Appendix/Ramblings/ConcentricEllipsoidalCoordinates - Revision history

Jet53man at 20:22, 23 July 2021

2021-07-23T20:22:37Z

Jet53man at 20:20, 23 July 2021

2021-07-23T20:20:55Z

Jet53man at 20:19, 23 July 2021

2021-07-23T20:19:59Z

@@ Line 890: / Line 890: @@
 \biggl( - \frac{\lambda_2}{p^2z} \biggr)^2
 \biggr]^{-1}
 </math>
    </td>

Jet53man: /* Concentric Ellipsoidal (T6) Coordinates */

2021-07-23T20:18:29Z

Concentric Ellipsoidal (T6) Coordinates

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Jet53man: /* Other Coordinate Pair in the Tangent Plane */

2021-07-23T20:16:41Z

Other Coordinate Pair in the Tangent Plane

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Jet53man: Replaced content with "FORCETOC =Concentric Ellipsoidal (T6) Coordinates= ==Background== Building on our Appendix/Ramblings/DirectionCosines|general..."

2021-07-23T20:14:43Z

Replaced content with "__FORCETOC__  =Concentric Ellipsoidal (T6) Coordinates= ==Background== Building on our Appendix/Ramblings/DirectionCosines|general..."

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Jet53man: /* Other Coordinate Pair in the Tangent Plane */

2021-07-23T19:46:51Z

Other Coordinate Pair in the Tangent Plane

← Older revision		Revision as of 15:46, 23 July 2021
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	<tr>		<tr>
	<td align="right">		<td align="right">
	<math>~\ell_{3D}</math>		<math>\ell_{3D}</math>
	</td>		</td>
	<td align="center">		<td align="center">
	<math>~=</math>		<math>=</math>
	</td>		</td>
	<td align="left">		<td align="left">
	<math>~\biggl[ x_0^2 + q^4y_0^2 + p^4 z_0^2 \biggr]^{- 1 / 2} \, .</math>		<math>\biggl[ x_0^2 + q^4y_0^2 + p^4 z_0^2 \biggr]^{- 1 / 2} \, .</math>
	</td>		</td>
	</tr>		</tr>
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	----		----

	The two-dimensional plane that is tangent to the <math>~\lambda_1</math> = constant surface ''at this point'' is given by the expression,		The two-dimensional plane that is tangent to the <math>\lambda_1</math> = constant surface ''at this point'' is given by the expression,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Jet53man: /* COLLADA */

2021-07-23T19:37:06Z

COLLADA

← Older revision		Revision as of 15:37, 23 July 2021
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	=COLLADA=		=COLLADA=
	Here we try to use the 3D-visualization capabilities of COLLADA to test whether or not the three coordinates associated with the T6 Coordinate system are indeed orthogonal to one another. We begin by making a copy of the '''Inertial17.dae''' text file, which we obtain from [[~~User:Tohline/~~ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS#The_COLLADA_Code_.26_Initial_3D_Scene\|an accompanying discussion]]. When viewed with the Mac's '''Preview''' application, this group of COLLADA-based instructions displays a purple ellipsoid with axis ratios, (b/a, c/a) = (0.41, 0.385). This means that we are dealing with an ellipsoid for which,		Here we try to use the 3D-visualization capabilities of COLLADA to test whether or not the three coordinates associated with the T6 Coordinate system are indeed orthogonal to one another. We begin by making a copy of the '''Inertial17.dae''' text file, which we obtain from [[ThreeDimensionalConfigurations/MeetsCOLLADAandOculusRiftS#The_COLLADA_Code_.26_Initial_3D_Scene\|an accompanying discussion]]. When viewed with the Mac's '''Preview''' application, this group of COLLADA-based instructions displays a purple ellipsoid with axis ratios, (b/a, c/a) = (0.41, 0.385). This means that we are dealing with an ellipsoid for which,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

	<tr>		<tr>
	<td align="right">		<td align="right">
	<math>~q \equiv \frac{a}{b}</math>		<math>q \equiv \frac{a}{b}</math>
	</td>		</td>
	<td align="center">		<td align="center">
Line 7,661:		Line 7,661:
	===Tangent Plane===		===Tangent Plane===

	From our [[~~User:Tohline/~~Appendix/Ramblings/~~ConcentricEllipsodalCoordinates~~#Other_Coordinate_Pair_in_the_Tangent_Plane\|above derivation]], the plane that is tangent to the ellipsoid's surface at <math>~(x_0, y_0, z_0)</math> is given by the expression,		From our [[Appendix/Ramblings/ConcentricEllipsoidalCoordinates#Other_Coordinate_Pair_in_the_Tangent_Plane\|above derivation]], the plane that is tangent to the ellipsoid's surface at <math>~(x_0, y_0, z_0)</math> is given by the expression,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Jet53man: /* Other Coordinate Pair in the Tangent Plane */

2021-07-23T19:29:01Z

Other Coordinate Pair in the Tangent Plane

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Jet53man: /* Primary (radial-like) Coordinate */

2021-07-23T19:25:28Z

Primary (radial-like) Coordinate

← Older revision		Revision as of 15:25, 23 July 2021
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	</tr>		</tr>
	</table>		</table>
	From our [[~~User:Tohline/~~Appendix/Ramblings/DirectionCosines#Scale_Factors\|accompanying discussion of direction cosines]], it is clear, as well, that the scale factor associated with the <math>~\lambda_1</math> coordinate is,		From our [[Appendix/Ramblings/DirectionCosines#Scale_Factors\|accompanying discussion of direction cosines]], it is clear, as well, that the scale factor associated with the <math>~\lambda_1</math> coordinate is,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Appendix/Ramblings/ConcentricEllipsoidalCoordinates - Revision history

Jet53man at 20:22, 23 July 2021

Jet53man at 20:20, 23 July 2021

Jet53man at 20:19, 23 July 2021

Jet53man: /* Concentric Ellipsoidal (T6) Coordinates */

Jet53man: /* Other Coordinate Pair in the Tangent Plane */

Jet53man: Replaced content with "__FORCETOC__ =Concentric Ellipsoidal (T6) Coordinates= ==Background== Building on our Appendix/Ramblings/DirectionCosines|general..."

Jet53man: /* Other Coordinate Pair in the Tangent Plane */

Jet53man: /* COLLADA */

Jet53man: /* Other Coordinate Pair in the Tangent Plane */

Jet53man: /* Primary (radial-like) Coordinate */

Jet53man: Replaced content with "FORCETOC =Concentric Ellipsoidal (T6) Coordinates= ==Background== Building on our Appendix/Ramblings/DirectionCosines|general..."