Intelligent Systems

Nov 26 01:55

Justin: A Humanoid Sporting Two DLR III Lightweight Arms

I saw a presentation by Professor Siciliano from University of Naples a few weeks ago. During the presentation, he briefly mentioned (and had a video) of a very cool new humanoid named Justin.


Justin Humanoid Robot from DLR

Justin sports not one, but two of the DLR-III Light-Weight arms (now being manufactured by Kuka).


DLR-III Light-Weight Arm


These arms are impressive! They're the first robotic arms (to my knowledge) to have a 1-to-1 power-to-weight ratio (meaning they can lift their own mass). These are very "sexy" arms, and even more impressive in person (Georgia Tech has one in orange that I spent some time examining -- way cool).

Anyway, I was unable to find copies of the videos Professor Siciliano showed during his presentation. The best I could find was a video on Wired's site from ICRA-2007. They apparently do not allow downloads, so the following was the best I could muster: Justin-ICRA07

 

 



Oct 30 22:40

GA Tech DARPA Urban Grand Challenge -- No Luck in 2007

I'd like to make a quick note about the Georgia Tech DARPA Urban Grand Challenge team, Sting Racing.  Unfortunately, they did not qualify for the finals, do the dismay of all of us who do not get to watch the competition live.

You can learn more about the failure of the robot on the team's blog, but essentially,

In our Saturday afternoon test in Area A Sting 1 crashed head-on into a concrete barrier. The front sensor mount was bent severely and pushed into the front of the vehicle. Fortunately the protection offered by the design and strength of the sensor mount saved the sensors.

After assessing the log data we determined the cause of the accident was a failure in the communication link between our GPS/IMU and the main control computer. Without “pose” information the robot could not know that it was moving.

If you're in to robot carnage, you can watch the video below.

 


 

OK, time to get back to work. 

Aug 09 22:55

New Robot from Boston Dynamics: Little Dog (Big Dog's Little Brother)

Does everyone remember Boston Dynamics' Big Dog walking robot?


Well, as a quick refresh: 

BigDog is powered by a gasoline engine that drives a hydraulic actuation system. BigDog's legs are articulated like an animal’s, and have compliant elements that absorb shock and recycle energy from one step to the next. BigDog is the size of a large dog or small mule, measuring 1 meter long, 0.7 meters tall and 75 kg weight.

BigDog has an on-board computer that controls locomotion, servos the legs and handles a wide variety of sensors. BigDog’s control system manages the dynamics of its behavior to keep it balanced, steer, navigate, and regulate energetics as conditions vary. Sensors for locomotion include joint position, joint force, ground contact, ground load, a laser gyroscope, and a stereo vision system. Other sensors focus on the internal state of BigDog, monitoring the hydraulic pressure, oil temperature, engine temperature, rpm, battery charge and others.

So far, BigDog has trotted at 3.3 mph, climbed a 35 degree slope and carried a 120 lb load.

Big Dog could take a solid kick and still remain upright! It is probably one of the most impressive walking/running robots to date.  (See YouTube video below, or a different version from Boston Dynamics -- local copy)

 


 

Well, Popular Mechanics showed pictures of Little Dog (Big Dog's baby brother) from DARPA Tech 2007.

  

I had never heard of Little Dog, and was about to be all impressed until I read that...

Little Dog will never be as famous as its sibling, Big Dog. Why? It can't recover from a kick, and whereas Big Dog hops along at a jaunty sprint, the toy-size Little Dog takes careful, measured steps. That's because it's practically blind. It has no onboard sensors, and relies on cameras set up around the lab to guide it. Data from these infrared and visible cameras is turned into a motion-capture file, which is beamed wirelessly to the robot. Reflective markers lining the track and dotting the robot help the cameras correlate its position in relation to its environment (similar to the motion-capture suits actors wear during videogame development or visual effects scenes).

It's hard to come up with an accurate comparison, but Little Dog is essentially blindfolded, but following external advice. Currently, it's allowed a gradual, "stop-and-start" approach to navigating uneven terrain, but by the time the Learning Locomotion program ends in January 2009, Little Dog will be practically scrambling. The research will likely be used to improve Big Dog specifically, and walking robots in general, since data related to Little Dog and its environment can be scaled up to larger obstacles and roughly human-size limbs. So as quaint as it looked poking its way down an eight-foot stretch, what we learn from Little Dog could help every robot with legs a little more sure-footed.

