/// <summary>
/// 判断点是否在线上
/// </summary>
/// <param name="p">点</param>
/// <param name="line">线</param>
/// <returns>在线上则返回true否则返回false</returns>
/// 公式:Point on the Line of the Segment:(P - A)×(B - A) = 0
public static bool PointOnTheLine(Point p, LineSegment line)
{
if (!Rectangle.PointInRectangle(p, new Rectangle(line)))
return false;
double cross = Point.CrossProduct(p - line.A, line.B - line.A);
return Math.Abs(cross) < Polygon.DeviationValue;
}
public Rectangle(LineSegment line)
{
X = Math.Min(line.A.X, line.B.X);
Y = Math.Min(line.A.Y, line.B.Y);
Width = Math.Max(line.A.X, line.B.X) - X;
Height = Math.Max(line.A.Y, line.B.Y) - Y;
}
/// <summary>
/// 判断点在线的哪一边
/// </summary>
/// <param name="p">点</param>
/// <param name="line">线</param>
/// <returns>小于0则左边，大于0则右边，等于0则在线上</returns>
public static LineSideType PointOnTheLineWhichSide(Point p, LineSegment line)
{
double cross = Point.CrossProduct(p - line.A, line.B - line.A);
bool result = Math.Abs(cross) < Polygon.DeviationValue;
if (result)
return LineSideType.On;
result = cross < 0;
if (result)
return LineSideType.Left;
else
return LineSideType.Right;
}
/// <summary>
/// 判断两条线是否相交
/// </summary>
/// <param name="line1">线1</param>
/// <param name="line2">线2</param>
/// <returns>有相交返回true,否则返回false</returns>
public static bool LineSegmentIntersection(LineSegment line1, LineSegment line2)
{
if (!Rectangle.CheckTwoRectanglesIntersect(new Rectangle(line1), new Rectangle(line2)))
return false;
LineSideType line1ASideType = PointOnTheLineWhichSide(line1.A, line2);
LineSideType line1BSideType = PointOnTheLineWhichSide(line1.B, line2);
if (!Check(line1ASideType, line1BSideType))
return false;
line1ASideType = PointOnTheLineWhichSide(line2.A, line1);
line1BSideType = PointOnTheLineWhichSide(line2.B, line1);
if (!Check(line1ASideType, line1BSideType))
return false;
return true;
}
public static bool PointInTheMaxRectangle(Point p, Polygon polygon)
{
double maxX = polygon.Points.Max(u => u.X);
double minX = polygon.Points.Min(u => u.X);
double maxY = polygon.Points.Max(u => u.Y);
double minY = polygon.Points.Min(u => u.Y);
LineSegment line = new LineSegment(new Point(maxX, maxY), new Point(minX, minY));
Rectangle rec = new Rectangle(line);
return Rectangle.PointInRectangle(p, rec);
}
private static bool LineSegmentIntersectionInPolygonLine(Point p, Polygon polygon)
{
int intersectionCount = 0;
double maxX = GetMaxPointX(polygon.Points);
if (p.X > maxX)
{
maxX = p.X + 1;
}
else
{
maxX += 1;
}
LineSegment mainLine = new LineSegment(p, new Point(maxX, p.Y));
for (int i = 0, j = 1; j < polygon.Points.Count; i++, j++)
{
LineSegment line = new LineSegment(polygon.Points[i], polygon.Points[j]);
bool result = LineSegment.LineSegmentIntersection(mainLine, line);
if (result)
intersectionCount++;
}
LineSegment lastLine = new LineSegment(polygon.Points[polygon.Points.Count - 1], polygon.Points[0]);
bool lastResult = LineSegment.LineSegmentIntersection(mainLine, lastLine);
if (lastResult)
intersectionCount++;
if ((intersectionCount % 2) == 0)
return false;
return true;
}
private static bool CheckPointOnPolygonLine(Point p, Polygon polygon)
{
for (int i = 0, j = 1; j < polygon.Points.Count; i++, j++)
{
LineSegment line = new LineSegment(polygon.Points[i], polygon.Points[j]);
if (LineSegment.PointOnTheLine(p, line))
return true;
}
LineSegment lastLine = new LineSegment(polygon.Points[polygon.Points.Count - 1], polygon.Points[0]);
if (LineSegment.PointOnTheLine(p, lastLine))
return true;
return false;
}