Click or drag to resize

UtilsConvertEllipsePhaseAngleToElevationAngle Method

Converts the phase angle of an ellipse as used in the SP-ICE 3 API into an elevation angle as used in Microsoft's ellipse definition.

Namespace: RAYLASE.Marker.VectorGraphicElement
Assembly: RAYLASE.Marker.VectorGraphicElement (in RAYLASE.Marker.VectorGraphicElement.dll) Version: 2.19.0
Syntax
C#
Copy
public static double ConvertEllipsePhaseAngleToElevationAngle(
	double a,
	double b,
	double theta,
	bool isRad
)

Parameters

a  Double
semiaxis a of the ellipse
b  Double
semiaxis b of the ellipse
theta  Double
phase angle of a point on the ellipse
isRad  Boolean
if false, the phase angle is converted into deg and the result is returned in deg as well

Return Value

Double
the elevation angle eta as needed by Microsoft to get the same point; it is in the range of [0..2pi].
Remarks
a) Raylase definitions:
Copy
                             |     P = (x, y), x=a*cos(theta), y=b*sin(theta)}
                     ____ ---+--- *___
                __---        |   /    ---__         theta != eta
               -             |  /--.       -_
              ´              | /    \        `      eta counterclockwise from x axis
             |               |/ eta  |        |
-------------+---------------+----------------+-----------------
             |               |                |
              .              |              _.                y
               -__           |           __-       tan(eta) = -
                  ---____    |    ____---                     x
                          ---+---
                             |                                b*sin(theta)   b
                                                   tan(eta) = ------------ = - tan(theta)
                                                              a*cos(theta)   a
=> eta   = atan(tan(theta)*b/a)
=> theta = atan(tan(eta)*a/b)
This applies for the first quadrant only. Calculated eta is positive in the first and third quadrant, negative in the second and fourth. For the corrections see the code. b) Microsoft definitions:
Copy
                             |     P
                     ____ ---+--- *___
                __---        |        ---__
               -             |             -_
              ´              |               `
             |               |                |
-------------+---------------+----------------+-----------------
             |               |\ eta  |        |
              .              | \    /       _.     eta clockwise from x axis
               -__           |  \-´      __-
                  ---____    |   \ ___---
                          ---+--- *
                             |     Q
See Also