Oh well, still pretty cool.  I'm betting it could still move faster than an Aibo...

 

Aug 09 22:15

Georgia Tech DARPA Grand Challenge Team Qualifies for Finals


This is Sting 1, Georgia Tech's entry into the DARPA Grand Challenge.  The goal is to create an autonomous robotic vehicle that can brave America's insane city streets.  Anyway, I just found out today that Tech has officially made it in to the final round of competition.  Congratulations guys!  

I really wish I could say that I am a part of the team, but I just don't have the time right now to work on another project...

It is a very impressive piece of machinery!  In case you can't tell, that is a Porsche Cayenne modified for autonomous (or remote-conrol) operation.  The car uses myriad sensors (including laser range finders, radar, GPS, and IMUs).  It is all controlled by 16 (yes, sixteen) processors -- in the form of 8 dual-Pentiums -- running Ubuntu Linux.  Now that is impressive! 

From the team's official website

Sting Racing selected a Porsche Cayenne, designated Sting 1, as the base vehicle for its entry in the Urban Design Challenge. The high-end SUV comes from the factory with a significant degree of automation and computer control already built in. Most of the primary and secondary controls can be accessed through the factory-installed, integrated CAN network. In addition, its standard air-conditioning package is adequate to cool the computers that areinstalled on board to operate the vehicle.

Sting 1 has been retrofitted for complete computer control of steering, throttle and brakes as well as secondary systems such as lights and windshield wipers. The retrofit was performed by EMC.

The vehicle is controlled by eight dual Pentium computers installed in the trunk space and thye are all running Ubuntu Linux.

For navigation, tracking other vehicles and situation assessment, the car is equipped with Novatel GPS sensors, an inertial package (IMU), six cameras, six laser scanners (Riegl & SICK LMS) and three 22 GHz radar units (EATON).

Sting 1 conforms to Challenge vehicle requirements:

  • SUV-size vehicle, preferably stock (Porsche Cayennem, 2006 model)
  • Meets California emission standards
  • Weighs between 2,000 and 30,000 pounds
  • Fully autonomous operation
  • Equipped with warning light, audible alarm, blinkers and brake lights

Sting 1 meets Challenge performance requirements:

  • Maximum speed of 30 mph
  • Capable of emergency stops within 20 m
  • Maintains a 1-5 m distance from other vehicles
  • Stops within 1 meter of stop signs and street crossing lines

In addition, during testing and in preparation for the the race the vehicle chase car equipped with a manually operated pause and stop system that can be engaged in case of emergency.

I personally know a number of people working on this project, and I think they have a real shot at winning.  I think that would be great for Georgia Tech and our new robotics PhD, of which I'm (almost) officially a part.  Go Tech!

Jul 05 15:29

RoboCup 2007 (4th of July)


Well, among other things I spent my Independence Day volunteering at RoboCup 2007. After I finished volunteering, the girlfriend and I wandered around and took a bunch of pictures and videos from the event. We'd like to share them with you. This is a sort of continuation from my previous RoboCup 2007 post. As a side note, I am very proud that the previous post made Engadget! They've had a subsequent post that features a link to the RoboCup 2007 Flickr pool. Here you can find a ton of additional pictures from others (including Dr. Balch, a robotics professor at GA Tech).

First, I'd like to recant my statement about the humanoids soccer competition. While they may be a little slower and more cumbersome, they are a blast to watch during actual competition. Just check out the videos (goal, action, and practicing).


We had the opportunity to watch the 4-legged (Aibo) soccer league. These were a blast to watch, but we were somewhat disappointed with the mechanics... Everyone used purchased 4-legged Aibos rather than custom-designed robots. Does anyone know if this is a requirement, or just done for simplicity? Oh well, they are fun to watch. Check out the pictures and videos.

Overview of the 4-Legged League arena.


Aibo goalie reacting to a shot.


A line of Aibo robots sitting in the prep area. In total, this is probably the largest gathering of the discontinued Aibos I've ever seen! There must be almost 100 of them hanging around. It is quite a site to behold.


Aibo takes a shot and scores a goal. [video]


Aibo takes a shot. It's blocked by the goalie. The follow-up shot hits the goal-post and misses to the right. Close! [video]


Aibo takes a shot that is blocked by the goalie. The attacking Aibo's follow-up pays off with a goal! [video]


Aibo scores a goal against its human controller during practice. [video]


We had the chance to catch some more of the Middle-Size League robots. I still say these are the most entertaining and technically challenging, but that is just my bias. Below is a picture of a team working on their robots in the pits.


