Patent Publication Number: US-10311621-B2

Title: Held object stabilization in virtual reality

Description:
TECHNICAL FIELD 
     This description generally relates to the representation of objects in virtual reality (VR). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an example electronic environment for performing improved techniques described herein. 
         FIG. 2  is a flow chart depicting an example method according to the improved techniques. 
         FIG. 3  is a diagram depicting an example filtering of an object within the electronic environment shown in  FIG. 1 . 
         FIG. 4  is a diagram depicting another example deformation of an object within the electronic environment shown in  FIG. 1 . 
         FIG. 5  is a diagram depicting an example of a computer device that can be used to implement the improvement described herein. 
         FIG. 6  is a diagram depicting an example head mounted display (HMD) for use in a virtual reality (VR) environment. 
         FIGS. 7A, 7B, and 7C  are diagrams depicting the example VR HMD and an example controller. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     A virtual reality (VR) system that generates a virtual environment includes a VR computer and a controller. A human user experiences a virtual environment generated by the VR computer by interacting with various objects within the virtual environment. For example, the human user may use the controller to move an object through a translation and/or a rotation via a gesture. To provide a natural simulation of the motion of the object in response to a gesture from the human user, the VR computer performs an animation of the object according to a rigid transformation. 
     Approaches to animating objects can involve defining vertices of an object and rigid transformations of those vertices that represent movement of various parts of the object. In some cases, there is a filter applied to the rigid transformations to simulate mass of the object. 
     As a simple example, suppose that the object is a baseball bat. A baseball bat is a long, rigid object. If the bat is a single, rigid element, then the relative distance of each pair of points on the bat remains fixed through a motion (i.e., translation and rotation). That is, each point of the bat is translated the same amount and undergoes the same angle of rotation in response to translational and rotational motions. 
     Some approaches herein to animating objects in a virtual environment scale well to interactive animations such as those in virtual reality (VR). For example, the approaches may not account for sources of noise, including (i) measurement noise in hand-held controllers used by users to control objects in a virtual environment and (ii) natural hand vibrations. The noise sources produce unnaturally jittery motion in the virtual environment when the user holds the object relatively still. 
     The noise has a translational component and a rotational component. The rotational component of the noise is amplified for vertices far from a fixed anchor point, Larger objects are particularly sensitive to this rotational noise. 
     For example, referring back to bat example introduced above, the response of the bat to motion at one of its ends (i.e., a handle where a user nominally holds the bat) might not be uniform because the bat may not be perfectly rigid. Along these lines, the user may introduce rotational noise as he or she holds the bat. The rotational noise at the handle where the user holds the bat may be amplified at the other end of the bat farther away from the user. Such an amplified rotational noise may result in an unnatural look and feel of the bat as represented in the virtual environment. 
     Other, more complex objects such as people and animals may be modeled as having rigid elements (“bones”) linked together by non-rigid elements. In the case of people and animals, the non-rigid elements may include joints and other connective tissue. In these cases, rotational noise at one point, e.g., a hand, may produce unnaturally large rotational noise at a remote point, e.g., a shoulder. 
     Simply filtering this rotational noise is undesirable. The rigidity of the attachment to the user&#39;s hand when the user is holding an object in VR is important to maintain presence. If the object were to start lagging behind the hand, either rotationally or positionally, the user experience would be tainted. The filter applied to the rigid transformations to simulate mass of the object may dampen such high-frequency motion at a fixed anchor point, but such a filter may make unintended vibrations away from the anchor point worse and compromise the user&#39;s experience. 
     The techniques of animating objects in VR described herein involve applying a motion filter to the object that varies with vertices on an object. Along these lines, a VR computer generates an object for an interactive, three-dimensional game by generating the triangular mesh approximating the surface of the object as well as rigid elements, or bones including vertices that define the motion of the vertices based on motion of an anchor vertex. For example, a bat may be represented by (e.g., modeled using) a single bone. As another example, an arm or hand of an avatar in a virtual environment may be represented by multiple connected bones. 
     A bone of an object is a rigid element that includes vertices of the object such that, when the bone moves, each vertex of the bone moves in the same way. When a user selects a vertex of the object as an anchor vertex about which to move the object, the VR computer generates variable filters for each bone that restrict the motion of that bone based on the distance of that bone from the anchor vertex. The filters may restrict that motion by reducing the amount of high-frequency motion associated with rotational noise. Accordingly, when the user produces a gesture with a controller that defines a path of motion for the anchor vertex, the bone including the anchor vertex goes through an unfiltered motion while bones remote from the anchor vertex go through a more restricted motion. Meanwhile, in an interior region of the object in which there are no bones, the vertices of the surface of the object may be smoothly deformed so that rigidity of the object remote from the anchor vertex is achieved during motion. Nevertheless, the VR computer may perform a dual quaternion skinning operation that preserves the volume of the interior region of the object. 
     In some implementations, a dual object is a mathematical object of the form f+∈g, where ∈ 2 =0. That is, for example, (f+∈g) 2 =f 2 +∈·2fg. A quanternion is a quantity of the form a+bî+cĵ+d{circumflex over (k)}, where îĵ={circumflex over (k)}, ĵ{circumflex over (k)}=î,  , =ĵ are quarternion units, and î 2 =ĵ={circumflex over (k)} 2 =−1, with multiplication of the quarternion units being anticommutative. Accordingly, a dual quarternion is a quarternion in which the quantities a,b,c,d are dual objects. Representing the various rotational and translational operations with dual quarternions allows transformations of non-rigid portions of an object that preserve volume. 
