Oculus VR » General http://www.oculusvr.com Oculus VR, a technology company revolutionizing the way people experience video games. Thu, 10 Apr 2014 20:30:13 +0000 en-US hourly 1 http://wordpress.org/?v=3.6.1 Introducing Michael Abrash, Oculus Chief Scientist http://www.oculusvr.com/blog/introducing-michael-abrash-oculus-chief-scientist/ http://www.oculusvr.com/blog/introducing-michael-abrash-oculus-chief-scientist/#comments Fri, 28 Mar 2014 17:11:04 +0000 Oculus VR http://www.oculusvr.com/?p=5283 The Path to the Metaverse

I'm tremendously excited to join Oculus, and when I think back, it's astonishing how unlikely the path to this moment is. I've told most of the parts of this story before, but never all together, and the narrative, now spanning twenty years, just keeps getting more remarkable.
 

Image credit Steve Grever, PC Perspective
Palmer, Michael, and John @ QuakeCon 2012

Sometime in 1993 or 1994, I read Snow Crash, and for the first time thought something like the Metaverse might be possible in my lifetime. Around the same time, I saw the first leaked alpha version of Doom. I knew John Carmack from exchanges on the M&T bulletin board a couple of years earlier, when both John and I were learning how to write 3D graphics code, so I sent him mail saying how blown away I was.

John replied that his mother lived in Seattle, and maybe we could get together next time he was in town. Eventually he came by to visit, and we had a good conversation, in the course of which he asked if I'd like to come work at Id; being in the middle of shipping the first couple of versions of Windows NT, I politely declined.

In late 1994 or early 1995, John let me know he was going to be back in town, and asked if I wanted to have dinner. We met at Thai Chef in Bellevue. I knew he was going to try to hire me, and I knew I was going to say no. But he didn't get around to doing that until after he had talked for a good two hours about how he was going to build cyberspace, and by that time it was hard for me to imagine doing anything else. John was as good as his word, and Quake was the start of a world of connected gaming that thrives to this day.

Quake was seminal and high-impact – it's amazing what a team of ten mostly untrained twenty-somethings in the Black Cube in Mesquite, Texas, managed to accomplish – but it wasn't the Metaverse. It was still, in the end, images on a screen, not Hiro Protagonist literally fencing for his life. And so John and I went our separate ways, John to continue to refine what he had created, and me to wander through a series of interesting projects that, in the end, always left me wishing for the pure focus, intensity, and impact of those two years working with John.

Fast-forward fourteen years. I'm at Valve – which started its existence by licensing the Quake source code – looking for the next big platform shift, and I conclude that it's augmented reality. Thanks to Valve's unique structure, I'm able to start working on that, along with several other interested people, including Atman Binstock, who I recruited over coffee at St. James Espresso in Kirkland; Atman is thinking about moving to Paris and writing a debugger, but finally decides to join up. John, meanwhile, is poking at virtual reality, seeing if it's finally feasible. He sends me mail on the occasion of the 15th anniversary of Quake's release, saying that he has a feeling that something really big is just around the corner, something bigger than anything that's happened so far. He's talking about VR.

Then two things happen at about the same time. On one path, Palmer develops his first VR prototype, John and Palmer Luckey connect, Oculus forms and its Kickstarter is wildly successful, DK1 ships, and John becomes Oculus CTO. Meanwhile, I read Ready Player One, strongly recommend it to several members of the AR group, and we come to the conclusion that VR is potentially more interesting than we thought, and far more tractable than AR. We switch over to working on VR just as Palmer's homebrew project is morphing into Oculus.

From that point, both VR paths have been pretty well documented, Oculus's in this blog, in the press, and all over the Internet, and Valve's in my blog and talks. The end result, a year and a half later, is a VR system that can create a sense of presence – the feeling, below the conscious level, that you really are someplace. This is an experience that no one except a few researchers using awkward, hugely expensive equipment had ever had, but within the next couple of years it should be available in a comfortable form factor at a consumer price. In the space of two years, a relative handful of people at two companies, none of them VR experts at the start, somehow managed to resurrect VR from the trash heap of technologies-that-never-were and make it the most exciting technology around.

What VR Could, Should, and Almost Certainly Will Be within Two Years, Steam Dev Days 2014

That wouldn't have happened if Palmer hadn't developed his prototype. If John hadn't been investigating VR at the right time. If they hadn't run into each other. If I hadn't been looking for a new platform. If Palmer hadn't met up with the right people to form Oculus and build DK1. If the community hadn't been so overwhelmingly supportive of VR and the Kickstarter. If Atman had decided to go do a debugger instead. If a team hadn't assembled at Valve, done a bunch of hard work to show that low persistence, excellent tracking, and a well-calibrated and well-tuned system enabled presence, and shared that knowledge with Oculus. If I hadn't come across Ready Player One at the right time. Heck, if I hadn't come across Snow Crash all those years ago, or the Doom alpha, or known John from the M&T bulletin board, or if I hadn't known Gabe Newell and Mike Harrington from my days at Microsoft, in which case I would have had no reason to help them license the Quake source code…

You get the idea. We're on the cusp of what I think is not The Next Big Platform, but rather simply The Final Platform – the platform to end all platforms – and the path here has been so improbable that I can only shake my head.

The final piece of the puzzle fell into place on Tuesday. A lot of what it will take to make VR great is well understood at this point, so it's engineering, not research; hard engineering, to be sure, but clearly within reach. For example, there are half a dozen things that could be done to display panels that would make them better for VR, none of them pie in the sky. However, it's expensive engineering. And, of course, there's also a huge amount of research to do once we reach the limits of current technology, and that's not only expensive, it also requires time and patience – fully tapping the potential of VR will take decades. That's why I've written before that VR wouldn't become truly great until some company stepped up and invested the considerable capital to build the right hardware – and that it wouldn't be clear that it made sense to spend that capital until VR was truly great. I was afraid that that Catch-22 would cause VR to fail to achieve liftoff.

That worry is now gone. Facebook's acquisition of Oculus means that VR is going to happen in all its glory. The resources and long-term commitment that Facebook brings gives Oculus the runway it needs to solve the hard problems of VR – and some of them are hard indeed. I now fully expect to spend the rest of my career pushing VR as far ahead as I can.

It's great to be working with John again after all these years, and with that comes a sense of deja vu. It feels like it did when I went to Id, but on steroids – this time we're working on technology that will change not just computer gaming, but potentially how all of us interact with computers, information, and each other every day. I think it's going to be the biggest game-changer I've ever seen – and I've seen quite a lot over the last 57 years.