In the match we watched, one team was having major technical difficulties. Effectively, only a single one of their robots was functioning properly. However, that didn't stop them -- the 1-robot team managed to score a goal against their opponents! I'd rename that bot "Ronaldo!" [video]


Ultimately even Ronaldo suffered from technical glitches, and the opposition capitalized by scoring several "easy" goals. [video]


I finally got a close-up of some of the Small-Size League robots (that use the overhead camera). It turns out I was incorrect on my previous post -- most of them do use holonomic wheels. I'm amazed at how quickly they move with those wheels. There weren't any games playing while I was there, but I snagged a few pictures. Note the color codes on the top for recognition.


 


There is also a "Search and Rescue" event (basically, teleoperated all-terrain robots) at RoboCup, though I'm not sure I understand how it is related to soccer. If they're indiscriminately going to add events, I'd like to see robot-sumo and tetsujin (robot exo-skeletons) added. Both are present at RoboGames. Anyway, here are a few Search and Rescue robots, including the team from GA Tech.



 

Well, I suppose that about sums up my newest pictures and videos. I have also saved the full-res videos on my server for posterity. Again, I'd prefer you be gentle on my bandwidth by viewing the YouTube ones.

 

Jul 03 12:42

RoboCup 2007

UPDATE: I've got a bunch of new pictures and videos from RoboCup 2007 posted. 

I was really bummed this summer when I missed the RoboGames. However, I consciously made the decision not to go since the RoboCup 2007 is in Atlanta this year, and is being held at my graduate school -- Georgia Tech! Because of this, I will be volunteering for several of the days, and I get up-close contact with the robot-builders, spectators, and event organizers.


Anyone with a Georgia Tech ID can get a spectator seat for free. If you're not so privileged, tickets can be had for like $10 (weekdays) or $20 (weekends). There are a TON of events this year (Small, Mid, and Junior soccer, Humanoid Soccer, 4-Legged Soccer, Nanogram, etc). It is being held across about 4 different venues (Campus Rec Center, Tech Square Research Building, Student Center, and Fox Theater), so there is plenty to watch. It is difficult to describe how large this event is, and how wonderful the caliber of robot-builders is (especially compared to other events I've attended, even compared to RoboGames). Just look at these shots of the "main" venue (Campus Rec Center).

From the front of the spectator area:


From the back of the spectator area:



There is literally always something cool going on, and the robot-builders are very friendly (from many different countries). For traditional roboticists, this is like heaven. I still miss some aspects of the RoboGames (like mini-Sumo); however, I don't really miss the BattleBots. The glorified RC cars usually don't appeal to traditional roboticists, but I'm sure that many enthusiasts would be disappointed by their absence.

Official competition just began today (Tuesday, July 3rd), but the event continues up through July 10th. I haven't seen any coverage on other blogs about RoboCup 2007, so I figured I'd share a selection of my pictures and videos (from team practice day -- yesterday on July 2nd).

This is a Junior Soccer League robot from Team Takahama. I had a chance to speak with this team at length, and I found their robot rather interesting. It uses 3 holonomic wheels for propulsion (like most of the robot soccer bots), it has a few wheels near the front that spin the ball to "hold" on to it. Then, it can shoot the ball using a little flipper on the front. I have a few videos of it in action here and here.



I personally favor the Junior Soccer League robots. A team for the Junior Soccer League only consists of two, small robots instead of the 4+ of other events. Also, the ball contains a number of infrared emitters, which makes detection simple as well. These factors make the Junior League much less costly, and thus more accessible to hobbyists. Many of the other events require large capital investments or sponsorship (to purchase 4-5 Aibos, or 4-5 laptops, etc).

Below is another Junior Soccer League robot, which uses compressed air to shoot the ball. Again, it employs holonomic wheels.


Below is an image of the Small Size League arena. You can see the cameras suspended above the arena. These are hooked to computers that perform visual recognition, tracking, and control of the robots to play soccer. This league focuses on multi-agent robotic cooperation and strategy.



I'm actually not a huge fan of the Small-Size league, mostly due to the external infrastructure and centralized control. Usually these robots do not use holonomic wheels, but rather use differential drive for speed and agility.