       FIG. 1  is a block diagram depicting an example electronic environment  100  according to the improved techniques described herein. The electronic environment  100  includes a user  112  with a VR controller and display  110 , a VR computer  120 , and a network  180 . 
     The VR controller  110  may take the form of a head-mounted display (HMD) which is worn by the user  112  to provide an immersive virtual environment. In the example electronic environment  100 , the user  112  that wears the VR controller  110  holds a user device, i.e., user device  114 . The user device  114  may be, for example, a smartphone, a controller, a joystick, or another portable handheld electronic device(s) that may be paired with, and communicate with, the VR controller  110  for interaction in the immersive virtual environment. The user device  114  may be operably coupled with, or paired with the VR controller  110  via, for example, a wired connection, or a wireless connection such as, for example, a WiFi or Bluetooth connection. This pairing, or operable coupling, of the user device  114  and the VR controller  110  may provide for communication between the user device  114  and the VR controller  110  and the exchange of data between the user device  114  and the VR controller  110 . This may allow the user device  114  to function as a controller in communication with the VR controller  110  for interacting in the immersive virtual environment. That is, a manipulation of the user device  114 , such as, for example, a beam or ray emitted by the user device  114  and directed to a virtual object or feature for selection, and/or an input received on a touch surface of the user device  114 , and/or a movement of the user device  114 , may be translated into a corresponding selection, or movement, or other type of interaction, in the immersive virtual environment provided by the VR controller  110 . 
     The VR computer  120  is configured to generate virtual environment (VE) data  130  for the immersive virtual environment and transmit that data to the user device  114  over the network  180 . As illustrated in  FIG. 1 , the VR computer  120  is implemented as a computer system that is in communication with the user device  114  over the network  180 . 
     The VR computer  120  includes a network interface  122 , a set of processing units  124 , memory  126 , and a signal receiver  128 . The network interface  122  includes, for example, Ethernet adaptors, Token Ring adaptors, and the like, for converting electronic and/or optical signals received from the network  180  to electronic form for use by the virtual environment computer  120 . The set of processing units  124  include one or more processing chips and/or assemblies. The memory  126  includes both volatile memory (e.g., RAM) and non-volatile memory, such as one or more ROMs, disk drives, solid state drives, and the like. The set of processing units  124  and the memory  126  together form control circuitry, which is configured and arranged to carry out various methods and functions as described herein. 
     In some embodiments, one or more of the components of the VR computer  120  can be, or can include processors (e.g., processing units  124 ) configured to process instructions stored in the memory  126 . Examples of such instructions as depicted in  FIG. 1  include a virtual environment manager  160  and an object transform manager  170 . The memory  126  may also store various data passed by the processors into routines realized by the instructions. As depicted in  FIG. 1 , such data include the VE data  130 , which in turn includes object data  140 ( 1 ), . . . ,  140 (M). 
     The VE manager  160  is configured to generate VE data  130  to be realized as the immersive virtual environment by the VR controller  110 . For example, when the VR computer  120  is configured to process data for an interactive, immersive game, the VE data  130  generated by the VR computer  120  may include some background data that renders as the walls of a room or an outdoor environment. In addition, the VE data  130  also includes a set of objects  140 ( 1 ), . . . ,  140 (M) with which the user  112  may interact via the VR controller  110 . The VR computer  120  may render any of the objects  140 ( 1 ), . . . ,  140 (M) onto the display/controller  110  for viewing by the user  112 . 
     Each object, e.g., object  140 ( 1 ), represents some physical object within the virtual environment. For example, if the VR computer  120  is processing a dart game, one virtual object may be a dart, another a dartboard. In such a game, the user  112 , via the controller  110 , may interact with the object  140 ( 1 ) via an avatar of the controller. Along these lines, the user  112  moves the controller  110  to a point on the object  140 ( 1 ), i.e., an anchor vertex. The user may then manipulate the object  140 ( 1 ) by a series of gestures with the controller. That is, each gesture may be interpreted by the VR computer  120  as a command to move the object  140 ( 1 ) along a certain path. 
     The object  140 ( 1 ) includes a plurality of vertices  142 ( 1 ) that define the surface of the object  140 ( 1 ). Typically, the VR computer  120  constructs the object  140 ( 1 ) from a triangular mesh in three-dimensional space. Each of the vertices of the triangular mesh then forms a vertex  142 ( 1 ) of the surface of the object  140 ( 1 ). 
     In principle, when the object  140 ( 1 ) is fully rigid, the movement of the object  140 ( 1 ) through a path is represented by a rigid transformation of each of the vertices  142 ( 1 ). The movement typically has a translational component and a rotational component. In some implementations, the movement may be represented as a series of matrices added and/or multiplied together. In other implementations, however, such motion may be represented by dual quaternions. 
     In most cases, however, the object  140 ( 1 ) is not truly rigid and some deformation may be expected. For example, portions of the objects between bones may not be rigid and the vertices in such portions may all move differently with respect to one another. In these cases, the object also contains a set of bones, i.e., rigid elements  144 ( 1 )( 1 ), . . . ,  144 ( 1 )(N 1 ), each of which are rigid parts of the object  140 ( 1 ) and have at least one vertex  142 ( 1 ) of the surface of the object. Instead of associating a transformation with each vertex, a transformation is associated with each bone, e.g., bone  144 ( 1 )( 1 ). The vertices of each bone move according to the transformation to the bone. For example, if the bone is rotated, each of the vertices, which are fixed to the respective ends of the bone will rotate with the bone. As another example, if the bone is translated, each of the vertices, which are fixed to the respective ends of the bone will be translated with the bone. If one end of the bone is moved more than another end of the bone, then one vertex will be moved more than the other vertex based on the movement of the bone. 
