機場跑道入侵檢測（C++、Qt）

實現原理：

1、讀取並解析機場跑道、車道數據，顯示和存儲。
2、根據本機的經緯度座標，確定本機所在跑道，並計算出一個多邊形區域。
3、實時獲取它機、車輛座標數據，判斷是否位於本機起飛跑道的多邊形範圍內。
4、如果它機、車輛座標位於本機跑道，則預警。

通過面積法，判斷點P是否在四邊形(A,B,C,D)內。如果在四邊形內,則四邊形的面積=面積(P,A,B)+面積(P,B,C)+面積(P,C,D)+面積(P,D,A),反之不在四邊形內。

如下圖：

效果

視頻地址：https://www.bilibili.com/video/BV1bK4y147R1/

關鍵代碼（只提供思路和部分代碼，並非完整代碼。）

	//judge quadrangle is contain point p
	bool isInQuadrangle(QVector<QPointF> &pointfs, QPointF p);

	//calculate triangle area
	double getTriangleArea(QPointF p1, QPointF p2, QPointF p3);

	//get Vertex of Quadrangle 
	void getQuadrangleVertex(QPointF m1, QPointF m2, float direction, double len, QVector<QPointF> &pointfs);

	//polygon vertexes can be sorted clockwise
	void clockwiseSort(QVector<QPointF> & vPoints);

	bool PointCmp(const QPointF &a, const QPointF &b, const QPointF &center);

	double getAngle(const QPointF &oldPos, const QPointF &newPos) const;

//跑道入侵檢測
void runwayIncursionCheck(std::vector<OtherAircraftInfo> &aircraftInfo)
{
	for (std::vector<OtherAircraftInfo>::iterator itr = aircraftInfo.begin(); itr != aircraftInfo.end(); itr++)
	{
		if (mCurrentRunWay.count() == 4)
		{
			if (mCalculate.isInQuadrangle(mCurrentRunWay, QPointF(itr->lon, itr->lat)))
			{
				itr->incursion = true;
				qWarning() << "Runway Incursion: " << itr->ID;
			}
			else
			{
				itr->incursion = false;
			}
		}		
	}
}

計算本機所在的跑道
void whichRunWay(const AircraftInfo & aircraftInfo)
{
	//foreach runWay
	mCurrentRunWay.clear();
	for (int runwayIndex = 0; runwayIndex < mRunWays.count() ; runwayIndex++)
	{		
		QVector<QPointF> runWay(4);
		double angle = mCalculate.getAngle(mRunWays[runwayIndex].at(0), mRunWays[runwayIndex].at(1));  //calculate runway angle
		mCalculate.getQuadrangleVertex(mRunWays[runwayIndex].at(0), mRunWays[runwayIndex].at(1), angle , 60/1852.0, runWay);
		if (mCalculate.isInQuadrangle(runWay, QPointF(aircraftInfo.lon, aircraftInfo.lat)))
		{
			mCurrentRunWay = runWay;
		}
	}
}

//通過一個已知座標點、方位角、和距離，計算另一個點的經緯度座標
void CalculatePositionByAngle(double & DestLat, double & DestLon, double orgLat, double orgLon, double distNM, double angle)
{
    double rad_lati = ToRadian(orgLat);
    double rad_longi = ToRadian(orgLon);
    double Ec = PolarRadiusMeter + (EquatorRadiusMeter - PolarRadiusMeter)*(90.0 - orgLat) / 90.0;
    double Ed = EquatorRadiusMeter * cos(rad_lati);

    double difx = distNM * 1852.0 * cos(ToRadian(90 - angle));
    double dify = distNM * 1852.0 * sin(ToRadian(90 - angle));

    DestLat = ToAngle(1.0*dify / Ec + rad_lati);
    DestLon = ToAngle(1.0*difx / Ed + rad_longi);

    if (DestLon > 180)
    {
        DestLon = DestLon - 360;
    }
    if (DestLat > 180)
    {
        DestLat = DestLat - 360;
    }
}

const qreal pi = 3.141592653589793238462643383;
//判斷座標點，是否在一個四邊形區域內
bool isInQuadrangle(QVector<QPointF> &pointfs, QPointF p)
{
	double dTriangle = getTriangleArea(pointfs.at(0), pointfs.at(1), p) + getTriangleArea(pointfs.at(1), pointfs.at(2), p) + getTriangleArea(pointfs.at(2), pointfs.at(3), p) + getTriangleArea(pointfs.at(3), pointfs.at(0), p);
	double dQuadrangle = getTriangleArea(pointfs.at(0), pointfs.at(1), pointfs.at(2)) + getTriangleArea(pointfs.at(2), pointfs.at(3), pointfs.at(0));

	
	if ((dTriangle >0) && (dQuadrangle > 0) && (qAbs(dTriangle - dQuadrangle) < 0.00001))
	{
		qDebug() << "isInQuadrangle: " << qAbs(dTriangle - dQuadrangle);
		return true;
	}
	else
		return false;
	//return dTriangle == dQuadrangle;
}
//計算一個三角形的面積
double getTriangleArea(QPointF p1, QPointF p2, QPointF p3)
{
	return qAbs((p1.x()*p2.y() + p2.x()*p3.y() + p3.x()*p1.y() - p2.x()*p1.y() - p3.x()*p2.y() - p1.x()*p3.y()) / 2.0);
}

