/// <summary>
/// 获取一个向量的unit 法向量，该法向量位于向量右侧,向量不能为零向量
/// </summary>
/// <param name="vtr"></param>
public static OxyzPointF GetNormal(OxyzPointF vtr)
{
double iDX = vtr._X * vtr._X;
double iDY = vtr._Y * vtr._Y;
double dDistance = Math.Sqrt(iDX + iDY);
double dx = 0d;
double dy = 0d;
OxyzPointF p1 = new OxyzPointF(0f, 0f, 0f);
OxyzPointF p2 = new OxyzPointF(0f, 0f, 0f);
if (vtr._Y != 0)
{
dx = vtr._Y / dDistance;
dy = dx * vtr._X / vtr._Y;
p1 = new OxyzPointF((float)dx, (float)dy);
p2 = new OxyzPointF((float)-dx, (float)-dy);
}
else if (vtr._X != 0)
{
dy = vtr._X / dDistance;
dx = dy * vtr._Y / vtr._X;
p1 = new OxyzPointF((float)dx, (float)dy);
p2 = new OxyzPointF((float)-dx, (float)-dy);
}
if (VectorTool.GetVectorPos(p1, new OxyzPointF(vtr._X, vtr._Y)) == -1)
{
return(new OxyzPointF(p1._X, -p1._Y));
}
return(new OxyzPointF(p2._X, -p2._Y));
}
public static OxyzPointF mpBaseVector = new OxyzPointF(0, 1.0f);//使用x轴做基向量
/// <summary>
/// 按照参数2指定的向量与基向量的夹角计算参数1点的绝对元胞坐标
/// </summary>
/// <param name="vector"></param>
/// <returns></returns>
// public static Point GetRealXY(Point point, OxyzPointF newVector)
// {
// if (newVector == null)
// {
// throw new ArgumentException("输入的参数不能为零");
// }
// //获取正弦和余弦值并且进行旋转变换
// SinCos sc = VectorTools.GetSinCos(mpBaseVector, newVector);
// return Coordinates.Rotate(point, sc);
// }
/// <summary>
/// 两个点的欧式距离
/// </summary>
//public static int Distance(Point p1, Point p2)
//{
// int iX = Math.Abs(p1.X - p2.X);
// int iY = Math.Abs(p1.Y - p2.Y);
// return (int)Math.Round(Math.Sqrt(iX * iX + iY * iY));
//}
//------------------------20160202-------------------------计算两个点的欧式距离
public static double Distance(OxyzPointF p1, OxyzPointF p2)
{
double iX = Math.Abs(p1._X - p2._X);
double iY = Math.Abs(p1._Y - p2._Y);
double iZ = Math.Abs(p1._Z - p2._Z);
return(Math.Sqrt(iX * iX + iY * iY + iZ * iZ));
}
public static Point GetNormal(Point start, Point end)
{
if (start != end)
{
var vector = new OxyzPointF(end.X - start.X, end.Y - start.Y);
return(VectorTool.GetNormal(vector).ToPoint());
}
//return new OxyzPointF(-opVector._X, -opVector._Y);
throw new Exception();
}
/// <summary>
/// to enlarge a point for drawing.use screen coordinates
/// </summary>
/// <param name="mp"></param>
/// <param name="iWidth"></param>
/// <returns>new points</returns>
public static OxyzPointF Offset(OxyzPointF mOld, int iWidth)
{
double dWidth = -1 * iWidth;
mOld._X += dWidth;
mOld._Y += dWidth;
mOld._Z += dWidth;
return(mOld);
}
/// <summary>
/// to enlarge a point for drawing.use screen coordinates
/// </summary>
/// <param name="mp"></param>
/// <param name="iWidth"></param>
/// <returns>new points</returns>
public static OxyzPointF Offset(OxyzPointF mOld, int iWidth, OxyzPointF vector)
{
double dWidth = iWidth;
mOld._X += dWidth * vector._X;
mOld._Y += dWidth * vector._Y;
mOld._Z += dWidth * vector._Z;
return(mOld);
