//-------------------------------------------------------------------------------------------
//Плоскость, проходящая через три заданные точки
public static PlaneDescriptor GetPlaneByThreePoints(
Point3D point1,
Point3D point2,
Point3D point3
)
{
double subX2X1 = point2.X - point1.X;
double subY2Y1 = point2.Y - point1.Y;
double subZ2Z1 = point2.Z - point1.Z;
double subX3X1 = point3.X - point1.X;
double subY3Y1 = point3.Y - point1.Y;
double subZ3Z1 = point3.Z - point1.Z;
double coefficientOfX = subY2Y1 * subZ3Z1 - subZ2Z1 * subY3Y1;
double coefficientOfY = subZ2Z1 * subX3X1 - subX2X1 * subZ3Z1;
double coefficientOfZ = subX2X1 * subY3Y1 - subY2Y1 * subX3X1;
double absoluteTerm =
point1.X * subZ2Z1 * subY3Y1 - point1.X * subY2Y1 * subZ3Z1 +
point1.Y * subX2X1 * subZ3Z1 - point1.Y * subZ2Z1 * subX3X1 +
point1.Z * subY2Y1 * subX3X1 - point1.Z * subX2X1 * subY3Y1;
PlaneDescriptor planeDescriptor = new PlaneDescriptor
(coefficientOfX, coefficientOfY, coefficientOfZ, absoluteTerm);
return(planeDescriptor);
}
//----------------------------------------------------------------------------------------------
//Точка пересечения плоскости и прямой, заданной двумя точками
public Point3D GetPlaneAndLineIntersectionPoint(
PlaneDescriptor planeDescriptor, Point3D linePointOne, Point3D linePointTwo
)
{
double m = linePointTwo.X - linePointOne.X;
double n = linePointTwo.Y - linePointOne.Y;
double p = linePointTwo.Z - linePointOne.Z;
double a = planeDescriptor.CoefficientOfX;
double b = planeDescriptor.CoefficientOfY;
double c = planeDescriptor.CoefficientOfZ;
double d = planeDescriptor.AbsoluteTerm;
double t =
-(d + a * linePointOne.X + b * linePointOne.Y + c * linePointOne.Z) /
(a * m + b * n + c * p);
double x = m * t + linePointOne.X;
double y = n * t + linePointOne.Y;
double z = p * t + linePointOne.Z;
return(new Point3D(x, y, z));
}