//根據四邊形兩條對邊的中線，方位、寬度，計算出四個頂點座標
void getQuadrangleVertex(QPointF m1, QPointF m2, float direction, double len, QVector<QPointF> &pointfs)
{
	float angle1 = 0.0;
	float angle2 = 0.0;

	angle1 = (direction + 90.0) > 360.0 ? direction + 90.0 - 360.0 : direction + 90.0;
	angle2 = (direction + 270.0) > 360.0 ? direction + 270.0 - 360.0 : direction + 270.0;

	Conversions cver;
	cver.CalculatePositionByAngle(pointfs[0].ry(), pointfs[0].rx(), m1.y(), m1.x(), len / 2, angle1);
	cver.CalculatePositionByAngle(pointfs[1].ry(), pointfs[1].rx(), m1.y(), m1.x(), len / 2, angle2);
	cver.CalculatePositionByAngle(pointfs[2].ry(), pointfs[2].rx(), m2.y(), m2.x(), len / 2, angle1);
	cver.CalculatePositionByAngle(pointfs[3].ry(), pointfs[3].rx(), m2.y(), m2.x(), len / 2, angle2);

	clockwiseSort(pointfs);
}

//四邊形四個頂點 按照順時針排序
void clockwiseSort(QVector<QPointF>& vPoints)
{
	//calculate centre point
	QPointF center;
	double x = 0, y = 0;
	for (int i = 0; i < vPoints.size(); i++)
	{
		x += vPoints[i].x();
		y += vPoints[i].y();
	}
	center.rx() = (int)x / vPoints.size();
	center.ry() = (int)y / vPoints.size();
	
	//sort point
	for (int i = 0; i < vPoints.size(); i++)
	{
		for (int j = 0; j < vPoints.size() - i - 1; j++)
		{
			if (PointCmp(vPoints[j], vPoints[j + 1], center))
			{
				QPointF tmp = vPoints[j];
				vPoints[j] = vPoints[j + 1];
				vPoints[j + 1] = tmp;
			}
		}
	}
}

bool PointCmp(const QPointF &a, const QPointF &b, const QPointF &center)
{
	if (a.x() >= 0 && b.x() < 0)
		return true;
	/*if (a.x() == 0 && b.x() == 0)
		return a.y() > b.y();*/
	//向量OA和向量OB的叉積
	int det = (a.x() - center.x()) * (b.y() - center.y()) - (b.x() - center.x()) * (a.y() - center.y());
	if (det < 0)
		return true;
	if (det > 0)
		return false;
	//向量OA和向量OB共線，以距離判斷大小
	int d1 = (a.x() - center.x()) * (a.x() - center.x()) + (a.y() - center.y()) * (a.y() - center.y());
	int d2 = (b.x() - center.x()) * (b.x() - center.y()) + (b.y() - center.y()) * (b.y() - center.y());
	return d1 > d2;
}
//根據兩個點，計算方位
double getAngle(const QPointF &oldPos, const QPointF &newPos) const
{
	//根據兩個點的經緯度，以一個點（old）爲座標中心，y軸正方向爲正北方向（即爲 0°），求出另一個點（new）關於正北方向的角度（0° ~ 360°）

	double a = newPos.x() - oldPos.x();  //經度差
	double b = newPos.y() - oldPos.y();    //緯度差
	double c = hypot(fabs(a), fabs(b));
	double cosy = 0.0;
	double angle = 0;

	if (a > 0 && b > 0)         // 判斷road點在user點的東北位置
	{
		cosy = b / c;
		angle = 0;
	}
	else if ((a == 0) && (b > 0))  //在正北位置
	{
		angle = -90;
	}
	else if ((a > 0) && (b < 0))   // 判斷road點在user點的東南位置
	{
		cosy = a / c;
		angle = 90;
	}
	else if ((a > 0) && (b == 0))  //在正東位置
	{
		angle = 90;
	}
	else if ((a < 0) && (b < 0))    // 判斷road點在user點的西南位置
	{
		cosy = fabs(b) / c;
		angle = 180;
	}
	else if ((a == 0) && (b < 0))   //在正南位置
	{
		angle = 90;
	}
	else if ((a < 0) && (b > 0))    // 判斷road點在user點的西北位置
	{
		cosy = fabs(a) / c;
		angle = 270;
	}
	else if ((a < 0) && (b == 0))   //在正西位置
	{
		angle = 180;
	}

	double m = acos(cosy);
	//n 即以正北爲 0 的總角度
	double n = (m / pi) * 180 + angle;

	return n;
}