main/src/georegression/metric/Intersection3D_F64.java
public static boolean intersect(LineParametric3D_F64 line , Sphere3D_F64 sphere ,
									Point3D_F64 a, Point3D_F64 b ) {

		// this equation was found by solving for l:
		// ||(P + V*l) - X0|| == r

		double r2 = sphere.radius*sphere.radius;

		double PP = GeometryMath_F64.dot(line.p,line.p);
		double PV = GeometryMath_F64.dot(line.p,line.slope);
		double PX = GeometryMath_F64.dot(line.p,sphere.center);
		double VV = GeometryMath_F64.dot(line.slope,line.slope);
		double VX = GeometryMath_F64.dot(line.slope,sphere.center);
		double XX = GeometryMath_F64.dot(sphere.center,sphere.center);

		// Coefficients in the quadratic equation
		double A = VV;
		double B = 2.0*(PV-VX);
		double C = PP+XX-2.0*PX-r2;

		// solve for the quadratic equation
		double inner = B*B - 4.0*A*C;
		if( inner < 0 )
			return false;
		double sqrt = Math.sqrt(inner);

		double t0 = (-B + sqrt)/(2.0*A);
		double t1 = (-B - sqrt)/(2.0*A);

		line.setPointOnLine(t0,a);
		line.setPointOnLine(t1,b);

		return true;
	}
public static boolean intersect(LineParametric3D_F64 line , Sphere3D_F64 sphere ,
									Point3D_F64 a, Point3D_F64 b ) {

		// this equation was found by solving for l:
		// ||(P + V*l) - X0|| == r

		double r2 = sphere.radius*sphere.radius;

		double PP = GeometryMath_F64.dot(line.p,line.p);
		double PV = GeometryMath_F64.dot(line.p,line.slope);
		double PX = GeometryMath_F64.dot(line.p,sphere.center);
		double VV = GeometryMath_F64.dot(line.slope,line.slope);
		double VX = GeometryMath_F64.dot(line.slope,sphere.center);
		double XX = GeometryMath_F64.dot(sphere.center,sphere.center);

		// Coefficients in the quadratic equation
		double A = VV;
		double B = 2.0*(PV-VX);
		double C = PP+XX-2.0*PX-r2;

		// solve for the quadratic equation
		double inner = B*B - 4.0*A*C;
		if( inner < 0 )
			return false;
		double sqrt = Math.sqrt(inner);

		double t0 = (-B + sqrt)/(2.0*A);
		double t1 = (-B - sqrt)/(2.0*A);

		line.setPointOnLine(t0,a);
		line.setPointOnLine(t1,b);

		return true;
	}
public static boolean intersect ( LineParametric3D_F64 line , Sphere3D_F64 sphere , Point3D_F64 a , Point3D_F64 b ) { // this equation was found by solving for l: // ||(P + V*l) - X0|| == r double r2 = sphere . radius * sphere . radius ; double PP = GeometryMath_F64 . dot ( line . p , line . p ) ; double PV = GeometryMath_F64 . dot ( line . p , line . slope ) ; double PX = GeometryMath_F64 . dot ( line . p , sphere . center ) ; double VV = GeometryMath_F64 . dot ( line . slope , line . slope ) ; double VX = GeometryMath_F64 . dot ( line . slope , sphere . center ) ; double XX = GeometryMath_F64 . dot ( sphere . center , sphere . center ) ; // Coefficients in the quadratic equation double A = VV ; double B = 2.0 * ( PV - VX ) ; double C = PP + XX - 2.0 * PX - r2 ; // solve for the quadratic equation double inner = B * B - 4.0 * A * C ; if ( inner < 0 ) return false ; double sqrt = Math . sqrt ( inner ) ; double t0 = ( - B + sqrt ) / ( 2.0 * A ) ; double t1 = ( - B - sqrt ) / ( 2.0 * A ) ; line . setPointOnLine ( t0 , a ) ; line . setPointOnLine ( t1 , b ) ; return true ; }
Finds the intersection of a line and sphere.  There can be 0, 1, or 2 intersections.  If there is
1 intersection the same point is returned twice.

@param line line
@param sphere sphere
@param a (Output) Storage for point of intersection.  t = max(t0,t1), where t is location on line
@param b (Output) Storage for point of intersection.  t = max(t0,t1), where t is location on line
@return true if the line intersects the sphere
Finds the intersection of a line and sphere . There can be 0 1 or 2 intersections . If there is 1 intersection the same point is returned twice .