Control of display content by movement on a fixed spherical space

Abstract

The present invention addresses the above described problems by simplifying the assumptions on possible motions made by a user. This simplification process can take place by making an assumption that the motion of the device will travel along a certain preferential motion arc, which will be referred to herein as the “Javal arc.” Calculations of motions of the device can be made based on these Javal arcs. Additionally, the double integration of each accelerometer is now eliminated and the expensive accelerometers are replaced by two magnetic sensors.

Description

Appendix A
ϵ Sin γ|Cos θ|(H_// Cos Φ)−Cos γ(H_// Sin Φ)=[h_y′″−H_⊥ Sin γ Sin θ]
i.e.,
h_X′″=ϵ Cos γ|Cos θ|(H_// Cos Φ)−Sin γ(H_// Sin Φ)+H_⊥ Cos γ Sin θ  (35.1)
h_Y′″=ϵ Sin γ|Cos θ|(H_// Cos Φ)−Cos γ(H_// Sin Φ)+H_⊥ Sin γ Sin θ  (35.2)
Sin γh_X′″−Cos γh_Y′″=2ϵ Sin γ Cos γ|Cos θ|(H_// Cos Φ)−Cos γ Sin² γ(H_// Sin Φ)
Sin γh_X′″+Cos γh_Y′″=−(H_// Sin Φ)+2H_⊥ Sin γ Cos γ Sin Φ
i.e.,
2ϵ Sin γ Cos γ|Cos θ|(H_// Cos Φ)+Cos² γ Sin² γ(H_// Sin Φ)=(Sin γh_X′″−Cos γh_Y′″)   (36.1)
(H_// Sin Φ)+(2 Sin γ Cos γ Sin θ)H_⊥=(Sin γh_X′″+Cos γh_Y′″)   (36.2)
H_⊥=ϵ_M(1−H_//²)^1/2   (37)
Where ϵ_M is known (north or south of magnetic equator).

Thus:
2ϵ Sin γ Cos γ|Cos θ|(H_// Cos Φ)+(Cos² γ−Sin² γ)(H_// Sin Φ)=(Sin γh_X′″−Cos γh_Y′″)   (38.1)
(H_// Sin Φ)+ϵ_M(Sin γ Cos γ Sin θ)(H_poc²−H_//²)^1/2=(Sin γh_X′″+Cos γh_Y′″)   (38.2)
If the magnetic inclination δ and the field amplitude H_poc are assumed to be known:
H_//=H_poc Cos δ  (9.1)
H_⊥=H_poc Sin δ  (39.2)
[2H_// Sin γ Cos γ(ϵ|Cos θ|)]Cos Φ+(Cos² γ−Sin² γ)(H_// Sin Φ)=(Sin γh_X′″−Cos γh_Y′″)   (40.1)
H_// Sin Φ+2(Sin γ Cos γ Sin θ)H_⊥=(Sin γh_X′″+Cos γh_Y′″)   (40.2)
i.e.,
H_// Sin Φ=2(Sin γ Cos γ Sin θ)H_⊥−(Sin γh_X′″+Cos γh_Y′″)   (41.1)

$H_{\mathrm{ll}}\mathrm{Cos}\Phi =\frac{\left(\mathrm{Sin}\gamma h_{X^{\mathrm{\prime \prime \prime }}}-\mathrm{Cos}\gamma h_{Y^{\mathrm{\prime \prime \prime }}}\right)-\left({\mathrm{Cos}}^2\gamma -{\mathrm{Sin}}^2\gamma \right)H_{\mathrm{ll}}\mathrm{Sin}\varphi }{2\mathrm{Sin}\mathrm{\gamma Cos}\gamma \left(\varepsilon \mathrm{Cos}\delta \right)}$
γ≃0 then H_// Sin Φ≃Cos γh_Y′″
h_X′″≃ϵ|Cos θ|(H_// Cos Φ)+H_⊥ Sin θ
i.e.,
ϵ|Cos θ|(H_// Cos Φ)≃(h_X′″−H_⊥ Sin θ)
(Cos γh_X′″−Sin γh_y′″)=ϵ|Cos θ|(H_// Cos Φ)+(Cos² γ−Sin² γ)H_⊥ Sin θ
(Sin γh_X′″+Cos γh_y′″=−(H_// Sin Φ)+2(Sin γ Cos γ)H_⊥ Sin θ
i.e.,
ϵ|Cos θ|(H_// Cos Φ)+(Cos² γ−Sin² γ)(H_⊥ Sin Φ)=(Cos γh_X′″−Sin θh_y′″)   (42.1)
−(H_// Sin Φ)+2(Sin γ Cos γ)(H_⊥ Sin θ)=(Sin γh_X′″+Cos γh_y′″)   (42.2)
If γ=0, one has in first approximation:
ϵ|Cos θ|(H_// Cos Φ)+(H_⊥ Sin θ)=h_x′″
−H_// Sin Φ=h_y′″
i.e.,

