Bachelor Informatica
Short-lasting effects of
Redirected Walking in
Virtual Reality
Kwan Win Chung
June 29, 2018
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Abstract
Redirected walking is a method used to immersively explore big virtual spaces while having limited amounts of physical space, using natural walking. This research takes a look at the effects of Redirected Walking on users’ ability to orientate in a physical space. This is accomplished by creating an application using the Redirected Walking toolkit, a toolkit which was created for the implementation of Redirected Walking in virtual reality applications. Immediately after the experiments, the participants performed worse in a simple orientation test compared to usual. But the likelihood that random chance could explain the obtained results is too high to make any conclusions. On the small chance that the results are correct it would suggest that the use of Redirected Walking does indeed have a short-lasting effect on the user.
Contents
1 Introduction 7
1.1 Research Question . . . 8
2 Theoretical background 9 2.1 The concept and background of Redirected Walking . . . 9
2.1.1 Gains . . . 9
2.1.2 Redirection algorithms . . . 10
2.1.3 The Redirected Walking Toolkit (RWT) . . . 12
2.2 Previous work . . . 12
3 Short-lasting effects of Redirected Walking 15 3.1 Test environment . . . 15
3.1.1 Equipment . . . 15
3.1.2 Virtual Environment for Redirected walking . . . 16
3.1.3 Virtual Environment for measurements . . . 19
3.2 Study design . . . 20
3.3 Participants . . . 21
3.4 Method . . . 21
4 Results and discussion 23 4.1 Rotation . . . 23
4.2 Translation . . . 26
4.3 General and verbal feedback . . . 28
4.4 Discussion . . . 29
4.4.1 Rotation . . . 29
4.4.2 Translation . . . 29
CHAPTER 1
Introduction
Immersive virtual reality (VR) technology has been around for a while now. The interest in virtual reality has increased rapidly over the last few years [6]. The main cause for this is the increasing availability of affordable devices that support VR [2].
When using VR a common problem is using natural locomotion, in the virtual environment (VE), while playing in a small physical space [16]. Natural locomotion in this context refers to walking. Natural locomotion has many advantages. As stated by Suma et al [16] natural locomotion gives a greater sense of presence [21]. It improves the performance on travel and search tasks [12] [14]. And it is more beneficial for memory and maintaining attention [17]. But natural locomotion also limits the VEs to the size of the tracked space [9].
A solution for locomotion in VR that uses natural walking is by either using the “Virtuix Omni”1 or “The Kat Walk”2 shown in figure 1.1 and figure 1.2. These are specially created
devices with a low friction surface and a method to keep a person from falling off the device. By also using low friction boots, the illusion can be created that a user is actually walking around in the VR world, while using natural walking.
Figure 1.1: Example of the Omni Virtuix3. Figure 1.2: Example of The Kat Walk4.
1http://www.virtuix.com/
Another solution for locomotion in VR that uses natural walking is “Redirected walking” [9]. This method enables a person, with a limited amount of physical space, to immersively explore a bigger virtual space while using natural walking [9] Redirected walking can be achieved by changing the actual walking direction of users without them noticing where they are in the tracked space [9]. This is usually done by manipulating the mapping between physical and virtual motion. This is done by applying gains [2]. Gains are changes that are made in the translation and/or rotation in the VE, compared to the real world. These gains cause the user to translate and or rotate differently in the real world. This will be explained in more detail in chapter 2.
1.1
Research Question
When VEs are not used appropriately, it has been pointed out that in the worst case it can damage the health of the user [19]. Sn example of this is VR sickness, which is closely related to a persons’ spatial cognitive capability [19]. Symptoms of VR sickness are: general discomfort, headache, stomach awareness, nausea, vomiting, pallor, sweating, fatigue, drowsiness, disorien-tation, and apathy [7]. Other symptoms might include postural instability and retching [7]. An important cause of VR sickness is “a physical law inconsistency between the visual vestibu-lar and peculiar information provided by the VR environment to imply movement” [19]. The redirection applied on a user is meant to be kept at unnoticeable levels [2]. This is because the amount of gains that is applied should be kept below a calculated threshold [13]. Unless redirection efficacy is prioritized over perceptibility [2]. But even when redirection efficacy is prioritized, the amount of gains applied should still be taken into consideration. This should be done to prevent discomfort to the user. Because in Redirected Walking the user is deliber-ately influenced to change behaviour based on changes in the visual input, this may incur one or more of the previously described symptoms. This brings us to the research question of this thesis: Does the application of Redirected Walking have any short-lasting effects on a users’ ability to orientate in real life when used for short periods of time?
4https://en.wikipedia.org/wiki/Virtuix_Omni#/media/File:Virtuix_Omni_Skyrim_(cropped).jpg (Visited: 7-June-2018)
CHAPTER 2
Theoretical background
Redirected walking was shortly introduced in the introduction. This chapter will go more in-depth about how Redirected Walking works.
2.1
The concept and background of Redirected Walking
Redirected walking is an interactive locomotion technique for VEs, that captures the benefits of natural walking while extending the possible size of the VE [9]. This concept was introduced about 17 years ago [9]. In the extreme, Redirected Walking can cause the user to walk in a large circle while they think that they are walking a straight line in the VE [9].
People keep track of their position relative to the space that they are in [16]. This is called spatial updating, which makes use of both visual information and body-based information1, which
is also known as path integration [16]. While body-based information is important for spatial updating, studies have shown that only visual cues are sufficient as well for spatial updating [11]. Research in Redirected Walking has even found that visual information dominates over body-based information when the difference between the VE and physical law is below a certain detection threshold [8] [13]. Users generally will only maintain the virtual world model during an immersive VR experience, because “hanging on to the real world model when fully immersed seems to be very difficult, and requires active concentration” [16]. So all the changes performed on the VE will directly impact the user.
2.1.1
Gains
There are three different kind of gains that can be applied to redirect a user without breaking presence when orientating. These are: rotation, translation and curvature gains [15]. For a visual example of these gains see figure 2.1. Translation gains consists of scaling the translation of the user such that the user moves faster/slower in the VE compared to the real world. Rotation gains consists of scaling the rotation of the user such that the user rotates more/less in the VE compared to the real world. Curvature gains consists of rotations during translation. This is usually applied when the user walks towards a point in the VE [2]. This will result in a curved path towards the point of interest that is perceived as a straight path.
Figure 2.1: Example of rotation, translation and curvature gains3. The orange lines represents
the users’ movement in the VE and the black lines represents the users’ movement in the real world.