I can't wait to see how far we can take it.

- Michael

www.oculus.com/careers

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Oculus Joins Facebook http://www.oculusvr.com/blog/oculus-joins-facebook/ http://www.oculusvr.com/blog/oculus-joins-facebook/#comments Tue, 25 Mar 2014 21:35:41 +0000 Oculus VR http://www.oculusvr.com/?p=5266 We started Oculus with a vision of delivering incredible, affordable, and ubiquitous consumer virtual reality to the world. We’ve come a long way in the last 18 months: from foam core prototypes built in a garage to an incredible community of active and talented developers with more than 75,000 development kits ordered. In the process, we’ve defined what consumer virtual reality needs to be and what it’s going to require to deliver it.

A few months ago, Mark, Chris, and Cory from the Facebook team came down to visit our office, see the latest demos, and discuss how we could work together to bring our vision to millions of people. As we talked more, we discovered the two teams shared an even deeper vision of creating a new platform for interaction that allows billions of people to connect in a way never before possible.

Today, we’re pleased to announce that we’ve joined forces with Facebook to create the best virtual reality platform in the world.

At first glance, it might not seem obvious why Oculus is partnering with Facebook, a company focused on connecting people, investing in internet access for the world and pushing an open computing platform. But when you consider it more carefully, we’re culturally aligned with a focus on innovating and hiring the best and brightest; we believe communication drives new platforms; we want to contribute to a more open, connected world; and we both see virtual reality as the next step.

Most important, Facebook understands the potential for VR. Mark and his team share our vision for virtual reality’s potential to transform the way we learn, share, play, and communicate. Facebook is a company that believes that anything is possible with the right group of people, and we couldn’t agree more.

This partnership is one of the most important moments for virtual reality: it gives us the best shot at truly changing the world. It opens doors to new opportunities and partnerships, reduces risk on the manufacturing and work capital side, allows us to publish more made-for-VR content, and lets us focus on what we do best: solving hard engineering challenges and delivering the future of VR.

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Over the next 10 years, virtual reality will become ubiquitous, affordable, and transformative, and it begins with a truly next-generation gaming experience. This partnership ensures that the Oculus platform is coming, and that it’s going to change gaming forever.

We’ll see you in the Metaverse!

– Palmer, Brendan, John and the Oculus team

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The Future of Virtual Reality http://www.oculusvr.com/blog/the-future-of-virtual-reality/ http://www.oculusvr.com/blog/the-future-of-virtual-reality/#comments Tue, 25 Mar 2014 21:35:30 +0000 Oculus VR http://www.oculusvr.com/?p=5271 I’ve always loved games. They’re windows into worlds that let us travel somewhere fantastic. My foray into virtual reality was driven by a desire to enhance my gaming experience; to make my rig more than just a window to these worlds, to actually let me step inside them. As time went on, I realized that VR technology wasn’t just possible, it was almost ready to move into the mainstream. All it needed was the right push.

We started Oculus VR with the vision of making virtual reality affordable and accessible, to allow everyone to experience the impossible. With the help of an incredible community, we’ve received orders for over 75,000 development kits from game developers, content creators, and artists around the world.

When Facebook first approached us about partnering, I was skeptical. As I learned more about the company and its vision and spoke with Mark, the partnership not only made sense, but became the clear and obvious path to delivering virtual reality to everyone. Facebook was founded with the vision of making the world a more connected place. Virtual reality is a medium that allows us to share experiences with others in ways that were never before possible.

Facebook is run in an open way that’s aligned with Oculus’ culture. Over the last decade, Mark and Facebook have been champions of open software and hardware, pushing the envelope of innovation for the entire tech industry. As Facebook has grown, they’ve continued to invest in efforts like with the Open Compute Project, their initiative that aims to drive innovation and reduce the cost of computing infrastructure across the industry. This is a team that’s used to making bold bets on the future.

In the end, I kept coming back to a question we always ask ourselves every day at Oculus: what’s best for the future of virtual reality? Partnering with Mark and the Facebook team is a unique and powerful opportunity. The partnership accelerates our vision, allows us to execute on some of our most creative ideas and take risks that were otherwise impossible. Most importantly, it means a better Oculus Rift with fewer compromises even faster than we anticipated.

Very little changes day-to-day at Oculus, although we’ll have substantially more resources to build the right team. If you want to come work on these hard problems in computer vision, graphics, input, and audio, please apply!

This is a special moment for the gaming industry — Oculus’ somewhat unpredictable future just became crystal clear: virtual reality is coming, and it’s going to change the way we play games forever.

I’m obsessed with VR. I spend every day pushing further, and every night dreaming of where we are going. Even in my wildest dreams, I never imagined we’d come so far so fast.

I’m proud to be a member of this community — thank you all for carrying virtual reality and gaming forward and trusting in us to deliver. We won’t let you down.

– Palmer Luckey, Founder, Oculus

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Letter to the Team from Brendan Iribe http://www.oculusvr.com/blog/letter-to-the-team-from-brendan-iribe/ http://www.oculusvr.com/blog/letter-to-the-team-from-brendan-iribe/#comments Tue, 25 Mar 2014 21:35:19 +0000 Oculus VR http://www.oculusvr.com/?p=5270 Team,

As you may have heard this morning, Oculus has agreed to join Facebook.

Facebook shares our vision for connecting a billion people through virtual reality with the power of shared presence.

Oculus will continue to operate independently. We’re staying Oculus, we’re still building the Oculus Rift, our email addresses are remain @oculusvr.com, and most importantly, our hoodies will still say Oculus.

By partnering with Facebook, we’ll be able to build a better product with zero compromises and a focus on growth. We’ll also be investing more heavily in made-for-VR content and exploring other opportunities to accelerate our vision.

In broad strokes, here are a few key points to consider for the long-term strategy:

  • We’re able to tap into Facebook’s experience and back-end systems for our platform services. As an added bonus, Oculus now has a rock solid, global payments solution.
  • We’ll be able to leverage Facebook’s recruiting infrastructure, including hiring engineers from within Facebook, to supercharge our recruiting.
  • We can afford to always make the decision that is right for virtual reality and our customers in the long term – we don’t have to make short term compromises.
  • We’re going to invest in additional partnerships to build the best product and platform.

I’ll meet with everyone individually over the next few days to discuss what this means in terms of integration. In the meantime, know that things couldn’t be better.

No team, ever, has had a better shot at delivering on the dream of virtual reality. This will be the team that solves the hardest problems and delivers the final platform. We need you now, more than ever, to go out and find the very best engineers in the world to help us deliver the final platform, the Holodeck.

