The presently disclosed subject matter relates to head tracking and, more particularly, to head tracking in a non-static environment.
The positive and imperative effect of head tracking on simulating VR (Virtual Reality) or AR (Augmented Reality) or binaural audio rendering is a well-known phenomenon. In systems that implement such effects, head-tracking data is used in order to adjust the location of virtual objects (for example visual objects or sound sources) to a user's head movements in order to make them appear static in space rather than follow the user.
In a non-static environment, such as when the user is walking, riding a train, etc., the frame of reference of the user is constantly changing. In these situations, tracking head movements relative to a fixed reference becomes problematic and can lead to erroneous placement of virtual objects around the user.
Problems of head tracking in a non-static environment have been recognized in the conventional art and various techniques have been developed to provide solutions, for example:
United States Patent Publication No. US 2011/0293129 discloses a head tracking system that determines a rotation angle of a head of a user with respect to a reference direction, which is dependent on a movement of a user. Here the movement of a user should be understood as an act or process of moving including e.g. changes of place, position, or posture, such as e.g. lying down or sitting in a relaxation chair. The head tracking system according to the invention comprises a sensing device for measuring a head movement to provide a measure representing the head movement, and a processing circuit for deriving the rotation angle of the head of the user with respect to the reference direction from the measure. The reference direction used in the processing circuit is dependent on the movement of the user. The advantage of making the reference direction dependent on a movement of a user is that determining the rotation angle of the head is independent of the environment, i.e. not fixed to environment. Hence whenever the user is e.g. on the move and his body parts undergo movement the reference direction is adapted to this movement.
The reference(s) cited above teach background information that may be applicable to the presently disclosed subject matter. Therefore the full contents of these publications are incorporated by reference herein where appropriate for appropriate teachings of additional or alternative details, features and/or technical background.
General Description
In many cases of head tracking, the user's frame of reference also undergoes changes, for example in response to a change in the direction of linear motion of the user. For example, in a VR system for watching movies in airplane, simulating a cinema room with screen and speakers, and where the user is sitting. It is desired that the simulated cinema will remain stable relative to the user, rather than to the earth's ‘north’, such that when the airplane turns the cinema will remain in front of the user's eyes. Another example is listening to music with virtualized loudspeakers over headphones while walking and/or running. In this example it is desirable that the virtualized loudspeakers position will remain in front of the listener even when the user is turning a street corner.
The presently disclosed subject matter alleviates provides a method and system of head tracking for use in a non-static environment by adjusting the reference used for head tracking according to the movement of the user. Two or more inertial measurement units (IMU) or any other two or more sensors for acquiring location and/or movement and/or orientation data are used, in which at least one of the sensors is used for tracking orientation of the user's head, and at least another sensor is used for providing information indicating a possible need to adjust the frame of reference by which the head movements are tracked.
According to one aspect of the presently disclosed subject matter there is provided a system for providing head orientation relative to an adaptive reference orientation comprising a head sensor configured to provide head data describing a first head orientation associated with a user; one or more second sensors configured to provide second data; and a processing unit operatively coupled to the head sensor and the one or more second sensors and configured to: receive head data from the head sensor; receive second data from the one or more second sensors; adapt said adaptive reference orientation by moving it at least partly towards said first head orientation by an amount which is varied at least partly in accordance with said second data, thereby generating a new adaptive reference orientation; and generate, in accordance with said first head orientation and said new adaptive reference orientation, a second head orientation associated with the user as said first head orientation relative to said new adaptive reference orientation.
In addition to the above features, the system according to this aspect of the presently disclosed subject matter can comprise one or more of features (i) to (xii) listed below, in any desired combination or permutation which is technically possible:
(i) the amount is varied at least partly in accordance with changes in the statistical properties of said second data.
(ii) the adaptive reference orientation is adapted by rotating the adaptive reference orientation in accordance with an adjustment amount by interpolating between said adaptive reference orientation and said first head orientation. Interpolating can be performed using a quaternion spherical linear interpolation (“Slerp”) operation.