2.1.2
Redirection algorithms
A redirection algorithm usually uses some combination of gains to keep the user away from the edges of the tracked space [2]. These algorithms can be categorized into two kind of algorithms, namely reactive and predictive algorithms [2]. Reactive algorithms make decisions based on the current location and orientation of the user at each point, where it makes a choice based on a particular heuristic [2]. An example of a reactive algorithm is the Steer-To-Orbit algorithm, in which the algorithm uses rotation and curvature gains to steer the user in an orbit around the center of the tracked space, as can be seen in figure 2.2. Predictive algorithms predict the path that the user will take and uses that prediction to plan out a redirection strategy [2]. An example of a predictive algorithm is the zigzag algorithm [9], which originally only made use of rotation, but now also supports translation and curvature [2]. This algorithm makes use of a zig-zag shaped path in the VE which it changes to a simple back-and-forth path between two points (checkpoints) in the tracked space [2]. Redirection in the zigzag algorithm is only applied when the user reaches a point in the VE which corresponds with a checkpoint. Figure 2.3 shows an example of the zigzag algorithm.
While redirection algorithms can help exploring a vast VE with natural walking, it cannot guarantee that users stay in the tracked space [2]. Therefore when nearing the border a safety mechanism must activate. In 2007 a safety mechanism was introduced [22]. This is known as a reorientation technique (resets). The most well known form of reorientation technique is the 2:1-Turn [22]. This technique has the user rotate 360 degrees in the VE, which results in a 180 degrees turn in the real world this faces the user towards the tracked space again.
3https://i1.wp.com/www.interactivearchitecture.org/wp-content/uploads/2017/09/ 1Different-Gains-Used-In-Redirected-Walking-Techniques.png?resize=670%2C168 (Visited: 7-June-2018)
Figure 2.2: Example of the Steer-To-Orbit algorithm from “Performance of Redirected Walking Algorithms in a Constrained Virtual World”[3]. The algorithm tries to keep the user in the orbit of the center of the tracked space. The user experiences the feeling that they are walking a straight path.
Figure 2.3: Example of the zigzag algorithm taken from the original Redirected Walking paper [9]. Users walk the blue path in the VE. After reaching points that corresponds to checkpoints in the tracked space, redirection is applied. These points are indicated by the white ”X” marks. Users are actually walking back and forth between two points in the tracked space as seen in figure 2.4.
2.1.3
The Redirected Walking Toolkit (RWT)
“The Redirected Walking Toolkit is a unified platform for developing, benchmarking and de-ploying Redirected Walking algorithms” [2]. It was created because the Redirected Walking technique is still not being used too much because of its complexity and subtleties involved in successfully deploying redirection [2]. Currently version 0.3 of the toolkit [10] is available as a Unity3D package [20].
For adding Redirected Walking in an application the toolkit comes with three pre-prepared redirection algorithms, a reorientation algorithm, a simulated walker, a virtual path generator and analysis tools. Of the three pre-prepared redirection algorithms, two are reactive algorithms and one of them is an predictive algorithm. The simulated walker uses an abstract avatar to simulate the movement of a user in the VE by either keyboard input or by the simulation itself. The virtual path generator can generate a variety of virtual random paths that try and replicate realistic walking routes, which can be used to check the navigability of the VE. The analysis tools can be used in combination with the rest of the toolkit to analyze the simulation with either existing or self created redirection algorithms. The analysis tools keeps track of the total reset count, real and virtual distance travelled between resets, time elapsed between resets, overall gains applied, overall real and virtual distance travelled, real and virtual position at custom intervals and the amount of gains applied at custom intervals [2]. To make testing different conditions easier, the toolkit also supports batch testing which lets the user run multiple simulations with different user defined conditions.
The RWT features all three gains featured in section 2.1.1. However it has split them into 5 gain values that can be adjusted: minimum translation gain, maximum translation gain, mini-mum rotation gain, maximini-mum rotation gain and curvature gain.
• Minimum translation gain is applied when the amount of translation in the VE is less than the translation needed in the real world. This value decreases translation in the VE, by translating the VE in the same direction as where the user is heading. The gain applied can range between -0.99 and 0.00. So for every meter that the user walks in real life, the user will walk 0.00 to 0.99 meters less in the VE.
• Maximum translation gain is applied when the amount of translation in the VE is more than the translation needed in the real world. This value increases up translation in the VE, by translating the VE in the opposite direction of where the user is heading. The gain applied can range between 0.00 and 5.00. So for every meter that the user walks in real life, the user will walk 0.00 to 5.00 meters extra in the VE.
• Minimum rotation gain is applied when the rotation needed in the VE is less than the rotation needed in the real world. This value decreases rotation in the VE, by rotating the VE in the same direction as the user.The gain applied can range between -0.99 and 0.00. So for every degree that the user rotates in real life, the user will rotate 0.00 to 0.99 degrees less in the VE.
• Maximum rotation gain is applied when the rotation needed in the VE is more than the rotation needed in the real world. This value increases rotation in the VE, by rotating the VE in the opposite direction as the user. The gain applied can range between 0.00 and 5.00. So for every degree that the user rotates in real life, the user will rotate 0.00 to 5.00 degrees extra in the VE.
• Curvature gain is applied when the rotation gain values alone are not enough to keep the user in the tracked space. The gain applied can range between 1.00 and 23.00. So for every meter walked in real life, the orientation of the user will have changed by 1.00 to 23.00 degrees.
2.2
Previous work
Since Redirected Walking was introduced about 17 years ago it has been validated, the limits and capabilites have been evaluated and additional manipulation techniques have been tested [9] [2].
There are three approaches to redirecting users: redirecting at certain points, redirecting all the time and making use of change blindness. All three approaches have already been tested and verified in previous papers [2] [5] [18].
Redirection can be achieved with a simple approach in which redirection is only applied when the user gets close to a checkpoint somewhere in the tracked space. An example of this approach is the Near-Field VR demo [2]. In the Near-Field demo users visited points of interests in a 12 by 4 meters VE, while walking back and forth in a 3.5 by 1.2 meters tracked space. A scene from this demo is shown in figure 2.4.