     An example of a bone is illustrated in  FIG. 3 . In  FIG. 3 , an elongated object  300  is shown. The object  300  has two bones,  315  and  325  in respective, rigid regions  310  and  320 . Each of these bones  315 ,  325  is represented as dashed lines because the bones are not a real portion of the object  300  but rather a device that helps visualize how some portions of the object  300  move. Each of the bones, e.g., bone  315 , has two vertices: an anchor vertex  340  and a second vertex  350  that is adjacent to a non-rigid region  330  of the object. For example, suppose again that the object is a baseball bat. A user would hold the bat at one end (the handle), at point  340 . Any sort of noise induced in the motion of an anchor vertex at this end might cause very large amounts of rotational noise at point  380  at the other end of the bat. Nevertheless, by filtering at the far end (point  380 ) differently than at the handle or close end (point  340 ), then such filters that dampen motion at the point  380  can be used to reduce or eliminate that jitter at the point  380 . Referring back to  FIG. 1 , because it has been found that motion under which bones remote from the anchor vertex move is more sensitive to noise (e.g., natural human hand jitter as well as machine-induced noise from the controller  110 ), each bone  144 ( 1 )( 1 ) has its own respective motion filter  146 ( 1 )( 1 ). The filters  146 ( 1 )( 1 ), . . . ,  146 ( 1 )(N 1 ) may then be different. In some implementations, the filters  146 ( 1 ), . . . ,  146 ( 1 )(N 1 ), dampen such noise in the motion according to a distance from an anchor vertex. For the bone including the anchor vertex, e.g., bone  144 ( 1 )(N 1 ), the motion may be unfiltered, i.e., the filter  146 ( 1 )(N 1 ) is represented by an identity transformation. 
     Each of the filters  146 ( 1 )( 1 ) may take the form of a dual-quaternion quantity that multiplies or otherwise modifies a dual quaternion transformation that represents the motion of a bone  144 ( 1 )( 1 ). In some implementations, the filter  146 ( 1 )( 1 ) may take the form of a constant damping term. In other implementations, the filter  146 ( 1 )( 1 ) may take the form of a low-pass filter in frequency space that dampens or eliminates high-frequency motion such as jitter. 
     The object transform manager  170  is configured to transform a selected object, e.g., object  140 ( 1 )( 1 ) in response to a gesture from the user  112  via the controller  110 . As discussed above, the gesture is interpreted by the VR computer  120  as a request to move the object along a translational and rotational path. 
     The object transform manager  170  is also configured to generate and apply a filter  146 ( 1 )( 1 ) to each of the bones  144 ( 1 )( 1 ). Each filter may be computed, in some implementations, based on a distance from an anchor vertex. The application of the filter may be a matrix, quaternion, or dual quaternion multiplication. 
     The network  180  is configured and arranged to provide network connections between the VR controller  110  and the virtual environment computer  120 . The network  180  may implement any of a variety of protocols and topologies that are in common use for communication over the Internet or other networks. Further, the network  180  may include various components (e.g., cables, switches/routers, gateways/bridges, etc.) that are used in such communications. 
     In some implementations, the memory  126  can be any type of memory such as a random-access memory, a disk drive memory, flash memory, and/or so forth. In some implementations, the memory  126  can be implemented as more than one memory component (e.g., more than one RAM component or disk drive memory) associated with the components of the virtual environment computer  120 . In some implementations, the memory  126  can be a database memory. In some implementations, the memory  126  can be, or can include, a non-local memory. For example, the memory  126  can be, or can include, a memory shared by multiple devices (not shown). In some implementations, the memory  126  can be associated with a server device (not shown) within a network and configured to serve the components of the virtual environment computer  120 . 
     In some implementations, the VR computer  120  can be, for example, a wired device and/or a wireless device (e.g., WiFi enabled device) and can be, for example, a computing entity (e.g., a personal computing device), a server device (e.g., a web server), a mobile phone, a touchscreen device, a personal digital assistant (PDA), a laptop, a television, a tablet device, e-reader, and/or so forth. Such device(s) can be configured to operate based on one or more platforms (e.g., one or more similar or different platforms) that can include one or more types of hardware, software, firmware, operating systems, runtime libraries, and/or so forth. 
     The components (e.g., modules, processing units  124 ) of the VR computer  120  can be configured to operate based on one or more platforms (e.g., one or more similar or different platforms) that can include one or more types of hardware, software, firmware, operating systems, runtime libraries, and/or so forth. In some implementations, the components of the VR computer  120  can be configured to operate within a cluster of devices (e.g., a server farm). In such an implementation, the functionality and processing of the components of the VR computer  120  can be distributed to several devices of the cluster of devices. 
     The components of the VR computer  120  can be, or can include, any type of hardware and/or software configured to process attributes. In some implementations, one or more portions of the components shown in the components of the VR computer  120  can be, or can include, a hardware-based module (e.g., a digital signal processor (DSP), a field programmable gate array (FPGA), a memory), a firmware module, and/or a software-based module (e.g., a module of computer code, a set of computer-readable instructions that can be executed at a computer). For example, in some implementations, one or more portions of the components of the VR computer  120  can be, or can include, a software module configured for execution by at least one processor (not shown). In some implementations, the functionality of the components can be included in different modules and/or different components than those shown in  FIG. 1 . 
     Although not shown, in some implementations, the components of the VR computer  120  (or portions thereof) can be configured to operate within, for example, a data center (e.g., a cloud computing environment), a computer system, one or more server/host devices, and/or so forth. In some implementations, the components of the VR computer  120  (or portions thereof) can be configured to operate within a network. Thus, the components of the VR computer  120  (or portions thereof) can be configured to function within various types of network environments that can include one or more devices and/or one or more server devices. For example, the network can be, or can include, a local area network (LAN), a wide area network (WAN), and/or so forth. The network can be, or can include, a wireless network and/or wireless network implemented using, for example, gateway devices, bridges, switches, and/or so forth. The network can include one or more segments and/or can have portions based on various protocols such as Internet Protocol (IP) and/or a proprietary protocol. The network can include at least a portion of the Internet. 
