double crossTrackDistanceTo( StartX, StartY, StartZ, EndX, EndY, EndZ, PointX, PointY, PointZ ); needed about geodesy HOT 2 CLOSED

I managed to convert the X,Y,Z coordinates to lat, long with these functions, both work... but use different methods...

My distance to visualize the line was simply to great giving the impression that maybe the current crossTrackDistanceTo function wasn't working or something was wrong, but it turns alright, though it doesn't respect the line segment concept... I'll might make new pull request for that.

//**
// * converts a XYZ THREE.Vector3 to longitude latitude. beware, the vector3 will be normalized!
// * @param vector3
// * @returns an array containing the longitude [0] & the lattitude [1] of the Vector3
// */
procedure TLatLon.FromXYZ( ParaX, ParaY, ParaZ : double );
var
vVector : TVector3D;
lng, lat : double;
p : TVector3D;
begin

vVector.mX := ParaX;
vVector.mY := ParaY;
vVector.mZ := ParaZ;

vVector.Normalize();

//longitude = angle of the vector around the Y axis
//-( ) : negate to flip the longitude (3d space specific )
//- PI / 2 to face the Z axis
lng := -( System.Math.arctan2( -vVector.mz, -vVector.mx ) ) - (System.PI / 2);

//to bind between -PI / PI
if( lng < -System.PI ) then lng := lng + (System.PI * 2);

//latitude : angle between the vector & the vector projected on the XZ plane on a unit sphere

//project on the XZ plane
p.mX := vVector.mX;
p.mY := 0;
p.mZ := vVector.mZ;

//project on the unit sphere
p.normalize();

//commpute the angle ( both vectors are normalized, no division by the sum of lengths )
lat := System.Math.arccos( p.Dot( vVector ) );

//invert if Y is negative to ensure teh latitude is comprised between -PI/2 & PI / 2
if ( vVector.mY < 0 ) then lat := lat * -1;
mLon := lng;
mLat := lat;

end;

procedure TLatLon.FromXYZ2( ParaX, ParaY, ParaZ : double; ParaSphereRadius : double );
begin
mLat := System.Math.ArcCos(ParaY / ParaSphereRadius); //theta
mLon := System.ArcTan(ParaX / ParaZ); //phi
end;

from geodesy.

I consider this more or less solved for now :) though maybe it can be done a little bit more efficient, without needing these conversions... I think so, but not entirely sure yet ! ;)

This was my initial version, maybe it's good enough for this functionality, but now I need other functionality :):

This code illustrates the removal of toNVector...

function ClosestDistancePointToGreatCircleV1
(
ParaPointX, ParaPointY, ParaPointZ : double;
ParaStartX, ParaStartY, ParaStartZ : double;
ParaEndX, ParaEndY, ParaEndZ : double;
ParaRadius : double = 6371e3 // (Mean) radius of earth (defaults to radius in metres).
) : double;
var
// also a possibility, thank god it works ! ;) :)
{
vPoint : unit_CrossTrackDistance_version_001.unit_TVector3D_version_001.TVector3D;
vStart : unit_CrossTrackDistance_version_001.unit_TVector3D_version_001.TVector3D;
vEnd : unit_CrossTrackDistance_version_001.unit_TVector3D_version_001.TVector3D;

vGreatCircle : unit_CrossTrackDistance_version_001.unit_TVector3D_version_001.TVector3D;

}

vPoint : TCrossDistanceVector3D;
vStart : TCrossDistanceVector3D;
vEnd : TCrossDistanceVector3D;

vGreatCircle : TCrossDistanceVector3D;

vAlpha : double;

begin
// vPoint := ParaPoint.toNvector(); // converts itself... to a 3d vector apperently...
vPoint.mX := ParaPointX;
vPoint.mY := ParaPointY;
vPoint.mZ := ParaPointZ;

// vGreatCircle := ParaPathStart.toNvector().cross(ParaPathEnd.toNvector()); // great circle defined by two points
vStart.mX := ParaStartX;
vStart.mY := ParaStartY;
vStart.mZ := ParaStartZ;

if vStart = vPoint then
begin
	result := 0;
	exit;
end;

vEnd.mX := ParaEndX;
vEnd.mY := ParaEndY;
vEnd.mZ := ParaEndZ;

vGreatCircle := vStart.cross( vEnd );

// vAlpha := vGreatCircle.AngleTo(vPoint) - (System.PI / 2); // angle between point & great-circle
vAlpha := vGreatCircle.AngleTo(vPoint) - (System.PI / 2); // angle between point & great-circle

result := vAlpha * ParaRadius;

end;

from geodesy.