一、本節課程
C++ ARX二次開發點和閉合多段線的位置關係
二、本節要講解的知識點
結合自己的業務場景，想想自己開發中可能碰到的點和閉合多段線相對關係的需求：統計多段線內部的所有圖塊；還可以拓展判斷任意曲線跟多段線的相對關係。
三、具體內容
- 計算機圖形學、計算幾何。判斷點是否在多邊形內部，一般有以下方法：
- 叉乘判斷（適合凸多邊形）：如果將多邊形的所有頂點按逆時針排序，那麼判斷點和每一條邊的位置關係，如果點在多邊形每一條邊的左側，那麼點就在我們的多邊形內部。
- 射線法：從給定點出發，沿着X軸正方向或者負方向做一條射線（射線可能跟多邊形沒有交點），計算射線跟多邊形的交點數量，如果是奇數個交點，在內部；偶數個交點在外部。處理下點就在多邊形的頂點上的特例。
- 本節提供的算法的思路是：
- 計算點到多段線的最近點，如果兩點之間的距離少於容差，則認爲點就在多段線上。
- 從給定點（要判斷的點）出發，沿最近點到給定點（要判斷的點）的方向 做一個射線（之所以這麼來做射線，是爲了儘可能早可能早判斷出點不在多邊形內部的情況），計算射線和多段線的交點。如果交點中包含了多段線的頂點，就將射線旋轉2度繼續進行判斷；如果不包含多段線的頂點，則根據交點個數來判斷點和多段線的位置關係。
工具函數的添加：
- MathUtil.h頭文件中添加：
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static bool IsEqual(double a,double b,double tol=1.0*10E-7); static int GetRand(int minValue,int maxValue); static double Round(double a,int precision); static int Round(double a); |
- MathUtil.cpp文件中添加：
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bool CMathUtil::IsEqual(double a,double b,double tol/*=1.0*10E-7*/) { return (fabs(a-b)<tol); } //對一個數按照指定的小數位數進行四捨五入 double CMathUtil::Round(double a,int precision) { return (floor(a*pow(10.0,precision)+0.5))/pow(10.0,precision); } int CMathUtil::Round(double a) { return (int)(a+0.5); } int CMathUtil::GetRand(int minValue,int maxValue) { assert(maxValue-minValue>0); int value=rand(); int rc=minValue+(int)CMathUtil::Round(((double)value)/RAND_MAX*(maxValue-minValue));//將生成的隨機數映射到區間上。 return rc; } |
- GePointUtil.h頭文件中添加：
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static bool IsEqual(const AcGePoint3d &firstPoint,const AcGePoint3d &secondPoint,double tol=1.0E-7); static bool IsEqual(const AcGePoint2d &firstPoint,const AcGePoint2d &secondPoint,double tol=1.0E-7); static int FindPoint(const AcGePoint3dArray &points,const AcGePoint3d &point,double tol=1.0E-7); static int FindPoint(const AcGePoint2dArray &points,const AcGePoint2d &point,double tol=1.0E-7); static void FilterEqualPoints(AcGePoint3dArray &points,double tol=1.0E-7); static void FilterEqualPoints(AcGePoint3dArray &points,const AcGePoint2d &pt,double tol=1.0E-7); |
- GePointUtil.cpp頭文件中添加：
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bool CGePointUtil::IsEqual(const AcGePoint3d &firstPoint,const AcGePoint3d &secondPoint,double tol/*=1.0E-7*/) { return (fabs(firstPoint.x-secondPoint.x)<tol && fabs(firstPoint.y-secondPoint.y)<tol && fabs(firstPoint.z-secondPoint.z)<tol); }
bool CGePointUtil::IsEqual(const AcGePoint2d &firstPoint,const AcGePoint2d &secondPoint,double tol/*=1.0E-7*/) { return (fabs(firstPoint.x-secondPoint.x)<tol && fabs(firstPoint.y-secondPoint.y)<tol ); } //在數組中查找點，返回點在數組中的索引，如果沒有找到點就返回-1 int CGePointUtil::FindPoint(const AcGePoint3dArray &points,const AcGePoint3d &point,double tol/*=1.0E-7*/) { for (int i=0;i<points.length();i++) { if (IsEqual(points[i],point,tol)) { return i; } } return -1; }
//在數組中查找點，返回點在數組中的索引，如果沒有找到點就返回-1 int CGePointUtil::FindPoint(const AcGePoint2dArray &points,const AcGePoint2d &point,double tol/*=1.0E-7*/) { for (int i=0;i<points.length();i++) { if (IsEqual(points[i],point,tol)) { return i; } } return -1; }
//點數組本身去重複點 void CGePointUtil::FilterEqualPoints( AcGePoint3dArray &points,double tol/*=1.0E-7*/) { for (int i=points.length()-1;i>0;i--) { for (int j=0;j<i;j++) { if (CMathUtil::IsEqual(points[i].x,points[j].x,tol)&& CMathUtil::IsEqual(points[i].y,points[j].y,tol)&& CMathUtil::IsEqual(points[i].z,points[j].z,tol)) { points.removeAt(i); break; } } } } void CGePointUtil::FilterEqualPoints( AcGePoint3dArray &points,const AcGePoint2d &pt,double tol/*=1.0E-7*/) { AcGePoint3dArray tempPoints; for (int i=0;i<points.length();i++) { if (CConvertUtil::ToPoint2d(points[i]).distanceTo(pt)>tol) { tempPoints.append(points[i]); } } points=tempPoints; } |