$\begin{array}{cc}\mathrm{Sin}\Phi =\left(\frac{h_{y^{\mathrm{\prime \prime \prime }}}}{H_{\mathrm{ll}}}\right)& \left(43.1\right)\\ \mathrm{Cos}\Phi =\frac{h_{x^{\mathrm{\prime \prime \prime }}}-H_{\perp }\mathrm{Sin}\theta }{\mathrm{Cos}\theta H_{\mathrm{ll}}}& \left(43.2\right)\\ \mathrm{assuming}ϵ=-1\left(\theta >\frac{\pi }{2}\right)H_{\mathrm{ll}}^2={\left(h_{y^{\mathrm{\prime \prime \prime }}}\right)}^2+{\left(\frac{h_{x^{\mathrm{\prime \prime \prime }}}-H_{\perp }\mathrm{Sin}\theta }{\mathrm{Cos}\theta }\right)}^2\mathrm{Sin}\varphi =\left(\frac{-h_{y^{\mathrm{\prime \prime \prime }}}}{H_{\mathrm{ll}}}\right)& \left(44.1\right)\\ \mathrm{Cos}\varphi =\frac{H_{\perp }\mathrm{Sin}\theta -h_{x^{\mathrm{\prime \prime \prime }}}}{\mathrm{Cos}\theta H_{\mathrm{ll}}}& \left(44.2\right)\\ \mathrm{\Delta Sin}\varphi =\mathrm{Cos}\mathrm{\varphi \Delta }\varphi =\Delta \left\{\frac{\left(-h_{y^{\mathrm{\prime \prime \prime }}}\right)}{H_{\mathrm{ll}}}\right\}& \left(45.1\right)\\ \Delta \mathrm{Cos}\varphi =\mathrm{Sin}\mathrm{\varphi \Delta }\varphi =\Delta \left\{\frac{\left(H_{\perp }\mathrm{Sin}\theta -h_{x^{\mathrm{\prime \prime \prime }}}\right)}{\mathrm{Cos}\theta H_{\mathrm{ll}}}\right\}& \left(45.2\right)\\ \mathrm{Cos}\mathrm{\varphi \Delta Sin\varphi }-\mathrm{Sin}\mathrm{\varphi \Delta Cos}\varphi =\mathrm{\Delta \varphi }=\left\{\frac{\left(H_{\perp }\mathrm{Sin}\theta -h_{x^{\mathrm{\prime \prime \prime }}}\right)}{\mathrm{Cos}\theta H_{\mathrm{ll}}}\right\}\Delta \left\{\frac{\left(-h_{y^{\mathrm{\prime \prime \prime }}}\right)}{H_{\mathrm{ll}}}\right\}+\left\{\frac{\left(-h_{y^{\mathrm{\prime \prime \prime }}}\right)}{H_{\mathrm{ll}}}\right\}\Delta \left\{\frac{\left(H_{\perp }\mathrm{Sin}\theta -h_{x^{\mathrm{\prime \prime \prime }}}\right)}{\mathrm{Cos}\theta H_{\mathrm{ll}}}\right\}& \left(46\right)\\ v_O^{Y^{\mathrm{\prime \prime \prime }}}={R_{\mathrm{conf}}\left[{\left(\frac{{\gamma }_{x^{\mathrm{\prime \prime \prime }}}}{y}\right)}^2+{\left(\frac{{\gamma }_{y^{\mathrm{\prime \prime \prime }}}}{y}\right)}^2\right]}^{\frac{1}{2}}\frac{\Delta \varphi }{\mathrm{\Delta t}}& \left(47\right)\\ v_O^{X^{\mathrm{\prime \prime \prime }}}=R_{\mathrm{conf}}\Delta \theta =R_{\mathrm{conf}}\frac{\mathrm{\Delta Sin}\theta }{{\left(1-{\sin }^2\theta \right)}^{\frac{1}{2}}\mathrm{\Delta t}}& \left(48\right)\end{array}$

Claims

1. A method for controlling a display on a portable electronic device, the method comprising the computer-implemented acts of:

detecting sensor data indicative of a motion of said portable electronic device relative to a fixed point, wherein said motion follows a preferential motion arc that is natural to eye and/or hand coordination of a holder of said portable electronic device;

calculating a position on a spheroid of said portable electronic device based on said sensor data indicative of said motion that is relative to said fixed point;

calculating said motion with respect to said spheroid given said sensor data indicative of said motion and analyzing said sensor data indicative of said motion with respect to said spheroid;

determining that said motion corresponds to a display command; and

adjusting said display based on said motion and on an angle of said position, if on said spheroid in response to determining that said motion corresponds to a user said display command, said angle indicating an orientation of said portable electronic device relative to a line of sight of said holder.

2. The method of claim 1, wherein said act of detecting said sensor data indicative of said motion further comprising comprises:

receiving input from motion sensors which that can detect said sensor data indicative of said motion of said portable electronic device.

3. The method of claim 1, wherein said act of calculating a said position on said spheroid is based on a Javal coordinate system.

4. The method of claim 1, wherein said act of calculating said motion with respect to said spheroid and analyzing said sensor data indicative of said motion is are based on a Javal arc coordinate system.

5. The method of claim 1, wherein said act of calculating said motion with respect to said spheroid and analyzing said sensor data indicative of said motion further comprises measuring changes in a magnetic field.