This is an image of a single robot from a Middle-Size League team. Notice the omnidirectional camera on the top. This is used in visual recognition algorithms to detect and track the ball. You can also see (under the number) a small laptop that controls this robot. Since each team is comprised of 4-5 robots, this can be quite expensive. Again, this robot uses holonomic wheels. The robots in this league are entirely autonomous, although the robots on each team are allowed to communicate wirelessly. They are pretty awesome. Check out the other pictures from this league below.





I also have a number of videos from the Middle-Size League robots practicing. Check them out here, here, and here.



Many people are enamored with the humanoid soccer. The humanoids' complexity is impressive, but their movements are still rather slow and cumbersome. Check out some of these videos for proof: vision tracking and goal.


 

There are still a number of events I have not explored. One event is the 4-legged soccer, which usually features teams of Sony Aibos playing soccer. Another event that I'm really looking forward to (since it is related to my research interests) is the Nanogram league. From the RoboCup website (including the image below),

The RoboCup Nanogram competition challenges teams of students and researchers to construct microscopic robots that will compete against each other in soccer-related agility drills. These robots will measure a few tens of micrometers to a few hundred micrometers in their largest dimension and will have masses ranging from a few nanograms to a few hundred nanograms.


The competitions over the next week are going to be really great. Hopefully I'll find time to share more of my pictures and videos, and hopefully I'll see you there!

 

I've kept local copies of the videos for posterity; however, I'd prefer if you'd view the YouTube videos listed above. The local copies can be found here:

Jun 29 00:54

Miniature Robots Travelling In The Human Body

Roland Piquepaille had an interesting write-up on an Israeli teams' efforts to create a miniature, inductive-powered robot to explore the inside of the human body (blood vessels in particular).


At first, I thought the above image was the actual prototype, in which case I would have been very impressed. Then, I read on...

You can see above "an artist's rendition of what the tiny submarine robot would look like." (Credit: Unknown, via the Jerusalem Post)

"Artist's rendition," indeed.

The researchers stress that the project is an "interesting development, but it has a long way to go before it is used in medicine." Solomon says that the tiny robot could be controlled for an unlimited amount of time to carry out any necessary medical procedure. The power source is an external magnetic field created near the patient that does not cause any harm to humans but supplies an endless supply of power for it to function. The robot's special structure enables it to move while being controlled by the operator using the magnetic field.

Yep, makes sense to use inductive/magnetic coupling for power, create the smallest such robot (that I know of), and claim great aspirations about fighting cancer and malignant tumors, but where is the functional prototype? "A long way to go," no doubt. I think there needs to be a little more substantiation when making such extreme claims. Publications are always good, as are active project websites.

Anyway, I've have seen a fair number of actual gastrointestinal robots for endoscopies (aka, "inside the human body") that use a similar idea. Most use peristaltic (undulating) motions to prevent tearing, lacerations, and punctures. However, some designs still use "gripping" feet mechanisms. One great example is a hybrid design from Carnegie Mellon (project homepage here and press release here). Most importantly, they are already performing testing in plastic tubing and pig intestines.

This prototype shows a "six-legged" (actually, they apply pressure to the gastrointestinal tract walls) robot.
This is another prototype (apparently 3-legged?) robot in an actual capsule.
An overview of the CMU approach. Click on the image to enlarge.

Another great example comes from a New Scientist article entitled "Worm-inspired robot crawls through intestines." It features work performed by a multi-national European research team, and again, this research has produced working prototypes (with videos)!

A prototype crawling through a pig intestine. Be sure to check out the video here.

 

(Local copy of the video here)

A more recent prototype being held in a researcher's hand. Check out the video of the legs actuating here.

 

(Local copy of the video here)

I'd like to take a moment to rant about what seems to be "bad" journalism. First, I'd like to pardon Roland Piquepaille, as he represents a fair amount of skepticism in his article. However, the remainder of the blogosphere is taking this "advancement" on dogmatic faith as an absolute truth. Maybe the Israeli team's work is a huge advancement, but maybe it isn't (there just isn't enough data at this point to make a clear distinction). Either way, the blogosphere isn't helping science by disseminating (mis)information. This is just plain wrong, and I hypothesize (along with some colleagues) that this may be true of several other recent "advancements" featured on many blogs.