- 在PolylineUtil.h中添加：
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static bool PointIsPolyVert(AcDbPolyline* pPoly,const AcGePoint2d &pt,double tol=1.0E-7); static void IntersectWithGeRay(AcDbPolyline *pPoly,const AcGeRay2d &geRay,AcGePoint3dArray &intPoints,double tol=1.0E-7); static int PtRelationToPoly(AcDbPolyline *pPoly,const AcGePoint2d &pt,double tol=1.0E-7); |
- 在PolylineUtil.cpp中添加：
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void CPolylineUtil::IntersectWithGeRay(AcDbPolyline *pPoly,const AcGeRay2d &geRay,AcGePoint3dArray &intPoints,double tol/*=1.0E-7*/) { intPoints.setLogicalLength(0); AcGePoint2dArray intPoints2d;
AcGeTol geTol; geTol.setEqualPoint(tol); for (int i=0;i<(int)(pPoly->numVerts());i++) { if (i<(int)(pPoly->numVerts())-1||pPoly->isClosed()==Adesk::kTrue) { double bugle=0; pPoly->getBulgeAt(i,bugle); if (fabs(bugle)<1.0E-7) { AcGeLineSeg2d geLine; Acad::ErrorStatus es=pPoly->getLineSegAt(i,geLine); AcGePoint2d intPoint; if (geLine.intersectWith(geRay,intPoint,geTol)==Adesk::kTrue) { if (CGePointUtil::FindPoint(intPoints2d,intPoint,tol)<0) { intPoints2d.append(intPoint); } } } else { AcGeCircArc2d geArc; pPoly->getArcSegAt(i,geArc); AcGePoint2d pt1,pt2; int count=0; if (geArc.intersectWith(geRay,count,pt1,pt2,geTol)==Adesk::kTrue) { if (CGePointUtil::FindPoint(intPoints2d,pt1,tol)<0) { intPoints2d.append(pt1); } if (count>1 && CGePointUtil::FindPoint(intPoints2d,pt2,tol)<0) { intPoints2d.append(pt2); } } } } } double z=pPoly->elevation(); for (int i=0;i<intPoints2d.length();i++) { intPoints.append(AcGePoint3d(intPoints2d[i].x,intPoints2d[i].y,z)); } }
int CPolylineUtil::PtRelationToPoly(AcDbPolyline *pPoly,const AcGePoint2d &pt,double tol/*=1.0E-7*/) { assert (pPoly); //1.如果點在多段線的最近點和給定的點重合，表示點在多段線上 AcGePoint3d closestPoint; pPoly->getClosestPointTo(CConvertUtil::ToPoint3d(pt,pPoly->elevation()),closestPoint);
if (fabs(closestPoint.x-pt.x)<tol && fabs(closestPoint.y-pt.y)<tol) { return 0; } //2 第一個射線的方向是從最近點到當前點，起點是當前點 //射線的起點是pt，方向從最近點到pt，如果反向做判斷，則最近點距離pt太近的時候，最近點也會被作爲一個交點（這個交點不太容易被排除掉） //此外，這樣的射線方向很容易判斷出點不在內部的情況 AcGeVector3d vec(-(closestPoint[X]-pt[X]),-(closestPoint[Y]-pt[Y]),0); AcGeRay2d geRay(AcGePoint2d(pt.x,pt.y),AcGePoint2d(pt.x+vec.x,pt.y+vec.y));
//3、射線與多段線計算交點 AcGePoint3dArray intPoints; IntersectWithGeRay(pPoly,geRay,intPoints,1.0E-4);
// CGePointUtil::FilterEqualPoints(intPoints,1.0E-4);
RETRY: if(intPoints.length()==0) { return -1; } else { CGePointUtil::FilterEqualPoints(intPoints,CConvertUtil::ToPoint2d(closestPoint));
for (int i=intPoints.length()-1;i>=0;i--) { if ( (intPoints[i][X]-pt[X])*(closestPoint[X]-pt[X])>=0 && (intPoints[i][Y]-pt[Y])*(closestPoint[Y]-pt[Y])>=0 ) { intPoints.removeAt(i); } }
int count=intPoints.length(); for (int i=0;i<intPoints.length();i++) { if (PointIsPolyVert(pPoly,CConvertUtil::ToPoint2d(intPoints[i]),1.0E-4)) { if (PointIsPolyVert(pPoly,AcGePoint2d(pt.x,pt.y),1.0E-4)) { return 0; }
vec=vec.rotateBy(0.035,AcGeVector3d::kZAxis); geRay.set(AcGePoint2d(pt.x,pt.y),AcGePoint2d(pt.x+vec.x,pt.y+vec.y)); intPoints.setLogicalLength(0); IntersectWithGeRay(pPoly,geRay,intPoints,1.0E-4); goto RETRY; } } if (count%2==0) { return -1; } else { return 1; } } } |
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