       FIG. 2  is a flow chart depicting an example method  200  of animating an object in a virtual environment. The method  200  may be performed by software constructs described in connection with  FIG. 1 , which reside in memory  126  of the VR computer  120  and are run by the set of processing units  124 . 
     At  202 , the VR computer  120  generates an object in a virtual environment. The object has a surface and includes a plurality of bones. The surface of the object includes a plurality of vertices. Each of the plurality of vertices is included in a respective bone of the plurality of bones. Each of the plurality of bones defines a motion of each vertex of that bone according to a rigid transformation. 
     At  204 , the VR computer  120  receives a request to move a first vertex of the surface of the object included in a first bone of the plurality of bones and a second vertex of the surface of the object included in a second bone of the plurality of bones. 
     At  206 , the VR computer  120 , in response to the request, applies a first filter to a first bone of the set of bones and a second filter to a second bone of the set of bones. Each of the first filter and the second filter, upon respective application to the first bone and the second bone, restricts the motion of the first vertex of the first bone by a first amount and restricts the motion of the second vertex by a second amount different from the first amount. 
     Based on the filtering described above, an object that has portions far from an anchor point can be stable to, for example, rotational noise. Without the use of such distance-dependent filters, portions relatively far from an anchor point can have rotational noise that tend to be amplified at the distant vertices. Accordingly, a filter at a remote point would dampen the motion at the remote point relative to the motion at a near point. For example, suppose that the object is a baseball bat. A user would hold the bat at one end (the handle). Any sort of rotational noise induced in the motion of an anchor vertex at this end might cause there to be very large, noisy rotational motions at the other end of the bat. Nevertheless, by filtering at the far end differently than at the handle, then the filters can be used to dampen, i.e., reduce high-frequency motion associated with the rotational noise at the far end with respect to motion at the near end. 
     In typical cases, such non-uniform filtering may cause the object in intermediate, non-rigid regions to deform. That said, the deformation of the object in such non-rigid regions can be controlled, as will be described in connection with  FIGS. 3 and 4  below. 
       FIG. 3  is a diagram depicting an example filtering of an object  300 . As shown in  FIG. 3 , the object  300  is divided into three distance ranges, or regions. This division is a model of an object having two bones and a non-rigid connector between these bones. 
     The first region  310  has a first bone  315  which in turn includes an anchor vertex  340  and an interior endpoint  350 . The second region  320  has a bone  325  which in turn includes a remote vertex  380  of the surface of the object  300  and an interior endpoint  360 . The third region  330 , in between the first and second regions, is non-rigid and has no bone. Rather, the surface  370  includes vertices of the object  300  that may move differently with respect to one another and may be deformed. 
     Upon receipt of a command to move the object  300  with respect to the anchor vertex  340  (e.g., a gesture from a human user that moves the anchor point  340  and, hence, the bone  315  and vertex  350 ), the VR computer  120  ( FIG. 1 ), via the object transform manager  170 , computes the rigid transformation to move the bone  315  that includes the anchor vertex  340  to a final point along a path as well as the bone that contains the remote vertex  380  to another destination based on its initial position and orientation. The object transform manager  170  also generates a filter for the bone  325  including the remote vertex  380  so as to dampen high-frequency jitter. 
     The object  300  illustrated in  FIG. 3  is highly directional, while many objects in a virtual environment may not be so. For the general case of objects possessing both high and low degrees of directionality, it has been found to be advantageous to define the bone in region  320 , i.e., the bone  325  including the remote vertex  380 , to be identical to the bone  315  in the region  310 , i.e., that including the anchor vertex  340 . This would limit the VR computer  120  to filtering against a rotation around the anchor point, while at the same time the VR computer  120  would be able to handle arbitrary objects and not just highly directional ones. 
     In rigging terms, all vertices between the anchor vertex  340  and the endpoint  350  are 100% mapped to the anchor&#39;s transform; all vertices past the endpoint  360  are 100% mapped to the filtered (remote) transform, and vertices between points  350  and  360  may be mapped using a regular function using the distance between the vertex and the anchor point as input. 
       FIG. 4  is a diagram depicting an example mapping function  400  used to map the vertices in region  330  ( FIG. 3 ). In order to avoid artifacts, the mapping function may not introduce discontinuities in the surface. Thus, the object transform manager  170  may generate a weight mapping function that has a zero slope at the endpoints  350  and  360 . 
     As illustrated in  FIG. 4 , the weight mapping function takes the form f(x)=sin 2 (π/2x) when the distance along an axis of symmetry (i.e., a horizontal axis) in the non-rigid region  330  is mapped to the interval [0,1]. In this way, vertices further away from the endpoint  350  and closer to the endpoint  360 , i.e., further away from the anchor vertex, experience more distortion. 
     Returning to  FIG. 3 , such distortion as introduced in region  330  by the weight mapping function  400  is illustrated as the distorted surface  370  in region  330 . Here, the surface of the object  300  is tapered in this non-rigid region. Note that the actual taper will have cylindrical ends so as to satisfy the constraint of zero slope at the endpoints  350  and  360 . 
     In some arrangements, the filter for the bone in region  320  may take the form of an asymptotic filter with a filtering ratio proportional to a current angular distance between the unfiltered and previously filtered orientations. For example, suppose again that the object is the elongated object  300  (e.g., an animal leg) subject to rotational noise at the far end at point  380 . Then the asymptotic filter damps motion at the point  380  proportional to the difference in angle between unfiltered and previously filtered motion due to the rotational noise (“diff”). This filter restricts (e.g., dampens) the motion at the far end according to this filtering ratio (“strength_pct”) and dampens the effect of the rotational noise. Accordingly, application of this filter will cause the animal leg to be stable at both ends in response to rotational noise at one end. In this case, some pseudocode describing a computation of such a filter might take the following form. 
     
