//计算两点所形成B样条的长度
static public float CalculateBsplineLen(PointF point1, PointF point2, float angle1, float angle2)
{
PointF[] finalDataPoint = new PointF[6];
PointF[] dataPoint = new PointF[2];
float length = 0.0f;
const float CHANGE_TO_RADIAN = (3.1415927f / 180.0f);
PointF[] lines = new PointF[2];
length = 0.6f * (float)Math.Sqrt((point1.X - point2.X) * (point1.X - point2.X) + (point1.Y - point2.Y) * (point1.Y - point2.Y));
dataPoint[0].X = (int)((3 * point1.X + length * Math.Cos((angle1) * CHANGE_TO_RADIAN)) / 3.0f);
dataPoint[0].Y = (int)((3 * point1.Y + length * Math.Sin((angle1) * CHANGE_TO_RADIAN)) / 3.0f);
dataPoint[1].X = (int)((3 * point2.X - length * Math.Cos((angle2) * CHANGE_TO_RADIAN)) / 3.0f);
dataPoint[1].Y = (int)((3 * point2.Y - length * Math.Sin((angle2) * CHANGE_TO_RADIAN)) / 3.0f);
//复制最终控制点坐标
finalDataPoint[0] = point1;
finalDataPoint[1] = point1;
finalDataPoint[2] = dataPoint[0];
finalDataPoint[3] = dataPoint[1];
finalDataPoint[4] = point2;
finalDataPoint[5] = point2;
//从初始点开始
lines[0].X = (int)finalDataPoint[0].X;
lines[0].Y = (int)finalDataPoint[0].Y;
length = 0.0f;
for (int i = 0; i < 3; i++)
{
for (float u = 0.01f; u <= 1; u += 0.01f)
{
float b0 = 1.0f / 6 * (1 - u) * (1 - u) * (1 - u);
float b1 = 1.0f / 6 * (3 * u * u * u - 6 * u * u + 4);
float b2 = 1.0f / 6 * (-3 * u * u * u + 3 * u * u + 3 * u + 1);
float b3 = 1.0f / 6 * u * u * u;
lines[1].X = (b0 * finalDataPoint[i].X + b1 * finalDataPoint[i + 1].X + b2 * finalDataPoint[i + 2].X + b3 * finalDataPoint[i + 3].X);
lines[1].Y = (b0 * finalDataPoint[i].Y + b1 * finalDataPoint[i + 1].Y + b2 * finalDataPoint[i + 2].Y + b3 * finalDataPoint[i + 3].Y);
length += Bspline.CalculatePnt2Pnt(lines[0], lines[1]);
lines[0] = lines[1];
}
}
length += Bspline.CalculatePnt2Pnt(lines[0], point2);
return(length);
}
//进行整体分段处理，仅用于BsplineSegment,计算每段15cm处切线方向
static public float Segment(PointF[] inPoint, string BsplineWithDirTxt, StreamWriter lengthSegmentFile)
{
StreamWriter file = new StreamWriter(BsplineWithDirTxt, false);
int num = inPoint.Count();
//系数矩阵对角列
float[] a = new float[num];
//系数矩阵对角上列
float[] b = new float[num];
//系数矩阵对角下列
float[] c = new float[num];
//定义soluctionX、soluctionY为线性方程的解
float[] soluctionX = new float[num];
float[] soluctionY = new float[num];
//定义dataX和dataY,用来存放inPoint里的X和Y坐标
float[] dataX = new float[num];
float[] dataY = new float[num];
//定义controlPoint用来存放控制点
PointF[] controlPoint = new PointF[num + 4];
//存放画线的两个使用点
PointF[] lines = new PointF[2];
//初始化 a,b,c
a[0] = 18;
a[num - 1] = 18;
for (int i = 1; i < num - 1; i++)
{
a[i] = 4;
}
for (int i = 1; i < num - 1; i++)
{
b[i] = 1;
c[i] = 1;
}
c[num - 1] = -9;
b[0] = -9;
for (int i = 0; i < num; i++)
{
dataX[i] = 6.0f * inPoint[i].X;
dataY[i] = 6.0f * inPoint[i].Y;
}
dataX[0] *= 1.5f;
dataY[0] *= 1.5f;
dataX[num - 1] *= 1.5f;
dataY[num - 1] *= 1.5f;
//计算outdataX,outdataY;
Calculate math = new Calculate();
//调用Matrix用追赶法求解线性方程
math.Matrix(dataX, num, ref a, ref b, ref c, ref soluctionX);
math.Matrix(dataY, num, ref a, ref b, ref c, ref soluctionY);
controlPoint[num + 3].X = dataX[num - 1] / 9;
