3/20/2023 0 Comments Black canary injustice 2Expertise – Increase Character EXP gained by 5.44%.The Comeback – Upon losing her first Health Bar, Black Canary will instantly gain 1 bar of Super Meter.Villanous Might – Inflict 3.97% extra damage to Heroes (Multiverse Only)Įffect: Expertise – Increase Character EXP gained by 5.03%.Affluent – Increases the amount of Credits and Guild Credits earned by 4.60%.NameĮffect: Interaction Boost – Increases Environmental Interaction Damage by 4.17%.Įffect: Down to Earth – Gain 195 EXP bonus for not jumping in a match (Single Player Mode Only).Įffect: Down to Earth – Gain 225 EXP bonus for not jumping in a match (Single Player Mode Only)Įffect: Down to Earth – Gain 267 EXP bonus when you don’t jump in a match (Single Player Mode Only)Įffect: Expertise – Increase Character EXP gained by 3.08%.Įffect: Affluent – Increases all Currency gained by 4.37%.Įffect: Affluent – Increases all Currency gained by 1.29%. Green Arrow interrupts the Society by saying, 'But first, a few words from the Brave and the Bold. advertisement Base Stats Move List Combos This section uses the common terminology for buttons where Playstation/Xbox: 1. Dubai New Year 2019 fireworks in full 06:10. Showing results for injustice 2 black canada gameplay trailer instead of injustice 2 - black canary gameplay trailer. All Categories All Channels Random Videos (0) Hot on Facebook (0) Popular Right Now (0) Free Movies (0). However, nothing compares to when the two make their grand entrance in Gorilla City in Injustice 2. Black Canary is a character in Injustice 2. 0 results for 'injustice 2 - black canary gameplay trailer' Categories. Please bear with us for the moment until it comes out. 2/10 The Brave And The Bold As mentioned, Green Arrow and Black Canary have great banter with each other. We’re doing the best we can to find the armors. Connor like Dinah also has the Canary Cry. This page is solely dedicated to Black Canary. Black Canary in this story loves her child, of course as a mother would, wouldnt want her son to get hurt. Please continue to follow this page for further updates on the armor. Gimme That! – When Black Canary wins a match against an online player, she gains 15.00% bonus Credits based on her remaining health.Įffect: Environmental Resistance – Reduces damage taken by Environmental Interactions by 6.38%. 3-year protection plan from Allstate - 3.99. The first mission is in which they were sent to stop Scarecrow from shipping a quantity of fear gas to Grodd from a hideout in Slaughter Swamp. Hiya Toys Injustice 2: Black Canary 1: 18 Scale Action Figure, Multicolor. She was then sent with Harley Quinn and Green Arrow on two successive missions. The Black Canary is the name of two superheroines appearing in American comic books published by DC Comics: Dinah Drake and her daughter Dinah Laurel Lance. Effect: Pure Focus – Increase all EXP gained by 2.36%Įffect: Wisdom – Increases Profile EXP by 1.77%.Įffect: Pure Focus – Increase all EXP gained by 3.06%.Įffect: Transition Resistance – Reduces damage taken from Arena Transitions by 0.82%.Įffect: Transition Resistance – Reduces damage taken from Arena Transitions by 0.46%. Injustice 2 Black Canary is first seen waiting for Batman with her husband Green Arrow.
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3/20/2023 0 Comments Modbus server vs clientClients could be HMIs or PLCs, while servers could be input/. an input value of 3.14 with 100 as scale is sent as 314, then it can be divided by the same scale to obtain the real value of 3.14).Īddress offset and number of Coils to use (max 256).Īddress offset and number of Digital Inputs or Coils to use (max 256) - (select one option from the Read Digital list).Īddress offset and number of Holding Registers to use (max 64).Īddress offset and number of Input Registers or Holding Registers to use (max 64) - (select one option from the Read Register list). Instead of having one master attached to multiple slaves, the terms client and server are used. If you already have address locations such as. Using this approach, a floating sensor's value can be converted into an integer, sent to the client and converted back to a real number by dividing it by the scale factor (e.g. The most difficult part when configuring your PLC is determining whether you need a Modbus server or client. Server IP address (127.0.0.1 for localhost).įrom where to read Digital Inputs (Inputs or Coils).įrom where to read Registers (Input Registers or Holding Registers).įloating sensor values are multiplied by this value actuator values are divided by it. Under the current standard the address can be 0 - 65535 with the. The following object types may be provided by a Modbus server to a Modbus client device: The addresses are representative of the original Modicon specification. other manufacturers must be able to communicate with your client or server components by means of a standardized protocol - and Modbus fits). Modbus protocol itself provides no security against unauthorized commands or interception of data. Periodically tries to connect to the PLC until a successful connection is established. As you're developing your own client and server components, I suggest you to use Modbus only if strictly required or convenient with an eye to openness (i.e. You can't, however, change where to write values since a Modbus TCP/IP server only allows write operations on Coils and Holding Registers. Some of the Modbus devices can act as both servers and clients, in this. the response messages sent by the servers. The client can close a connection when required, and also process a message from server. These serve as indications of the requested services on the server side Modbus responses, i.e. (which support the Modbus TCP/IP protocol) but also a wide assortment of other clients and server. the messages sent on the network by the clients to initiate transactions. Compatible devices include not only Modicon processors. You can define from where to read