       
         
           
               
             
               
                   
               
             
            
               
                 dual_quat filt = get_unfiltered_transform( ); 
               
               
                 min_angle = degrees (2) 
               
               
                 max_angle = degrees (8) 
               
               
                 filt_min = 0.1 
               
               
                 filt_max = 0.8 
               
               
                 while(1) { 
               
               
                  // update here... 
               
               
                  dual_quat_unfilt = get_unfiltered_transform( ); // relative to the 
               
               
                  anchor 
               
               
                  diff = angle(filt.q, unfilt.q); 
               
               
                  // Compensate for pi-crossings. 
               
               
                  if (diff &gt; pi) { 
               
               
                  diff = abs (diff − two_pi); 
               
               
                  filt.q * = −1.0; 
               
               
                  } 
               
               
                  strength_pct = clamp((diff − min_angle) / (max_angle −  
               
               
                  min_angle), 0, 1) 
               
               
                  filt = mix(filt, unfilt, mix(filt_min, filt_max, strength_pct)); 
               
               
                  //render various viewports here... 
               
               
                 } 
               
               
                   
               
            
           
         
       
     
     In some arrangements, the object transform manager  170  performs a skinning operation on the object  300 . Skinning is a process that involves associating a portion of the surface of an object, i.e., a skin, with a bone of the object. In an object having many, independently movable bones, some portions of the skin may be associated with more than one bone, e.g., the skin associated with a joint between two bones of an animal leg. 
     In some implementations, the object transform manager  170  uses a dual quaternion skinning in order to take advantage of certain volume-preserving properties of such a transformation. In this case, some pseudocode describing such a skinning operation might take the following form. As the pseudocode makes clear, the mapping function only alters the vertex positions and not vertex normals so that the distortion in the non-rigid region  330  is not obvious (or perceptible) to the user. 
     As an example, an animal leg has two bones  315  and  325  and a non-rigid region  330  between these bones  315  and  325 . A skinning operation in the non-rigid region  330  (i.e., a joint between the bones) might be affected by unfiltered rotation noise at the point  380 , as the skin would be associated with the noisy motions resulting in the bone  325 . By damping the rotational noise as described above and introducing the weight function defined with respect to  FIG. 4 , a skinning process may be performed to map out the distortion of the surface of the object  300  in between the bones  315  and  325 . 
     
       
         
           
               
             
               
                   
               
             
            
               
                 #define dual_quat mat2x4 
               
               
                 uniform float influence_start; 
               
               
                 uniform float influence_end; 
               
               
                 uniform dual_quat filtered_dq; 
               
               
                 uniform mat4 object_to_anchor; uniform mat4 anchor_to_object; 
               
               
                 /*precomputed version of inverse(object_to_anchor)*/ 
               
               
                 float weight_map(float v) { 
               
               
                   /* Insert easing function such as that described in FIG. 4 */ 
               
               
                 } 
               
               
                 vec4 dquat_transform(dual_quat dq, vec4 v) { 
               
               
                   /* Insert known dual quaternion transformation code */ 
               
               
                 } 
               
               
                 /* Notice that only the vertex position is altered, and not the per- 
               
               
                 vertex normal. This helps in hiding the distortion. */ 
               
               
                 vec4 distort(vec4 vertex) { 
               
               
                  vec4 v = object_to_anchor * vertex; 
               
               
                  dual_quat unfiltered = unit_dquat; 
               
               
                  float weight = weight_map(clamp( 
               
            
           
           
               
               
               
               
               
               
            
               
                  (length(v)  
                 −  
                 influence_start) 
                 /  
                 (influence_end 
                 − 
               
            
           
           
               
            
               
                 influence_start), 
               
               
                  0 , 1)); 
               