(iii) the second data can be used to compute or derive the adjustment amount by computing one or more measures based on the second data, and converting the one or more measures to the adjustment amount.
(iv) the one or more measures can be converted to the adjustment amount by comparing one or more of the one or more measures to one or more respective thresholds.
(v) the one or more measures can include one or more of relative stability, relative deviation, and/or absolute deviation.
(vi) the adjustment amount can be further processed for smoothing.
(viii) the adjustment amount can be further processed to control one or more of rise time, hold time, and decay time of the adjustment amount.
(ix) the second data includes data indicative of a need to change the adaptive reference orientation.
(x) the second data includes data indicative of at least one of: location, motion, orientation, velocity and acceleration associated with the user in at least one dimension of a three dimensional coordinate system.
(xi) binaural audio can be rendered in accordance with the second head orientation and delivered to headphones worn by the user.
(xii) at least one of virtual reality (VR) video and/or augmented reality (AR) video can be rendered in accordance with the second head orientation.
According to another aspect of the presently disclosed subject matter there is provided a computer implemented method of providing a head orientation relative to an adaptive reference orientation comprising, by a processing unit, receiving head data from a head sensor, the head data describing a first head orientation associated with a user; receiving second data from one or more second sensors; adapting the adaptive reference orientation by moving it at least partly towards said first head orientation by an amount which is varied at least partly in accordance with said second data, thereby generating a new adaptive reference orientation; and generating, in accordance with said first head orientation and said new adaptive reference orientation, a second head orientation associated with the user as said first head orientation relative to said new adaptive reference orientation.
This aspect of the disclosed subject matter can comprise one or more of features (i) to (xii) listed above with respect to the system, mutatis mutandis, in any desired combination or permutation which is technically possible.
According to another aspect of the presently disclosed subject matter there is provided a non-transitory program storage device readable by a computer, tangibly embodying computer readable instructions executable by the computer to perform a method of providing a head orientation relative to an adaptive reference orientation comprising, by a processing unit, receiving head data from a head sensor, the head data describing a first head orientation associated with a user; receiving second data from one or more second sensors; adapting the adaptive reference orientation by moving it at least partly towards said first head orientation by an amount which is varied at least partly in accordance with said second data, thereby generating a new adaptive reference orientation; and generating, in accordance with said first head orientation and said new adaptive reference orientation, a second head orientation associated with the user as said first head orientation relative to said new adaptive reference orientation.
This aspect of the disclosed subject matter can optionally comprise one or more of features (i) to (xii) listed above with respect to the system, mutatis mutandis, in any desired combination or permutation which is technically possible.
Among the technical advantages of the presently disclosed subject matter is the ability to perform head tracking in a non-static environment by using data from one or more second sensors operating independently of the head sensor to detect when the user's frame of reference has changed.
Among further advantages is the ability to continually generate an adaptive reference orientation for use in head tracking, thereby enabling the proper placement of virtual objects around the user's head in a non-static environment.
In order to understand the invention and to see how it can be carried out in practice, embodiments will be described, by way of non-limiting examples, with reference to the accompanying drawings, in which:
In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be understood by those skilled in the art that the presently disclosed subject matter may be practiced without these specific details. In other instances, well-known methods, procedures, components and circuits have not been described in detail so as not to obscure the presently disclosed subject matter.
Unless specifically stated otherwise, as apparent from the following discussions, it is appreciated that throughout the specification discussions utilizing terms such as “processing”, “computing”, “calculating”, “adapting”, “generating”, or the like, refer to the action(s) and/or process(es) of a computer that manipulate and/or transform data into other data, said data represented as physical, such as electronic, quantities and/or said data representing the physical objects. The term “computer” should be expansively construed to cover any kind of hardware-based electronic device with data processing capabilities including, by way of non-limiting example, the processing circuitry disclosed in the present application.
