在CAD的二次开发中，点和多段线的关系是一个非常重要且常见的问题，本文实现例程以张帆所著《ObjectARX 开发基础与实例教程》为基础，并完善和修复了部分问题。

1 基本思路

 点和多段线的关系判断算法有两个思路：叉乘判断法（适用于凸多边形）和射线法，本文以射线法进行代码实现。其基本思路为：

1. 如果点在多段线上，返回该结果。
2. 从给定点出发，沿某个方向做一条射线，计算射线与多边形交点的数量。如果交点数量为奇数，那么点在图形内部；如果交点数量为偶数，那么点在图形外部。
3. 在第2条的基础上，排除交点在多段线的顶点上的情况；若出现该情况，需要旋转射线重新判断。

2 相关知识点

2.1 ECS坐标系概述

 在该例程中，有一个关键点是理解ECS(或者OCS)坐标系统。
 ECS是实体（对象）坐标系，其原点是WCS的原点，X和Y轴所在平面的法向量是实体的法向量。ECS的 X 轴和Y轴的方向由任意轴算法确定，也就是X、Y轴的方向是由法向量与 WCS 的关系来确定的。因此，ECS的X 轴和Y轴是唯一且仅由法向量决定的。另外，ECS的Z坐标是指xy平面距离WCS原点的距离（有正负）。
 在ObjectARX有一个暴露的接口可以完成WCS→ECS的转换

bool acdbWcs2Ecs(ads_point p,ads_point q,ads_point norm,bool vec);

 上述接口的实现应该是下列办法

//将WCS转为一个平面实体的ECS坐标
int Wcs2Ecs(const AcGeVector3d vtNorm, const AcGePoint3d ptWcs, BOOL bDisp, AcGePoint3d& ptEcs)
{struct resbuf fromrb, torb;fromrb.restype = RTSHORT;fromrb.resval.rint = 0; // WCS  torb.restype = RT3DPOINT;ads_point_set(asDblArray(vtNorm), torb.resval.rpoint);return acedTrans(asDblArray(ptWcs), &fromrb, &torb, bDisp, asDblArray(ptEcs));
}

 理解了上述知识点，我们之后在判断射线和多段线关系的时候，就可以把射线转为多段线的ECS坐标，然后在多段线所在的ECS平面上，比较射线和多段线的每一条线段的相交关系。从而可以优化算法。

2.2 其他点坐标转换接口

1. 点或向量坐标变换

函数名	作用
acdbUcs2Ecs	UCS→ECS
acdbEcs2Ucs	ECS→UCS
acdbUcs2Wcs	UCS→WCS
acdbWcs2Ucs	WCS→UCS
acdbEcs2Wcs	ECS→WCS
acdbWcs2Ecs	WCS→ECS

2. AcGePoint3d和ads_point互转

函数名	作用
AcGePoint3d (AcGePoint2d ) → ads_point	asDblArray
ads_point → AcGePoint3d (AcGePoint2d )	aspnt3d 或 asPnt2d

2.3 如何获取多段线的顶点ECS坐标

 多段线获取顶点坐标有两种重载形式：

Acad::ErrorStatus getPointAt(unsigned int, AcGePoint3d& pt
) const;
Acad::ErrorStatus getPointAt(unsigned int index, AcGePoint2d& pt
) const;