This is a truly special moment. The work we’ve done has captured the world’s attention and changed the perception of the medium forever. This partnership is a huge affirmation of everything we’ve done. Congratulations, guys.

Now, let’s get back to changing the world.

– Brendan

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Announcing the Oculus Rift Development Kit 2 (DK2) http://www.oculusvr.com/blog/announcing-the-oculus-rift-development-kit-2-dk2/ http://www.oculusvr.com/blog/announcing-the-oculus-rift-development-kit-2-dk2/#comments Wed, 19 Mar 2014 15:05:31 +0000 Oculus VR http://www.oculusvr.com/?p=5230 Since the launch of the Oculus Kickstarter, we’ve been focused on building the best virtual reality platform. The original development kit was a strong starting point that showed the world a glimpse of presence, but its shortcomings prevented it from delivering great VR.

Almost exactly one year after shipping the original dev kit, we’re pleased to announce DK2, the second development kit for the Oculus Rift!

The second development kit features many of the key technical breakthroughs and core elements of the consumer Rift including a low-persistence, high-definition display and precise, low-latency positional head tracking.

DK2 isn’t identical to the consumer Rift, but the fundamental building blocks for great VR are there. All the content developed using DK2 will work with the consumer Rift. And while the overall experience still needs to improve before it’s consumer-ready, we’re getting closer everyday — DK2 is not the Holodeck yet, but it’s a major step in the right direction.

Like the Crystal Cove prototype, DK2 uses a low persistence OLED display to eliminate motion blur and judder, two of the biggest contributors to simulator sickness. Low persistence also makes the scene appear more visually stable, increasing the potential for presence. The high-definition 960×1080 per-eye display reduces the screen-door effect and improves clarity, color, and contrast.

DK2 also integrates precise, low-latency positional head tracking using an external camera that allows you to move with 6-degrees-of-freedom and opens up all sorts of new gameplay opportunities like peering around corners, leaning in to get a closer look at objects in the world, and kicking back on a virtual beach.
 



Precise positional tracking is another key requirement for comfortable virtual reality; without it, an enormous amount of your real world movement is lost. We’re looking forward to seeing the new experiences the community creates now that positional head tracking is a core element of the platform.

We’ve also included updated orientation tracking, a built-in latency tester, an on-headset USB accessory port, new optics, elimination of the infamous control box, a redesigned SDK and further optimized Unity and Unreal Engine 4 integrations.
 



All in, DK2 delivers a massive leap forward in terms of the quality of the VR experiences you’re able to create and enjoy. The consumer Rift will be another major step beyond that, but in the meantime DK2 brings the world closer to great consumer virtual reality than ever before.

Even with all these changes, we’ve tried to keep the price as low as possible. DK2 will be $350 at launch and you can pre-order the hardware starting today at www.oculusvr.com/order. We expect to begin shipping the first batch of DK2s in July, and we’ll ramp up production based on interest.
 

GDC 2014

We’re debuting the second development kit this week at the Game Developers Conference in San Francisco with EVE: Valkyrie by CCP, UE4 Elemental Defense by Epic, and a new demo, UE4 Couch Knight!
 



Couch Knight was built by the team at Epic Games to showcase the positional tracking and basic avatars in a setting with shared presence. The tech demo juxtaposes a realistic scene with two cartoon knights, controlled by the players, who burst to life and battle throughout the room on couches, shelves and even the players’ avatars.

The players’ head movements and position are actually mapped to the avatars using UE4’s inverse kinematic system, which makes for a taste of a social experience.

A huge thank you to the team at Epic for bringing Couch Knights to life! If you’re at the show this week, be sure to swing by the booth and check it out.
 

What’s Next?

We’re deep into development on the consumer Rift. We have a lot more planned, including improvements to comfort, resolution, tracking, software, ergonomics, optics, industrial design, and the overall experience.
 



Virtual reality is going to continue to evolve rapidly in the coming years. There’s no cutting corners or ‘good enough’ when it comes to VR; the consumer Rift needs to be perfect and we’re dedicated to getting it right. We’re moving as fast as possible and promise it’ll be worth the wait.

The passion of the VR community is what has made all this possible, from the Kickstarter campaign to the hundreds of games and experiences we've seen so far. And this is still just the beginning.

We truly believe virtual reality will change the world — Thanks for being part of the journey with us.

– The Oculus Team

 

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Welcome Atman Binstock, Chief Architect http://www.oculusvr.com/blog/welcome-atman-binstock-chief-architect/ http://www.oculusvr.com/blog/welcome-atman-binstock-chief-architect/#comments Tue, 11 Mar 2014 15:18:03 +0000 Oculus VR http://www.oculusvr.com/?p=5204 We’re thrilled to introduce Atman Binstock, Oculus’ new Chief Architect!

Atman was one of the lead engineers and driving forces behind Valve’s VR project, creating the ‘VR Room’ demo that garnered so much excitement at Steam Dev Days. Prior to Valve, Atman led several projects at top companies in the industry, including RAD, DICE, and Intel.

Atman and the Valve VR team helped prove simulator sickness could be overcome and a true sense of "presence" could be delivered. He helped set the bar for consumer virtual reality and is dedicated to making sure Oculus delivers the highest quality VR experience.

Atman wanted to share his start in VR with the community:

“Just over two years ago, Michael Abrash and I were sitting in a coffee shop in Kirkland. He was trying to convince me to come work on AR and VR with him at Valve.

At the time, I was trying to wrap my head around two questions: ‘Why me?’ and ‘Why now?’ Michael did a good job of explaining that a confluence of technologies was developing that could make compelling virtual experiences possible, but I still wrestled with ‘Why me?’ After all, if the technology was really ready, surely people more capable than me would figure it out.

But Michael convinced me that this was basically the myth of technological inevitability: the idea that because technologies were possible, they would just naturally happen. Instead, the way technological revolutions actually happen involve smart people working hard on the right problems at the right time. And if I wanted a revolution, and I thought I was capable of contributing, I should be actively pushing it forward.

I signed up.

Two years later, we’ve solved some of the basic problems, proven great VR is not only possible but truly magical, and now I want to bring it to the world. I’m incredibly excited and humbled by the opportunity — We’re just scratching the surface of what’s possible, and I can’t wait to discover what’s next!”


Image courtesy Serenity Forge.

