public Angle(double radian)
{
if (GeoUtils.Equals(radian, 0))
{
_radian = 0;
}
else if (GeoUtils.Equals(radian, PI2))
{
_radian = PI2;
}
else
{
while (radian < 0)
{
radian += PI2;
}
while (radian > PI2)
{
radian -= PI2;
}
_radian = radian;
}
}
/// <summary>
/// 二分法查找参数对应区间
/// </summary>
/// <param name="par">参数</param>
/// <returns>参数对应区间</returns>
public int FindSpan(double par)
{
var n = _knots.Count - 1;
if (GeoUtils.Equals(par, _knots[_knots.Count - 1]))
{
return(n + Degree - 1);
}
int low = 0, high = n;
int mid = (low + high) / 2;
while (par < _knots[mid] || par >= _knots[mid + 1])
{
if (par < _knots[mid])
{
high = mid;
}
else
{
low = mid;
}
mid = (low + high) / 2;
}
return(mid + Degree);
}
private void AddAttribute(XElement xe, string name, double value)
{
if (!GeoUtils.Equals(value, 0))
{
xe.Add(new XAttribute(name, value));
}
}
/// <summary>
/// 按直线的镜像矩阵
/// </summary>
/// <param name="start"></param>
/// <param name="vec"></param>
/// <returns></returns>
public static Matrix2D Mirror(Point2D start, 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), start));
}
else if (ex)
{
return(new Matrix2D(-1, 0, 0, 1, start.X * 2, 0));
}
else if (ey)
{
return(new Matrix2D(1, 0, 0, -1, 0, start.Y * 2));
}
double k = vec.Y / vec.X;
double b = (start.Y - k * start.X);
double x0 = b / k;
double angle = vec.Angle * 2;
double s2 = Math.Sin(angle);
double c2 = Math.Cos(angle);
return
(new Matrix2D(c2, s2, s2, -c2, -b * s2, x0 * s2));
}
public Angle(double radian, bool format)
{
if (format)
{
if (GeoUtils.Equals(radian, PI2))
{
_radian = PI2;
}
else
{
while (radian < 0)
{
radian += PI2;
}
while (radian > PI2)
{
radian -= PI2;
}
_radian = radian;
}
}
else
{
_radian = radian;
}
}
public override bool Equals(object obj)
{
if (obj is Vector2D)
{
var v2 = (Vector2D)obj;
return
(GeoUtils.Equals(X, v2.X, GeoUtils.EqualsVector) &&
GeoUtils.Equals(Y, v2.Y, GeoUtils.EqualsVector));
}
return(false);
}
public override bool Equals(object obj)
{
if (obj is Point2D)
{
var p2 = (Point2D)obj;
return
(GeoUtils.Equals(X, p2.X, GeoUtils.EqualsPoint) &&
GeoUtils.Equals(Y, p2.Y, GeoUtils.EqualsPoint));
}
return(false);
}
public int Compare(Vector2D v1, Vector2D v2)
{
if (GeoUtils.Equals(v1.X, v2.X, GeoUtils.EqualsVector))
{
if (GeoUtils.Equals(v1.Y, v2.Y, GeoUtils.EqualsVector))
{
return(0);
}
else
{
return(v1.Y.CompareTo(v2.Y));
}
}
return(v1.X.CompareTo(v2.X));
}
public int Compare(Point2D p1, Point2D p2)
{
if (GeoUtils.Equals(p1.X, p2.X, GeoUtils.EqualsPoint))
{
if (GeoUtils.Equals(p1.Y, p2.Y, GeoUtils.EqualsPoint))
{
return(0);
}
else
{
return(p1.Y.CompareTo(p2.Y));
}
}
return(p1.X.CompareTo(p2.X));
}
public IEnumerator <Curve2D> GetEnumerator()
{
for (int i = 0; i < SegmentCount; i++)
{
var pt1 = Vertexs[i];
var pt2 =
i == Vertexs.Count - 1 ?
Vertexs[0] :
Vertexs[i + 1];
if (GeoUtils.Equals(pt1.Bulge, 0))
{
yield return(new LineSegment2D(pt1.Position, pt2.Position));
}
else
{
yield return(new CircleArc2D(pt1.Position, pt2.Position, pt1.Bulge));
}
}
}
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 static bool operator ==(Point2D p1, Point2D p2)
{
return
(GeoUtils.Equals(p1.X, p2.X, GeoUtils.EqualsPoint) &&
GeoUtils.Equals(p1.Y, p2.Y, GeoUtils.EqualsPoint));
}
public bool IsZero()
{
return(GeoUtils.Equals(_radian, 0));
}
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 IsWholeCircle()
{
return(GeoUtils.Equals(_radian, PI2));
}
public bool Equals(Angle x, Angle y)
{
return(GeoUtils.Equals(x._radian, y._radian));
}