The terms “non-transitory memory” and “non-transitory storage medium” used herein should be expansively construed to cover any volatile or non-volatile computer memory suitable to the presently disclosed subject matter.
The operations in accordance with the teachings herein may be performed by a computer specially constructed for the desired purposes or by a general-purpose computer specially configured for the desired purpose by a computer program stored in a non-transitory computer-readable storage medium.
The term “user” used in this patent specification should be expansively construed to cover an individual whose head movements are desirous of being tracked.
The term “head orientation” used in this patent specification should be expansively construed to cover any kind of data (e.g. in the form of a quaternion, rotation matrix or set of Euler angles, etc.) describing the rotation of the user's head in three dimensions (i.e. roll, pitch, yaw), which could also be described in relative terms relative to some other orientation.
The term “frame of reference” used in this patent specification should be understood as a non-mathematical term describing the scene (e.g. audio and/or visual) relative to which the user's head orientation is tracked.
The term “reference orientation” used in this patent specification should be expansively construed to cover any kind of data (e.g. in the form of a quaternion, rotation matrix or set of Euler angles, etc.) describing the rotation of the frame of reference relative to which the head orientation is described.
Embodiments of the presently disclosed subject matter are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of the presently disclosed subject matter as described herein.
Bearing this in mind, attention is drawn to
Processing circuitry (102) is further operatively coupled to one or more second sensors S1-Sn (116) which are configured to provide second data indicative of a need to change the reference orientation and which are configured to operate independently of head sensor (114). That is, head sensor (114) and second sensor(s) (116) do not sense one another or otherwise share data with one another. In certain embodiments, second sensor(s) (116) can include, e.g. one or more of an IMU, accelerometer, gyroscope, magnetometer, or other sensor capable of detecting changes to at least one of location, motion (e.g. kinetic motion, physical motion, three-dimensional motion, etc.), orientation, velocity, and/or acceleration associated with the user.
In certain embodiments, processing circuitry (102) can be comprised in a mobile device carried by the user, e.g. a smartphone, tablet, etc. In certain embodiments, the second sensor(s) (116) (or some of them) can also be comprised in a mobile device (which can be the same or different mobile device in which the processing circuitry may be comprised) carried by the user, sitting in the user's pocket, or otherwise physically situated in close proximity to the user, such that second sensor(s) are responsive to changes in the movement of the user.
Processing circuitry (102) can further comprise or be coupled to one or more processing units (104). Processing unit (104) can be, e.g., a processor, a microprocessor, a microcontroller or any other computing device or module, including multiple and/or parallel processing units. Processing circuitry (102) can further comprise (or be otherwise associated with) one or more memories, such as the illustrated data repository (106), configured to store data including, inter alia, received head data and/or second data, as will further be detailed below.
Processing circuitry (102) can further comprise (or be otherwise associated with) one or more of the following modules: Adjustment amount calculation (AAC) module (108), Reference orientation calculation (ROC) module (110), and a Relative head orientation calculation (RHOC) module (112).
In certain embodiments, the AAC module (108) can be configured to continually receive second data from second sensor(s) (116) and to compute a value indicative of an adjustment amount based on said data, as will further be detailed below with reference to
In certain embodiments, the ROC module (110) can be configured to receive a head orientation from head sensor (114), an adjustment amount from the AAC module, and an adaptive reference orientation, and to adapt the adaptive reference orientation by moving it toward the head orientation, thereby generating a new adaptive reference orientation, as will further be detailed below with reference to
In certain embodiments, the new adaptive reference orientation is fed back to the ROC module (110) as the next input adaptive reference orientation. For example, the ROC module (110) can include or be associated with a recursive filter (e.g. a smoothing filter, averaging filter, infinite impulse response (IIR) filter, finite impulse response (FIR) filter, etc.) configured to continually receive as input a reference orientation Qref[n] and a time constant Tc for averaging, and to continually output a new reference orientation Qref[n+1] by performing a smoothing operation in accordance with Tc. The output reference orientation Qref[n+1] is then fed back into the filter as the next input reference orientation Qref[n]. The time constant Tc may also be continually varied, as will be detailed below.