controlPoint[num + 2].X = dataX[num - 1] / 9;
controlPoint[0].X = dataX[0] / 9;
controlPoint[1].X = dataX[0] / 9;
for (int i = 0; i < num; i++)
{
controlPoint[i + 2].X = soluctionX[i];
}
controlPoint[num + 3].Y = dataY[num - 1] / 9;
controlPoint[num + 2].Y = dataY[num - 1] / 9;
controlPoint[0].Y = dataY[0] / 9;
controlPoint[1].Y = dataY[0] / 9;
for (int i = 0; i < num; i++)
{
controlPoint[i + 2].Y = soluctionY[i];
}
//计算型值点，画出曲线
////从初始点开始
//lines[0].X = controlPoint[0].X;
//lines[0].Y = controlPoint[0].Y;
float length = 0.0f;
float lengthOrigin = 0.0f;
const float CHANGE_TO_ANGLE = (180.0f / 3.1415927f);
int count = 0;
for (int i = 0; i < num + 1; i++)
{
for (float u = 0.01f; u <= 1; u += 0.01f)
{
float b0 = 1.0f / 6 * (1 - u) * (1 - u) * (1 - u);
float b1 = 1.0f / 6 * (3 * u * u * u - 6 * u * u + 4);
float b2 = 1.0f / 6 * (-3 * u * u * u + 3 * u * u + 3 * u + 1);
float b3 = 1.0f / 6 * u * u * u;
lines[1].X = (b0 * controlPoint[i].X + b1 * controlPoint[i + 1].X + b2 * controlPoint[i + 2].X + b3 * controlPoint[i + 3].X);
lines[1].Y = (b0 * controlPoint[i].Y + b1 * controlPoint[i + 1].Y + b2 * controlPoint[i + 2].Y + b3 * controlPoint[i + 3].Y);
lengthOrigin += Bspline.CalculatePnt2Pnt(lines[0], lines[1]);
length += Bspline.CalculatePnt2Pnt(lines[0], lines[1]);
if (length > 300.0)
{
length = 0;
float Db0 = -1.0f / 2 * (u - 1) * (u - 1);
float Db1 = 1.0f / 2 * (3 * u * u - 4 * u);
float Db2 = 1.0f / 2 * (-3 * u * u + u * 2 + 1);
float Db3 = 1.0f / 2 * u * u;
float angle = CHANGE_TO_ANGLE * (float)Math.Atan2((Db0 * controlPoint[i].Y + Db1 * controlPoint[i + 1].Y
+ Db2 * controlPoint[i + 2].Y + Db3 * controlPoint[i + 3].Y),
(Db0 * controlPoint[i].X + Db1 * controlPoint[i + 1].X
+ Db2 * controlPoint[i + 2].X + Db3 * controlPoint[i + 3].X));
if (count == 0)
{
file.Write(inPoint[0].X.ToString() + "," + inPoint[0].Y.ToString() + "," + (Math.Atan2(lines[1].Y - inPoint[0].Y, lines[1].X - inPoint[0].X) * 180.0f / 3.14159f).ToString() + "\r\n");
file.Write(lines[1].X.ToString() + "," + lines[1].Y.ToString() + "," + angle.ToString() + "\r\n");
}
else
{
file.Write(lines[1].X.ToString() + "," + lines[1].Y.ToString() + "," + angle.ToString() + "\r\n");
}
count++;
//并没有记录第一点和最后一点
lengthSegmentFile.WriteLine(lengthOrigin);
}
lines[0] = lines[1];
}
}
lengthOrigin += Bspline.CalculatePnt2Pnt(inPoint[num - 1], lines[1]);
file.Write(inPoint[num - 1].X.ToString() + "," + inPoint[num - 1].Y.ToString() + "," + (Math.Atan2(inPoint[num - 1].Y - lines[1].Y, inPoint[num - 1].X - lines[1].X) * 180.0f / 3.14159f).ToString() + "\r\n");
file.Close();
return(lengthOrigin);
}
//计算所绘制B样条曲线关键点路径长度，并存在txt文件中,用于切分姿态角度所用
static public void CalculateBsplineInfo(string txtAdress)
{
//创建临时文件
StreamWriter tempFile = new StreamWriter(Directory.GetCurrentDirectory() + "\\eeww.txt", true);
//////////////////////////////////从TXT文档读取数据点/////////////////////////////////////
//数据读取
StreamReader pathFile = File.OpenText(txtAdress);
List <string> tempString = new List <string>();
while (!pathFile.EndOfStream)
{
tempString.Add(pathFile.ReadLine());
}
pathFile.Close();
//如果点数小于2，不能规划出轨迹