Redirection can also be achieved by continuously applying redirection while the user moves through the VE. An example of this approach is the unlimited corridor [5]. Users walked alongside a curved wall while touching it, which enhanced the illusion that they were walking straight lines in the VE. Users could walk endlessly and even multiple users could experience this system at the same time without colliding with each other. A scene from this demo is shown in figure 2.5. Lastly, redirection can also be achieved without manipulation of the mapping between phys-ical and virtual motions like with the previous two approaches. Instead this method takes ad-vantage of change blindness. “Change blindness is a perceptual phenomenon that occurs when a person fails to detect a visual change to an object or scene” [18]. While change blindness can give the impression of exploring a vast VE, even more than with continuous rotation techniques, it comes at the cost of negatively impacting spatial knowledge acquisition [15]. An example of this approach is the change blindness experiment introduced by Suma et al in 2011 [18] in which users had to complete a set of tasks at different locations in the VE with the scene changing when the users were busy with the task at hand, keeping the users in the tracked space. A scene from this experiment is shown in figure 2.6
Figure 2.4: Example of the Near-Field VR demo from “The Redirected Walking Toolkit” [2]. Here user walks back and forth between two points in the tracked area. The lower part of the image shows the route that the user has travelled in the VE.
Figure 2.5: Example of the unlimited corridor from “Unlimited Corridor Redirected walking techniques using visuo haptic interactions” [5]. On the left we see two users simultaniously using the system. Both of them are walking alongside the construction. The users feel like they are walking straight lines as shown on the right.
Figure 2.6: Change blindness example from “Leveraging Change Blindness for Redirection in Virtual Environments” [18]. Here we see a change in the scene, while the user had his back turned towards the door. Only one participant out of 37 noticed this change.
CHAPTER 3
Short-lasting effects of Redirected Walking
Manipulating the mapping between physical and virtual motion for longer periods of time may have short term consequences [19]. To investigate if applying Redirected Walking for a limited period of time also has short term consequences, a study will be conducted to look at the short-lasting effects of short term usage of Redirected Walking. This study will look at short term changes of the real life rotation and translation of users specifically, when used for short periods of time. Although curvature gain is implemented in the Redirected Walking experiment, it will almost never be applied. This is the reason why users’ curvature changes in the real world will not be tested.
For this research a limited amount of space is available. This means that redirection efficacy is prioritized over perceptibility. But while redirection efficacy is prioritized, caution should be exercised when choosing the gains that will be applied, to prevent VR sickness.
3.1
Test environment
This section describes the equipment and applications used for the experiments.
3.1.1
Equipment
For the experiments a HTC VIVE system [4] was used, which included 2 base stations, a head-mounted display (HMD) and two controllers. The HMD had a dual AMOLED 3.6” diagonal screen with a resolution of 1080 x 1200 pixels per eye, which is 2160 x 1200 pixels when combined. It had a refresh rate of 90 HZ and a field of view of 110 degrees. This setup was connected to a 64-bit windows 10 PC with the following specifications: Intel Core i7-7700k 4.20GHz processor, NVIDIA GeForce GTX 1080 Ti graphics card and 32 GB Ram. Each eye was rendered at 60 frames per second using the Unity 3D engine [20]. The HTC VIVE has an estimated precision of RMS (root mean square) 1.55mm and an estimated accuracy of RMS 1.9mm [1].
Figure 3.1: The HTC VIVE headset, controllers and base stations1.
3.1.2
Virtual Environment for Redirected walking
For the experiments a VE was created that made use of the Redirected Walking toolkit. Due to the limited size and shape of the available physical space, a predictive redirection algorithm was used instead of a reactive algorithm. The algorithm used was the zigzag algorithm which is the same algorithm as used in the near-field demo [2]. Therefore redirection will only be applied at the checkpoints.
The experiment will have users explore a virtual hallway, as shown in figure 3.2. The choice was made to make a hallway instead of a larger room because this made it easier to have users follow a certain path in the VE. Users will walk back and forth between two checkpoints in the tracked space, while they explore the hallway in the VE. In the VE the positions of these two checkpoints are spread out in a zigzag pattern. Figures 3.2 and 3.3 shows the path users walk, both in the VE and in the real world also showing the location of the checkpoints. When reaching a checkpoint, gains will be applied to ensure that the user reaches the next checkpoint safely. If the user were to directly rotate to the next checkpoint the VE would rotate in the same direction as the user. This could cause the user to feel off balance, as was experienced during the creation of the Redirected Walking experiment. This is caused by the large difference between the angle that the user has to rotate in real life and in the VE. Whenever the amount of rotation needed in the VE is smaller than the amount of rotation needed in real life this problem would occur. The solution for this problem was to increase the rotation needed in the VE by having the user rotate in the opposite direction before heading to the next checkpoint.
To help achieve this, destroyable blocks were added to the VE, as shown in figures 3.5 and 3.6. Users have to grab a weapon with their controller and destroy blocks that were strategically placed throughout the VE. Figure 3.7 shows a user destroying a block with a sword. The yellow blocks spawn more blocks to ensure players rotate a certain amount before heading to the next checkpoint. The black blocks are placed in the VE to keep the player distracted while walking from checkpoint to checkpoint. They are also added to take some attention off of the yellow blocks. A direction indicator was added to help users find the nearest block, because some users had trouble paying attention to the blocks. Figure 3.6 shows the direction indicator mentioned. The Redirected Walking experiment ends when the user reaches the final point in the VE, as shown in figure 3.8.
The Redirected Walking experiment implements all the gains discussed in section 2.1.1. The exact value of the gains can be found in figure 3.4. The maximum translation gain, minimum translation gain, maximum rotation gain and curvature gain values are low enough to not be
1
https://www.vive.com/media/filer_public/8f/ef/8fef879f-c986-4c89-a0b3-12126e8ba6f7/ vive-pdp-hero-desktop-031918-v3.jpg
noticed. That is unless you explicitly pay attention to them. The minimum rotation gain however is very noticeable this is the reason why the destroyable blocks were added. If the minimum rotation gain would be closer to zero there is a risk that users will go out of the tracked space, but this would make the minimum rotation gain less noticeable.
Although curvature gain is implemented in the Redirected Walking experiment, it will almost never be applied. It will only be applied if the user walks through the walls in the VE. When redirection efficacy is prioritized you should not rely on curvature, because users might still go out of bounds. As was experienced during the creation of the Redirected Walking experiment. Instead of relying on curvature gains, the tweaking of the amount of rotation gains was prioritized.
Figure 3.2: The virtual hallway that users have to navigate through. In this demo translation, rotation and curvature gains are applied. The values of these gains can be seen in figure 3.4. The user follows the green path in the VE, while they walk back and forth between two points in the tracked space, as shown in figure 3.3. The blue circle indicates the begin location of the user and the red circle indicates the end location of the user. The gray squares are the locations of the checkpoints in the VE. Each one of those checkpoints in the VE corresponds to one of two checkpoints in the tracked space.
