GIS中的基本算法之判断点是否在直线上
注：算法的原理描述均来自《地理信息系统算法基础》一书；
原理：设点为Q，线段为P1P2，判断点Q在线段上的依据是：(Q-P1)×(P2-P1)=0（注意这里的减法和乘法均是向量算法，有不懂向量运算原理的可以在网上搜一下）且Q在以P1P2为对角定点的矩形内。前者保证Q点在直线上，后者保证Q点不在线段的延长线或反向延长线上，这一步骤其实就是分别判断一下Q点的x、y坐标是否在P1、P2点的x、y坐标之间；
实现：
#region==判断点是否在直线上 ==
/// <summary>
/// Determines whether [is point on line] [the specified points].
/// </summary>
/// <param name="points">The point.</param>
/// <param name="lineStartPoint">The line start point.</param>
/// <param name="lineEndPoint">The line end point.</param>
/// <returns>
/// <c>true</c> if [is point on line] [the specified points]; otherwise, <c>false</c>.
/// </returns>
public static bool isPointOnLine(Point point,Point lineStartPoint,Point lineEndPoint )
{
//(P-P1)*(P2-P1)=0 向量差乘是否为0;
double X21,Y21,X10,Y10;
X21 = lineEndPoint.X-lineStartPoint.X;
Y21 = lineEndPoint.Y-lineStartPoint.Y;
X10 = point.X-lineStartPoint.X;
Y10 = point.Y-lineStartPoint.Y;
//向量乘积为0则该点在线上
double vectorValue = X21*Y10-X10*Y21;
if (vectorValue != 0.0)
return false;
else
{
double xMin = Math.Min(lineStartPoint.X,lineEndPoint.X);
double xMax = Math.Max(lineEndPoint.X,lineStartPoint.X);
double yMin = Math.Min(lineStartPoint.Y,lineEndPoint.Y);
double yMax = Math.Max(lineEndPoint.Y,lineStartPoint.Y);
//判断点是否是在该线的延长线上
if (xMin <= point.X && point.X <= xMax && yMin <= point.Y && point.Y <= yMax)
return true;
else
return false;
}
}
#endregion转载自：https://blog.csdn.net/kangming310/article/details/9397287