if (tempString.Count() < 2)
{
return;
}
List <PointF> tempPnts = new List <PointF>();
Pen myPen = new Pen(Color.Black, 1);
foreach (string str in tempString)
{
string[] sArray = str.Split(',');
tempPnts.Add(new PointF(float.Parse(sArray[0]), float.Parse(sArray[1])));
}
System.Drawing.PointF[] tempPoint = tempPnts.ToArray();
//////////////////////////////////////////////////////////////////////////////////////////////
int num = tempPoint.Count();
float[] pntLen = new float[num];
//系数矩阵对角列
float[] a = new float[num];
//系数矩阵对角上列
float[] b = new float[num];
//系数矩阵对角下列
float[] c = new float[num];
//定义soluctionX、soluctionY为线性方程的解
float[] soluctionX = new float[num];
float[] soluctionY = new float[num];
//定义dataX和dataY,用来存放inPoint里的X和Y坐标
float[] dataX = new float[num];
float[] dataY = new float[num];
//定义controlPoint用来存放控制点
PointF[] controlPoint = new PointF[num + 4];
//存放画线的两个使用点
PointF[] lines = new PointF[2];
//初始化 a,b,c
a[0] = 18;
a[num - 1] = 18;
for (int i = 1; i < num - 1; i++)
{
a[i] = 4;
}
for (int i = 1; i < num - 1; i++)
{
b[i] = 1;
c[i] = 1;
}
c[num - 1] = -9;
b[0] = -9;
for (int i = 0; i < num; i++)
{
dataX[i] = 6.0f * tempPnts[i].X;
dataY[i] = 6.0f * tempPnts[i].Y;
}
dataX[0] *= 1.5f;
dataY[0] *= 1.5f;
dataX[num - 1] *= 1.5f;
dataY[num - 1] *= 1.5f;
//计算outdataX,outdataY;
Calculate math = new Calculate();
//调用Matrix用追赶法求解线性方程
math.Matrix(dataX, num, ref a, ref b, ref c, ref soluctionX);
math.Matrix(dataY, num, ref a, ref b, ref c, ref soluctionY);
controlPoint[num + 3].X = dataX[num - 1] / 9;
controlPoint[num + 2].X = dataX[num - 1] / 9;
controlPoint[0].X = dataX[0] / 9;
controlPoint[1].X = dataX[0] / 9;
for (int i = 0; i < num; i++)
{
controlPoint[i + 2].X = soluctionX[i];
}
controlPoint[num + 3].Y = dataY[num - 1] / 9;
controlPoint[num + 2].Y = dataY[num - 1] / 9;
controlPoint[0].Y = dataY[0] / 9;
controlPoint[1].Y = dataY[0] / 9;
for (int i = 0; i < num; i++)
{
controlPoint[i + 2].Y = soluctionY[i];
}
float threshold = 1.0f;
while (true)
{
//计算型值点，画出曲线
//从初始点开始
lines[0] = tempPoint[0];
pntLen[0] = 0.0f;
int count = 1;
float length = 0.0f;
for (int i = 0; i < num + 1; i++)
{
for (float u = 0.01f; u <= 1; u += 0.01f)
{
float b0 = 1.0f / 6 * (1 - u) * (1 - u) * (1 - u);
float b1 = 1.0f / 6 * (3 * u * u * u - 6 * u * u + 4);
float b2 = 1.0f / 6 * (-3 * u * u * u + 3 * u * u + 3 * u + 1);
float b3 = 1.0f / 6 * u * u * u;
lines[1].X = (b0 * controlPoint[i].X + b1 * controlPoint[i + 1].X + b2 * controlPoint[i + 2].X + b3 * controlPoint[i + 3].X);
lines[1].Y = (b0 * controlPoint[i].Y + b1 * controlPoint[i + 1].Y + b2 * controlPoint[i + 2].Y + b3 * controlPoint[i + 3].Y);
length += Bspline.CalculatePnt2Pnt(lines[0], lines[1]);
if (Bspline.CalculatePnt2Pnt(lines[1], tempPnts[count]) < threshold)
{
pntLen[count++] = length;
}
lines[0] = lines[1];
}
}
if (count == num - 1)
{
length += Bspline.CalculatePnt2Pnt(lines[0], tempPoint[num - 1]);
pntLen[num - 1] = length;
break;
}
else
{
threshold *= 2.0f;
}
}
int ii = 0;
foreach (string str in tempString)
{
tempFile.WriteLine(str + "," + pntLen[ii++].ToString());
}
tempFile.Close();
//清空txt文档