digital values (Inputs or Coils) and register values (Input Registers or Holding Registers). Modbus messaging is based on a client/server model and employs the following messages: Modbus requests, i.e. This driver implements a Modbus TCP/IP Client (master). Sample: Sorting with Unity Pro Soft PLC through Modbus TCP/IP 3/20/2023 0 Comments Black light colorSo after you look at the features, take a look at the price too and try to determine if the product is worth the money you’ll spend on it. Whether you want to use it for tasks at home, to improve your work, and more, a black light can be very beneficial. No matter how you look at it, a black light can serve as an investment. Set your budget and search for products which fall within your budget. There are many products out there which come in various price ranges. You don’t have to break the bank just to buy a black light for your home or office. You should also think about the price of the black light too. The filters for these products are quite expensive which is why short-wave black lights of a high-quality are more expensive compared to long-wave black lights. This is because when there’s too much visible light, the objects won’t glow as much.Ĭonversely, the filtered short-wave black lights filter out most of the visible light, only permitting the short-wave UV light to pass through. This makes it useless for the purpose of finding minerals. Unfiltered short-wave black lights permit a huge amount of visible light. When it comes to short-wave light, there are two types namely filtered and unfiltered. Do this if you only need long-wave light. Either that or you can choose a product which already has this feature. If you need this option in your black light, you can purchase the filter separately to make your black light more versatile. Long-wave black lights include filters which have the ability to screen out most of the visible light they emit but not all of it. Therefore, if you see any of these products, it’s best to keep on looking. Such products emit a genuine UV light, but they won’t provide you with the black light experience you want. These lights have similar properties to lighting fixtures which you may find in tanning salons or in animal cages if the animal needs regular daylight exposure. There are some products which provide white-colored UV light too. Black lights with short-wave features can be very beneficial for eliminating germs rather than for use as a household tool. This isn’t ideal for flashlights because of the light’s strength. Some black lights provide the option of short-wave light. Next, think about the light of the product. When you know what style you want, the choice becomes easier. You may need a wider beam for a stage or a smaller beam with a brighter light so you can go searching for minerals, scorpions, and more. These are also the most affordable styles of black lights, but they have a lot of functions.Īs you look at different products, think about which style would suit your needs. Homeowners generally prefer bulbs and flashlights because they are the most convenient and easy to use. You can choose a screw bulb, a flashlight, a string light, a bar, and more. Styleīlack lights come in a wide range of powers and styles. If you want to find the best black light for you, think about what you need first. Some people use black lights to find spots and stains in their homes while others use them for performances. For instance, such lights are especially popular during Halloween as they can provide special effects to haunted houses. When choosing a black light, think about your purpose for needing one. The objects which get illuminated by a black light are lightly colored, or white in color and such objects will give off a very bright glow. In a dark room, the light emitted by a black light can illuminate specific objects and also provide a stunning and unique glow known as fluorescence. The main purpose of a black light is to emit UV light which differs from other kinds of light. What important factors should you consider when buying black lights?įeatures to consider in Good Black Lights Purpose.Vansky UV Flashlight Black light UV Lights Features to consider in Good Black Lights. 3/20/2023 0 Comments Model based flight control systemIn addition, there are many other methods that have been proposed, such as those involving a linear quadratic regulator, sliding mode control, and control. In, a robust linear parameter-varying observer was designed, and then, a comparator integrator was used to design the feedback controller. In, a new asymptotic tracking controller was proposed, adopting the robust integral of the signum of the error method and an immersion and invariance-based adaptive control methodology. In, a robust nonlinear controller that combines sliding mode control with backstepping control to improve the antidisturbance ability of the system was proposed. However, PID parameter tuning is difficult and it is sensitive to disturbances. As a classical controller, proportional integral derivative (PID) controllers have been widely used recently. In the past few years, researchers worldwide have proposed many controllers for UAVs. In controller design, it is necessary to simultaneously take into account the amount of algorithm calculation and the control effect. Moreover, a mathematical model of the UAV is difficult to accurately establish, so it is difficult to control a quadrotor UAV for position trajectory tracking. During flight, quadrotors are generally affected by body vibration and external air flow. Quadrotors have the characteristics of nonlinearity, strong coupling, and sensitivity to disturbance. Quadrotors not only play the important role in the military field but also have been widely used in the civil field. Quadrotors have many advantages, such as a simple structure, good flexibility, and vertical take-off and landing. In recent years, quadrotors have gradually become a popular research topic. Finally, simulation results of a spiral ascent and a climbing maneuver flight illustrate that the controller proposed in this paper has high tracking accuracy and strong robustness under different flight scenarios the average tracking error of the outdoor flight experiment is about 0.22 m, which further verifies the effectiveness of the proposed controller. Secondly, the RBF network is used to estimate the unknown parameter of the system and the Lyapunov function is constructed to prove the stability of the closed-loop system. Firstly, the dynamic model of a quadrotor with disturbance is analyzed and the controller is designed based on the ADRC method. In order to solve the problems of internal uncertainty and external disturbance of an unmanned aerial vehicle (UAV), this paper proposes the active disturbance rejection controller (ADRC) based on the adaptive radial basis function (RBF) neural network. 