In certain embodiments, the RHOC module (112) can be configured to receive the most current adaptive reference orientation from the ROC module and the most current head orientation from head sensor (114), and to calculate the user's relative head orientation relative to the current adaptive reference orientation, as will be detailed below with reference to
In certain embodiments, the RAS (100) detailed above can be used for rendering binaural audio, virtual or augmented reality scenes, or any other application that requires placement of virtual objects around the head of the user. By way of non-limiting example,
It should be appreciated by those skilled in the art that while
In certain embodiments, after having calculated the one or more measures indicative of a need to change the reference orientation (300-1)-(300-N), the AAC module (108) converts the one or more measures to a value indicative of an adjustment amount (302). This conversion can be carried out by comparison of one or more measures to one or more thresholds. For example, the adjustment amount can be a derived value between 0 and 1 which is calculated based on one or a combination of two or more measures, as will be more fully detailed below and illustrated by way of certain examples. The adjustment amount can then be further filtered (304) linearly or non-linearly, e.g. to control one or more of rise time, hold time and decay time, or for smoothing.
The adjustment amount is the amount that the previous reference orientation will move towards the head orientation per time unit. This determines the velocity (e.g. angular velocity) at which the adaptive reference orientation will follow the head. The velocity being some measure of the speed of adaptation of the reference orientation towards the head orientation. This velocity is continuously varied in accordance with data from the second sensor.
Having now calculated an adjustment amount which is based at least in part on the most current second data (and which can be continually recalculated in real-time in response to changes in second data), the current adjustment amount is then fed to the ROC module (110) which uses the adjustment amount and current head orientation for adapting the adaptive reference orientation (306).
The process of adapting the reference orientation is repeated continuously such that the reference orientation is gradually converged toward the current head orientation by an amount which is dictated at least in part by the second data (as illustrated for a single dimension in
For example, if Qref is a quaternion representation of the reference orientation and Qhead is a quaternion representation of the current head orientation. Qref can be continuously converged towards Qhead with the computed AdjustAmount using a spherical linear interpolation operation (“Slerp”) in a first order feedback loop, as in Equation 1:
Qref[n]=Slerp(Qref[n−1],Qhead[n],AdjustAmout[n]) (1)
Equation 1 can be described as a first order IIR filter.
In general, a Slerp operation refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1 (see, e.g. Ken Shoemake: Animating Rotation with Quaternion Curves. SIGGRAPH, Volume 19, Number 3 (1985)). Thus in this example, Qref and Qhead would be the “ends” while the adjustment amount would be the interpolation parameter.
It should be appreciated by a person skilled in the art that there are many methods of calculating a linear interpolation between two orientations, and that Slerp example of Equation 1 is but a single non-limiting example.
As detailed above, each time a new reference orientation is generated by the ROC module (110), the new reference orientation is fed back into the ROC module (110) for generating the next reference orientation. In addition, new reference orientation is also fed to the RHOC module (112) which uses the new reference orientation and the current head orientation to determine the user's relative head orientation (308) relative to the new reference orientation. For example, the relative orientation Qhead/ref can be determined from the reference orientation Qref and the head orientation Qhead by multiplication with the inverse quaternion as in Equation 2:
Qhead/ref=Qref−1Qhead (2)
The above process is repeated continuously such that the user's relative head orientation is continuously being determined, and possibly in real-time response to the user's head movements, according to which Qhead/ref can be used as the head orientation in any moving VR, AR or binaural environment.