6. The method of claim 1, wherein said act of calculating said motion with respect to said spheroid and analyzing said sensor data indicative of said motion further comprises measuring one or more angles corresponding to a position of said portable electronic device relative to said fixed point.

7. The method of claim 1, wherein said motion is modeled mathematically by a virtual surface of a virtual thin-walled shell that is approximately spherical in shape.

8. The method of claim 4, wherein an origin of said Javal arc is said fixed point.

9. A controller for a display on a portable electronic device, the controller comprising:

at least one accelerometer for measuring a sensor data indicative of a motion of said portable electronic device relative to a fixed point, wherein said motion follows a preferential motion arc that is natural to eye and/or hand coordination of a holder of said portable electronic device;

at least one magnetic sensor for measuring said motion; and

logic for calculating said motion with respect to a spheroid given said senor data indicative of said motion, and for calculating a position on said spheroid of said portable electronic device based on one or more measurements from said at least one accelerometer and said at least one magnetic sensor;

logic for determining that said motion corresponds to a display command; and

logic for adjusting said display based on said motion and on an angle of said position on said spheroid in response to determining that said motion corresponds to said display command, said angle indicating an orientation of said portable electronic device relative to a line of sight of said holder.

10. The controller of claim 9, wherein said motion is modeled by a pre-defined path.

11. The controller of claim 9, wherein said motion is modeled by a Javal arc.

12. The controller of claim 9, wherein said motion is based on a Javal coordinate system.

13. A method for controlling a portable electronic device, the method comprising the computer-implemented acts of:

calculating and analyzing a motion of said portable electronic device with respect to a spheroid given sensor data indicative of said motion with respect to said spheroid;

analyzing said sensor data indicative of said motion with respect to said spheroid;

calculating a position on said spheroid of said portable electronic device based on said sensor data indicative of said motion that is relative to a fixed point from said portable electronic device, wherein said motion follows a preferential motion arc that is natural to eye and/or hand coordination of a holder of said portable electronic device; and

determining if that said motion corresponds to a user display command; and

adjusting at least one aspect of a display on said portable electronic device based on said motion when said motion corresponds to a user command and on an angle of said position on said spheroid in response to determining that said motion corresponds to said display command, said angle indicating an orientation of said portable electronic device relative to a line of sight of said holder.

14. The method of claim 13, wherein said acts of calculating said motion of said portable electronic device and analyzing said sensor data indicative of said motion further comprising comprises:

receiving input from motion sensors which that can detect said sensor data indicative of said motion of said portable electronic device.

15. The method of claim 14, wherein said motion sensors are attached to said portable electronic device.

16. The method of claim 13, further comprising:

calculating a position of said device based on said motion that is relative to said fixed point.

17. A controller for a display on a portable electronic device, the controller comprising:

only two accelerometers for measuring sensor data indicative of a motion of said portable electronic device relative to a fixed point, wherein said motion follows a preferential motion arc that is natural to eye and/or hand coordination of a holder of said portable electronic device;

at least one magnetic sensor for measuring said motion; and

logic for calculating said motion with respect to a spheroid given said sensor data indicative of said motion, and for calculating a position on said spheroid of said portable electronic device based on one or more measurements from said only two accelerometers and said at least one magnetic sensor;

logic for determining that said motion corresponds to a display command; and

logic for adjusting said display based on said motion and on an angle of said position on said spheroid in response to determining that said motion corresponds to said display command, said angle indicating an orientation of said portable electronic device relative to a line of sight of said holder.

18. A controller for a display on a portable electronic device, the controller comprising:

one gyroscope for measuring sensor data indicative of a motion of said portable electronic device relative to a fixed point, wherein said motion follows a preferential motion arc that is natural to eye and/or hand coordination of a holder of said portable electronic device;

at least one magnetic sensor for measuring said motion; and

logic for calculating said motion with respect to a spheroid given said sensor data indicative of said motion, and for calculating a position on said spheroid of said portable electronic device based on one or more measurements from said one gyroscope and said at least one magnetic sensor;

logic for determining that said motion corresponds to a display command; and

logic for adjusting said display based on said motion and on an angle of said position on said spheroid in response to determining that said motion corresponds to said display command, said angle indicating an orientation of said portable electronic device relative to a line of sight of said holder.

19. A controller for a display on a portable electronic device, the controller comprising:

only one accelerometer for measuring sensor data indicative of a motion of said portable electronic device relative to a fixed point, wherein said motion follows a preferential motion arc that is natural to eye and/or hand coordination of a holder of said portable electronic device;

only two magnetic sensors for measuring said motion; and

logic for calculating said motion with respect to a spheroid given said sensor data indicative of said motion, and for calculating a position on said spheroid of said portable electronic device based on one or more measurements from said only one accelerometer and said only two magnetic sensors;

logic for determining that said motion corresponds to a display command; and

logic for adjusting said display based on said motion and on an angle of said position on said spheroid in response to determining that said motion corresponds to said display command, said angle indicating an orientation of said portable electronic device relative to a line of sight of said holder.