               
                  dual_quat distortion = mix(unfiltered, filtered_dq, weight); 
               
               
                  return anchor_to_object * dquat_transform(distortion, v); 
               
               
                 } 
               
               
                   
               
            
           
         
       
     
       FIG. 5  shows an example of a generic computer device  500  and a generic mobile computer device  550 , which may be used with the techniques described here in the context of applications involving VR. Computing device  500  includes a processor  502 , memory  504 , a storage device  506 , a high-speed interface  508  connecting to memory  504  and high-speed expansion ports  510 , and a low speed interface  512  connecting to low speed bus  514  and storage device  506 . Each of the components  502 ,  504 ,  506 ,  508 ,  510 , and  512 , are interconnected using various busses, and may be mounted on a common motherboard or in other manners as appropriate. The processor  502  can process instructions for execution within the computing device  500 , including instructions stored in the memory  504  or on the storage device  506  to display graphical information for a GUI on an external input/output device, such as display  516  coupled to high speed interface  508 . In other implementations, multiple processors and/or multiple buses may be used, as appropriate, along with multiple memories and types of memory. In addition, multiple computing devices  500  may be connected, with each device providing portions of the necessary operations (e.g., as a server bank, a group of blade servers, or a multi-processor system). 
     The memory  504  stores information within the computing device  500 . In one implementation, the memory  504  is a volatile memory unit or units. In another implementation, the memory  504  is a non-volatile memory unit or units. The memory  504  may also be another form of computer-readable medium, such as a magnetic or optical disk. 
     The storage device  506  is capable of providing mass storage for the computing device  500 . In one implementation, the storage device  506  may be or contain a computer-readable medium, such as a floppy disk device, a hard disk device, an optical disk device, or a tape device, a flash memory or other similar solid state memory device, or an array of devices, including devices in a storage area network or other configurations. A computer program product can be tangibly embodied in an information carrier. The computer program product may also contain instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer- or machine-readable medium, such as the memory  504 , the storage device  506 , or memory on processor  502 . 
     The high speed controller  508  manages bandwidth-intensive operations for the computing device  500 , while the low speed controller  512  manages lower bandwidth-intensive operations. Such allocation of functions is exemplary only. In one implementation, the high-speed controller  508  is coupled to memory  504 , display  516  (e.g., through a graphics processor or accelerator), and to high-speed expansion ports  510 , which may accept various expansion cards (not shown). In the implementation, low-speed controller  512  is coupled to storage device  506  and low-speed expansion port  514 . The low-speed expansion port, which may include various communication ports (e.g., USB, Bluetooth, Ethernet, wireless Ethernet) may be coupled to one or more input/output devices, such as a keyboard, a pointing device, a scanner, or a networking device such as a switch or router, e.g., through a network adapter. 
     The computing device  500  may be implemented in a number of different forms, as shown in the figure. For example, it may be implemented as a standard server  520 , or multiple times in a group of such servers. It may also be implemented as part of a rack server system  524 . In addition, it may be implemented in a personal computer such as a laptop computer  522 . Alternatively, components from computing device  500  may be combined with other components in a mobile device (not shown), such as device  550 . Each of such devices may contain one or more of computing device  500 ,  550 , and an entire system may be made up of multiple computing devices  500 ,  550  communicating with each other. 
     Computing device  550  includes a processor  552 , memory  564 , an input/output device such as a display  554 , a communication interface  566 , and a transceiver  568 , among other components. The device  550  may also be provided with a storage device, such as a microdrive or other device, to provide additional storage. Each of the components  550 ,  552 ,  564 ,  554 ,  566 , and  568 , are interconnected using various buses, and several of the components may be mounted on a common motherboard or in other manners as appropriate. 
     The processor  552  can execute instructions within the computing device  550 , including instructions stored in the memory  564 . The processor may be implemented as a chipset of chips that include separate and multiple analog and digital processors. The processor may provide, for example, for coordination of the other components of the device  550 , such as control of user interfaces, applications run by device  550 , and wireless communication by device  550 . 
     Processor  552  may communicate with a user through control interface  558  and display interface  556  coupled to a display  554 . The display  554  may be, for example, a TFT LCD (Thin-Film-Transistor Liquid Crystal Display) or an OLED (Organic Light Emitting Diode) display, or other appropriate display technology. The display interface  556  may comprise appropriate circuitry for driving the display  554  to present graphical and other information to a user. The control interface  558  may receive commands from a user and convert them for submission to the processor  552 . In addition, an external interface  562  may be provided in communication with processor  552 , so as to enable near area communication of device  550  with other devices. External interface  562  may provide, for example, for wired communication in some implementations, or for wireless communication in other implementations, and multiple interfaces may also be used. 
     The memory  564  stores information within the computing device  550 . The memory  564  can be implemented as one or more of a computer-readable medium or media, a volatile memory unit or units, or a non-volatile memory unit or units. Expansion memory  574  may also be provided and connected to device  550  through expansion interface  572 , which may include, for example, a SIMM (Single In Line Memory Module) card interface. Such expansion memory  574  may provide extra storage space for device  850 , or may also store applications or other information for device  550 . Specifically, expansion memory  574  may include instructions to carry out or supplement the processes described above, and may include secure information also. Thus, for example, expansion memory  574  may be provided as a security module for device  550 , and may be programmed with instructions that permit secure use of device  550 . In addition, secure applications may be provided via the SIMM cards, along with additional information, such as placing identifying information on the SIMM card in a non-hackable manner. 