Atman will be spearheading the new Oculus R&D team based in the Seattle area. We’re looking for exceptional engineers to help research and develop the future of virtual reality. If you’re interested in working with us, please visit oculus.com/careers or email careers+seattle@oculusvr.com.

End of Rift Development Kit Sales

We’re quickly running out of stock for the Rift development kit, so we’ve shut down sales in most regions. A handful of the hardware components are no longer being manufactured, and as a result, we’re ramping down production and distribution of the original kits.

We never expected to sell so many Rift development kits and the fact that we’re close to being sold out after 60,000 kits is nothing short of incredible — Thank you for your support!

We’ll have more news on this soon, so stay tuned!

GDC, PAX East, and E3

We just wrapped up SXSW in Austin where we did a live Q&A panel and the first public demo of the Crystal Cove prototype since CES:

CNN“SXSW: Demo of 'Game of Thrones' on Oculus Rift wows virtual reality fans”

Wired“How It Felt to Experience Game of Thrones Through an Oculus Rift”

Palmer, Ryan and Nate on the SXSW panel, “Exploring the Future of Virtual Reality with Oculus”:

The team is heads-down in the run up to GDC 2014 next week. We’re giving two talks at the show, along with hosting a booth on the expo floor (with 20 demo stations!):

Working with the Latest Oculus Rift Hardware and Software
Michael Antonov and Nate Mitchell – Wednesday, March 19th @ 11am – 12pm

Developing Virtual Reality Games and Experiences
Tom Forsyth – Thursday, March 20th @ 2:30pm – 3:30pm

If you’re at the show, make sure to stop by and say Hello! And just in case you missed it, here’s Palmer’s talk from Steam Dev Days in January:

We’ll see you at GDC!

– The Oculus Team

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EVE: Valkyrie, Open Source Hardware, and the Best Practices Guide http://www.oculusvr.com/blog/eve-valkyrie-open-source-hardware-and-the-best-practices-guide/ http://www.oculusvr.com/blog/eve-valkyrie-open-source-hardware-and-the-best-practices-guide/#comments Wed, 05 Feb 2014 16:42:20 +0000 Oculus VR http://www.oculusvr.com/?p=5122 The intersection of transparency and open collaboration between Oculus and the development community often leads to amazing content and inspiring breakthroughs. Today, we’re excited to share a few great examples.

Oculus Co-Publishing EVE: Valkyrie for the Rift

First, we’re thrilled to announce that the first Oculus co-publishing project is none other than EVE: Valkyrie, making Valkyrie an exclusive Oculus Rift launch title.

EVE: Valkyrie, developed by the team at CCP Games (creators of EVE Online and DUST 514), is one of the first AAA games designed exclusively for the Rift. The project, initially called “EVE-VR”, was born from a small, passionate team within CCP who supported Oculus during the Kickstarter campaign.

Since its debut at EVE Fanfest last year, Valkyrie has been a brilliant showcase for the power of VR and hands-down one of our favorite Rift games. At E3 2013, Valkyrie came away with a half-dozen awards including Best Game of E3 from PC Gamer and Most Innovative Game from IGN. Valkyrie was also a key part of the award-winning Crystal Cove demos at CES this year.

The original EVE-VR team.

“We strongly believe the best VR experiences are going to be the ones built from the ground up for VR, and we’ve kept that in mind whilst developing Valkyrie.

We wanted people to really feel like they were there – to sense the vastness of space, feel the confined area of the cockpit and get that adrenaline rush as you see an exploding fighter whizz past your head.

In a very short amount of time this passion project became a full fledged CCP project which we’re now working on in Newcastle. It’s hard to believe how far we’ve come in a year!”

– CCP EVE Valkyrie team members Robert Clarke, Programmer, and Sigurður Gunnarsson, Senior Programmer

We couldn’t be more excited for the future of Valkyrie, and we’re thrilled to help CCP bring the best possible made-for-VR experience to the Rift.

We’re looking for more great developers to partner with on made-for-VR content. If you’re interested in potentially teaming up, email us at publishing@oculusvr.com to learn more!

Open Sourcing the Latency Tester

A key part of the Oculus culture is a drive for openness. We believe that making Oculus more open and transparent will ultimately accelerate and improve virtual reality technology for everyone.

As part of this effort, today we’ve released the Oculus Latency Tester as open source hardware. This includes the firmware as a CooCox project, the schematic and board layout in Eagle, STLs of a 3D printable enclosure, and documentation of the interface. The entire package is available to view, download, and fork in a GitHub repository.

The Latency Tester is now under permissive licenses that let you freely use, modify, distribute, tear apart, and even sell the project or pieces of it to your heart’s content. The firmware, excluding vendor libraries, is released under the Apache 2.0 License. The schematic, board layout, and enclosure are available under Creative Commons Attribution 4.0. These licenses make working with the Latency Tester source as convenient as possible.

The Latency Tester contains a Cortex M3-based microcontroller, a digitally interfaced RGB color sensor, and a 3 digit 7 segment display. Testing the latency of the Rift is just one use case. You could build a display color calibrator, an ambient light detector, a general purpose tester of video game latency with external trigger input, or a myriad of other projects with a little hacking on the firmware or hardware.

The files are available for you to build your own, but if you don’t want to break out the soldering iron or toaster oven, you can order a Latency Tester here. A new production run was just completed and will be shipping out shortly.

We’re always looking at open-sourcing other aspects of the Oculus hardware and software stack that can be useful to the community. We’ll keep you posted on future developments!

Best Practices Guide

Photo courtesy Dave Oshry.

At Steam Dev Days, Palmer announced that we’ve released the Oculus Best Practices Guide, a collection of suggestions and basic guidelines for developing VR content. The guide is the result of months of research, prototyping, and testing by the Oculus team along with key members of the community.

If you’re interested in developing VR games or experiences, we highly recommend giving it a read. Here’s a very brief section from the introduction for inspiration:

“VR is an immersive medium. It creates the sensation of being entirely transported into a virtual (or real, but digitally reproduced) three-dimensional world, and it can provide a far more visceral experience than screen-based media. Enabling the mind’s continual suspension of disbelief requires particular attention to detail. It can be compared to the difference between looking through a framed window into a room, versus walking through the door into the room and freely moving around.”

You can download the guide now from the Oculus Developer Center here:

http://static.oculusvr.com/sdk-downloads/documents/OculusBestPractices.pdf

The Best Practices Guide is an ever-evolving document, and we’re always reviewing and adding emerging insights from the developer community. If you have suggestions, let us know by emailing bestpractices@oculusvr.com!

What’s Next?

