveElementCount, true);
crv.TransitionCurve = PHCurve;
#endregion
return(crv);
}