Figure 3.3: The 3.5m x 2m tracked space in which the user walks around in. During the Redirected Walking experiment users walk back and forth between the two blue circles. These indicate the locations of the checkpoints.
Figure 3.4: The value of the gains used in the Redirected Walking Toolkit
Figure 3.5: An overview of the stage. The red circle indicates the user. The orange circles indicates the destroyable black blocks. The white circles indicate the destroyable yellow blocks. The green circle indicates the weapon that is used to destroy these blocks. The purple circle indicates the target indicator, which shows the next block that should be destroyed. The blue circle indicates a checkpoint. There are more checkpoints spread throughout the stage, as can be seen in figure 3.2. But these only become visible one by one, after their previous checkpoints are reached.
Figure 3.6: An overview of the stage, from the perspective of the player. The orange circles indicates a destroyable black block. The white circles indicate a destroyable yellow block. The green circle indicates the weapon that is used to destroy these blocks. The purple circle indicates the target indicator, which shows the next block that should be destroyed. The blue circle indicates a checkpoint.
Figure 3.7: A user destroying a block, by stabbing their sword into it. The target indicator jumps to the next target.
Figure 3.8: The last checkpoint to be reached. This is made clear to the user by having a red color and the text: “End” on it.
3.1.3
Virtual Environment for measurements
experiment” (Baseline), “Directly after the Redirected Walking experiment” and “5 minutes after the Redirected Walking experiment” will be measured. These measurements will be explained in more detail in section 3.2. For these measurements a different VE was created. The top view of this VE is shown in figure 3.9. Users will have to wear a HMD and hold one of the VIVE controllers during the measurements. This however might cause trouble with the cables of the HMD, but during the actual measurements no participants complained about the cables being in the way. It also cannot be made sure that users have their eyes closed during a test. So the fact that participants will have their eyes closed when they need to close it is an assumption based on trust. The reason why this method was chosen instead of just using a controller without HMD, was because using only a controller lead to strange values being measured. Due to a tight schedule it was faster to use the HMD instead of finding the cause of this problem. The controllers are only used to capture the orientation and location of the HMD when certain buttons are pressed. The white circle shown in figure 3.9 is the center of the stage and acts as a starting point for the tests. The white and yellow blocks are marks that users can focus on to get an indication of which direction they are looking at. Two different buttons on the HTC VIVE controller were used for the tests. One of the button saved the current orientation of the HMD. The other button saved the location of the HMD. By comparing the orientation before and after a rotation, the amount rotated could be calculated. By comparing the locations before and after translation, the amount translated could be calculated.
Figure 3.9: A top view of the test environment that was made to do the translation and rotation tests in. The white circle represents the center of the stage. The white and yellow blocks are marks to show the user which direction they are looking at.
3.2
Study design
The study takes place in a 3.5 by 2 meters sized tracked space. For the Redirected Walking experiment participants will start at one side of the area and walk back and forth between two points which are 3.5 meters apart from each other, see figure 3.3. The VE for this is a zigzag shaped hallway like the path that is portrayed in figure 3.2. Participants are asked to walk through the hallway while destroying some block with their weapon.
To check for short-lasting effects of Redirected Walking, the users will be tested on changes in rotation and translation. These tests will be done “Before the Redirected Walking experi-ment” (Baseline), “Directly after the Redirected Walking experiexperi-ment” and “5 minutes after the Redirected Walking experiment”. The results after the Redirected Walking experiment will be compared with the baseline to see if there are any effects on the users’ ability to orientate in real life. If there are effects, the final results will be used to see if these effects linger. During the
experiments participants only have to take of their HMD during the 5 minute break to fill in a questionnaire, which can be found in the appendix.
The tests are also performed in a VR environment, as shown in figure 3.9. For both tests users have to wear the HMD and hold one of the VIVE controllers in their hand. For the rotation test users have to stand in the center of the VE, indicated by the white circle shown in figure 3.9. Users are asked to face the yellow block while standing in the center of the VE, which is indicated by a white dot as shown in figure 3.9. To start the test they have to close their eyes, press a button on the controller and try to rotate a 180 degrees. After rotating they are asked to press the same button again and open their eyes. By pressing the button the current orientation of the HTC VIVE is captured. By looking at the difference before and after the rotation the amount rotated can be calculated. This is repeated 5 times before the Redirected Walking experiment, 5 times after the Redirected Walking experiment and 5 times after the 5 minute break. To summarize the rotation tests.
1. Stand in the center and face the yellow block. 2. Press the button and close your eyes.
3. Try to rotate 180 degrees.
4. Press the button again and open eyes.
5. Return to start position and repeat 4 more times.
After the rotation test comes the translation test. For the translation test users also have to start in the center of the VE, but they have to face the white block located 2 meters from the center. To start the test users have to close their eyes and press a button. After translating users have to press this button again after which they can open their eyes and get back into the starting position. By pressing this button the current location of the user is captured. By looking at the differences between the values of the before and after, the amount translated can be calculated. This is repeated 5 times before the Redirected Walking experiment, 5 times after the Redirected Walking experiment and 5 times after the 5 minute break. To summarize the translation tests.
1. Stand in the center and face the white block. 2. Press the button and close your eyes.
3. Try and get as close as possible to the white block. 4. Press the button again and open eyes.
5. Return to start position and repeat 4 more times.
3.3
Participants
A total of 20 people participated in the study. The average age of the participants was 22. Of the participants 90% were male and 10% were female. 35% of the participants had previous experience with VR and none of them had heard of Redirected Walking before. Participants were required to be over 18 years old. People who had a history of epilepsy or seizures, VR Sickness or any other kind of motion sickness were excluded from this study. If anything didn’t feel right, participants could stop at any given moment. This did not happen though.
3.4
Method
The study took about 15 to 25 minutes to complete for each participant. Before they arrived, participants were asked to read and fill in the consent form which can be found in the appendix. Only those that did fill it in were selected. Participants were then taken to the tracked area and
the equipment and their tasks were explained. When the participants were ready, they put on the HMD to complete the rotation and translation tests.
After these tests were completed the experimenter explained about the checkpoints, blocks, weapon and target indicator of the Redirected Walking experiment. When the experimenter was done explaining everything, the participants ran the Redirected Walking experiment. After reaching the end of the VE the participants ran the rotation and translation tests again. After taking off the HMD the participants took a small 5 minute break. Immediately at the start of this break they were asked to fill in a feedback questionnaire. Most participants took about 4 minutes to finish the questionnaire, no one took longer than the five minutes given. Lastly the participants were asked to run the rotation and translation tests again. This concluded the experiments and participants got the opportunity to ask questions or give comments.