     The memory may include, for example, flash memory and/or NVRAM memory, as discussed below. In one implementation, a computer program product is tangibly embodied in an information carrier. The computer program product contains instructions that, when executed, perform one or more methods, such as those described above. The information carrier is a computer- or machine-readable medium, such as the memory  564 , expansion memory  574 , or memory on processor  552 , that may be received, for example, over transceiver  568  or external interface  562 . 
     Device  550  may communicate wirelessly through communication interface  566 , which may include digital signal processing circuitry where necessary. Communication interface  566  may provide for communications under various modes or protocols, such as GSM voice calls, SMS, EMS, or MMS messaging, CDMA, TDMA, PDC, WCDMA, CDMA2000, or GPRS, among others. Such communication may occur, for example, through radio-frequency transceiver  568 . In addition, short-range communication may occur, such as using a Bluetooth, Wi-Fi, or other such transceiver (not shown). In addition, GPS (Global Positioning System) receiver module  570  may provide additional navigation- and location-related wireless data to device  550 , which may be used as appropriate by applications running on device  550 . 
     Device  550  may also communicate audibly using audio codec  560 , which may receive spoken information from a user and convert it to usable digital information. Audio codec  560  may likewise generate audible sound for a user, such as through a speaker, e.g., in a handset of device  550 . Such sound may include sound from voice telephone calls, may include recorded sound (e.g., voice messages, music files, etc.) and may also include sound generated by applications operating on device  550 . 
     The computing device  550  may be implemented in a number of different forms, as shown in the figure. For example, it may be implemented as a cellular telephone  580 . It may also be implemented as part of a smart phone  582 , personal digital assistant, or other similar mobile device. 
     Various implementations of the systems and techniques described here can be realized in digital electronic circuitry, integrated circuitry, specially designed ASICs (application specific integrated circuits), computer hardware, firmware, software, and/or combinations thereof. These various implementations can include implementation in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, coupled to receive data and instructions from, and to transmit data and instructions to, a storage system, at least one input device, and at least one output device. 
     These computer programs (also known as programs, software, software applications or code) include machine instructions for a programmable processor, and can be implemented in a high-level procedural and/or object-oriented programming language, and/or in assembly/machine language. As used herein, the terms “machine-readable medium” “computer-readable medium” refers to any computer program product, apparatus and/or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and/or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The term “machine-readable signal” refers to any signal used to provide machine instructions and/or data to a programmable processor. 
     To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form, including acoustic, speech, or tactile input. 
     The systems and techniques described here can be implemented in a computing system that includes a back end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front end component (e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include a local area network (“LAN”), a wide area network (“WAN”), and the Internet. 
     The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. 
     In some implementations, the computing devices depicted in  FIG. 5  can include sensors that interface with a virtual reality (VR headset  590 ). For example, one or more sensors included on a computing device  550  or other computing device depicted in  FIG. 5 , can provide input to VR headset  590  or in general, provide input to a VR space. The sensors can include, but are not limited to, a touchscreen, accelerometers, gyroscopes, pressure sensors, biometric sensors, temperature sensors, humidity sensors, and ambient light sensors. The computing device  550  can use the sensors to determine an absolute position and/or a detected rotation of the computing device in the VR space that can then be used as input to the VR space. For example, the computing device  550  may be incorporated into the VR space as a virtual object, such as a controller, a laser pointer, a keyboard, a weapon, etc. Positioning of the computing device/virtual object by the user when incorporated into the VR space can allow the user to position the computing device to view the virtual object in certain manners in the VR space. For example, if the virtual object represents a laser pointer, the user can manipulate the computing device as if it were an actual laser pointer. The user can move the computing device left and right, up and down, in a circle, etc., and use the device in a similar fashion to using a laser pointer. 
     In some implementations, one or more input devices included on, or connect to, the computing device  550  can be used as input to the VR space. The input devices can include, but are not limited to, a touchscreen, a keyboard, one or more buttons, a trackpad, a touchpad, a pointing device, a mouse, a trackball, a joystick, a camera, a microphone, earphones or buds with input functionality, a gaming controller, or other connectable input device. A user interacting with an input device included on the computing device  550  when the computing device is incorporated into the VR space can cause a particular action to occur in the VR space. 
     In some implementations, a touchscreen of the computing device  550  can be rendered as a touchpad in VR space. A user can interact with the touchscreen of the computing device  550 . The interactions are rendered, in VR headset  590  for example, as movements on the rendered touchpad in the VR space. The rendered movements can control objects in the VR space. 
     In some implementations, one or more output devices included on the computing device  550  can provide output and/or feedback to a user of the VR headset  590  in the VR space. The output and feedback can be visual, tactical, or audio. The output and/or feedback can include, but is not limited to, vibrations, turning on and off or blinking and/or flashing of one or more lights or strobes, sounding an alarm, playing a chime, playing a song, and playing of an audio file. The output devices can include, but are not limited to, vibration motors, vibration coils, piezoelectric devices, electrostatic devices, light emitting diodes (LEDs), strobes, and speakers. 
