public static double[] AnglesCrossLine(Point centre, double r, Point pt1, Point pt2)
{
Point t = Funcs2D.PointToLine(pt1, pt2, centre);
if (Funcs2D.IsEqual(t, centre))
{
double an = Funcs2D.LineAngle(pt1, pt2);
return(new double[] { Funcs2D.PureRadianAngle(an + Math.PI), an });
}
double z = Funcs2D.Distance(centre, t);
double a = Funcs2D.LineAngle(centre, t);
if (z.IsGreater(r))
{
return(null); // mimo
}
if (z.IsEqual(r)) // tecna
{
return(new double[] { a });
}
//secna
double aa = Math.Acos(z / r); // uhel pulky tetivy
return(new double[] { Funcs2D.PureRadianAngle(a + aa), Funcs2D.PureRadianAngle(a - aa) });
}
/// <summary>
/// otestuje zda prislusny bot lezi na oblouku
/// </summary>
/// <param name="pt">testovany bod</param>
/// <returns></returns>
public bool IsPointOn(Point pt)
{
Circle2D?c = GetAngles(out double st, out double an);
if (c == null)
{
return(false);
}
if (!Funcs2D.Distance(pt, c.Value.Center).IsEqual(Math.Abs(Radius)))
{
return(false);
}
st = Funcs2D.PureRadianAngle(st);
double angle = Funcs2D.LineAngle(c.Value.Center, pt);
if (an > 0)
{
an = st + an;
return(angle.IsGreaterOrEqual(st) && angle.IsLesserOrEqual(an));
}
else
{
an = st + an;
return(angle.IsGreaterOrEqual(an) && angle.IsLesserOrEqual(st));
}
}
/// <summary>
/// kruznice urcena tremi body na obvodu
/// </summary>
/// <param name="pt1">prvni bod</param>
/// <param name="pt2">druhy bod</param>
/// <param name="pt3">treti bod</param>
public Circle2D(Point pt1, Point pt2, Point pt3)
{
Radius = 0;
Center = pt1;
Point[] p = new Point[2];
Vector[] v = new Vector[2];
p[0].X = (pt1.X + pt2.X) / 2;
p[0].Y = (pt1.Y + pt2.Y) / 2;
p[1].X = (pt2.X + pt3.X) / 2;
p[1].Y = (pt2.Y + pt3.Y) / 2;
v[0].X = pt2.Y - pt1.Y;
v[0].Y = -(pt2.X - pt1.X);
v[1].X = pt3.Y - pt2.Y;
v[1].Y = -(pt3.X - pt2.X);
TwoLine2D.CrossStatus st = TwoLine2D.CrossStatus.Infinite;
if (TwoLine2D.CrossAbs(p[0], st, v[0], st, p[1], st, v[1], st, out Center))
{
Radius = Funcs2D.Distance(pt1, Center);
}
}
/// <summary>
/// oblouk zadany stredem , pocatecnim bodem a vektorem ne kterem lezi kocovy bod
/// </summary>
/// <param name="center">stred</param>
/// <param name="pt">pocatecni bod</param>
/// <param name="vector">vektor na kterem lezi koncovy bod</param>
/// <param name="shortangle">true = kratky oblouk (mezi nulou az 180 stupni), false = dlouhy oblouk (doplnek do 360 stupnu)</param>
public Arc2D(Point center, Point pt, Vector vector, bool shortangle = true)
{
Radius = Funcs2D.Distance(center, pt);
Begin = pt;
double a = Funcs2D.Radian(Vector.AngleBetween(new Vector(1, 0), vector));
End = Circle2D.PointOn(center, Radius, a);
if (!shortangle)
{
Radius *= -1;
}
a = Vector.AngleBetween(pt.Minus(center), vector);
Clockwise = !(a > 0 && shortangle || a < 0 && !shortangle);
}
/// <summary>
/// kruznice zadana dvema body na obvodu a polomerem
/// , pokud je polomer mensi nez polovina vzdalenosti bodu, umisti se stred kruznice do stredoveho bodu tvoriciho obema ridicimi body
/// , stred kruznice se umisti do poloroviny urcene ridicimi body, podle znamenka polomeru
/// </summary>
/// <param name="pt1">prvni bod na obvodu</param>
/// <param name="pt2">druhy bod na ovodu</param>
/// <param name="r">polomer</param>
public Circle2D(Point pt1, Point pt2, double r)
{