CHAPTER 4
Results and discussion
To prove that Redirected Walking has an effect on users two null hypothesis will be formed and a p-value of lower than 0.05 should be calculated for both to reject both null hypothesis. This will be done using the obtained data. These two null hypothesis are created to look at the rotation and translation separately.
• The null hypothesis for rotation is: the means of the rotations after the Redirected Walking experiment should be the same as the base measurements.
• The alternative hypothesis is that the means of the rotations after the Redirected Walking experiment should be different from the base measurements.
• The null hypothesis for translation is: the means of the translations after the Redirected Walking experiment should be the same as the base measurements.
• The alternative hypothesis is that the means of the translations after the Redirected Walk-ing experiment should be different than the base measurements.
If both null hypothesis can be disproved a null hypothesis concerning the lingering of the effects can be tested.
• This null hypothesis is: the change in the means after using Redirected Walking does not last.
• The alternative hypothesis is that the change in the means after using Redirected Walking does last.
If the alternative hypothesis is true, a follow-up study can be performed to measure how long this effect lasts for different usage periods.
4.1
Rotation
Each measurement gave the result in degrees in. These values are given in 4 or more decimals after the point. The results can be found in the appendix. As mentioned in section 3.1.1 the HTC VIVE has an estimated precision of RMS 1.55mm and accuracy of RMS 1.9mm. To take this into account we will round the results to 2 decimals after the point. In the data each participant has 15 different rotation values. Five values are from before the Redirected Walking experiment. These values are labeled as Base 1 - 5. Another five values are taken after the Redirected Walking experiment. These values are labeled Post VR 1 - 5. And the five values labeled as Post break 1 - 5 are the values taken after the 5 minute break. Each participant has the mean calculated for each of these three categories. These are labeled as AVG Base, AVG post VR and AVG post break.
• Range AVG post VR: 164.94 to 198.07 degrees. • Range AVG post break: 165.64 to 194.91 degrees.
In figures 4.1, 4.2 and 4.3 the means are put into histograms with a bin size of 2 degrees. These three histograms can be compared to each other to see if there is an overall change in how people rotated at different moments in the experiment. Figure 4.4 shows a scatter plot so you can compare the 3 different moments per user. The error bars show the range of the 5 measurements of each specific moment.
A t-test can be used to determine if two sets of data are significantly different from each other. Doing a paired test on the AVG Base and AVG post VR values using a two tailed distribution gave a t-value of: 0.046. By using the obtained t-value with a degree of freedom of 19 we got a p-value of 0.96. This means that we cannot reject the null hypothesis and the results are not statistically significant. The likelihood that random chance can explain the results is very high. The standard deviation(σ) for the base and post VR data is 8.95.
Figure 4.1: Experimental results of test subjects’ ability to make a 180 degrees turn with their eyes closed, before the Redirected Walking experiment, put in a histogram with a bin size of 2 degrees.
Figure 4.2: Experimental results of test subjects’ ability to make a 180 degrees turn with their eyes closed, directly after the Redirected Walking experiment, put in a histogram with a bin size of 2 degrees.
Figure 4.3: Experimental results of test subjects’ ability to make a 180 degrees turn with their eyes closed, after a 5 minute break, put in a histogram with a bin size of 2 degrees.
Figure 4.4: Experimental results of test subjects’ ability to make a 180 degrees turn with their eyes closed, before the Redirected Walking experiment, directly after the Redirected Walking experiment and 5 minutes after the Redirected Walking experiment. This scatter plot allows you to quickly compare the 3 different means of a user. The error bars shows the range of the five measurements at each timeframe.
4.2
Translation
Each measurement gave the result in meters. These values are given in 4 or more decimals after the point. The results can be found in the appendix. As mentioned in section 3.1.1 the HTC VIVE has an estimated precision of RMS 1.55mm and accuracy of RMS 1.9mm. To take this into account We will round the results to 2 decimals after the point. In the data each participant has 15 different translation values. Five values are from before the Redirected Walking experiment. These values are labeled as Base 1 - 5. Another five values are taken after the Redirected Walking experiment. These values are labeled Post VR 1 - 5. And the five values labeled as Post break 1 - 5 are the values taken after the 5 minute break. Each participant has the mean calculated for each of these three categories. These are labeled as AVG Base, AVG post VR and AVG post break.
• Range AVG Base: 1.68 to 2.18 meters. • Range AVG post VR: 1.78 to 2.19 meters. • Range AVG post break: 1.80 to 2.18 meters.
The data is stored in meters, but when we use them for calculations we convert them to centimeters. In figures 4.5, 4.6 and 4.7 the means are put into histograms with a bin size of 3 centimeter. These three histograms can be compared to each other to see if there is an overall change in how people translated at different moments in the experiment. Figure 4.8 shows a scatter plot so you can compare the 3 different moments per user. The error bars show the range of the 5 measurements of each specific moment.
A t-test can be used to determine if two sets of data are significantly different from each other. Doing a paired test on the AVG Base and AVG post VR values using a two tailed distribution gave a t-value of: 0.68. By using the obtained t-value with a degree of freedom of 19 we got a p-value of 0.51. This means that we cannot reject the null hypothesis and the results are not
statistically significant. The likelihood that random chance can explain the results is very high. The standard deviation(σ) for the base and post VR data is 11.26.
Figure 4.5: Experimental results of test subjects’ ability to walk 2 meters with their eyes closed, before the Redirected Walking experiment, put in a histogram with a bin size of 3 centimeter.
Figure 4.6: Experimental results of test subjects’ ability to walk 2 meters with their eyes closed, directly after the Redirected Walking experiment, put in a histogram with a bin size of 3 cen-timeter.
Figure 4.7: Experimental results of test subjects’ ability to walk 2 meters with their eyes closed, after a 5 minute break, put in a histogram with a bin size of 3 centimeter.
Figure 4.8: Experimental results of test subjects’ ability to walk 2 meters with their eyes closed, before the Redirected Walking experiment, directly after the Redirected Walking experiment and 5 minutes after the Redirected Walking experiment. This scatter plot allows you to quickly compare the 3 different means of a user. The error bars shows the range of the five measurements at each timeframe.
4.3
General and verbal feedback
The feedback about the Redirected Walking experience was positive overall. Two participants felt a bit lost during the Redirected Walking experiment because they did not know where they
were in the tracked space. This caused their experience to be less enjoyable. They were afraid that they would hit something. But they stated that it was pretty cool nonetheless. While most feedback was positive there were a few negative comments. Two participants felt a bit dizzy after each checkpoint. This was caused by the fact that they did not pay much attention to the blocks. So they kept rotating against the recommended direction. This behaviour did not change even after the experimenter advised them to pay more attention to the blocks. The biggest complaint was about the cables of the HTC VIVE. During the Redirected Walking experiment some of the participants stated that: “they were in the way”. While no one tripped over them, they still caused inconvenience for some of the participants.