The team will be at a ton of upcoming events, including at IndieCade East, SXSW, and GDC. If you’re at one of the shows, swing by and say “Hi”. Brendan and Palmer are also giving a talk on the future of virtual reality on Thursday at 2:30pm PST from DICE, which will be livestreamed at http://www.twitch.tv/DICE.

Finally, as always, we’re recruiting the best and the brightest, especially:

- Senior 3D Artists and Modelers

- Senior Animators

- Senior Gameplay Engineers

…to help us build next-gen VR content!

You can find all the latest opportunities for Oculus’ Irvine, San Francisco, and Dallas offices at www.oculusvr.com/careers.

Hope to see you soon!

– The Oculus Team

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Crystal Cove Debut, CES Recap, and Steam Dev Days http://www.oculusvr.com/blog/crystal-cove-debut-ces-recap-and-steam-dev-days/ http://www.oculusvr.com/blog/crystal-cove-debut-ces-recap-and-steam-dev-days/#comments Fri, 24 Jan 2014 17:44:09 +0000 Oculus VR http://www.oculusvr.com/?p=5094 January has been an incredible month for virtual reality. Between the debut of the Crystal Cove prototype, numerous awards at CES, Valve’s VR demo, the inspiring Steam Dev Days presentations, and an amazing reception at the Sundance Film Festival, it’s becoming clear to the world that virtual reality is on the horizon, and it’s going to change everything.

The Crystal Cove Prototype

Starting with CES, we revealed a new Oculus Rift feature prototype, codenamed “Crystal Cove”. Crystal Cove is the most immersive and comfortable hardware that we’ve shown to date, and demonstrates two key features that we’ll be including in the consumer Rift: positional tracking and low persistence.

The result is a powerful sense of presence — the magic of being completely convinced that you’re actually someplace else.

Positional Tracking

We’ve said before that precise, low-latency positional tracking is a requirement for great VR since the virtual world can be accurately synced to the player’s real world movements. Crystal Cove introduces a new 6-degrees-of-freedom positional tracking system, resulting in a much more comfortable and immersive experience.

It also opens up completely new opportunities for gameplay that would be impossible without position data (eg. peeking around corners or out windows, examining an object from multiple angles, and dodging bullets a la ‘The Matrix’).

Crystal Cove’s positional tracking system is optically-based, with an external camera tracking LEDs on the the headset. By referencing the LEDs on the headset against a virtual model of the headset, it can determine the Rift’s location in physical space. The system was designed by the Oculus team, with a custom vision pipeline that we’ll continue to optimize and build on.

Low Persistence

Crystal Cove also incorporates “low persistence” display technology, which we see as another major breakthrough for VR.

Low persistence delivers the most comfortable and natural experience yet by eliminating motion blur and judder, which also increases the visual stability of the scene. It doesn’t sound very flashy on paper, but it makes a huge impact on immersion that can only be appreciated once you see it firsthand.

By driving a modified OLED display at a high refresh rate and only illuminating the pixels on the screen for a tiny fraction of each frame length, low-persistence eliminates the outdated display data that your eyes would normally see between frames.

If you’re interested to learn more about the technical and physiological details that make low persistence so key, Michael Abrash at Valve has a great blog post explaining the technique in more detail: http://blogs.valvesoftware.com/abrash/down-the-vr-rabbit-hole-fixing-judder/

We’d like to throw a special thank-you to Valve for their collaboration and support in developing the tech behind Crystal Cove.

UE4 Strategy VR and EVE: Valkyrie

We showcased two demos on Crystal Cove: Unreal Engine 4 Strategy VR and EVE: Valkyrie, both optimized for positional tracking and low persistence.

UE4 Strategy VR is a tower-defense game, where players take on the Lava Lord in a match-up that pits waves of dwarves against their arrow, cannon, and flame towers. The demo is perfect for showcasing positional tracking, where players can actually lean over and into the board to get a better look at the scene, or peek around a wall to look at oncoming attackers.

A huge thank you to the amazing team at Epic Games, particularly Nick Whiting, Alan Willard, and Nick Donaldson, who designed, built, and optimized the demo from top to bottom for CES!


The EVE: Valkyrie demo was built on an early build of the game that was originally shown at Gamescom. Valkyrie continues to be one of the hands-down, best Rift experiences, and we’d like to thank the entire team at CCP for making such a great game. We’re looking forward to Valkyrie’s bright future!

Highlights from CES

It’s truly hard to capture the excitement and momentum around Oculus at CES, but Crystal Cove was a huge hit at the show, taking home more than 10 awards, including Best in Show from Engadget (the official awards for CES), the Verge, and Wired.

Winning Best in Show marks a huge victory for VR, especially being selected from thousands of incredible products at the biggest consumer electronics show in the world.

Photo courtesy of Engadget.

A few of the press highlights from the week:

“I Wore the New Oculus Rift and I Never Want to Look at Real Life Again” – Gizmodo

“Mere Words Can’t Do Justice To How Awesome The New Oculus Rift Gaming Headset Is — And I Don’t Even Like Video Games” – Business Insider

Steam Dev Days

After CES, we headed to Steam Dev Days in Seattle, where thousands of the industry’s best game developers gathered to discuss the future of Steam and VR.

Palmer gave a talk, providing his top suggestions for aspiring VR game developers in 25-short minutes. All of the talks were recorded, and Valve has said they’ll share them in the next few weeks, so stay tuned for the video in a future update.

Michael Abrash also gave a powerful talk on the future of virtual reality that you can read here:

http://media.steampowered.com/apps/abrashblog/Abrash%20Dev%20Days%202014.pdf

The inspiring start to his talk:

“Compelling consumer-priced VR hardware is coming, probably within two years.

It’s for real this time – we’ve built prototypes, and it’s pretty incredible.

Our technology should work for consumer products.

VR will be best and will evolve most rapidly on the PC.

Steam will support it well.

And we think it’s possible that it could transform the entire entertainment industry.”

- Michael Abrash

We couldn’t agree more.

Valve also shared their VR tech demo with developers at the show. We’ve tried it, and it really is one of the best VR experiences in the world. As Palmer mentioned during his talk, their demo sets the bar for virtual reality “presence”, and we intend to deliver that quality of experience to the world with the consumer Rift.

Building the Future

If you’re interested in being part of that future, building and shipping the world’s best consumer VR platform, we’re always looking for the brightest engineers in:

Computer Vision

Software Engineering

Mechanical Engineering

Web Services

…and just about everything else too.

There’s a lot more exciting advancements ahead for VR in 2014. Thanks again for your support — We’re just getting started, and none of this would be possible without you.