     In some implementations, the computing device  550  may appear as another object in a computer-generated, 3D environment. Interactions by the user with the computing device  550  (e.g., rotating, shaking, touching a touchscreen, swiping a finger across a touch screen) can be interpreted as interactions with the object in the VR space. In the example of the laser pointer in a VR space, the computing device  550  appears as a virtual laser pointer in the computer-generated, 3D environment. As the user manipulates the computing device  550 , the user in the VR space sees movement of the laser pointer. The user receives feedback from interactions with the computing device  850  in the VR space on the computing device  550  or on the VR headset  590 . 
     In some implementations, one or more input devices in addition to the computing device (e.g., a mouse, a keyboard) can be rendered in a computer-generated, 3D environment. The rendered input devices (e.g., the rendered mouse, the rendered keyboard) can be used as rendered in the VR space to control objects in the VR space. 
     Computing device  500  is intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. Computing device  550  is intended to represent various forms of mobile devices, such as personal digital assistants, cellular telephones, smart phones, and other similar computing devices. The components shown here, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the inventions described and/or claimed in this document. 
       FIG. 6  illustrates an example implementation of a head-mounted display as shown in  FIGS. 3 and 4 . In  FIG. 6 , a user wearing an HMD  600  is holding a portable handheld electronic device  602 . The handheld electronic device  602  may be, for example, a smartphone, a controller, a joystick, or another portable handheld electronic device(s) that may be paired with, and communicate with, the HMD  600  for interaction in the immersive virtual environment generated by the HMD  600 . The handheld electronic device  602  may be operably coupled with, or paired with the HMD  600  via, for example, a wired connection, or a wireless connection such as, for example, a WiFi or Bluetooth connection. This pairing, or operable coupling, of the handheld electronic device  602  and the HMD  600  may provide for communication between the handheld electronic device  602  and the HMD  600  and the exchange of data between the handheld electronic device  602  and the HMD  600 . This may allow the handheld electronic device  602  to function as a controller in communication with the HMD  600  for interacting in the immersive virtual environment generated by the HMD  600 . That is, a manipulation of the handheld electronic device  602 , such as, for example, a beam or ray emitted by the handheld electronic device  602  and directed to a virtual object or feature for selection, and/or an input received on a touch surface of the handheld electronic device  602 , and/or a movement of the handheld electronic device  602 , may be translated into a corresponding selection, or movement, or other type of interaction, in the immersive virtual environment generated by the HMD  600 . For example, the HMD  600 , together with the handheld electronic device  602 , may generate a virtual environment as described above, and the handheld electronic device  602  may be manipulated to effect a change in scale, or perspective, of the user relative to the virtual features in the virtual environment as described above. 
       FIGS. 7A and 7B  are perspective views of an example HMD, such as, for example, the HMD  600  worn by the user in  FIG. 6 , and  FIG. 7C  illustrates an example handheld electronic device, such as, for example, the handheld electronic device  602  shown in  FIG. 6 . 
     The handheld electronic device  702  may include a housing  703  in which internal components of the device  702  are received, and a user interface  704  on an outside of the housing  703 , accessible to the user. The user interface  704  may include a touch sensitive surface  706  configured to receive user touch inputs. The user interface  704  may also include other components for manipulation by the user such as, for example, actuation buttons, knobs, joysticks and the like. In some implementations, at least a portion of the user interface  704  may be configured as a touchscreen, with that portion of the user interface  704  being configured to display user interface items to the user, and also to receive touch inputs from the user on the touch sensitive surface  706 . The handheld electronic device  702  may also include a light source  708  configured to selectively emit light, for example, a beam or ray, through a port in the housing  703 , for example, in response to a user input received at the user interface  704 . 
     The HMD  700  may include a housing  710  coupled to a frame  720 , with an audio output device  730  including, for example, speakers mounted in headphones, also be coupled to the frame  720 . In  FIG. 7B , a front portion  710   a  of the housing  710  is rotated away from a base portion  710   b  of the housing  710  so that some of the components received in the housing  710  are visible. A display  740  may be mounted on an interior facing side of the front portion  710   a  of the housing  710 . Lenses  750  may be mounted in the housing  710 , between the user&#39;s eyes and the display  740  when the front portion  710   a  is in the closed position against the base portion  710   b  of the housing  710 . In some implementations, the HMD  700  may include a sensing system  760  including various sensors and a control system  770  including a processor  790  and various control system devices to facilitate operation of the HMD  700 . 
     In some implementations, the HMD  700  may include a camera  780  to capture still and moving images. The images captured by the camera  780  may be used to help track a physical position of the user and/or the handheld electronic device  702  in the real world, or physical environment relative to the virtual environment, and/or may be displayed to the user on the display  740  in a pass through mode, allowing the user to temporarily leave the virtual environment and return to the physical environment without removing the HMD  700  or otherwise changing the configuration of the HMD  700  to move the housing  710  out of the line of sight of the user. 
     In some implementations, the HMD  700  may include a gaze tracking device  765  to detect and track an eye gaze of the user. The gaze tracking device  765  may include, for example, an image sensor  765 A, or multiple image sensors  765 A, to capture images of the user&#39;s eyes, for example, a particular portion of the user&#39;s eyes, such as, for example, the pupil, to detect, and track direction and movement of, the user&#39;s gaze. In some implementations, the HMD  700  may be configured so that the detected gaze is processed as a user input to be translated into a corresponding interaction in the immersive virtual experience. 
     A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the specification. 
     In addition, the logic flows depicted in the figures do not require the particular order shown, or sequential order, to achieve desirable results. In addition, other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Accordingly, other embodiments are within the scope of the following claims.