As detailed above, in certain embodiments, prior to being fed to the ROC module (110), the adjustment amount may undergo a filtering process, e.g. to control the adjustment amount according to a predetermined minimum and/or maximum and/or filtered linearly and/or non-linearly to control one or more of the rise time, hold time, and decay time in order to create an optimal and natural motion of the reference orientation. For example, a maximum time constant of 60 sec corresponding to some minimum amount will ensure that the reference orientation will always be slowly moving towards the head direction to compensate for small or slowly accumulating drifts. In another example, a short rise time (0 sec) and longer hold and decay times (2 secs) could be set on the amount such that if a sudden, short transient occurred, the amount would respond immediately causing the reference orientation to tightly follow the head (to compensate for the drastic change) all through the hold time. Then, slowly as the decay time fades out, the reference orientation eventually stay static and normal tracking would be resumed.
Line graph (418) of
Line graph (420) of
Line graph (422) of
As illustrated in
It should be noted that due to the zoom level of the graph shown in
In certain embodiments, as detailed above, the one or measures can include one or a combination of one or more of relative stability, relative deviation, and absolute deviation. Each of these measures will be now be discussed in more detail and examples will be provided.
This measure compares the current short time sample variance to an earlier long term sample variance and returns an indicator of relative increase in variance. Let the variance S of each sensor (per axis) over the samples between n−N and n be denoted using Equation 3:
The relative stability per axis (not normalized) is given by Equation 4:
RS_UNNORMperSensorPerAxis[n]=max((S{n,n−N1}−S{n−N1,n−N1−N2}),0) (4)
where N1 and N2 are sample groups (time windows) over which the variances are computed, and n is the current sample. Normalizing this for total variance of variances using the variance of a variance for normal distribution is given by:
which translates to a pooled variance of the two sets given by:
Thus the normalized relative stability per axis per sensor can be written as Equation 5:
The denominator normalizes the variances by the total variance of variance, and thus the variance is used as a random variable to achieve a unit-less measure of change in variance. A unit-less measure is critical in order to set one threshold for different device and sensors types.
Finally, the relative stability calculated for each axis per sensor can be combined by root mean square (RMS) and also combined between sensors by a weighted RMS to allow different weighting per sensor, e.g. using Equation 6:
where K is the number of sensors. For example, for three axis gyro and three axis accelerometer, K=2. Then, for example at 100 Hz, if T1=0.5 sec and T2=2.0 sec, then N1=50, N2=200. In this example, the stability of the current half second (short term) is compared to that of the preceding two seconds (long term).
This measure compares the mean reference orientation between two adjacent time spans. Computing the geometrical mean quaternion of a set of four-dimensional quaternions can be achieved using the ‘Slerp’ operation described above. This operation ensures that the interpolation between two quaternions is done via the shortest path (i.e. the greater circle). In order to compute the mean over period of Tc, the Slerp operation can be used in a recursive fashion as in Equation 7:
Qmean[n]=Slerp(Qmean[n−1],Qin[n],α) (7)
where α is the relative amount to Slerp over each step, and is defined by the time constant Tc and the tracking sample rate Fs as per Equation 8:
α=1−e−1/(F
To compute a variance for quaternions, a distance measure is defined, e.g. the angle between the two quaternions computed by the dot product as in Equation 9:
The variance can then be computed as in Equation 10:
It should be noted that Qmean is a vector, but the variance SQ is a scalar in units of squared angles.
The means and variances are computed twice, once over the last second (or any other time span), and again over the preceding second (or any other time span). i.e.:
Qmean1=Qmean(t,t−T) and Qmean2=Qmean(t−T,t−2T); and
SQ1=SQ(t,t−T) and SQ2=SQ(t−T,t−2T)
T is a time constant over which the mean and variance of orientations are computed. For example, when T=1 sec, the orientation in the current second is compared to that of the previous second.
Using the means and variances, the relative deviation can be computed which is also unit-less, using Equation 11:
This measure is computed by combining the measures of relative stability and relative deviation which were detailed above. These measures can be combined, e.g. using root mean squares as in Equation 12:
In certain embodiments, the individual measures (i.e. relative stability and relative deviation) can each be assigned a respective weight.