4.4
Discussion
After having obtained the data and having calculated the p-values of 0.964 for rotation and 0.505 for translation, we can conclude that we cannot reject either null hypothesis and the results are not statistically significant. The likelihood that random chance can explain the results is very high. But there is still a small chance that this might not be the case. As such we will still look at the data and try to draw a conclusion.
4.4.1
Rotation
By comparing figures 4.1 and 4.2 we see that after the Redirected Walking experiment users in general rotate differently than their base values. Figure 4.3 shows that after taking the 5 minute break alot of the users rotated less compared to directly after the Redirected Walking experiment. Using figure 4.4 to see more quickly what kind of changes there are between the three means of each person, we can see that there is indeed a chance in the rotation of most users after Redirected Walking. For example if we were to look at the first user we see that after the Redirected Walking experiment this user shows a noticeable decrease from their base value. After taking a break this user slowly gets back to their base value. The fourth user for example shows a noticeable increase in rotation after the Redirected Walking experiment, which stays more or less the same after the 5 minute break. This might suggest that there is indeed an effect after using Redirected Walking that lingers.
For a 95% confidence interval for our rotation experiment we would have needed a sample size of n = 40.05σ
2
= 48.950.05
2
= 128.164. This assumes the population is normally distributed with a known standard deviation.
4.4.2
Translation
By comparing figures 4.5 and 4.6 we see that after the Redirected Walking experiment users in general do not translate alot differently than their base values. Figure 4.7 also shows that after taking the 5 minute break alot of the users translated more or less the same. But using figure 4.8 to see more quickly what kind of changes there are between the three means of each person, we can see that there are indeed users who translate alot differently after Redirected Walking. For example if we were to look at the fifth user we see that after the Redirected Walking experiment this user shows a noticeable increase from their base value. After taking a break this user slowly gets back to their base value. The seventh user for example shows a noticeable decrease in translation after the Redirected Walking experiment, which stays more or less the same after the 5 minute break.
This might suggest that there is indeed a effect after using Redirected Walking that lingers. For a 95% confidence interval for our translation experiment we would have needed a sample size of n = 411.26σ
2
= 411.260.05
2
= 202.860. This assumes the population is normally distributed with a known standard deviation.
CHAPTER 5
Conclusion and future work
Redirected walking is a method to immersively explore big virtual environments, while having a limited amount of physical space, using natural walking. The Redirected Walking toolkit is a good place to start when implementing Redirected Walking in your application. In this study we took a look at possible changes in rotation and translation of users who used Redirected Walking. Our sample size was too small and the likelihood that random chance could explain the results is very high. There is a confidence interval of 4% that Redirected Walking does indeed have effects on certain users. If a follow-up study would be planned it would need a too high of a sample size if we were to use the same parameters and redirection technique. It would be suggested to create a follow up study that used continuous redirection algorithms like the Steer-To-Orbit algorithm to get better and maybe more reliable results. It would also be suggested to use a wireless HTC VIVE to prevent issues with cables.
Bibliography
[1] Analysis of valves lighthouse tracking system reveals accuracy. June 2018. url: https : //www.roadtovr.com/analysis-of-valves-lighthouse-tracking-system-reveals-accuracy/.
[2] Mahdi Azmandian et al. “The redirected walking toolkit: a unified development platform for exploring large virtual environments”. In: Everyday Virtual Reality (WEVR), 2016 IEEE 2nd Workshop on. IEEE. 2016, pp. 9–14.
[3] Eric Hodgson, Eric R. Bachmann, and Tyler Thrash. “Performance of Redirected Walking Algorithms in a Constrained Virtual World”. In: IEEE Transactions on Visualization and Computer Graphics 20 (2014), pp. 579–587.
[4] HTC VIVE. June 2018. url: https://www.vive.com/eu/product/.
[5] Keigo Matsumoto et al. “Unlimited corridor: redirected walking techniques using visuo haptic interaction”. In: ACM SIGGRAPH 2016 Emerging Technologies. ACM. 2016, p. 20. [6] Zahira Merchant et al. “Effectiveness of virtual reality-based instruction on students’ learn-ing outcomes in K-12 and higher education: A meta-analysis”. In: Computers & Education 70 (2014), pp. 29–40.
[7] Eugenia M.Kolasinski. Simulator sickness in virtual environments. Tech. rep. U.S. Army Research Institute, May 1995.
[8] Sharif Razzaque. Redirected walking. PhD Thesis, University of North Carolina at Chapel Hill, 2005.
[9] Sharif Razzaque, Zachariah Kohn, and Mary C Whitton. “Redirected walking”. In: Pro-ceedings of EUROGRAPHICS. Vol. 9. Citeseer. 2001, pp. 105–106.
[10] Redirected walking toolkit. June 2018. url: http://projects.ict.usc.edu/mxr/rdwt/. [11] Bernhard E Riecke, Douglas W Cunningham, and Heinrich H B¨ulthoff. “Spatial updating
in virtual reality: the sufficiency of visual information”. In: Psychological research 71.3 (2007), pp. 298–313.
[12] Roy A Ruddle and Simon Lessels. “The benefits of using a walking interface to navigate virtual environments”. In: ACM Transactions on Computer-Human Interaction (TOCHI) 16.1 (2009), p. 5.
[13] Frank Steinicke et al. “Estimation of detection thresholds for redirected walking tech-niques”. In: IEEE transactions on visualization and computer graphics 16.1 (2010), pp. 17– 27.
[14] Evan Suma et al. “Evaluation of the cognitive effects of travel technique in complex real and virtual environments”. In: IEEE Transactions on Visualization and Computer Graphics 16.4 (2010), pp. 690–702.
[15] Evan A Suma et al. “A taxonomy for deploying redirection techniques in immersive virtual environments”. In: Virtual Reality Short Papers and Posters (VRW), 2012 IEEE. IEEE. 2012, pp. 43–46.
[16] Evan A Suma et al. “Effects of redirection on spatial orientation in real and virtual envi-ronments”. In: 3D User Interfaces (3DUI), 2011 IEEE Symposium on. IEEE. 2011, pp. 35– 38.