}
/// <summary>
/// offset中x和y的值向左上偏移，其xy都为负值
/// </summary>
/// <param name="scrnPoint">原坐标系</param>
/// <param name="offset">偏移坐标</param>
// /// <returns>返回值为新参数</returns>
// public static PointF Offset(PointF scrnPoint, PointF offset)
// {
// //计算平移(偏移)
//// scrnPoint.X += offset.X;
//// scrnPoint.Y += offset.Y;
//// return scrnPoint;//这个是个结构参数复制，然后返回新的结果
// return Coordinates.Offset(new OxyzPointF(scrnPoint.X,scrnPoint.Y,0f),new OxyzPointF(offset.X,offset.Y,0f)).ToPointF();
// }
/// <summary>
/// vector use math coordinates .while offset servers screen coordinates,Y is reversed .so .Y needs to be reverse
/// </summary>
/// <param name="scrnPoint"></param>
/// <param name="offset"></param>
/// <returns></returns>
public static OxyzPointF Offset(OxyzPointF scrnPoint, OxyzPointF offset)
{
OxyzPointF mp = new OxyzPointF(scrnPoint._X, scrnPoint._Y);
//计算平移(偏移)
mp._X += offset._X;
//mp._Y -= offset._Y;
mp._Y += offset._Y;
return(mp);
}
/// <summary>
/// 以点mpA和点mpB为终点建立的直线方程，然后判断点mpNew在直线的上方还是下方
/// </summary>
/// <param name="mpA">直线起点坐标</param>
/// <param name="mpB">直线终点坐标</param>
/// <param name="mpNew">要检验的点坐标</param>
/// <returns>返回0表示点mpNew位于直线上，返回1表示点mpNew位于向量上方，返回-1表示点mpNew位于直线下方</returns>
public static int GetPointPosition(OxyzPointF mpA, OxyzPointF mpB, OxyzPointF mpNew)
{
if (mpB._X == mpA._X && mpB._Y == mpA._Y)
{
throw new ArgumentException("直线的两个端点不能相同");
}
double fResult = (mpNew._Y - mpA._Y) * (mpB._X - mpA._X) - (mpNew._X - mpA._X) * (mpB._Y - mpA._Y);
if (Math.Abs(fResult) < 0.9f) //绝对值在1之内，因为点坐标系有误差造成的
{
return(0); //返回0 表示向量在直线上
}
return(fResult >= 0.9f ? 1 : -1);
}
///// <summary>
///// convert cartesian coordinates to screen coordinates and enlarge it 转换为屏幕坐标系;
///// </summary>
///// <param name="iScaleFactor"></param>
// public static PointF Project(OxyzPointF p, int iScaleFactor)
// {
// return Coordinates.Project(p, iScaleFactor).ToPointF();
// }
/// <summary>
/// screen coordinates scalaor
/// </summary>
/// <param name="mp">cartesian coordinates</param>
/// <param name="iScaleFactor">一个元胞长度对应的屏幕像素点数</param>
/// <returns></returns>
public static OxyzPointF Project(OxyzPointF mp, int iScaleFactor)
{
OxyzPointF scrnPoint = new OxyzPointF();
scrnPoint._X = (float)Math.Round(iScaleFactor * mp._X);
scrnPoint._Y = (float)Math.Round(iScaleFactor * mp._Y);
// //计算平移(偏移)
// scrnPoint.X -= Coordinates.GraphicsOffset.X;
// scrnPoint.Y -= Coordinates.GraphicsOffset.Y;
return(Coordinates.Offset(scrnPoint, Coordinates.GraphicsOffset));
//return scrnPoint;//这个是个结构参数复制，然后返回新的结果
}
/// <summary>
/// 这个是Cartesian笛卡尔坐标系下的结果
///利用两点式，建立基础方程，并且利用这个方程计算输入点与基方程的联系,调用三参数的重载，第一个参数默认为零,返回-1表示位于基向量下方或者是右方，返回1表示位于基向量上方或者是左方
/// </summary>
/// <param name="vBase">基向量的终点坐标，起点坐标为0</param>
/// <param name="vNew">要检验的点的坐标如果是向量，应当输入向量的终点坐标</param>
/// <returns>返回-1表示位于基向量下方或者是右方，返回1表示位于基向量上方或者是左方</returns>
