/// <summary>
/// 获取逆矩阵
/// </summary>
/// <returns></returns>
public Matrix2D?Inverse()
{
Matrix2D mat = Clone();
if (GeoUtils.Inverse(ref mat._elements, 3))
{
return(mat);
}
else
{
return(null);
}
}
/// <summary>
/// 插值点反求控制点
/// </summary>
/// <param name="closed"></param>
/// <param name="fitPoints"></param>
public Spline2D(bool closed, IEnumerable <Point2D> fitPoints)
{
Periodic = false;
HasFitPoints = true;
FitPoints = new List <Point2D>(fitPoints);
//参数区间数
int n = FitPoints.Count - 1;
//参数化
List <double> knots = new List <double>();
knots.Add(0);
double totalLength = 0;
for (int i = 0; i < n; i++)
{
totalLength += (FitPoints[i + 1] - FitPoints[i]).Length;
knots.Add(totalLength);
}
if (closed)
{
totalLength += (FitPoints[0] - FitPoints[FitPoints.Count - 1]).Length;
knots.Add(totalLength);
}
NurbsData = new NurbsData(knots, 3, closed);
if (closed)
{
//构建矩阵方程组
double[,] mat = new double[n + 1, n + 1];
for (int i = 0; i < n + 1; i++)
{
var par = NurbsData.Knots[i + Degree];
int span = NurbsData.Knots.FindSpan(par);
var nn = NurbsData.Knots.BasicFuns(span, par);
for (int j = 0; j < Degree; j++)
{
mat[i, (span - Degree + j) % (n + 1)] = nn[j];
}
}
var fpts = new List <Point2D>(FitPoints);
//求解
GeoUtils.Inverse(ref mat, n + 1);
for (int i = 0; i < n + 1; i++)
{
NurbsData.AddControlPoint(new Point2D());
for (int j = 0; j < n + 1; j++)
{
NurbsData.ControlPoints[i] += fpts[j] * mat[i, j];
}
}
}
else
{
//构建矩阵方程组
double[,] mat = new double[n + 3, n + 3];
//计算插值点的非零幂基函数值
for (int i = 1; i < n; i++)
{
var par = NurbsData.Knots[i + Degree];
int span = NurbsData.Knots.FindSpan(par);
var nn = NurbsData.Knots.BasicFuns(span, par);
for (int j = 0; j < Degree; j++)
{
mat[i + 1, span - Degree + j] = nn[j];
}
}
mat[1, 0] = mat[n + 1, n + 2] = 1;
//使用自由边界条件，即端点处二阶导数为0
var t1 = totalLength / NurbsData.Knots[Degree + 1];
var t2 = totalLength / NurbsData.Knots[Degree + 2];
mat[0, 0] = t1;
mat[0, 1] = -t1 - t2;
mat[0, 2] = t2;
t1 = totalLength / (totalLength - NurbsData.Knots[n + Degree - 2]);
t2 = totalLength / (totalLength - NurbsData.Knots[n + Degree - 1]);
mat[n + 2, n] = t1;
mat[n + 2, n + 1] = -t1 - t2;
mat[n + 2, n + 2] = t2;
var fpts = new List <Point2D>();
fpts.Add(Point2D.Origin);
fpts.AddRange(FitPoints);
fpts.Add(Point2D.Origin);
//求解
GeoUtils.Inverse(ref mat, n + 3);
for (int i = 0; i < n + 3; i++)
{
NurbsData.AddControlPoint(new Point2D());
for (int j = 0; j < n + 3; j++)
{
NurbsData.ControlPoints[i] += fpts[j] * mat[i, j];
}
}
}
}
