[mapguide-internals] 3D CircularArc issues

[Maksim Sestic]

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