FileStream fs = new FileStream(txtAdress, FileMode.Create, FileAccess.Write);
fs.Close();
//FileTxt.FileTxtCopy(Directory.GetCurrentDirectory() + "\\eeww.txt", txtAdress);
//删除临时文件
System.IO.File.Delete(Directory.GetCurrentDirectory() + "\\eeww.txt");
}
//计算b样条长度，端点条件为自由端点条件
static public float CalculateBsplineLenWithoutDir(PointF[] inPoint)
{
int num = inPoint.Count();
//系数矩阵对角列
float[] a = new float[num];
//系数矩阵对角上列
float[] b = new float[num];
//系数矩阵对角下列
float[] c = new float[num];
//定义soluctionX、soluctionY为线性方程的解
float[] soluctionX = new float[num];
float[] soluctionY = new float[num];
//定义dataX和dataY,用来存放inPoint里的X和Y坐标
float[] dataX = new float[num];
float[] dataY = new float[num];
//定义controlPoint用来存放控制点
PointF[] controlPoint = new PointF[num + 4];
//存放画线的两个使用点
PointF[] lines = new PointF[2];
//初始化 a,b,c
a[0] = 18;
a[num - 1] = 18;
for (int i = 1; i < num - 1; i++)
{
a[i] = 4;
}
for (int i = 1; i < num - 1; i++)
{
b[i] = 1;
c[i] = 1;
}
c[num - 1] = -9;
b[0] = -9;
for (int i = 0; i < num; i++)
{
dataX[i] = 6.0f * inPoint[i].X;
dataY[i] = 6.0f * inPoint[i].Y;
}
dataX[0] *= 1.5f;
dataY[0] *= 1.5f;
dataX[num - 1] *= 1.5f;
dataY[num - 1] *= 1.5f;
//计算outdataX,outdataY;
Calculate math = new Calculate();
//调用Matrix用追赶法求解线性方程
math.Matrix(dataX, num, ref a, ref b, ref c, ref soluctionX);
math.Matrix(dataY, num, ref a, ref b, ref c, ref soluctionY);
controlPoint[num + 3].X = dataX[num - 1] / 9;
controlPoint[num + 2].X = dataX[num - 1] / 9;
controlPoint[0].X = dataX[0] / 9;
controlPoint[1].X = dataX[0] / 9;
for (int i = 0; i < num; i++)
{
controlPoint[i + 2].X = soluctionX[i];
}
controlPoint[num + 3].Y = dataY[num - 1] / 9;
controlPoint[num + 2].Y = dataY[num - 1] / 9;
controlPoint[0].Y = dataY[0] / 9;
controlPoint[1].Y = dataY[0] / 9;
for (int i = 0; i < num; i++)
{
controlPoint[i + 2].Y = soluctionY[i];
}
//计算型值点，画出曲线
//从初始点开始
lines[0] = inPoint[0];
float length = 0.0f;
const float CHANGE_TO_ANGLE = (180.0f / 3.1415927f);
for (int i = 0; i < num + 1; i++)
{
for (float u = 0.01f; u <= 1; u += 0.01f)
{
float b0 = 1.0f / 6 * (1 - u) * (1 - u) * (1 - u);
float b1 = 1.0f / 6 * (3 * u * u * u - 6 * u * u + 4);
float b2 = 1.0f / 6 * (-3 * u * u * u + 3 * u * u + 3 * u + 1);
float b3 = 1.0f / 6 * u * u * u;
lines[1].X = (b0 * controlPoint[i].X + b1 * controlPoint[i + 1].X + b2 * controlPoint[i + 2].X + b3 * controlPoint[i + 3].X);
lines[1].Y = (b0 * controlPoint[i].Y + b1 * controlPoint[i + 1].Y + b2 * controlPoint[i + 2].Y + b3 * controlPoint[i + 3].Y);
length += Bspline.CalculatePnt2Pnt(lines[0], lines[1]);
float Db0 = -1.0f / 2 * (u - 1) * (u - 1);
float Db1 = 1.0f / 2 * (3 * u * u - 4 * u);
float Db2 = 1.0f / 2 * (-3 * u * u + u * 2 + 1);
float Db3 = 1.0f / 2 * u * u;
float angle = CHANGE_TO_ANGLE * (float)Math.Atan2((Db0 * controlPoint[i].Y + Db1 * controlPoint[i + 1].Y
+ Db2 * controlPoint[i + 2].Y + Db3 * controlPoint[i + 3].Y),
(Db0 * controlPoint[i].X + Db1 * controlPoint[i + 1].X
+ Db2 * controlPoint[i + 2].X + Db3 * controlPoint[i + 3].X));
lines[0] = lines[1];
}
}
length += Bspline.CalculatePnt2Pnt(lines[0], inPoint[num - 1]);
return(length);
}