We’ll see you in the Rift!

– The Oculus Team

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Fostering the Oculus Ecosystem http://www.oculusvr.com/blog/fostering-the-ecosystem/ http://www.oculusvr.com/blog/fostering-the-ecosystem/#comments Fri, 20 Dec 2013 16:44:05 +0000 Oculus VR http://www.oculusvr.com/?p=4897 Over the last year, we've seen the Oculus community share some of the most innovative and compelling VR experiences in the history of the medium. It’s been inspiring to see so many of these projects and teams go on to raise investment from the community and venture capital groups to build something special. And this is only just the beginning.

One of the key components for truly awe-inspiring virtual reality is great content. At Oculus, we’re constantly looking at new ways to support Oculus developers, foster the ecosystem, and truly fuel the future of virtual reality. One of our long-time, favorite ideas has been to actually fund and publish Oculus games, applications, and experiences ourselves by providing additional support and resources for key developers building the games and content that we believe will define the platform.

We’ve been working quietly, behind the scenes with a select group of amazing developers on this new publishing initiative. Now, we’d like to introduce you to a new team member who'll be leading this effort full-time!

Welcome David De Martini!

We're thrilled to introduce David De Martini, our new Head of Worldwide Publishing!

David brings an incredible amount of game development and publishing expertise to Oculus. David was formerly at EA, where he worked on a huge number of games and franchises, including NASCAR, March Madness, Tiger Woods PGA Tour (2002-2006), and The Godfather. Eventually, he moved to EA Partners, EA's co-publishing arm dedicated to publishing games developed by external developers, where he worked with top development studios around the world to create hit games like Rock Band, the Crysis series, and Titanfall.

David will be leading Oculus’s publishing initiative, providing Oculus developers additional resources to help them achieve their vision. This means new opportunities for key developers for direct support from Oculus, and ultimately, more great content on the Oculus platform.

Please join us in welcoming David to the team! We couldn’t be more excited to have him.

We'll have more news on the publishing initiative and some of the key developers that we're working early next year. Stay tuned!

New Blog Post: “Help! My Cockpit is Drifting Away!”

Steve LaValle has written a new blog post on magnetometers, sensor data, and the science behind drift correction in the Rift. If you've ever wondered why your virtual reality cockpit will sometimes begin drifting away, and what we're working on at Oculus to address it, this post has your answers.

“It turns out that the Rift Development Kit similarly suffers from yaw drift error, which is a steadily growing error in the estimated “forward” direction. Fortunately, the sensor board inside the Rift contains a magnetometer. Determining which way your Rift is facing ought to be as simple as reading the magnetometer values to obtain a virtual compass arrow, right? Like most research pursuits, however, the quest to solve a problem leads to several waves of confusion and further enlightenment. In this post, I will explain how we correct yaw drift error in the Rift. The key for me, at least, was to shatter my belief in the perfect compass, and understand what a magnetometer, the real sensor, is actually trying to measure.”

You can read the full post over on the Oculus Blog or via this direct link.

Quick Shipping Update

We're finally shipping development kits within 3-5 days of the order being placed! It certainly took us longer than expected to reach this point, and we appreciate everyone's patience as we worked to get here.

If you're interested in purchasing additional Oculus Rift development kits or the Oculus Latency Tester, you can learn more at oculusvr.com/order.

VR Jam Shirts Shipping

The VR Jam shirts are now shipping out to teams who submitted a build for each of the jam's milestones. If you were on one of these teams, you should receive your shirts within the next few weeks, depending on region.

Thanks again to all the teams for making VR Jam 2013 such a success!

Happy Holidays from Oculus!

It's been an incredible year, and we owe an enormous thank you to you, the community. We wouldn't be here without you.

We wish you all the best this holiday season, and we'll see you in 2014!

– The Oculus Team

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Help! My Cockpit Is Drifting Away http://www.oculusvr.com/blog/magnetometer/ http://www.oculusvr.com/blog/magnetometer/#comments Fri, 20 Dec 2013 14:50:38 +0000 Steve LaValle http://www.oculusvr.com/?p=4561 When I was a kid, my dad gave me this nice compass:

compass

I was amazed that the arrow in this magical device always seemed to point North. I carried this belief about compasses into my adult life. They are well known to help people overcome dead reckoning problems, which prevent them from traveling along a straight course. Robots face similar problems: In my previous research, I imagined that we can simply give a mobile robot a sensor called a “compass”, which allows it to know which direction it is facing.

It turns out that the Rift Development Kit similarly suffers from yaw drift error, which is a steadily growing error in the estimated “forward” direction. Fortunately, the sensor board inside the Rift contains a magnetometer. Determining which way your Rift is facing ought to be as simple as reading the magnetometer values to obtain a virtual compass arrow, right? Like most research pursuits, however, the quest to solve a problem leads to several waves of confusion and further enlightenment. In this post, I will explain how we correct yaw drift error in the Rift. The key for me, at least, was to shatter my belief in the perfect compass, and understand what a magnetometer, the real sensor, is actually trying to measure.

The Yaw Drift Problem

In an earlier blog post, I explained the basic head tracking problem and our solution. When we integrate gyroscope readings of angular velocity, the resulting, estimated head orientation gradually drifts away from the true orientation. An accelerometer is used to compensate for tilt drift error, which leaves one important component: yaw drift error. This is incorrect rotation about a vertical axis (aligned with gravity).

In some games, such a first-person shooter, yaw drift error may be inconsequential because you can re-orient your avatar without reference to a fixed direction; however, in others it becomes quite an annoyance. For example, if you are in a cockpit game, you may start off facing forward (Hawken is shown here):

CockpitNormal

but over time, the cockpit will drift the side, even though you are still facing forward in the physical world:

CockpitDrift

You could rotate your chair to compensate, but we should be solving this problem, rather than you!

Magnetic Field Sensing

The interaction of magnetic materials and electric currents is conveniently described by a 3D vector field. At every point in the space around you, a 3D magnetic field vector exists that has both magnitude and direction. You can visualize the vector at each point as an arrow of some length that points in some direction (including upward or downward). In a constant vector field the field vector does not depend on the particular time or position; all arrows have the same length and point in the same direction:

ConstantField

Although not true in practice, it is a convenient approximation within a small area.

Now consider measuring this field vector. We are fortunate that magnetic field sensing has come a long way over the past century. Magnetometers have followed the same rapid trend we have observed across many technologies: They have become smaller and cheaper at an exponential rate. Further helping this trend is the proliferation of MEMS-based magnetometers in recent smartphones to provide help with directions. Even as a hobbyist, you can now buy a tiny, three-axis magnetometer online for around $1 US.

