/// <summary>
/// 判断点是否在圆上(CKY标准，点到圆弧最近距离)
/// </summary>
/// <returns></returns>
public static bool CKYIsOnCircle(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3, DataType.BasicDataType.vector x_vVector4, double x_nLinePrecision, double x_nCirclePrecision, ref double x_nActualError)
{
bool l_bResult = false;
DataType.BasicDataType.vector l_vCenterPoint;
DataType.BasicDataType.PlaneCoefficient l_pCoefficient;
double l_nRadius;
l_bResult = CreatPlane(x_vVector1, x_vVector2, x_vVector3, x_nLinePrecision, out l_pCoefficient);
if (l_bResult == true)
{
l_bResult = IsOnPlane(x_vVector4, l_pCoefficient, x_nCirclePrecision);
if (l_bResult == true)
{
l_bResult = CreatCircle(x_vVector1, x_vVector2, x_vVector3, out l_vCenterPoint, out l_nRadius);
double l_nDistance = BasicMathTool.VectorDistance(l_vCenterPoint, x_vVector4);
double l_nPointToPlaneDistance = PointToPlaneDistance(x_vVector4, l_pCoefficient);
double l_nActualError = Math.Sqrt(Math.Pow(l_nDistance - l_nRadius, 2) + Math.Pow(l_nPointToPlaneDistance, 2));
if (l_nActualError <= x_nCirclePrecision)
//if (Math.Abs(l_nDistance - l_nRadius) <= x_nPrecision)
{
l_bResult = true;
x_nActualError = l_nActualError;
}
else
{
l_bResult = false;
}
}
}
return(l_bResult);
}
/// <summary>
/// 判断点是否在圆上
/// </summary>
/// <returns></returns>
public static bool IsOnCircle(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3, DataType.BasicDataType.vector x_vVector4, double x_nLinePrecision, double x_nPrecision)
{
bool l_bResult = false;
DataType.BasicDataType.vector l_vCenterPoint;
DataType.BasicDataType.PlaneCoefficient l_pCoefficient;
double l_nRadius;
l_bResult = CreatPlane(x_vVector1, x_vVector2, x_vVector3, x_nLinePrecision, out l_pCoefficient);
if (l_bResult == true)
{
l_bResult = IsOnPlane(x_vVector4, l_pCoefficient, x_nPrecision);
if (l_bResult == true)
{
l_bResult = CreatCircle(x_vVector1, x_vVector2, x_vVector3, out l_vCenterPoint, out l_nRadius);
double l_nDistance = BasicMathTool.VectorDistance(l_vCenterPoint, x_vVector4);
if (Math.Abs(l_nDistance - l_nRadius) <= x_nPrecision)
{
l_bResult = true;
}
else
{
l_bResult = false;
}
}
}
return(l_bResult);
}
/// <summary>
/// 向量差
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <returns></returns>
public static DataType.BasicDataType.vector SubVector(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2)
{
DataType.BasicDataType.vector l_vV1;
l_vV1.x = x_vVector2.x - x_vVector1.x;
l_vV1.y = x_vVector2.y - x_vVector1.y;
l_vV1.z = x_vVector2.z - x_vVector1.z;
return(l_vV1);
}
/// <summary>
///
/// </summary>
/// <param name="x_vVector"></param>
/// <param name="x_pPlaneCoefficient"></param>
/// <param name="x_nPrecision"></param>
/// <returns></returns>
//public static bool CKYIsOnPlane(DataType.BasicDataType.vector x_vVector, DataType.BasicDataType.PlaneCoefficient x_pPlaneCoefficient, double x_nPrecision)
//{
// bool l_bResult = false;
// double l_nValue = x_pPlaneCoefficient.a * x_vVector.x + x_pPlaneCoefficient.b * x_vVector.y + x_pPlaneCoefficient.c * x_vVector.z + x_pPlaneCoefficient.d;
