public void ToX(XElement xe)
{
var closed = Closed;
if (GeoUtils.Equals(ControlPoints[0], ControlPoints[ControlPoints.Count - 1]))
{
closed = true;
}
xe.Add(new XAttribute("Closed", closed));
xe.Add(new XAttribute("Degree", Degree));
var controlPoints = new XElement("ControlPoints");
xe.Add(controlPoints);
foreach (var pt in ControlPoints)
{
controlPoints.Add(pt.ToX("Point"));
}
xe.Add(Knots.ToX());
}
public Curve2D GetSegmentAt(int index)
{
if (index < 0 || index >= SegmentCount)
{
return(null);
}
var pt1 = Vertexs[index];
var pt2 =
index == Vertexs.Count - 1 ?
Vertexs[0] :
Vertexs[index + 1];
if (GeoUtils.Equals(pt1.Bulge, 0))
{
return(new LineSegment2D(pt1.Position, pt2.Position));
}
else
{
return(new CircleArc2D(pt1.Position, pt2.Position, pt1.Bulge));
}
}
public CircleArc2D(Point2D pt1, Point2D pt2, Point2D pt3, bool isWholeCircle)
{
if (isWholeCircle)
{
var xy1 = Math.Pow(pt1.X, 2) + Math.Pow(pt1.Y, 2);
var xy2 = xy1 - Math.Pow(pt3.X, 2) - Math.Pow(pt3.Y, 2);
var xy3 = xy1 - Math.Pow(pt2.X, 2) - Math.Pow(pt2.Y, 2);
xy1 = (pt1.X - pt2.X) * (pt1.Y - pt3.Y) - (pt1.X - pt3.X) * (pt1.Y - pt2.Y);
if (GeoUtils.Equals(xy1, 0))
{
throw new Exception("无法创建圆!");
}
Center =
new Point2D(
(xy3 * (pt1.Y - pt3.Y) - xy2 * (pt1.Y - pt2.Y)) / (2 * xy1),
(xy2 * (pt1.X - pt2.X) - xy3 * (pt1.X - pt3.X)) / (2 * xy1));
Radius = (pt1 - Center).Length;
if (GeoUtils.Equals(Radius, 0))
{
throw new Exception("半径为零!");
}
StartAngle = Angle.Zero;
EndAngle = Angle.Degree360;
}
else
{
CircleArc2D cir = new CircleArc2D(pt1, pt2, pt3, true);
Center = cir.Center;
Radius = cir.Radius;
IsClockWise =
Vector2D.IsClockWise(
pt1 - cir.Center,
pt2 - cir.Center,
pt3 - cir.Center);
}
}
/// <summary>
/// 按向量的镜像矩阵
/// </summary>
/// <param name="start"></param>
/// <param name="end"></param>
/// <returns></returns>
public static Matrix2D Mirror(Vector2D vec)
{
bool ex = GeoUtils.Equals(vec.X, 0);
bool ey = GeoUtils.Equals(vec.Y, 0);
if (ex && ey)
{
return(Rotation(new Angle(Math.PI)));
}
else if (ex)
{
return(new Matrix2D(-1, 0, 0, 1, 0, 0));
}
else if (ey)
{
return(new Matrix2D(1, 0, 0, -1, 0, 0));
}
double angle = vec.Angle * 2;
double s2 = Math.Sin(angle);
double c2 = Math.Cos(angle);
return(new Matrix2D(c2, s2, s2, -c2, 0, 0));
}
public void ToX(XElement xe)
{
xe.Add(new XAttribute("X", GeoUtils.Round(X)));
xe.Add(new XAttribute("Y", GeoUtils.Round(Y)));
}
public bool IsPerpendicularTo(Vector2D vec)
{
return(GeoUtils.Equals(DotProduct(vec), 0));
}
public bool IsParallelTo(Vector2D vec)
{
return(GeoUtils.Equals(CrossProduct(vec), 0));
}
public static bool operator ==(Vector2D v1, Vector2D v2)
{
return
(GeoUtils.Equals(v1.X, v2.X, GeoUtils.EqualsPoint) &&
GeoUtils.Equals(v1.Y, v2.Y, GeoUtils.EqualsPoint));
}
public bool Equals(Angle x, Angle y)
{
return(GeoUtils.Equals(x._radian, y._radian));
}
public bool IsWholeCircle()
{
return(GeoUtils.Equals(_radian, PI2));
}
public bool IsZero()
{
return(GeoUtils.Equals(_radian, 0));
}
/// <summary>
/// 交换矩阵元素
/// </summary>
/// <param name="x1"></param>
/// <param name="y1"></param>
/// <param name="x2"></param>
/// <param name="y2"></param>
public void Swap(int x1, int y1, int x2, int y2)
{
GeoUtils.Swap(ref _elements, x1, y1, x1, y1);
}
public override string ToString()
{
return(string.Format("{0},{1}", GeoUtils.Round(X), GeoUtils.Round(Y)));;
}
public static bool operator ==(Point2D p1, Point2D p2)
{
return
(GeoUtils.Equals(p1.X, p2.X, GeoUtils.EqualsPoint) &&
GeoUtils.Equals(p1.Y, p2.Y, GeoUtils.EqualsPoint));
}
/// <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];
}
}
}
}