public static int GetVectorPos(OxyzPointF vBase, OxyzPointF vNew)
{
if (vBase._X == 0 && vBase._Y == 0 ||
vNew._X == 0 && vNew._Y == 0)
{
throw new ArgumentException("基向量或者要判定的向量不能为0向量");
}
int iReturn = VectorTool.GetPointPosition(new OxyzPointF(0.0f, 0.0f), vBase, vNew);
if (iReturn == 0 && vNew._X < vBase._X)
{
iReturn = 2;
}
return(iReturn);
}
/// <summary>
/// 获取两个向量的夹角的余弦值，该值的区间是-1到1闭区间,两个参数向量都不能是0向量
/// </summary>
public static double GetCosine(OxyzPointF vBase, OxyzPointF vNew)
{
//向量的数量积
double fNumerator = vBase._X * vNew._X + vBase._Y * vBase._Y;
//第一个向量（基向量）的摸
double dBaseM = vBase._X * vBase._X + vBase._Y * vBase._Y;
double dBase = Math.Sqrt(dBaseM);
//第二个向量的模
double dNewM = vNew._X * vNew._X + vNew._Y * vNew._Y;
double dNew = Math.Sqrt(dNewM);
//两个向量的模的乘积
double dDenominator = dBase * dNew;
if (dDenominator == 0.0)
{
throw new DivideByZeroException("向量的模为0是不允许的，无法计算0向量的角度");
}
///返回余弦值
return(fNumerator / dDenominator);
}
/// <summary>
/// 判定角度并且输出角度的正弦和余弦值，315-45 为0度 45-135度变为90度,135-225 为180度 225-315度变为270度，
/// </summary>
public static SinCos GetSinCos(OxyzPointF mpBaseVector, OxyzPointF mpVector)
{
//由于0.707小于根号2的一半所以45度变为90度
double dCosineValue = VectorTool.GetCosine(mpBaseVector, mpVector);
//-45 180 +45度的左开右闭闭区间
if (-1.001 <= dCosineValue && dCosineValue < -0.708) //-根号2的是是1.414 其一半 是0.707
{
return(new SinCos(0, -1)); //cosine 180 是-1；
}
int irtlPos = VectorTool.GetVectorPos(mpBaseVector, mpVector);
if (-0.708 <= dCosineValue && dCosineValue < 0.708)
{ //判断y位于基向量的上方还是下方
if (irtlPos < -0.1) //-45 270 +45度
{
return(new SinCos(-1, 0)); //270
}
if (irtlPos > 0.1) // -45 90 +45度
{
return(new SinCos(1, 0)); //90
}
if (-0.1 < irtlPos && irtlPos < 0.1)
{
return(new SinCos(1, 0));
}
else//iPos==0 当前角度下 这是不可能出现的
{
throw new Exception("不可能出现的值");
}
}
//这之间的有可能是零度，有可能是360度
if (0.708 <= dCosineValue && dCosineValue <= 1.001)
{
//315度到44度之间全部当作0度处理
return(new SinCos(0, 1));
}
throw new Exception("不可能没有捕获所有的角度值");
}
/// <summary>
/// 获取向量的逆向量
/// </summary>
/// <param name="opVector"></param>
/// <returns></returns>
public static OxyzPointF GetInverse(OxyzPointF opVector)
{
return(new OxyzPointF(-opVector._X, -opVector._Y));
}
/// <summary>
/// 获取一个单位向量的倍数向量
/// </summary>
/// <param name="uniVector"></param>
/// <param name="iMuti"></param>
/// <returns></returns>
public static OxyzPointF GetMultiNormal(OxyzPointF uniVector, int iMuti)
{
return(new OxyzPointF(uniVector._X * iMuti, uniVector._Y * iMuti, uniVector._Z * iMuti));
}
public static OxyzPointF Offset(OxyzPoint scrnPoint, OxyzPointF offset)
{
return(Coordinates.Offset(scrnPoint.ToOxyzPointF(), offset));
}
public static OxyzPointF Muilt(OxyzPointF a, Int32 iScaler)
{
return(new OxyzPointF(a._X * iScaler, a._Y * iScaler, a._Z * iScaler));
}
public OxyzPoint(OxyzPointF opF)
{
this._X = Convert.ToInt32(opF._X);
this._Y = Convert.ToInt32(opF._Y);
this._Z = Convert.ToInt32(opF._Z);
}