// if (l_nValue <= x_nPrecision)
// {
// l_bResult = true;
// }
// else
// {
// l_bResult = false;
// }
// return l_bResult;
//}
public static double PointToPlaneDistance(DataType.BasicDataType.vector x_vVector, DataType.BasicDataType.PlaneCoefficient x_pPlaneCoefficient)
{
double l_nValue1 = new double();
double l_nValue2 = new double();
l_nValue1 = x_pPlaneCoefficient.a * x_vVector.x + x_pPlaneCoefficient.b * x_vVector.y + x_pPlaneCoefficient.c * x_vVector.z + x_pPlaneCoefficient.d;
l_nValue2 = Math.Abs(l_nValue1) / Math.Sqrt(Math.Pow(x_pPlaneCoefficient.a, 2) + Math.Pow(x_pPlaneCoefficient.b, 2) + Math.Pow(x_pPlaneCoefficient.c, 2));
return(l_nValue2);
}
/// <summary>
/// 判断向量是否相等
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <param name="x_nPrecision"></param>
/// <returns></returns>
public static bool IsEqualVector(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, double x_nPrecision)
{
bool l_bResult = false;
if (x_vVector1.x - x_vVector2.x <= x_nPrecision & x_vVector1.y - x_vVector2.y <= x_nPrecision & x_vVector1.z - x_vVector2.z <= x_nPrecision)
{
l_bResult = true;
}
return(l_bResult);
}
/// <summary>
/// 空间点到直线距离 test success
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <param name="x_vVector3"></param>
/// <returns></returns>
public static double PointToLineDistance(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3)
{
double l_nDistance = 0;
//d=l_x/l_y
DataType.BasicDataType.vector l_MA = BasicMathTool.SubVector(x_vVector1, x_vVector2);
DataType.BasicDataType.vector l_MB = BasicMathTool.SubVector(x_vVector1, x_vVector3);
DataType.BasicDataType.vector l_MAB = BasicMathTool.Vect3CrossPord(l_MB, l_MA);
double l_x = BasicMathTool.VectorNorm(l_MAB);
double l_y = BasicMathTool.VectorNorm(l_MA);
l_nDistance = (double)l_x / l_y;
return(l_nDistance);
}
public static bool VectAngle(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, ref double x_nAngle)
{
double l_CosAngle = Vect3ScalorProd(x_vVector1, x_vVector2) / (VectorNorm(x_vVector1) * VectorNorm(x_vVector2));
//double l_SinAngle =VectorNorm(Vect3CrossPord(x_vVector1, x_vVector2)) / (VectorNorm(x_vVector1) * VectorNorm(x_vVector2));
//double l_tanAngle = l_SinAngle / l_CosAngle;
if (l_CosAngle <= 1 && l_CosAngle >= -1)
{
x_nAngle = Radian2Angle(Math.Acos(l_CosAngle));
return(true);
}
else
{
return(false);
}
}
/// <summary>
/// 判断三点共线
/// </summary>
/// <returns>true：共线</returns>false：不共线
public static bool ThreeColline(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3, double x_nPrecision)
{
bool l_bOk = false;
DataType.BasicDataType.vector l_V1, l_V2;
l_V1 = BasicMathTool.SubVector(x_vVector1, x_vVector2);
l_V2 = BasicMathTool.SubVector(x_vVector2, x_vVector3);
if (Math.Abs(l_V2.x * l_V1.y - l_V1.x * l_V2.y) <= x_nPrecision & Math.Abs(l_V2.x * l_V1.z - l_V2.z * l_V1.x) <= x_nPrecision)
{
l_bOk = true;
}
else
{
l_bOk = false;
}
return(l_bOk);
}
/// <summary>
/// 判断点是否在平面上
/// </summary>
/// <param name="x_vVector"></param>
/// <param name="x_pPlaneCoefficient"></param>