[17] Evan A Suma et al. “Effects of travel technique and gender on a divided attention task in a virtual environment”. In: 3D User Interfaces (3DUI), 2010 IEEE Symposium on. IEEE. 2010, pp. 27–34.
[18] Evan A Suma et al. “Leveraging change blindness for redirection in virtual environments”. In: Virtual Reality Conference (VR), 2011 IEEE. IEEE. 2011, pp. 159–166.
[19] Nobuhisa Tanaka and Hideyuki Takagi. “Virtual reality environment design of managing both presence and virtual reality sickness”. In: Journal of physiological anthropology and applied human science 23.6 (2004), pp. 313–317.
[20] Unity3D game engine. June 2018. url: https://unity3d.com/.
[21] Martin Usoh et al. “Walkin>walking-in-place>flying, in virtual environments”. In: Pro-ceedings of the 26th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co. 1999, pp. 359–364.
[22] Betsy Williams et al. “Exploring large virtual environments with an HMD when physical space is limited”. In: Proceedings of the 4th symposium on Applied perception in graphics and visualization. ACM. 2007, pp. 41–48.
6/8/2018 RDW experiment registratieformulier
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RDW experiment registratieformulier
Heel erg bedankt dat je wilt helpen met mijn scriptie.Door je op te geven geef je aan het volgende gelezen en geaccepteerd te hebben: * Je wordt niet snel misselijk.
* Je hebt geen vorm van epilepsie.
* Je hebt geen vorm van motorische beperkingen.
* Je hebt geen aandoening dat invloed heeft op oriëntatie en evenwicht. * Je bent zowel fysiek als mentaal in staat om Virtual Reality te gebruiken. Het experiment zal plaatsvinden op Science Park, 1098 Amsterdam, Nederland.
De hele sessie zal ongeveer 15 - 25 minuten duren, waarbij er gebruik gemaakt zal worden van de HTC Vive.
* Required
1. Email address *
2. Datum *
Geef hier aan wanneer je het experiment het liefst doet. Ik zal dan van tevoren contact opnemen of de tijdslot beschikbaar is. Alsjeblieft een datum kiezen tussen 1 juni en 7 juni.
Example: December 15, 2012 11:03 AM
6/8/2018 RDW in Virtual Reality questionnaire
RDW in Virtual Reality questionnaire
* Required
1. Wat is je geslacht? *
Check all that apply. Man
Vrouw Anders 2. Wat is je leeftijd? *
3. Heb je eerder gebruik gemaakt van Virtual Reality applicaties? *
Mark only one oval. Ja
Nee
4. Heb je al eerder gehoord van redirected walking in VR of heb je het al eerder meegemaakt? *
Mark only one oval.
Ja, ik had er al eerder over gehoord. Ja, ik heb het zelfs al eerder meegemaakt. Nee
RDW in Virtual Reality questionnaire
5. Was er een moment tijdens de test, waar je opmerkte dat er iets vreemds of onnatuurlijk gebeurde dat wegnam van de ervaring? Als dit het geval is, leg dan uit wat je opmerkte en hoe je je voelde.
6/8/2018 RDW in Virtual Reality questionnaire
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6. Was er een moment tijdens de test, waar je je verdwaald voelde? Als dit het geval is, leg dan uit hoe je je voelde en wanneer je dit voelde. *
7. Je hebt een grote virtuele ruimte doorgelopen, terwijl de fysieke ruimte kleiner was dan deze ruimte. Hoe denk je dat dit gebeurd was? Als je het niet zeker weet geef dit dan aan. *
8. Wanneer je draaide aan het einde van een gang, draaide de virtuele wereld ook, zodat je niet tegen de grenzen van de fysieke ruimte aankwam. Merkte je dit op? Als dit het geval is, leg dan uit hoe je je voelde. *
9. Was er een specifiek element aan de simulatie dat de ervaring in virtual reality negatief/positief beinvloedde? Als dit het geval is, geef dit dan aan.
ROTATION in degrees.
Base 1 - 5, Post VR 1 - 5 and Post break 1 - 5 show the amount that users rotated during the rotation tests. AVG Base, AVG post VR and AVG post break takes the mean of the 5 values of their category
Range AVG Base: 159.48 - 194.15 Range AVG post VR: 164.94 - 198.07 Range AVG post break: 165.64 - 194.91
Testpersonen Base1 Base2 Base3 Base4 Base5 Post VR 1 Post VR 2 Post VR 3
Persoon 1 177.62 178.51 180.32 183.38 185.07 164.76 164.12 175.18 Persoon 2 200.75 180.59 184.11 178.39 182.58 183.27 186.19 203.86 Persoon 3 193.19 188.27 180.97 176.92 180.28 195.69 171.13 170.76 Persoon 4 154.56 159.16 153.75 159.46 170.46 175.60 174.79 177.43 Persoon 5 171.11 178.66 181.03 174.80 182.50 187.68 188.01 173.74 Persoon 6 168.26 181.19 202.19 196.33 196.58 192.33 187.17 192.03 Persoon 7 210.12 205.13 190.37 185.12 180.02 225.11 195.63 200.57 Persoon 8 189.03 192.33 167.07 182.33 195.21 200.51 195.32 184.12 Persoon 9 156.34 163.00 177.12 165.21 166.13 180.31 185.63 171.29 Peroon 10 179.99 181.23 188.29 179.21 183.55 178.11 188.36 182.12 Persoon 11 182.33 181.22 180.33 181.12 178.12 191.92 190.68 188.00 Persoon 12 183.99 178.22 177.66 181.00 180.22 187.31 189.57 184.72 Persoon 13 162.10 159.09 174.39 162.32 167.00 180.10 165.52 175.32 Persoon 14 195.10 189.23 200.55 190.21 185.54 192.39 176.31 200.68 Persoon 15 167.29 171.99 180.10 173.99 172.12 185.22 188.58 176.45 Persoon 16 177.78 180.23 181.24 180.11 179.88 179.33 192.39 176.99 Persoon 17 155.64 170.33 162.30 172.32 165.44 166.31 154.82 170.34 Persoon 18 180.00 180.91 181.12 179.57 182.78 212.33 204.22 210.22 Persoon 19 181.04 179.10 175.00 178.88 183.66 172.31 176.22 174.23 Persoon 20 178.46 182.60 189.46 186.06 187.35 185.41 184.81 180.27
ROTATION in degrees.