This measure aims to cope with situations where slow motion occurs which might not be caught by the two examples above. This measure (provided in angular units) compares the mean second-sensor's orientation with some reference anchor, the anchor being some past orientation. When the deviation from the anchor exceeds a threshold the anchor is set to the current second-sensor's orientation, as in Equation 13:
AbsDeviationMeasure=|θdiff(Qmean,Qanchor)| (13)
Conversion of Measures to Adjustment Amount
As detailed above, the adjustment amount can be derived from one or a combination of two or more measures. For example, referring to the example measures of relative stability, relative deviation and absolute deviation which were detailed above, the adjustment amount can be calculated as per Equation 14:
where p is some power value.
If the absolute deviation measure exceeds the absolute threshold (e.g. in degrees or other unit of orientation), the AdjustAmount is set to 1, otherwise, it is set smoothly in the range 0-1 with the position and shape of the slope controlled by the RelThreshold and p respectively as illustrated in
As detailed above, the example linear interpolation operation provided in Equation 1 can be described as a first order IIR filter. In systems such as this it is typical to define a filter time constant Tc over which the value of the output reaches a value of
of the target value. Under these definitions, the relation between the adjustment amount and the Tc is described in Equations 15 and 16:
where log is the natural logarithm and Fs is the sample rate.
However, the adjustment amount varies based on second sensor data so Tc is not constant as described in Equation 17:
Using Tc[n], the reference orientation can be described as adapting at a velocity proportional to 1/Tc[n].
At block 702, processing unit receives head data from head sensor (114). The head data describes a first head orientation associated with a user. In certain embodiments, head data is continually being received from the head sensor, for example at a predetermined sampling rate, such that the most recently received head data thereby describes the current first head orientation.
Substantially concurrently with receiving head data, at block 704 the processing unit receives second data from the one or more second sensors (116). In certain embodiments, second data is continually received from the one or more second sensors, for example at respective predetermined sampling rates, such that the most recently received second data thereby describes the most current second data. In certain embodiments, as detailed above, the second data comprises data indicative of a need to change the adaptive reference orientation, e.g. data indicative of location, motion, orientation, velocity and/or acceleration associated with the user in at least one dimension of a three dimensional coordinate system.
At block 706, the processing unit. e.g. AAC module (108), continually calculates a value indicative of an adjustment amount at least partly in accordance with the most current second data. In certain embodiments, the adjustment amount can be derived or computed from the second data, for example by computing one or more measures from the second data (e.g. based on changes in statistical properties of the second data) and converting the one or more measures to an adjustment amount. In certain embodiments, the one or more measures can be converted to an adjustment amount by comparing one or more of the measures to one or more respective thresholds. The one or more measures can include, e.g. relative stability, relative deviation and/or absolute deviation. In certain embodiments, the adjustment amount may be further filtered for smoothing and/or to control one or more of rise time, hold time, and decay time.
At block 708, the processing unit, e.g. ROC module (110), continually adapts the adaptive reference orientation by moving it at least partly toward the head orientation (as provided by the head data) by an amount which is varied at least partly in accordance with the second data, thereby generating a new adaptive reference orientation. In certain embodiments, the amount can be determined by the adjustment amount. In certain other embodiments, the amount can be derived from a filter time constant Tc over which the value of the reference orientation will converge at least partly towards the current head orientation. In certain embodiments, adapting the adaptive reference orientation can include rotating the adaptive reference orientation in accordance with the adjustment amount calculated at block 706. The rotating can be achieved, e.g. by means of a quaternion “Slerp” between the adaptive reference orientation and the first head orientation.