 其中第一种获取的是顶点的WCS坐标，第二种获取的是顶点的ECS 2D坐标。这个区别一定要看仔细。

3 实现例程

3.1 接口实现

 该例程在张帆所著方法的基础上，增加了对UCS坐标系的支持。在此，再次向原书作者表达敬意。

#include "dbxutil.h"
#define POINT_POLY_INSIDE 1
#define POINT_POLY_OUTSIDE 0
#define POINT_POLY_ONEDGE 2// 在数组中查找某个点，返回点在数组中的索引，未找到则返回-1
int FindPoint(const AcGePoint2dArray &points, const AcGePoint2d &point, double tol /*= 1.0E-7*/)
{TADSGePoint3d pt1;TADSGePoint3d pt2(point);for (int i = 0; i < points.length(); i++){pt1 = points[i];if (IsEqual(pt1, pt2, tol)){return i;}}return -1;
}//-----------------------------------------------------------------------------+
//=Description:     几何类射线和多段线的交点
//=Parameter:	   	pPoly[in]	多段线
//=Parameter:	   	geRay[in]	射线（位于多段线的OCS平面上）
//=Parameter:	   	arptIntersect[in] 返回的交点（坐标系为多段线的OCS坐标系）
//=Parameter:	   	tol[in]		容差
//-----------------------------------------------------------------------------+
static void IntersectWithGeRay(const AcDbPolyline *pPoly, const AcGeRay2d &geRay, AcGePoint2dArray& arptIntersect, double tol = 1.0E-7)
{arptIntersect.removeAll();//设置容差，该容差为两点相同时的容差AcGeTol geTol;geTol.setEqualPoint(tol);// 多段线的每一段分别与射线计算交点AcGePoint2d pt2d;for (int i = 0; i < pPoly->numVerts(); i++){if (i < pPoly->numVerts() - 1 || pPoly->isClosed() == Adesk::kTrue){double dBulge = 0;pPoly->getBulgeAt(i, dBulge);if (fabs(dBulge) < 1.0E-7){// 构建几何类的线段来计算交点AcGeLineSeg2d geLine;Acad::ErrorStatus es = pPoly->getLineSegAt(i, geLine);AcGePoint2d ptIntersect;if (geLine.intersectWith(geRay, ptIntersect, geTol) == Adesk::kTrue){if (FindPoint(arptIntersect, ptIntersect, tol) < 0)arptIntersect.append(ptIntersect);}}else{// 构建几何类的圆弧来计算交点AcGeCircArc2d geArc;pPoly->getArcSegAt(i, geArc);AcGePoint2d pt1, pt2;int iCount = 0;if (Adesk::kTrue == geArc.intersectWith(geRay, iCount, pt1, pt2, geTol)){if (FindPoint(arptIntersect, pt1, tol) < 0)arptIntersect.append(pt1);if (iCount > 1 && FindPoint(arptIntersect, pt2, tol) < 0)arptIntersect.append(pt2);}}}}
}// 点是否是多段线的顶点
static bool PointIsPolyVert(AcDbPolyline *pPoly, const AcGePoint2d &pt, double tol)
{AcGeTol geTol;geTol.setEqualPoint(tol);AcGePoint2d ptVert;for (int i = 0; i < (int)pPoly->numVerts(); i++){pPoly->getPointAt(i, ptVert);if (ptVert.isEqualTo(pt, geTol)){return true;}}return false;
}// 从数组中过滤掉重复点
static void FilterEqualPoints(AcGePoint2dArray &points, double tol = 1.0E-7)
{AcGeTol geTol;geTol.setEqualPoint(tol);for (int i = points.length() - 1; i > 0; i--){for (int j = 0; j < i; j++){if (points[i].isEqualTo(points[j],geTol)){points.removeAt(i);break;}}}
}// 从数组中过滤掉某个点
static void FilterEqualPoints(AcGePoint2dArray &points, const AcGePoint2d &pt, double tol = 1.0E-7)
{AcGeTol geTol;geTol.setEqualPoint(tol);for (int i = points.length() - 1; i >= 0; i--)if (points[i].isEqualTo(pt, geTol))points.removeAt(i);
}//-----------------------------------------------------------------------------+
//=Description:     判断点是否在多段线内部
//=Return:          0多段线外，1多段线内，2多段线上
//=Parameter:	   	pPoly[in] 
//=Parameter:	   	ptPickWcs[in] 
//=Parameter:	   	tol[in] 
//-----------------------------------------------------------------------------+
int IsPointInPoly(AcDbPolyline *pPoly, const AcGePoint3d &ptPickWcs, double tol = 1.0E-7)
{if(!pPoly || !pPoly->isClosed())return POINT_POLY_OUTSIDE;AcGeTol geTol;geTol.setEqualPoint(tol);//转换坐标，将点转为ECS坐标系AcGePoint3d ptPick;acdbWcs2Ecs(asDblArray(ptPickWcs), asDblArray(ptPick), asDblArray(pPoly->normal()), false);//判断点和多段线平面是否共面double dElevation = pPoly->elevation();if (fabs(dElevation - ptPick.z) > tol)return POINT_POLY_OUTSIDE;//如果点到多段线的最近点和给定的点重合，表示点在多段线上AcGePoint3d ptClosestWcs;pPoly->getClosestPointTo(ptPickWcs, ptClosestWcs);if (ptPickWcs.isEqualTo(ptClosestWcs, geTol))return POINT_POLY_ONEDGE;//转换最近点为ECS坐标系下AcGePoint3d ptClosest;acdbWcs2Ecs(asDblArray(ptClosestWcs), asDblArray(ptClosest), asDblArray(pPoly->normal()), false);// 第一个射线的方向是从最近点到当前点，起点是当前点// 射线的起点是pt，方向为从最近点到pt，如果反向做判断，则最近点距离pt太近的时候，// 最近点也会被作为一个交点（这个交点不太容易被排除掉）AcGeVector2d vtRay((ptPick - ptClosest).x, (ptPick - ptClosest).y);AcGeRay2d geRay(AcGePoint2d(ptPick.x, ptPick.y), vtRay);// 判断点和多段线的位置关系while (true){bool bContinue = false;AcGePoint2dArray arptIntersect;IntersectWithGeRay(pPoly, geRay, arptIntersect, 1.0E-4);FilterEqualPoints(arptIntersect, 1.0E-4);// IntersectWith函数经常会得到很近的交点，这些点必须进行过滤if (arptIntersect.length() == 0)return POINT_POLY_OUTSIDE;// 没有交点，表示点在多段线的外部else{//特殊情况1：过滤掉由于射线被反向延长带来的影响,当pt距离最近点比较近的时候，//最近点竟然被当作一个交点,所以，首先删除最近点（如果有的话）FilterEqualPoints(arptIntersect, AcGePoint2d(ptClosest.x, ptClosest.y));//特殊情况2：如果某个交点与最近点在给定点的同一方向，要去掉这个点//,这个点明显不是交点，还是由于intersectwith函数的Bugfor (int i = arptIntersect.length() - 1; i >= 0; i--){if ((arptIntersect[i].x - ptPick.x) * (ptClosest.x - ptPick.x) >= 0 &&(arptIntersect[i].y - ptPick.y) * (ptClosest.y - ptPick.y) >= 0)arptIntersect.removeAt(i);}for (i = 0; i < arptIntersect.length(); i++){if (PointIsPolyVert(pPoly, arptIntersect[i], 1.0E-4))	// 只要有交点是多段线的顶点就重新进行判断{// 处理给定点很靠近多段线顶点的情况(如果与顶点距离很近，就认为这个点在多段线上，因为这种情况没有什么好的判断方法)if (PointIsPolyVert(pPoly, AcGePoint2d(ptPick.x, ptPick.y), 1.0E-4))return POINT_POLY_ONEDGE;// 将射线旋转一个极小的角度(2度)再次判断（假定这样不会再通过上次判断到的顶点）vtRay = vtRay.rotateBy(0.035);geRay.set(AcGePoint2d(ptPick.x, ptPick.y), vtRay);bContinue = true;break;}}if (!bContinue){if (0 == arptIntersect.length() % 2)return POINT_POLY_OUTSIDE;elsereturn POINT_POLY_INSIDE;}}}
}