Now imagine placing a tiny sensor into the world to measure the magnetic field vector (m_x, m_y, m_z). The sensor cannot simply output the three components m_x, m_y, and m_z because it measures the field relative to its own orientation. A three-axis magnetometer measures the magnetic field vector projected along each of its three perpendicular axes. Each axis reads a single intensity value that corresponds to the projection along the axis. The figure shows a 2D version of this, in which there are two perpendicular axes:

RotMag

If the sensor is rotated counterclockwise by \theta, then the measured field vector is rotated by -\theta. For the 3D case, this means that if the sensor is rotated, then the sensor reading of the field vector should appear rotated by the inverse rotation. This implies that a magnetometer reading from inside of the Rift allows us infer something about its orientation based on the sensed magnetic field vector.

The Earth’s Strange Magnetic Field

What magnetic field should we use to align the Rift? It is popular fiction that the Earth produces a magnetic field vector that points North, perfectly horizontally, from every point on the Earth. If you believe this, then you are in for three surprises. The first is that the field vector points upward or downward a significant amount, depending on the location. Here is a map of the so-called inclination angles:

EarthMagInclination

Here at Oculus Headquarters in Irvine, the field vector points 60 degrees into the Earth! Off the coast of Antarctica, the vector may point straight up. If the vector is close to parallel with gravity, then the magnetic field becomes useless as an additional source of information because the accelerometer already estimates alignment with respect to this direction (up or down).

The second surprise is that the vectors do not actually point North, resulting in a declination angle:

EarthMagDeclination

It is rumored that downtown Portland, Oregon has misaligned streets due to 19th century debates on magnetic versus true North. However, most people live in a place where the declination angle is within 10 degrees, which can go unnoticed. If you need accuracy to within a degree, for example to point a satellite dish using a compass, then it becomes important.

The final surprise is that the intensity varies substantially around the world:

EarthMagIntensity

In Paraguay, the field intensity is only around 0.22 Gauss, whereas in Central Asia it is over 0.6 Gauss— expect strong readings in Siberia! If we want to use a magnetometer directly as a high-precision compass, which calculates the exact direction of North, then we need to take these field variations into account.

This presents no trouble for us, however. We can consistently align the Rift without knowing which way is North. All we need is a vector field that is constant in our small work area while also having a substantial horizontal component (at least 0.1 Gauss, for example, when projected into the horizontal plane).

All the Other Magnetic Fields

If you can place your magnetometer in an isolated spot on the Earth, then the Earth’s magnetic field will dominate the sensor reading. If you are using it in the vicinity of other magnetic materials or electric circuits, then it will happily observe magnetic fields caused by these as well. Unfortunately, they are superimposed onto the Earth’s field, resulting in a jumble that is difficult to disentangle. This situation occurs for almost everyone using the Rift.

First consider materials inside the Rift, including the screen and other components on the sensor circuit board. In any coordinate frame attached to the Rift, the materials move together with the sensor. Although numerous materials may generate or interfere with magnetic fields, they are commonly grouped into two classes based on their magnetic properties: hard iron and soft iron [5]. These need not contain iron; for example, nickel and cobalt are ferromagnetic materials. Hard iron simply generates a magnetic field around it. This will combine additively with the Earth’s field, but note that it is vector addition. If placed correctly, it is even possible to completely cancel the Earth’s field and obtain zero. Soft iron cannot generate its own field, but it distorts any field around it in an orientation-dependent way.

The net effect of all hard iron in the Rift is to generate a constant magnetic field vector at the sensor. This means that a fixed offset is produced for each of the three magnetometer sensor axes. If you hold the magnetometer fixed in space and bring it through all possible orientations, we expect the observed values to lie on a sphere (ignoring noise). The sensor observes the same field vector, but from different relative directions. The distortion caused by soft iron generally warps the sphere into an ellipsoid [1, 4, 10].

Calibration: One Step Closer to a Compass

The first step toward making the magnetometer useful for yaw drift correction is to transform its output to compensate for the hard and soft-iron biases. We consider two cases: A crude method and a careful method. For the crude method, ignore soft-iron bias and focus only on determining the offset due to hard-iron bias. In this case, the magnetometer values should lie on a sphere. How many sensor readings are needed to find the sphere? Dropping down to 2D helps. A basic fact from planar geometry is that any three non-collinear points determines a unique circle [3]. This result extends to 3D (and higher!) to obtain that any four linearly independent points uniquely determines a sphere. Through several 4×4 matrix determinant calculations, the sphere center can be quickly found [8]. Once the center is found, its three coordinates are subtracted from the magnetometer output values.

Because only four magnetometer readings are needed, the center can be estimated automatically, without the user even being aware. Due to noise, the points need to be well-separated: Far from each other and far from being linearly dependent.

The crude method has the advantage of requiring minimal effort and disruption to the user; however, after much experimentation, it seems preferable to request the user to perform a more intensive, once-in-a-while task that gathers hundreds of magnetometer readings. In this case, we request the user to spin the Rift around through as many orientations as possible. An ellipsoid is fit to the data using least-squares minimization of the algebraic distance. (Some technical issues arise due to implicit surface fitting; these are covered in [7,9].)

The figure shows the effect of careful calibration:

magellipse

This plot is a 2D slice of the 3D data. Once the ellipsoid parameters are obtained, they are applied to offset, scale, and rotate the raw magnetometer readings. This causes all transformed readings to lie roughly on a sphere centered at the origin. The process helps to fix the direction of the sensed magnetic field vector; however, it does not recover the true intensity (length of the vector). This is not important for yaw drift correct and we transform the readings so that they approximately have unit intensity. Only the direction is critical.

Detecting Drift with Reference Points

BoatStar

Once we have a calibrated magnetometer, it is ready for use by our drift correction method. The next step is to save a reference point. For intuition, imagine you are sailing the seas on a ship and decide to measure the yaw (azimuth) angle between the direction that the ship is facing and your favorite star. If at any time you want to make sure that the ship is pointing in the same direction, then you can check the angle again. If the angle is wrong, you should turn the ship to correct it. I think of a reference point as a “virtual star”.

To store a reference point, we simply record the magnetometer reading together with the estimate of the Rift orientation at which it was taken.

