[mapguide-internals] 3D CircularArc issues

[Gavin Cramer]

Hello, Maksim.  Finally, someone take a look at this!  I posed a similar question years ago... which I noticed because I wrote the original FDO code from which this package is copied.  I would like to take a look at it again, but I am swamped until at least early October.

What I recall of this is that better precautions against ill-conditioning were taken in ComputeLengthFromCenterRadiusAnglesAndNormal(), but that ComputeCenterRadiusAnglesFromThreePositionsAndNormal was not revisited for the same issue.

For those who do not know what ill-conditioning is, I left comments in ComputeLengthFromCenterRadiusAnglesAndNormal()...

        // In the 3D case, use spherical trigonometry.  To avoid ill-conditioning
        // of the arccosine  and arcsine functions, this will be the two-parameter
        // arctangent form of the Haversine formula (e.g. rather than the Law of Cosines).
        //
        // The ill-conditioning of certain angles stretch
        // the accuracy of the trig functions.  For example, the arcosine
        // function breaks down for values near 1.0...
        //       cos (5 degrees) = 0.996194698
        //       cos (1 degree) = 0.999847695
        //       cos (1 minute) = 0.9999999577
        //       cos (1 second) = 0.9999999999882
        //       cos (0.05 sec) = 0.999999999999971
        // Credits:
        //       http://www.census.gov/cgi-bin/geo/gisfaq?Q5.1
        //       http://mathforum.org/library/drmath/view/51879.html
        //       http://mathforum.org/library/drmath/view/51711.html
        //       http://mathforum.org/library/drmath/view/54680.html

Maksim, is this the issue of concern for you?  Do you have the wherewithal to make a code fix?  If so, it should be applied to the original FdoSpatial package as well.

Gavin


-----Original Message-----
From: mapguide-internals-bounces at lists.osgeo.org [mailto:mapguide-internals-bounces at lists.osgeo.org] On Behalf Of Maksim Sestic
Sent: Monday, September 19, 2011 7:59 AM
To: mapguide-internals at lists.osgeo.org
Subject: [mapguide-internals] 3D CircularArc issues

Hi all,

 

It seems that there's issues with CircularArc implementation, or maybe I'm
having problems understanding source code:

 

In file SpatialUtilityCircularArc.cpp:

 

Method void
MgSpatialUtilityCircularArc::ComputeCenterRadiusAnglesFromThreePositionsAndN
ormal() defines Start/End angle theta and phi values as follows:

 

// Compute start_angle and end_angle

 

    m_startAngle.m_theta = atan2(m_start->GetY() - m_center->GetY(),

                                 m_start->GetX() - m_center->GetX());

 

    if (m_startAngle.m_theta == -MgMathUtility::GetPi())

        m_startAngle.m_theta = MgMathUtility::GetPi();

 

    m_startAngle.m_phi = m_hasZ? asin((m_start->GetZ() - m_center->GetZ()) /
m_radius) : 0.0;

 

    m_endAngle.m_theta = atan2(m_end->GetY() - m_center->GetY(),

                               m_end->GetX() - m_center->GetX());

 

    if (m_endAngle.m_theta == -MgMathUtility::GetPi())

        m_endAngle.m_theta = MgMathUtility::GetPi();

 

    m_endAngle.m_phi = m_hasZ? asin((m_end->GetZ() - m_center->GetZ()) /
m_radius) : 0.0;

 

Please note that Start/End angle phi value is prone to error, e.g. using
following values for stard (SP), mid (MP) and end point (EP) of an 3D
circular arc:

 

SP = 220932.945, 205589.3036, 60.834

MP = 220957.505, 205585.6127, 60.882

EP = 220962.4382, 205584.7477, -38.525

 

for this particular part:

 

asin((m_end->GetZ() - m_center->GetZ())

 

obviuously fails if difference between EndPoint.Z and CenterPoint.Z exceeds
-1/1 range.

 

Above errors affect following method: void
MgSpatialUtilityCircularArc::ComputeLengthFromCenterRadiusAnglesAndNormal()

 

...making 3D arc's length computation impossible (via spherical
trigonometry).

 

Regards,

Maksim Sestic

_______________________________________________
mapguide-internals mailing list
mapguide-internals at lists.osgeo.org
http://lists.osgeo.org/mailman/listinfo/mapguide-internals