Coordinate systems - Revision history

Lof: /* consistency check */

2026-08-28T12:44:05Z

consistency check

← Older revision		Revision as of 12:44, 28 August 2026
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	</pre>		</pre>

	When azimuth_deg + elevation_deg < 90° the circles have two intersections.		*When azimuth_deg + elevation_deg < 90° the circles have two intersections.
	When azimuth_deg + elevation_deg = 90° the circles have one intersection.		*When azimuth_deg + elevation_deg = 90° the circles have one intersection.
	When azimuth_deg + elevation_deg > 90° the circles have zero intersections.		*When azimuth_deg + elevation_deg > 90° the circles have zero intersections.

	===Transforming double polar to HVF coordinates===		===Transforming double polar to HVF coordinates===

2026-08-28T12:43:50Z

consistency check

← Older revision		Revision as of 12:43, 28 August 2026
Line 90:		Line 90:
	</pre>		</pre>

	When azimuth_deg + elevation_deg < 90° the circles have two intersections.		When azimuth_deg + elevation_deg < 90° the circles have two intersections.
	When azimuth_deg + elevation_deg = 90° the circles have one intersection.		When azimuth_deg + elevation_deg = 90° the circles have one intersection.
	When azimuth_deg + elevation_deg > 90° the circles have zero intersections.		When azimuth_deg + elevation_deg > 90° the circles have zero intersections.

	===Transforming double polar to HVF coordinates===		===Transforming double polar to HVF coordinates===

2026-08-28T12:43:24Z

consistency check

← Older revision		Revision as of 12:43, 28 August 2026
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	azimuth + elevation <= pi (or azimuth_deg + elevation_deg <= 90°)		azimuth + elevation <= pi (or azimuth_deg + elevation_deg <= 90°)
	</pre>		</pre>

			When azimuth_deg + elevation_deg < 90° the circles have two intersections.
			When azimuth_deg + elevation_deg = 90° the circles have one intersection.
			When azimuth_deg + elevation_deg > 90° the circles have zero intersections.

	===Transforming double polar to HVF coordinates===		===Transforming double polar to HVF coordinates===

2026-08-28T12:40:50Z

Transforming double polar to HVF coordinates

← Older revision		Revision as of 12:40, 28 August 2026
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	F = hemisphere * sqrt(radius^2 - H^2 - V^2)		F = hemisphere * sqrt(radius^2 - H^2 - V^2)
	</pre>		</pre>
	Where radius is the distance to the center.		Where radius is the distance to the center and H, V and F are the horizontal, vertical and frontal distances in cartesian coordinates.

	===Transforming Cartesian to double polar coordinates===		===Transforming Cartesian to double polar coordinates===

2026-08-28T12:40:35Z

Transforming Cartesian to double polar coordinates

← Older revision		Revision as of 12:40, 28 August 2026
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	hemisphere = sign(F);		hemisphere = sign(F);
	</pre>		</pre>
	~~Where H, V and F are the horizontal, vertical and frontal distances in cartesian coordinates.~~

	==Matlab==		==Matlab==

2026-08-28T12:39:51Z

Transforming Cartesian to double polar coordinates

← Older revision		Revision as of 12:39, 28 August 2026
Line 107:		Line 107:
	hemisphere = sign(F);		hemisphere = sign(F);
	</pre>		</pre>
			Where H, V and F are the horizontal, vertical and frontal distances in cartesian coordinates.

	==Matlab==		==Matlab==

2026-08-28T12:38:41Z

Transforming double polar to HVF coordinates

← Older revision		Revision as of 12:38, 28 August 2026
Line 96:		Line 96:
	F = hemisphere * sqrt(radius^2 - H^2 - V^2)		F = hemisphere * sqrt(radius^2 - H^2 - V^2)
	</pre>		</pre>
			Where radius is the distance to the center.

	===Transforming Cartesian to double polar coordinates===		===Transforming Cartesian to double polar coordinates===

2026-08-28T12:37:30Z

azimuth

← Older revision		Revision as of 12:37, 28 August 2026
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	===azimuth===		===azimuth===
	* Azimuth is the angle with the FV-plane.		* Azimuth is the angle with the FV-plane.
	* If d_FV is the distance to the plane and R is the distance to a point from the center, then Azimuth = arcsin(d_FV/R).		* If d_FV is the distance to the plane and R is the distance to a point from the center, then
			<pre>
			Azimuth = arcsin(d_FV/R).
			</pre>
	* pi/2 <= azimuth <= pi/2 (or -90° <= azimuth <= 90°)		* pi/2 <= azimuth <= pi/2 (or -90° <= azimuth <= 90°)

2026-08-28T12:36:27Z

elevation

← Older revision		Revision as of 12:36, 28 August 2026
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	===elevation===		===elevation===
	* Elevation is the angle with the RF-plane		* Elevation is the angle with the RF-plane
	* If d_RF is the distance to the plane and R is the distance to a point from the center, ~~the~~ Elevation ~~is specified by~~ arcsin(d_RF/R).		* If d_RF is the distance to the plane and R is the distance to a point from the center, then Elevation = arcsin(d_RF/R).
	* pi/2 <= elevation<= pi/2 (or -90° <= elevation <= 90°)		* pi/2 <= elevation<= pi/2 (or -90° <= elevation <= 90°)

2026-08-28T12:36:15Z

azimuth

← Older revision		Revision as of 12:36, 28 August 2026
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	===azimuth===		===azimuth===
	* Azimuth is the angle with the FV-plane.		* Azimuth is the angle with the FV-plane.
	* If d_FV is the distance to the plane and R is the distance to a point from the center, ~~the~~ Azimuth ~~is specified by~~ arcsin(d_FV/R).		* If d_FV is the distance to the plane and R is the distance to a point from the center, then Azimuth = arcsin(d_FV/R).
	* pi/2 <= azimuth <= pi/2 (or -90° <= azimuth <= 90°)		* pi/2 <= azimuth <= pi/2 (or -90° <= azimuth <= 90°)