double d = Funcs2D.Distance(pt1, pt2) / 2;
if (Math.Abs(r) <= d)
{
Radius = d;
Center = new Point((pt1.X + pt2.X) / 2, (pt1.Y + pt2.Y) / 2);
}
else
{
Radius = Math.Abs(r);
double v = Math.Sqrt(Math.Pow(Radius, 2) - Math.Pow(d, 2));
Center = Funcs2D.LineRelPtOffset(pt1, pt2, 0.5, r < 0 ? -v : v);
}
}
/// <summary>
/// oblouk zadany stredem , pocatecnim bodem a uhlem
/// </summary>
/// <param name="center">stred</param>
/// <param name="pt">pocatecni bod</param>
/// <param name="angle">uhel v radianech , smer podle znamenka ( - = clockwise)</param>
public Arc2D(Point center, Point pt, double angle)
{
Radius = Funcs2D.Distance(center, pt);
Begin = pt;
if (Math.Abs(angle) > Math.PI * 2)
{
angle = angle % (Math.PI * 2);
}
Clockwise = angle < 0;
double a = Funcs2D.Radian(Vector.AngleBetween(new Vector(1, 0), pt.Minus(center)));
a += angle;
End = Circle2D.PointOn(center, Radius, a);
if (Math.Abs(angle) > Math.PI)
{
Radius *= -1;
}
}
/// <summary>
/// oblouk tvoreny dvema po sobe jdoucimi useckami a polomerem
/// takzvane zaobleni rohu
/// pokud je polomer zaporny vytvori se tzv. vykousnuti se stredem ve spolecnem bode
/// objekt se nastavi na empty pokud jsou usecky rovnobezne nebo jedna z nich ma nulovou delku
/// </summary>
/// <param name="pt1">pocatecni bod prvni ridici usecky</param>
/// <param name="pt2">spolecny bod ridicich usecek</param>
/// <param name="pt3">konecny bod druhe ridici usecky</param>
/// <param name="radius">polomer zaobleni, zaporny polomer provede vykousnuti</param>
/// <param name="testPt">pokud se pocatecni nebo koncovy bod vypocita mimo usecku, objekt se nastavi na Empty</param>
public Arc2D(Point pt1, Point pt2, Point pt3, double radius, bool testPt = false)
{
// zjistim smer offsetu
double a = Vector.AngleBetween(pt2.Minus(pt1), pt3.Minus(pt2));
if (a > 0)
{
a = -Math.Abs(radius);
Clockwise = false;
}
else
{
a = Math.Abs(radius);
Clockwise = true;
}
// vypocitam prusecik offsetovanych primek
Point[] p1 = Funcs2D.LineOffset(pt1, pt2, a);
Point[] p2 = Funcs2D.LineOffset(pt2, pt3, a);
if (p1 == null || p2 == null || !TwoLine2D.CrossRel(p1[0], p1[1], p2[0], p2[1], out Point rr))
{
// tri body na jedne primce
Begin = pt1; End = pt3;
Radius = 0;
return;
}
if (radius > 0)
{
if (testPt)
{
if (!TwoLine2D.TestRelOnLine(TwoLine2D.CrossStatus.And, rr.X) || !TwoLine2D.TestRelOnLine(TwoLine2D.CrossStatus.And, rr.Y))
{
// body jsou mimo usecky
Begin = pt1; End = pt3;
Radius = 0;
return;
}
}
// koeficienty prenesu do puvodnich usecek a spocitam body
Begin = Funcs2D.PointOnLine(pt1, pt2, rr.X);
End = Funcs2D.PointOnLine(pt2, pt3, rr.Y);
Radius = radius;
}
else
{
Radius = -radius;
if (testPt)
{
if (Funcs2D.Distance(pt1, pt2) < Radius || Funcs2D.Distance(pt2, pt3) < Radius)
{
// body jsou mimo usecky
Begin = pt1; End = pt3;
Radius = 0;
return;
}
}
// bod na prvni primce ve vzdalenosti abs(radius) od spolecneho bodu
Begin = Funcs2D.PointOnLineLen(pt2, pt1, Radius);
// bod na druhe primce
End = Funcs2D.PointOnLineLen(pt2, pt3, Radius);
Clockwise = !Clockwise;
}
}
/// <summary>
/// kruznice zadana stredem a bodem na obvodu
/// </summary>
/// <param name="center">stred</param>
/// <param name="pt">bod na obvodu</param>
public Circle2D(Point center, Point pt)
{
Radius = Funcs2D.Distance(center, pt);
Center = center;
}