Assume a right-handed coordinate system with “up” being the y axis. The following steps are used to detect yaw drift error:

  1. Take the reference point and transform the magnetometer into the fixed, world frame using the quaternion (Rift orientation) at which it was stored. This yields m_w = (m_x,m_y,m_z).
  2. Take the current magnetometer reading transform it into the world frame using the current Rift orientation. Let the result be denoted by n_w = (n_x,n_y,n_z).
  3. The two readings m_w and n_w are projected into the horizontal plane by setting their y components to 0.
  4. Convert the projected readings into angles as \theta = {\rm atan2}(m_z,m_x) and \theta' = {\rm atan2}(n_z,n_x). Here, {\rm atan2} denotes the 360-degree arctangent function, a standard C++ library function.

    MagAtan

  5. The yaw drift error is e = \theta - \theta'. Be careful to correctly handle the 2 \pi angle wraparound, to ensure that e always lies between -\pi and \pi.

What happens when a larger error is detected? There are many possibilities; however, one of the worst would be to immediately yaw the camera in the virtual world by -e because the user would notice and perhaps be unhappy. A better idea is to gradually apply the corrective rotations. We would like the corrections to be so slow that the user does not notice, while being fast enough so that they are sufficient to overcome the maximum drift rate during ordinary use. We determined the appropriate rate after careful analysis of experiments involving both humans using the Rift and a robot arm that systematically moves the sensor around. We apply the corrections using a complementary filter. In the simplest case, the filter would apply a tiny correction that is proportional to e in each iteration of our sensor fusion code, which operates at 1000Hz. In the current software, we apply a second-order complementary filter, which combines tilt correction, yaw correction, and gyro bias error estimation into a single, simple framework. We chose complementary filters for their simplicity. One could alternatively use Kalman filters, but they are equivalent at a basic level [2], and the Kalman filter model of a known system with Gaussian noise does not closely match the behavior of humans moving their heads around. The complementary filter provides a small number of simple constants that can be tuned based on perceptual experiments (can the human notice it being applied?) and mathematical proofs of convergence [6].

An important limitation remains. If the magnetometer calibration is not perfect, then yaw error could be incorrectly measured. The ellipsoid center or curvature (eccentricity) are subject to error. This problem becomes worse as the distance between the current orientation and the reference point orientation increases. To handle this problem, we impose a maximum angular limit on the angle between the orientation at which the reference point was saved and the orientation at which it is used. A typical value is 10 degrees. To enable drift correction when facing other directions, we simply generate more reference points. Think star charts! A table of reference points is constructed by adding a new one every time the orientation is far from all of the previous ones in the table. Only the nearest reference point is used for correction at a particular iteration. For improved robustness, we sometimes detect and remove bad reference points. This could happen, for example, if you set the Rift down on a desk (especially one containing hard iron!) for an hour and put it back on again without stopping your program. Our current SDK allows up to 1000 reference points, but the typical amount used in practice is 200 because it is difficult to cover all 3D rotations by turning your head. By using multiple reference points, we can even get reasonably good performance by using the crude four-point method to estimate a sphere center, instead of performing a careful ellipsoidal fit. This way, the magnetometer could be calibrated and used without the user knowing. In our latest software, we require that the magnetometer is carefully calibrated in advance using the profile tool.

Performance

We performed several experiments in which a user sits and plays a VR game for over twenty minutes. To provide “ground truth” against which to compare our yaw correction methods, we measured their head orientations using an OptiTrack motion capture system. The average amount of yaw error was around 3.7 degrees, while the worst-case performance was within 10 degrees. Several performance plots are shown below.

yaw1

yaw3

yaw2

Although we are satisfied with performance, a reasonable future goal is to keep the error to within one degree. Some unavoidable problems also remain. If the magnetic field, when measured indoors, is nearly aligned with gravity or has nearly zero magnitude, then the magnetometer cannot provide useful readings for yaw correction. (Although this happens outdoors only in exotic locations on Earth, it could occur indoors due to iron reinforcements.) Trouble is also caused by fields that vary highly by position or over time.

Conclusions

Through calibration and the use of reference points, we were able to get a magnetometer to perform almost as well as using a compass in the woods. When performing yaw drift correction, the particular magnetic field intensity and the direction of absolute North are not important. What remains important is to provide a reference direction that is fixed in the physical world. Our methods use the direction of a nearby reference point to gradually correct the yaw drift error. The result is consistent maintenance of “forward”, rather than having a cockpit drift to the side. We have obtained an effective solution by carefully sidestepping the fundamental limitations of passive magnetic field sensing.

Acknowledgments

Thanks to Lee Cooper, Max Katsev, Brant Lewis, and Anna Yershova for their contributions to the ideas, implementations, and experiments described in this post.

References

[1] Gebre-Egziabher, D., Elkaim, G., Powell, J., and Parkinson, B., Calibration of Strapdown Magnetometers in Magnetic Field Domain. ASCE Journal of Aerospace Engineering, Vol. 19, No. 2, Pages 1–16, April 2006.

[2] Higgins, W. T., A Comparison of Complementary and Kalman Filtering. IEEE Transactions on Aerospace and Electronic Systems, Vol. 11, No. 3, Pages 321-325, May 1975.

[3] Khan, Sal, Three Points Defining a Circle. Khan Academy online video. Oct 13, 2011.

[4] Konvalin, C., Compensating for Tilt, Hard-Iron and Soft-Iron Effects. Sensors. December 1, 2009.

[5] Macintyre, S. A., Magnetic Field Measurement, Chapter 48, The Measurement, Instrumentation, and Sensors Handbook, J. G. Webster, Editor, CRC Press, 1999.

[6] Mahoney, R., Hamel, T., and Pflimlin, J.-L., Nonlinear Complementary Filters on the Special Orthogonal Group. In Proceedings IEEE Conference on Decision and Control, 2008.

[7] Markovsky, I., Kukush, A., and Van Huffel, S., Consistent Least Squares Fitting of Ellipsoids. Numerische Mathematik, Vol. 98, No. 1, Pages 177-195, 2004.

[8] Schmitt, S. R., Center and Radius of a Sphere from Four Points. Chegg-Study, Free Textbook Solutions, 2013.

[9] Taubin, G., Cukierman, F., Sullivan, S., Ponce, J., and Kriegman, D. J., Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 16, No. 3, March 1994.

[10] Vasconcelos, J. F., Elkaim, G., Silvestre, C., Oliveira, P., Cardeira, B., A Geometric Approach to Strapdown Magnetometer Calibration in Sensor Frame. IEEE Transactions on Aerospace and Electronic Systems, Vol. 47, No. 2, Pages 1293-1306, April 2011.

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