//пока что не ясно
private static Point[] bezierCoeffs(MyPoint bezierStartPoint, MyPoint bezierPoint1, MyPoint bezierPoint2, MyPoint bezierEndPoint)
{
Point[] coeffs = new Point[4];
double bezierStartPointX_M_3 = bezierStartPoint.X * 3.0;
double bezierPoint1X_M_3 = bezierPoint1.X * 3.0;
double bezierPoint2X_M_3 = bezierPoint2.X * 3.0;
coeffs[0].X = -bezierStartPoint.X + bezierPoint1X_M_3 - bezierPoint2X_M_3 + bezierEndPoint.X;
coeffs[1].X = bezierStartPointX_M_3 - 6.0 * bezierPoint1.X + bezierPoint2X_M_3;
coeffs[2].X = -bezierStartPointX_M_3 + bezierPoint1X_M_3;
coeffs[3].X = bezierStartPoint.X;
double bezierStartPointY_M_3 = bezierStartPoint.Y * 3.0;
double bezierPoint1Y_M_3 = bezierPoint1.Y * 3.0;
double bezierPoint2Y_M_3 = bezierPoint2.Y * 3.0;
coeffs[0].Y = -bezierStartPoint.Y + bezierPoint1Y_M_3 - bezierPoint2Y_M_3 + bezierEndPoint.Y;
coeffs[1].Y = bezierStartPointY_M_3 - 6.0 * bezierPoint1.Y + bezierPoint2Y_M_3;
coeffs[2].Y = -bezierStartPointY_M_3 + bezierPoint1Y_M_3;
coeffs[3].Y = bezierStartPoint.Y;
return(coeffs);
}
public static MyPoint GetStartPointDiagonal(MyPoint a1, MyPoint b1)
{
return(new MyPoint(Math.Min(a1.X, b1.X), Math.Min(a1.Y, b1.Y)));
}
public static MyPoint GetEndPointDiagonal(MyPoint a1, MyPoint b1)
{
return(new MyPoint(Math.Max(a1.X, b1.X), Math.Max(a1.Y, b1.Y)));
}
//основная функция
public static bool ComputeIntersections(MyPoint bezierStartPoint, MyPoint bezierPoint1, MyPoint bezierPoint2, MyPoint bezierEndPoint, MyPoint lineStartPoint, MyPoint lineEndPoint)
{
double A = lineEndPoint.Y - lineStartPoint.Y; // A = y2 - y1
double B = lineStartPoint.X - lineEndPoint.X; // B = x1 - x2
double C = -lineStartPoint.X * A - lineStartPoint.Y * B; //C=x1*(y1-y2)+y1*(x2-x1) = x1*(-A)+y1*(-B)=-x1*(A)-y1*(B)
var coeffs = bezierCoeffs(bezierStartPoint, bezierPoint1, bezierPoint2, bezierEndPoint);
double[] P = new double[4];
P[0] = A * coeffs[0].X + B * coeffs[0].Y; // t^3
P[1] = A * coeffs[1].X + B * coeffs[1].Y; // t^2
P[2] = A * coeffs[2].X + B * coeffs[2].Y; // t
P[3] = A * coeffs[3].X + B * coeffs[3].Y + C;
var r = cubicRoots(P[0], P[1], P[2], P[3]);
List <MyPoint> X = new List <MyPoint>();
double t;
MyPoint p;
double s;
double tMt;
double tMtMt;
for (int i = 0; i < 3; i++)
{
t = r[i];
tMt = t * t; //Это выражение используется несколько раз. Небольшая оптимизация
tMtMt = tMt * t; //Это выражение используется несколько раз. Небольшая оптимизация
p = new MyPoint
(
coeffs[0].X * tMtMt + coeffs[1].X * tMt + coeffs[2].X * t + coeffs[3].X,
coeffs[0].Y * tMtMt + coeffs[1].Y * tMt + coeffs[2].Y * t + coeffs[3].Y
);
if ((lineEndPoint.X - lineStartPoint.X) != 0)
{
s = (p.X - lineStartPoint.X) / (lineEndPoint.X - lineStartPoint.X);
}
else
{
s = (p.Y - lineStartPoint.Y) / (lineEndPoint.Y - lineStartPoint.Y);
}
if (t < 0 || t > 1.0 || s < 0 || s > 1.0)
{
continue;
}
X.Add(p);
}
return(X.Count > 0);
}