Post VR 4 Post VR 5 Post break 1 Post break 2 Post break 3 Post break 4 Post break 5 AVG Base AVG post VR
165.78 177.71 174.85 171.02 195.71 169.86 168.95 180.98 169.51 179.39 179.39 192.18 192.92 187.30 187.37 195.90 185.28 186.42 178.30 164.66 196.24 171.06 170.48 171.97 192.30 183.93 176.11 168.91 190.51 171.11 178.66 181.03 174.80 182.50 159.48 177.45 182.07 194.90 176.34 108.66 210.25 182.25 179.23 177.62 185.28 196.57 187.56 183.01 178.32 176.92 180.52 192.25 188.91 191.13 179.03 189.99 165.05 198.77 190.01 202.55 180.78 194.15 198.07 179.46 184.21 174.25 183.12 185.21 178.33 183.23 185.19 188.73 179.22 167.53 160.21 172.31 156.68 177.24 164.23 165.56 176.80 181.21 176.24 180.51 182.32 179.98 180.21 182.82 182.46 181.21 179.31 187.00 180.00 179.90 182.00 180.03 178.91 180.63 187.38 187.56 182.57 180.31 183.21 177.88 179.99 181.37 180.22 186.34 173.57 182.51 156.02 177.31 166.79 155.52 175.99 164.98 175.41 202.31 194.47 192.21 185.66 198.49 197.57 189.51 192.13 193.23 169.88 174.57 155.00 167.67 170.78 166.00 175.44 173.10 178.94 185.63 180.33 180.00 181.21 180.31 178.67 183.42 179.85 182.94 168.21 165.00 166.56 160.00 163.42 174.00 164.21 165.21 164.94 188.42 172.33 192.32 180.00 176.52 190.22 187.65 180.88 197.50 180.57 179.51 184.22 181.22 178.40 181.66 177.51 179.54 176.57 167.17 187.34 198.01 190.27 198.52 193.89 193.84 184.79 181.00
ROTATION in degrees.
AVG post break
176.08 191.13 180.41 177.62 171.34 182.20 187.43 180.83 166.14 181.17 180.17 180.55 166.33 192.69 166.98 180.72 165.64 185.35 180.60 194.91
TRANSLATION in meters
Base 1 - 5, Post VR 1 - 5 and Post break 1 - 5 show the amount that users translated AVG Base, AVG post VR and AVG post break takes the mean of the 5 values of their category
Range AVG Base: 1.68 - 2.18
Range AVG post VR: 1.78 - 2.19 Range AVG post break: 1.80 - 2.18
Testpersonen Base1 Base2 Base3 Base4 Base5 Post VR 1 Post VR 2 Post VR 3
Persoon 1 2.41 1.87 1.91 2.05 1.99 2.10 2.00 2.05 Persoon 2 1.96 2.21 1.94 1.92 1.90 1.96 1.97 1.95 Persoon 3 2.37 2.19 2.12 2.01 2.05 2.15 2.07 2.13 Persoon 4 2.32 2.24 2.17 2.04 1.97 2.16 2.28 2.00 Persoon 5 2.19 1.99 2.17 2.02 2.14 2.11 2.22 2.17 Persoon 6 1.64 1.89 1.88 2.15 2.08 2.01 1.92 1.96 Persoon 7 2.31 2.20 2.25 1.99 2.15 2.16 2.06 2.13 Persoon 8 2.12 1.97 2.25 2.11 2.12 2.12 2.05 2.13 Persoon 9 1.64 1.72 1.67 1.90 1.76 1.79 1.92 1.76 Peroon 10 2.02 1.98 2.01 2.10 1.98 1.97 2.02 2.07 Persoon 11 2.11 2.05 2.01 1.98 2.00 2.01 1.95 2.00 Persoon 12 2.00 2.32 1.99 2.00 2.05 2.12 1.90 2.06 Persoon 13 1.78 2.03 1.90 2.01 1.96 2.00 1.88 2.03 Persoon 14 2.15 1.99 1.89 2.12 2.01 2.12 1.90 1.98 Persoon 15 1.79 1.81 1.80 1.96 1.86 1.88 1.79 1.78 Persoon 16 2.00 2.00 2.02 1.99 2.03 2.05 1.99 1.98 Persoon 17 1.79 1.92 2.01 2.10 1.95 2.21 1.83 2.00 Persoon 18 2.21 2.05 1.97 2.00 2.07 1.96 2.05 2.01 Persoon 19 1.99 1.97 2.06 1.99 2.03 2.02 2.10 1.96 Persoon 20 1.52 1.75 1.62 1.66 1.85 1.95 1.61 1.85
TRANSLATION in meters
Post VR 4 Post VR 5 Post break 1 Post break 2 Post break 3 Post break 4 Post break 5 AVG Base AVG post VR
2.02 2.03 2.19 1.92 2.02 1.99 1.94 2.05 2.04 1.94 2.10 2.15 2.18 2.04 2.11 1.97 1.99 1.99 2.02 2.19 2.16 2.10 2.15 2.05 2.19 2.15 2.11 2.16 2.16 2.10 2.25 2.01 2.00 2.20 2.15 2.15 2.33 2.14 2.17 2.16 2.35 2.17 2.03 2.10 2.19 1.89 2.01 2.07 1.72 1.98 2.10 2.09 1.93 1.96 2.03 2.00 2.15 2.08 2.01 2.09 2.12 2.18 2.08 2.00 2.08 2.14 2.00 2.11 2.09 2.09 2.11 2.08 2.11 1.55 1.90 1.73 1.80 1.68 1.91 1.74 1.82 2.01 2.10 2.01 1.99 2.00 2.02 2.01 2.02 2.04 2.03 2.00 1.99 2.01 1.99 2.00 1.90 2.03 2.00 2.00 1.98 2.00 1.97 2.08 1.98 2.01 2.07 2.01 1.92 2.00 2.06 2.06 1.98 2.01 1.96 1.94 1.97 2.02 2.10 2.02 1.99 2.07 1.98 1.97 2.03 2.02 1.87 2.05 1.78 1.92 2.12 1.57 1.64 1.84 1.87 2.11 2.01 2.22 1.91 2.13 1.97 2.06 2.01 2.03 1.92 1.90 2.13 1.84 1.92 1.87 2.00 1.95 1.97 1.99 2.00 2.00 1.97 2.07 1.99 2.02 2.06 2.00 1.99 2.06 2.05 1.98 1.97 2.09 2.12 2.01 2.02 1.70 1.79 2.35 1.73 1.72 1.92 1.68 1.68 1.78
TRANSLATION in meters
AVG post break
2.01 2.09 2.13 2.11 2.18 1.99 2.09 2.09 1.80 2.00 1.98 2.01 2.01 2.00 1.81 2.06 1.95 2.01 2.04 1.88