I make a pledge to represent anything I post as accurately as possible, and to the best of my knowledge (what little I have). Hopefully the other blogs will too.

May 24 09:29

Electroactive Polymer Application -- Biomimetric Animatronics

Electroactive polymers (EAPs) can provide low-power, life-like, compliant actuation. This makes them well-suited for applications in animatronics (life-like robots). Some of the more striking examples are shown below.

This is probably the most striking biomimetric animatronic example, from Eamex. The eye and eyelid have extremely realistic motion, and the motion is achieved without complex and bulky motor/pulley systems. Be sure to check out the video!

(Local copy of the video here)

This robotic head also shows lifelike facial expressions. It was a platform for EAP demonstrations, photographed at the NASA Jet Propulsion Lab (via David Hanson at UT Dallas). Again, be sure to check out the video.

(Local copy of the video here)

This small, stuffed toy from Eamex is actuated using EAPs. The motion is designed to be "cute" for children. The compliance (reduced torque) of the EAP actuation makes them safe around children. The movements remind me of the Teddy Bear from the movie "AI - Artificial Intelligence." Check out the video.

(Local copy of the video here)

These dinosaur toys (T-Rex, Triceratops, and Brontosaurus) are actuated using EAPs, again from Eamex. The motion is interesting, and not over-powering (so no worries about cutting off a child's finger from too much torque). The video can be found here.

(Local copy of the video here)

 

Apr 29 16:46

Troody the Robotic Dinosaur (and the story of disappearing web content)

One of my favorite robots of all time was the Troody robotic dinosaur from MIT.



From the MIT archives page:

Troody, the creation of Peter Dilworth, is a 16 DOF autonomously powered and controlled biped robot built to resemble a Troodon, a small carnivorous dinosaur that lived in the Cretaceous. In this video (below), Troody is shown standing up and walking across a desk (the cables provide power, start/stop control, and safety in case of a fall). Next Troody is shown taking a sharp left turn. Finally, Troody is shown taking a long battery-powered walk from our basement laboratory to visit Cog on the 9th floor (via the elevator). It only fell 4 times along the way.


The frustrating thing is that Peter Dilworth's page on Troody is no longer available (that link to his page returns a 404 error). I find that this happens all too often, and it appears that all the technical specifications of Troody are lost to history (I'll run a publication search later to see if I can find the details there). If anyone knows where all that valuable information can be found, please let me know. I guess this illustrates one of the reasons I started my webpage -- an archive of all the science and technology content that interests me.

Anyway, the archived video is shown below.


Of course, I don't want to lose the video if YouTube ever disappears, so here is a local copy for posterity (it's quite large).

 

Mar 18 22:13

1000-Core Processor - The Vision of AsAP

Hopefully people aren't naive enough to fall for a "number of cores" competition, much like the Intel/AMD "number of Mega/Giga Hertz" competition a while back. Intel and AMD are now planning quad-core and 8-core chips for future desktop PCs, and I'm sure this will usher in a new era of performance computing. This is all well-and-good, but why a 1000 core processor?!?

OK, clearly a 1000-core chip isn't going to be used for general purpose computing (at least not at this time). But power-performance ratios are really the future of embedded and special-purpose computing. Consider the Asynchronous Array of Simple Processors (AsAP) project, which implements 36 cores (6x6 array) of 32-bit processors (9-stage pipeline, 54 32-bit instructions, and 16-bit datapath).

AsAP processor operates at 475 MHz; and each processor dissipates 32 mW while executing applications, 84 mW while 100% active, and 144 mW worst-case at 1.8 V. Most of AsAP's area (66%) is for the core which is a high area utilization. Each processor occupies 0.66 mm2, which is more than 20 times smaller than the other traditional processors such as ARM. AsAP processor also achieves more than 5 times higher performance density and energy efficiency compared with others, as shown at below.


One really unique thing about the AsAP (at least from my perspective) is its asynchronous FIFO buffers that allow each core to talk to its surrounding ones despite the differences in clock rates/latencies (see this paper -- or locally here). In this fashion, a core is only active (consuming power) when it has data in its buffer to process. Each processor is programmed with a small code snippet (in C or assembly), which can be assigned (or auto-mapped) into the AsAP. Now for the really cool part. With 36 cores each with a small instruction set (54 possible instructions), 64 words of RAM, 128 words of ROM, you can do some really amazing things!

