//-------------------------------------------------------------------------------------------
//Ближайшая точка эллипса
public Point2D GetNearestEllipsePoint(Point2D point)
{
double a = this.radiusX;
double b = this.radiusY;
double x = point.X;
double y = point.Y;
double a0 = (b * b * b * b * y * y) / (a * a);
double a1 = 2 * b * b * (1 - (b * b) / (a * a)) * y;
double a2 =
a * a - 2 * b * b - x * x + (b * b * b * b) / (a * a) -
(b * b * y * y) / (a * a);
double a3 = 2 * ((b * b) / (a * a) - 1) * y;
double a4 = -Math.Pow((a * a - b * b) / (a * b), 2);
Complex[] roots = QuarticEquation.GetRoots(a4, a3, a2, a1, a0);
Complex[] integerRoots = NumbersManager.GetNumbersWithZeroImaginaryPart(roots);
double[] coordinatesY = NumbersManager.GetRealParts(integerRoots);
double[] coordinatesX = this.GetCoordinatesXOfPossiblePoints(point, coordinatesY);
Point2D[] possiblePoints = PlaneManager.CreatePoints2D(coordinatesX, coordinatesY);
Point2D[] ellipsePoints = this.SelectPoints(possiblePoints, 0.01);
Point2D nearestPoint = PlaneManager.GetNearestPoint(point, ellipsePoints);
return(nearestPoint);
}
//-----------------------------------------------------------------------------------------------
//Перемещение точек в первый квадрант
public static Point2D[] DisplacePointsToFirstQuadrant(Point2D[] points)
{
double[] minimalCoordinates = PlaneManager.GetMinimalCoordinates(points);
double displacementX = minimalCoordinates[0];
double displacementY = minimalCoordinates[1];
Point2D[] newPoints = PlaneManager.DisplacePoints(points, -displacementX, -displacementY);
return(newPoints);
}
//-----------------------------------------------------------------------------------------------
//Расстояния между точками массива и заданной точкой
public static double[] GetDistances(Point2D[] points, Point2D targetPoint)
{
double[] distances = new double[points.Length];
for (int index = 0; index < points.Length; index++)
{
Point2D point = points[index];
double distance = PlaneManager.DistanceBetweenTwoPoints(point, targetPoint);
distances[index] = distance;
}
return(distances);
}
//-----------------------------------------------------------------------------------------------
//Минимальные координаты точек
public static double[] GetMinimalCoordinates(Point2D[] points)
{
double[] coordinatesX = PlaneManager.GetCoordinatesX(points);
double[] coordinatesY = PlaneManager.GetCoordinatesY(points);
double minX = coordinatesX.Min();
double minY = coordinatesY.Min();
double[] minimalCoordinates = new double[] { minX, minY };
return(minimalCoordinates);
}
//----------------------------------------------------------------------------------------------
//Повернуть векторы
public static RealVector[] RotateVectros(
RealVector[] vectors,
RealMatrix rotationMatrix
)
{
RealVector[] newVectors = new RealVector[vectors.Length];
for (int index = 0; index < vectors.Length; index++)
{
RealVector vector = vectors[index];
RealVector newVector = PlaneManager.RotateVector(vector, rotationMatrix);
newVectors[index] = newVector;
}
return(newVectors);
}
//-----------------------------------------------------------------------------------------------
//Выбрать ближайшую к данной точке точку из массива
public static Point2D GetNearestPoint(Point2D point, Point2D[] points)
{
if (points.Length == 1)
{
return(points[0]);
}
Point2D nearestPoint = points[0];
double minDistance = PlaneManager.DistanceBetweenTwoPoints(point, nearestPoint);
for (int index = 1; index < points.Length; index++)
{
Point2D currentPoint = points[index];
double distance = PlaneManager.DistanceBetweenTwoPoints(point, currentPoint);
if (distance < minDistance)
{
minDistance = distance;
nearestPoint = currentPoint;
}
}
return(nearestPoint);
}
//------------------------------------------------------------------------------------------------
//Расстояние до заданной точки
public double GetDistanceToPoint(Point2D point)
{
double distance = PlaneManager.DistanceBetweenTwoPoints(this, point);
return(distance);
}