At block 710, the processing unit, e.g. RHOC module (112), generates data indicative of a second head orientation associated with the user in accordance with the user's first head orientation (received at block 702) and the new adaptive reference orientation (generated at block 708), in which the second head orientation describes the user's first head orientation relative to the new adaptive reference orientation. In certain embodiments, the user's second head orientation can be used for rendering at least one of binaural audio, VR video and/or AR video, which can then be delivered to the user via headphones, oculus, or other listening and/or viewing apparatus. Execution then returns to block 702 and the sequence of operations 702-710 is repeated wherein the new adaptive reference orientation generated at block 710 constitutes the next reference orientation to be adapted at block 708.
At each execution of block 710, the user's most current relative head orientation is generated relative to the adaptive reference orientation, thereby enabling the delivery of the rendered audio and/or video to the user in response to the user's head movements in real-time or near real-time with the user's head movements.
It is noted that the teachings of the presently disclosed subject matter are not bound by the system described with reference to
It is noted that the teachings of the presently disclosed subject matter are not bound by the flow chart illustrated in
It is to be understood that the invention is not limited in its application to the details set forth in the description contained herein or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Hence, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting. As such, those skilled in the art will appreciate that the conception upon which this disclosure is based may readily be utilized as a basis for designing other structures, methods, and systems for carrying out the several purposes of the presently disclosed subject matter.
It will also be understood that the system according to the invention may be, at least partly, implemented on a suitably programmed computer. Likewise, the invention contemplates a computer program being readable by a computer for executing the method of the invention. The invention further contemplates a non-transitory computer-readable memory tangibly embodying a program of instructions executable by the computer for executing the method of the invention.
Those skilled in the art will readily appreciate that various modifications and changes can be applied to the embodiments of the invention as hereinbefore described without departing from its scope, defined in and by the appended claims.
The present application claims benefit from U.S. Provisional Patent Application No. 62/330,267 filed on May 2, 2016, which is incorporated hereby by reference in its entirety.
Filing Document | Filing Date | Country | Kind |
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PCT/IL2017/050484 | 5/1/2017 | WO | 00 |
Publishing Document | Publishing Date | Country | Kind |
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WO2017/191631 | 11/9/2017 | WO | A |
Number | Name | Date | Kind |
---|---|---|---|
5742264 | Inagaki et al. | Apr 1998 | A |
5959597 | Yamada et al. | Sep 1999 | A |
6009210 | Kang | Dec 1999 | A |
6474159 | Foxlin et al. | Nov 2002 | B1 |
9268136 | Starner et al. | Feb 2016 | B1 |
9271103 | Wells | Feb 2016 | B2 |
9821920 | Cole et al. | Nov 2017 | B2 |
20080170730 | Azizi et al. | Jul 2008 | A1 |
20090058606 | Munch et al. | Mar 2009 | A1 |
20090147993 | Hoffmann et al. | Jun 2009 | A1 |
20090189830 | Deering | Jul 2009 | A1 |
20090219224 | Elg | Sep 2009 | A1 |
20110193883 | Palais et al. | Aug 2011 | A1 |
20110293129 | Dillen et al. | Dec 2011 | A1 |
20130236040 | Crawford et al. | Sep 2013 | A1 |
20140232637 | Park et al. | Aug 2014 | A1 |
20140354515 | LaValle et al. | Dec 2014 | A1 |
20160363992 | Welti | Dec 2016 | A1 |
20170050743 | Cole | Feb 2017 | A1 |
20170083084 | Tatsuta et al. | Mar 2017 | A1 |
20180081426 | Rothkopf | Mar 2018 | A1 |
Entry |
---|
“Slerp,” Wikipedia, [https://en.wikipedia.org/wiki/Slerp]. |
“Quaternion,” Wolfram MathWorld, [http://mathworld.wolfram.com/Quaternion.html]. |
“Quaternions and spatial rotation,” Wikipedia, [https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation]. |
Blow, Jonathan, “Understanding Slerp, Then Not Using It,” The Inner Product, Apr. 2004, [http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/]. |
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20190064519 A1 | Feb 2019 | US |
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