bool calcRayEarthIntersection(const Vec3 &linePoint,
const Vec3 &lineDirn,
Vec3 &nearXsecPoint)
{
// the solution for intersection points between a ray
// and the Earth's surface is a quadratic equation
// first calculate the quadratic equation params:
// a(x^2) + b(x) + c
// a, b and c are found by substituting the parametric
// equation of a line into the equation for a ellipsoid
// and solving in terms of the line's parameter
// * http://en.wikipedia.org/wiki/Ellipsoid
// * http://gis.stackexchange.com/questions/20780/...
// ...point-of-intersection-for-a-ray-and-earths-surface
std::vector<double> listRoots;
double a = (pow(lineDirn.x,2) / ELL_SEMI_MAJOR_EXP2) +
(pow(lineDirn.y,2) / ELL_SEMI_MAJOR_EXP2) +
(pow(lineDirn.z,2) / ELL_SEMI_MINOR_EXP2);
double b = (2*linePoint.x*lineDirn.x/ELL_SEMI_MAJOR_EXP2) +
(2*linePoint.y*lineDirn.y/ELL_SEMI_MAJOR_EXP2) +
(2*linePoint.z*lineDirn.z/ELL_SEMI_MINOR_EXP2);
double c = (pow(linePoint.x,2) / ELL_SEMI_MAJOR_EXP2) +
(pow(linePoint.y,2) / ELL_SEMI_MAJOR_EXP2) +
(pow(linePoint.z,2) / ELL_SEMI_MINOR_EXP2) - 1;
calcQuadraticEquationReal(a,b,c,listRoots);
if(!listRoots.empty())
{ // ensure poi lies along ray dirn
if((listRoots[0] > 0) && (listRoots[1] > 0))
{
Vec3 point1;
point1.x = linePoint.x + listRoots.at(0)*lineDirn.x;
point1.y = linePoint.y + listRoots.at(0)*lineDirn.y;
point1.z = linePoint.z + listRoots.at(0)*lineDirn.z;
Vec3 point2;
point2.x = linePoint.x + listRoots.at(1)*lineDirn.x;
point2.y = linePoint.y + listRoots.at(1)*lineDirn.y;
point2.z = linePoint.z + listRoots.at(1)*lineDirn.z;
// save the point nearest to the ray's origin
if(linePoint.DistanceTo(point1) > linePoint.DistanceTo(point2))
{ nearXsecPoint = point2; }
else
{ nearXsecPoint = point1; }
return true;
}
}
return false;
}