/// <param name="x_nPrecision"></param>
/// <returns></returns>
public static bool IsOnPlane(DataType.BasicDataType.vector x_vVector, DataType.BasicDataType.PlaneCoefficient x_pPlaneCoefficient, double x_nDistancePrecision)
{
bool l_bResult = false;
//double l_nValue = x_pPlaneCoefficient.a * x_vVector.x + x_pPlaneCoefficient.b * x_vVector.y + x_pPlaneCoefficient.c * x_vVector.z + x_pPlaneCoefficient.d;
//l_nValue = Math.Abs(l_nValue) / Math.Sqrt(Math.Pow(x_pPlaneCoefficient.a, 2) + Math.Pow(x_pPlaneCoefficient.b, 2) + Math.Pow(x_pPlaneCoefficient.c, 2));
double l_nValue = PointToPlaneDistance(x_vVector, x_pPlaneCoefficient);
if (l_nValue <= x_nDistancePrecision)
{
l_bResult = true;
}
else
{
l_bResult = false;
}
return(l_bResult);
}
/// <summary>
/// 向量叉乘
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <returns></returns>
public static DataType.BasicDataType.vector Vect3CrossPord(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2)
{
double[] x = new double[3];
double[] y = new double[3];
double[] z = new double[3];
DataType.BasicDataType.vector l_vResule;
x[0] = x_vVector1.x;
x[1] = x_vVector1.y;
x[2] = x_vVector1.z;
y[0] = x_vVector2.x;
y[1] = x_vVector2.y;
y[2] = x_vVector2.z;
z = Vect3CrossPord(x, y);
l_vResule.x = z[0];
l_vResule.y = z[1];
l_vResule.z = z[2];
return(l_vResule);
}
/// <summary>
/// 三点建圆
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <param name="x_vVector3"></param>
/// <param name="x_vCenterPoint"></param>圆心
/// <param name="x_nRadius"></param>半径
/// <returns></returns>
public static bool CreatCircle(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3, out DataType.BasicDataType.vector x_vCenterPoint, out double x_nRadius)
{
x_vCenterPoint.x = 0;
x_vCenterPoint.y = 0;
x_vCenterPoint.z = 0;
x_nRadius = 0;
bool l_bOk = false;
l_bOk = ThreeColline(x_vVector1, x_vVector2, x_vVector3, 0.0000001);
//l_bOk = ThreeColline(x_vVector1, x_vVector2, x_vVector3, 0.01);
if (l_bOk == false)
{
double[,] l_nMatrix = new double[3, 3];
l_nMatrix[0, 0] = (x_vVector1.y - x_vVector3.y) * (x_vVector2.z - x_vVector3.z) - (x_vVector2.y - x_vVector3.y) * (x_vVector1.z - x_vVector3.z);
l_nMatrix[0, 1] = (x_vVector2.x - x_vVector3.x) * (x_vVector1.z - x_vVector3.z) - (x_vVector1.x - x_vVector3.x) * (x_vVector2.z - x_vVector3.z);
l_nMatrix[0, 2] = (x_vVector1.x - x_vVector3.x) * (x_vVector2.y - x_vVector3.y) - (x_vVector2.x - x_vVector3.x) * (x_vVector1.y - x_vVector3.y);
l_nMatrix[1, 0] = x_vVector2.x - x_vVector1.x;
l_nMatrix[1, 1] = x_vVector2.y - x_vVector1.y;
l_nMatrix[1, 2] = x_vVector2.z - x_vVector1.z;
l_nMatrix[2, 0] = x_vVector3.x - x_vVector2.x;
l_nMatrix[2, 1] = x_vVector3.y - x_vVector2.y;
l_nMatrix[2, 2] = x_vVector3.z - x_vVector2.z;
double[] l_Matrix_b = new double[3];
l_Matrix_b[0] = l_nMatrix[0, 0] * x_vVector3.x + l_nMatrix[0, 1] * x_vVector3.y + l_nMatrix[0, 2] * x_vVector3.z;
l_Matrix_b[1] = (l_nMatrix[1, 0] * (x_vVector2.x + x_vVector1.x) + l_nMatrix[1, 1] * (x_vVector2.y + x_vVector1.y) + l_nMatrix[1, 2] * (x_vVector2.z + x_vVector1.z)) / 2;