  • FIR Filters
  • Signal Convolution
  • Sorting
  • CORDIC sin, cos, arcsin, arccos, arctan
  • Pseudo Random Number Generators (LFSR)
  • CRC Calculations
  • Huffman Encoding
  • FFTs
  • JPEG Encoders (9 cores, 224mW @ 300 MHz) (shown below)
  • A complete 802.11a/g wireless LAN base-band transmitter (22 cores, 407mW @ 300 MHz)


All of these applications offer huge power and performance savings compared to other, traditional solutions (as explained in this presentation -- or locally here). The fully-functional, complete 802.11a/g wireless LAN base-band transmitter implemented in 22 cores at a mere 407 mW is perhaps the most impressive application to date! Check out the diagram below to see what each core is doing!


But wait, the title of this post mentions a 1000-core processor, not 36. Well, that is all just a matter of scaling. Additional cores can be (easily?) added into the array.

We have designed a 0.18 μm CMOS chip that was fabricated during the summer of 2005 (the 36-core chip). Early testing in the fall of 2005 has shown it is fully functional! We believe it is the highest clock rate fabricated processor designed in any university. A 13 mm x 13 mm chip utilizing the exact same design in 90 nm CMOS would contain more than 1000 processors and be capable of more than 1 Tera-op/sec peak performance.

Just imagine what would be possible with 1000 cores! (see the image below) One could argue, "This can be done with FPGAs." And you'd be correct (in fact, they already have the AsAP architecture loaded into FPGAs for testing). However, having the processors in silicon gives you additional benefits.

  • Performance increases (FPGAs are limited because of general-purpose nature)
  • Power decreases (FPGAs logic is always active, the AsAP only runs when it has data)
  • Easy functional decomposition and mapping
  • Programming each core (and then auto-mapping) in C or assembly instead of Verilog and VHDL

I hope they work with a chip-fab to make some of these chips available to hobbyists. These chips would be really valuable in robotics, as you could activate and deactivate the different cores depending on your power budget (not to mention the power savings inherent with the AsAP design).


As a side-note, I almost worked with Dr. Baas on these project(s) for my PhD. Ultimately, I decided chip design wasn't my thing (at least not for a PhD, but it would have been great for a MS). However, my good friend Toney is doing some work on the project. Last I knew, he was working with the test setup, shown below. It should be obvious that this group at UC Davis does some amazing work. Good job guys!

 



You can find out more about the AsAP project here.

Mar 11 19:53

Simultaneous Localization and Mapping

I'd like to pose a question: "How can you know the location of a robot when you don't have GPS?" Obviously, absolute position would be extremely difficult. Even if you had the stars to navigate (like sailors), your resolution is not so good. Further, not all environments have stars visible (indoors, subterranean, etc.).

One solution is to keep track of your relative displacement using an inertial measurement unit (IMU), such as the one pictured (a low-res MEMS IMU from Cloud Cap Technologies). These devices measure acceleration and rotation in all three axes. You can fuse the sensor data using a Kalman filter to give your displacement and heading. Of course, the measurements are noisy, and thus (even if sitting still) your perceived location will drift from your actual location over time. One possible solution to this problem is Simultaneous Localization and Mapping (or SLAM).

Dr. John Leonard of MIT does some very cool work in Simultaneous Localization and Mapping (SLAM). To quote his website:

The problem of SLAM is stated as follows: starting from an initial position, a mobile robot travels through a sequence of positions and obtains a set of sensor measurements at each position. The goal is for the mobile robot to process the sensor data to produce an estimate of its position while concurrently building a map of the environment. While the problem of SLAM is deceptively easy to state, it presents many theoretical challenges. The problem is also of great practical importance; if a robust, general-purpose solution to SLAM can be found, then many new applications of mobile robotics will become possible.

So not only do you know your location, but you're left with an internal map -- a good thing for us humans who use robots to explore remote or isolated environments. I always think the concepts are best explained by a video. Notice how the robot uses dead reckoning to estimate its position. When a loop is completed, SLAM automatically corrects the internal map by "recognizing" familiar terrain. It is a very powerful algorithm. If you'd like more details, here (or locally here) is a good article that describes the algorithm. Of course, most of the time the algorithm is applied in 2-dimensions, as computation complexity increases very rapidly in 3-dimensions.

Again, while I prefer you view the video from the Dr. Leonard's website, I've placed a copy on my site for posterity (here).

 

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