// ReSharper disable once InconsistentNaming
public static BezierCurve ResolveXY(PointD point0, PointD point1, PointD point2, PointD point3, PointD vector0,
PointD vector3)
{
var B0 = Polynomial.GetBernstein(0, 3);
var B1 = Polynomial.GetBernstein(1, 3);
var B2 = Polynomial.GetBernstein(2, 3);
var B3 = Polynomial.GetBernstein(3, 3);
const double eps = 0.000001D;
const double step = 0.001D;
// ReSharper disable once InconsistentNaming
var uuu_tuu3 = B0 + B1;
// ReSharper disable once InconsistentNaming
var ttt_ttu3 = B3 + B2;
var z1 = ((point1 - point0) * (point2 - point1)).Z;
var z2 = ((point2 - point1) * (point3 - point2)).Z;
//Точки находятся почти на одной линии
if (Math.Abs(z1) < eps && Math.Abs(z2) < eps)
{
return(new BezierCurve(point0, point0, point3, point3));
}
var method1 = new PointD(vector3.Y, -vector3.X);
var method2 = new PointD(vector0.Y, -vector0.X);
var dot1 = vector0.DotProduct(method1);
var dot2 = vector3.DotProduct(method2);
var distance = (point0 - point3).Length;
//double kMax1 = 10000D * distance / vector0.Length;
//double kMax2 = 10000D * distance / vector3.Length;
var kMax1 = 1D * distance / vector0.Length;
var kMax2 = 1D * distance / vector3.Length;
#region Полезные комменты
//Идеальный случай
//double kMin1 = 0;
//double kMin2 = 0;
//Классический случай
//double kMin1 = 0.001D * distance / vector0.Length;
//double kMin2 = 0.001D * distance / vector3.Length;
//Point3D s1 = new Point3D(Math.Cos(angle0), Math.Sin(angle0), 0);
//Point3D s2 = new Point3D(Math.Cos(angle3), Math.Sin(angle3), 0);
//point1 = u1 * u1 * u1 * point0 + 3 * t1 * u1 * u1 * (point0 + k1 * s1) + 3 * t1 * t1 * u1 * (point3 + k2 * s2) + t1 * t1 * t1 * point3;
//point2 = u2 * u2 * u2 * point0 + 3 * t2 * u2 * u2 * (point0 + k1 * s1) + 3 * t2 * t2 * u2 * (point3 + k2 * s2) + t2 * t2 * t2 * point3;
//3 * t1 * u1 * u1 * k1 * s1 = point1 - u1 * u1 * u1 * point0 - 3 * t1 * u1 * u1 * point0 - 3 * t1 * t1 * u1 * point3 - 3 * t1 * t1 * u1 * k2 * s2 - t1 * t1 * t1 * point3
//3 * t2 * u2 * u2 * k1 * s1 = point2 - u2 * u2 * u2 * point0 - 3 * t2 * u2 * u2 * point0 - 3 * t2 * t2 * u2 * point3 - 3 * t2 * t2 * u2 * k2 * s2 + t2 * t2 * t2 * point3
#endregion
//Иначе Corel Draw не распознает слишком близкие числа
var kMin1 = 0.01D / vector0.Length;
var kMin2 = 0.01D / vector3.Length;
var min = double.PositiveInfinity;
double k1Min = kMin1, k2Min = -kMin2;
var px1 = uuu_tuu3 * point0.X + ttt_ttu3 * point3.X - point2.X;
var px2 = B1 * vector0.X;
var px3 = B2 * vector3.X;
var py1 = uuu_tuu3 * point0.Y + ttt_ttu3 * point3.Y - point2.Y;
var py2 = B1 * vector0.Y;
var py3 = B2 * vector3.Y;
var polyDenomX = point1.X - uuu_tuu3 * point0.X - ttt_ttu3 * point3.X;
var polyDenomY = point1.Y - uuu_tuu3 * point0.Y - ttt_ttu3 * point3.Y;
for (var t1 = step; t1 < 1D; t1 += step)
{
#region Находим k1 и k2 для текущего t1
var u1 = 1D - t1;
//PointD denominator = point1 - u1 * u1 * u1 * point0 - 3 * t1 * u1 * u1 * point0 - 3 * t1 * t1 * u1 * point3 - t1 * t1 * t1 * point3;
var denominator = new PointD(polyDenomX.GetValue(t1), polyDenomY.GetValue(t1));
var k1 = denominator.DotProduct(method1) / (3 * t1 * u1 * u1 * dot1);
//double k1 = denominator.DotProduct(method1) / (B1.GetValue(t1) * dot1);
if (k1 > kMax1 || k1 < kMin1)
{
continue;
}
var k2 = denominator.DotProduct(method2) / (3 * t1 * t1 * u1 * dot2);
//double k2 = denominator.DotProduct(method2) / (B0.GetValue(t1) * dot2);
if (k2 < -kMax2 || k2 > -kMin2)
{
continue;
}
#endregion
#region Находим время
//Polynomial polynomX = B0 * point0.X + b3 * point3.X - point2.X + B1 * (point0.X + k1 * vector0.X) + B0 * (point3.X + k2 * vector3.X);
//Polynomial polynomY = B0 * point0.Y + b3 * point3.Y - point2.Y + B1 * (point0.Y + k1 * vector0.Y) + B0 * (point3.Y + k2 * vector3.Y);
var polynomX = px1 + k1 * px2 + k2 * px3;
var polynomY = py1 + k1 * py2 + k2 * py3;
//Находим корни кубического уравнения
var resolve = polynomX.Resolve(false);
foreach (var time in resolve)
{
if (time < 0 || time > 1)
{
continue;
}
var value = Math.Abs(polynomY.GetValue(time));
if (value < min)
{
min = value;
k1Min = k1;
k2Min = k2;
}
}
#endregion
#region Второй метод
/*
*
* for (double t2 = t1 + step; t2 < 1D; t2 += step)
* {
* double u2 = 1D - t2;
*
* PointD denominator2 = point2 - u2 * u2 * u2 * point0 - 3 * t2 * u2 * u2 * point0 - 3 * t2 * t2 * u2 * point3 - t2 * t2 * t2 * point3;
* double k12 = denominator2.DotProduct(method1) / (3 * t2 * u2 * u2 * dot1);
* double k22 = denominator2.DotProduct(method2) / (3 * t2 * t2 * u2 * dot2);
*
* if (k12 < 0 || k22 > 0)
* {
* continue;
* }
*
* double d1 = k12 - k1;
* double d2 = k22 - k2;
* value = d1 * d1 + d2 * d2;
*
* if (value < min)
* {
* min = value;
* k1min = k1;
* k2min = k2;
* }
* }
*/
#endregion
}
//k1min = 0.001D;
//k2min = -0.001D;
return(new BezierCurve(point0, point0 + k1Min * vector0, point3 + k2Min * vector3, point3));
}