l_Matrix_b[2] = (l_nMatrix[2, 0] * (x_vVector3.x + x_vVector2.x) + l_nMatrix[2, 1] * (x_vVector3.y + x_vVector2.y) + l_nMatrix[2, 2] * (x_vVector3.z + x_vVector2.z)) / 2;
double[,] l_inverse = new double[3, 3];
l_bOk = MatrixTool.MatrixInverse(l_nMatrix, ref l_inverse);
if (l_bOk == true)
{
double[] l_CenterPoint = new double[3];
l_bOk = MatrixTool.MatrixDotMultiply(l_inverse, l_Matrix_b, out l_CenterPoint);
if (l_bOk == true)
{
x_vCenterPoint.x = l_CenterPoint[0];
x_vCenterPoint.y = l_CenterPoint[1];
x_vCenterPoint.z = l_CenterPoint[2];
x_nRadius = Math.Sqrt(Math.Pow(x_vVector1.x - x_vCenterPoint.x, 2) + Math.Pow(x_vVector1.y - x_vCenterPoint.y, 2) + Math.Pow(x_vVector1.z - x_vCenterPoint.z, 2));
}
}
}
return(l_bOk);
}
public static bool VectAngle(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3, ref double x_nAngle)
{
DataType.BasicDataType.vector l_vCenter = new BasicDataType.vector();
double l_nRadius = new double();
bool l_bResult = PointTool.CreatCircle(x_vVector1, x_vVector2, x_vVector3, out l_vCenter, out l_nRadius);
if (l_bResult == true)
{
double l_nDistance1 = VectorDistance(x_vVector1, x_vVector2);
double l_nDistance2 = VectorDistance(x_vVector2, x_vVector3);
double l_ntheta1 = 2 * Math.Asin(l_nDistance1 / (2 * l_nRadius));
double l_ntheta2 = 2 * Math.Asin(l_nDistance2 / (2 * l_nRadius));
double l_ntheta = l_ntheta1 + l_ntheta2;
x_nAngle = Radian2Angle(l_ntheta);
return(true);
}
else
{
return(false);
}
}
//public static bool CKYIsOnCircle(DataType.StaubliRobotData.St_PointRx x_pPoint1, DataType.StaubliRobotData.St_PointRx x_pPoint2, DataType.StaubliRobotData.St_PointRx x_pPoint3, DataType.StaubliRobotData.St_PointRx x_pPoint4, double x_nLinePrecision, double x_nCirclePrecision,ref double x_nPreviousRadius,ref double x_nSubsequentRadius, ref double x_nActualError)
//{
// bool l_bResult = false;
// DataType.BasicDataType.vector l_v1, l_v2, l_v3, l_v4;
// l_v1 = Point2Vector(x_pPoint1);
// l_v2 = Point2Vector(x_pPoint2);
// l_v3 = Point2Vector(x_pPoint3);
// l_v4 = Point2Vector(x_pPoint4);
// l_bResult = CKYIsOnCircle(l_v1, l_v2, l_v3, l_v4, x_nLinePrecision, x_nCirclePrecision,ref x_nPreviousRadius,ref x_nSubsequentRadius ,ref x_nActualError);
// return l_bResult;
//}
///// <summary>
///// 判断点是否在圆上(CKY标准，点到圆弧最近距离)
///// </summary>
///// <returns></returns>
//public static bool CKYIsOnCircle(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3, DataType.BasicDataType.vector x_vVector4, double x_nLinePrecision, double x_nCirclePrecision,ref double x_nPreviousRadius,ref double x_nSubsequentRadius ,ref double x_nActualError)
//{
// bool l_bResult = false;
// DataType.BasicDataType.vector l_vCenterPoint1,l_vCenterPoint2;
// DataType.BasicDataType.PlaneCoefficient l_pCoefficient;
// double l_nRadius1,l_nRadius2;
// l_bResult = CreatPlane(x_vVector1, x_vVector2, x_vVector3, x_nLinePrecision, out l_pCoefficient);
// if (l_bResult == true)
// {
// l_bResult = IsOnPlane(x_vVector4, l_pCoefficient, x_nCirclePrecision);
// if (l_bResult == true)
// {