3.2 测试代码

void CmdPtInPoly()
{struct resbuf* rb = NULL;rb = acutBuildList(RTDXF0, _T("LWPOLYLINE"), RTNONE);TCHAR* prompts[2] = { _T("\n请选择了一个实体:"),_T("\n取消了一个实体") };ads_name ssPick;if (RTNORM == acedSSGet(_T(":S:$-M"), prompts, NULL, rb, ssPick)){ads_name ent;if (RTNORM == acedSSName(ssPick, 0, ent)){AcDbObjectId id;acdbGetObjectId(id, ent);AcDbPolyline* pPoly;if (Acad::eOk == acdbOpenObject(pPoly, id, AcDb::kForRead)){ads_point ptRet;while (RTNORM == acedGetPoint(NULL, _T("\n请任意点选一点:"), ptRet)){//判断点是否在多段线以内int iRelation = IsPointInPoly(pPoly, Ucs2Wcs(ptRet));if (POINT_POLY_INSIDE == iRelation)acutPrintf(_T("\n\t点在多段线内"));else if (POINT_POLY_ONEDGE == iRelation)acutPrintf(_T("\n\t点在多段线上"));else if (POINT_POLY_OUTSIDE == iRelation)acutPrintf(_T("\n\t点在多段线外"));}pPoly->close();}}acedSSFree(ssPick);}acutRelRb(rb);
}

4 实现效果