main/src/georegression/fitting/line/FitLine_F64.java
public static LinePolar2D_F64 polar( List<Point2D_F64> points , double weights[] , LinePolar2D_F64 ret ) {

		final int N = points.size();
		double totalWeight = 0;
		for( int i = 0; i < N; i++ ) {
			totalWeight += weights[i];
		}

		if( totalWeight == 0 )
			return null;

		if( ret == null )
			ret = new LinePolar2D_F64();

		double meanX = 0;
		double meanY = 0;

		for( int i = 0; i < N; i++ ) {
			Point2D_F64 p = points.get(i);
			double w = weights[i];
			meanX += w*p.x;
			meanY += w*p.y;
		}
		meanX /= totalWeight;
		meanY /= totalWeight;

		double top = 0;
		double bottom = 0;

		for( int i = 0; i < N; i++ ) {
			Point2D_F64 p = points.get(i);
			double w = weights[i];
			double dx = meanX - p.x;
			double dy = meanY - p.y;

			top += w*dx*dy;
			bottom += w*(dy*dy - dx*dx);
		}
		top /= totalWeight;
		bottom /= totalWeight;

		ret.angle = Math.atan2(-2.0*top , bottom)/2.0;
		ret.distance = (double)( meanX*Math.cos(ret.angle) + meanY*Math.sin(ret.angle));

		return ret;
	}
public static LinePolar2D_F64 polar( List<Point2D_F64> points , double weights[] , LinePolar2D_F64 ret ) {

		final int N = points.size();
		double totalWeight = 0;
		for( int i = 0; i < N; i++ ) {
			totalWeight += weights[i];
		}

		if( totalWeight == 0 )
			return null;

		if( ret == null )
			ret = new LinePolar2D_F64();

		double meanX = 0;
		double meanY = 0;

		for( int i = 0; i < N; i++ ) {
			Point2D_F64 p = points.get(i);
			double w = weights[i];
			meanX += w*p.x;
			meanY += w*p.y;
		}
		meanX /= totalWeight;
		meanY /= totalWeight;

		double top = 0;
		double bottom = 0;

		for( int i = 0; i < N; i++ ) {
			Point2D_F64 p = points.get(i);
			double w = weights[i];
			double dx = meanX - p.x;
			double dy = meanY - p.y;

			top += w*dx*dy;
			bottom += w*(dy*dy - dx*dx);
		}
		top /= totalWeight;
		bottom /= totalWeight;

		ret.angle = Math.atan2(-2.0*top , bottom)/2.0;
		ret.distance = (double)( meanX*Math.cos(ret.angle) + meanY*Math.sin(ret.angle));

		return ret;
	}
public static LinePolar2D_F64 polar ( List < Point2D_F64 > points , double weights [ ] , LinePolar2D_F64 ret ) { final int N = points . size ( ) ; double totalWeight = 0 ; for ( int i = 0 ; i < N ; i ++ ) { totalWeight += weights [ i ] ; } if ( totalWeight == 0 ) return null ; if ( ret == null ) ret = new LinePolar2D_F64 ( ) ; double meanX = 0 ; double meanY = 0 ; for ( int i = 0 ; i < N ; i ++ ) { Point2D_F64 p = points . get ( i ) ; double w = weights [ i ] ; meanX += w * p . x ; meanY += w * p . y ; } meanX /= totalWeight ; meanY /= totalWeight ; double top = 0 ; double bottom = 0 ; for ( int i = 0 ; i < N ; i ++ ) { Point2D_F64 p = points . get ( i ) ; double w = weights [ i ] ; double dx = meanX - p . x ; double dy = meanY - p . y ; top += w * dx * dy ; bottom += w * ( dy * dy - dx * dx ) ; } top /= totalWeight ; bottom /= totalWeight ; ret . angle = Math . atan2 ( - 2.0 * top , bottom ) / 2.0 ; ret . distance = ( double ) ( meanX * Math . cos ( ret . angle ) + meanY * Math . sin ( ret . angle ) ) ; return ret ; }
<p>
Computes the weighted best fit line to the set of points using the polar line equation. The solution
is optimal in the Euclidean sense, see [1] for more details.
</p>

<p>
[1] K. Arras, R. Siegwart, "Feature Extraction and Scene Interpretation for Map-Based Navigation
and Map Building" Proc. SPIE, Mobile Robotics XIII, Vol. 3210, 1997
</p>

@param points Set of points on the line.
@param weights Weight for each point.  weights[i] &ge; 0
@param ret Storage for the line.  If null a new line will be declared.
@return Best fit line. or null if sum of weights is zero
<p > Computes the weighted best fit line to the set of points using the polar line equation . The solution is optimal in the Euclidean sense see [ 1 ] for more details . < / p >