// l_bResult = CreatCircle(x_vVector1, x_vVector2, x_vVector3, out l_vCenterPoint1, out l_nRadius1);
// l_bResult = CreatCircle(x_vVector1, x_vVector2, x_vVector4, out l_vCenterPoint2, out l_nRadius2);
// if (l_bResult == true)
// {
// //double l_nActualError = BasicMathTool.VectorDistance(l_vCenterPoint1, l_vCenterPoint2);
// double l_nActualError = Math.Abs(l_nRadius1 - l_nRadius2);
// if (l_nActualError <= x_nCirclePrecision)
// {
// l_bResult = true;
// x_nActualError = l_nActualError;
// x_nPreviousRadius = l_nRadius1;
// x_nSubsequentRadius = l_nRadius2;
// }
// else
// {
// l_bResult = false;
// }
// }
// else
// {
// l_bResult = false;
// }
// }
// }
// return l_bResult;
//}
/// <summary>
/// 三点建立平面 test success
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <param name="x_vVector3"></param>
/// <param name="x_pPlaneCoefficient"></param>
/// <returns>false 三点共线
/// </returns>true 成功
public static bool CreatPlane(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2, DataType.BasicDataType.vector x_vVector3, double x_nLinePrecision, out DataType.BasicDataType.PlaneCoefficient x_pPlaneCoefficient)
{
x_pPlaneCoefficient.a = 0;
x_pPlaneCoefficient.b = 0;
x_pPlaneCoefficient.c = 0;
x_pPlaneCoefficient.d = 0;
bool l_bResule = false;
//l_bResule = ThreeColline(x_vVector1, x_vVector2, x_vVector3,x_nLinePrecision);
l_bResule = ThreeColline(x_vVector1, x_vVector2, x_vVector3, 0.0000001);
if (l_bResule == false)
{
DataType.BasicDataType.vector l_vVector1 = BasicMathTool.SubVector(x_vVector1, x_vVector2);
DataType.BasicDataType.vector l_vVector2 = BasicMathTool.SubVector(x_vVector1, x_vVector3);
DataType.BasicDataType.vector l_vVector3 = BasicMathTool.Vect3CrossPord(l_vVector1, l_vVector2);
x_pPlaneCoefficient.a = l_vVector3.x;
x_pPlaneCoefficient.b = l_vVector3.y;
x_pPlaneCoefficient.c = l_vVector3.z;
x_pPlaneCoefficient.d = -x_pPlaneCoefficient.a * x_vVector1.x - x_pPlaneCoefficient.b * x_vVector1.y - x_pPlaneCoefficient.c * x_vVector1.z;
l_bResule = true;
}
return(l_bResule);
}
/// <summary>
/// 两点间距离
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <returns></returns>
public static double VectorDistance(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2)
{
double l_nValue = Math.Sqrt(Math.Pow(x_vVector2.x - x_vVector1.x, 2) + Math.Pow(x_vVector2.y - x_vVector1.y, 2) + Math.Pow(x_vVector2.z - x_vVector1.z, 2));
return(l_nValue);
}
/// <summary>
/// 向量点积
/// </summary>
/// <param name="x_vVector1"></param>
/// <param name="x_vVector2"></param>
/// <returns></returns>
public static double Vect3ScalorProd(DataType.BasicDataType.vector x_vVector1, DataType.BasicDataType.vector x_vVector2)
{
return(x_vVector1.x * x_vVector2.x + x_vVector1.y * x_vVector2.y + x_vVector1.z * x_vVector2.z);
}
/// <summary>
/// 向量的模
/// </summary>
/// <param name="x_vVector"></param>
/// <returns></returns>
public static double VectorNorm(DataType.BasicDataType.vector x_vVector)
{
return(Math.Sqrt(Math.Pow(x_vVector.x, 2) + Math.Pow(x_vVector.y, 2) + Math.Pow(x_vVector.z, 2)));
}