3/20/2023 0 Comments Dog trainer wiSoon thereafter, I developed a special interest in teaching K9 Nose Work®, and earned my Certified Nose Work Instructor™ certification in March of 2016. I started teaching group classes for a local training company in 2011 and since that time, have earned my certification from the Certification Council for Professional Dog Trainers, taught classes ranging from puppy preschool to reactive rover. So how exactly did I become a dog trainer? I would say that Fanny introduced me to the concepts of training, but going through the experiences with Oscar catapulted me into wanting to learn all I could about dog training, behavior-and more importantly-the significance of building a true partnership with your canine companion. We started to explore other activities that we could actually enjoy (hint: a big part of this was letting him "be more dog"), which has facilitiated an amazing transformation we both needed. I was clearly not listening to him and needed to adjust the world he lived in. I kept asking, "If Fanny could do it, why can't Oscar?" After lots of mutual frustration, I realized I had to stop trying to "fix" my boy. I tried all the reward-based methods I had successfully used with Fanny, but it just wasn’t resonating with Oscar. He was rushed by another dog in agility class and started to develop fear reactions in the training room. Oscar started to exhibit “stranger danger” at unfamiliar people and dogs. I had dreams of doing therapy work with him and, as a puppy he was a wonderful little bundle of joy. On New Year’s Eve that year, we drove to Northern Wisconsin to pick up Oscar, a pure-bred White Shepherd, who was eight-weeks old at the time. Aaron and I decided to add a second dog to our family. Dogs are dogs - they don't come with an intuitive understanding of how to live in a human world, and they certainly do not speak English.įast-forward to 2009. Working with Fanny taught me that training isn't about trying to suppress a dog’s natural instincts, but rather, trying to understand them and set up an environment that offers them a better lifestyle. As soon as we started working with Jan's methods, Fanny improved drastically as my husband, Aaron, and I set up routines that were comfortable for all three of us. She introduced me to positive reinforcement training and helped me understand behaviors from a dog's perspective. Soon thereafter I met a Milwaukee-based trainer who worked exclusively with reward-based training methods. "This is not right," I realized, "There's gotta be a different way. As I was trying one of the recommendations by "The Dog Whisperer," Fanny locked eyes with me, and her distress hit me hard. One specific interaction with Fanny changed everything. We started training with the practices I thought were best at the time made popular by a certain T.V. I knew we'd need to work together to help her feel safe at home and in our neighborhood. It was clear that she had issues with men. By the time I adopted Fanny in 2003, she'd already lived in three different homes. After spending my childhood pretending to be a dog (thanks for not thinking I was crazy, Mom & Dad!), I was so excited to finally get a dog my senior year of college. 3/20/2023 0 Comments Tank in kokonoThe entire second floor is oak, as are the doors and the closets of the bedrooms. The main entrance door is made of iroko wood, one of the most expensive African woods highly resistant to moisture and changeable to light. The ground floor is made of marble with a special treatment to look like wood. The quality of construction of the villa is unquestionable as the materials used are carefully selected. The impressive wooden staircase leads to the upper floor where there are another three large bedrooms, a large bathroom, a living room, a storage room and a huge covered terrace with wonderful views. On this level there is also a large bedroom, a bathroom and an extra room where at the moment is the billiard. Next to the kitchen there is a second living room, a very special and warm space with unobstructed sea views. It is made of solid wood (oak), has many cabinets, large countertops and an auxiliary storage room. Next to the open space but also discreetly hidden is the kitchen. The large openings around the perimeter allow you to see the sea from anywhere in the area. It is built on a plot with a total area of 2,200sqm and has the right to build for additional 500sqm.Įntering from the main entrance we meet the wonderful large open space that includes the living room with the imposing fireplace and the dining room. The property has a total surface of 250 sqm and consists of two levels. It is located in a truly privileged spot in a green landscape and at the same time enjoys unobstructed panoramic views of the endless blue of the sea. Septic Tank Pumping in Greensboro, IndianaVilla with unique architectural design and construction of excellent quality.Septic Tank Pumping in Pierceton, Indiana.Septic Tank Pumping in Portland, Indiana.Septic Tank Pumping in Jonesville, Indiana.Septic Tank Pumping in Rosedale, Indiana.Septic Tank Pumping in Kingman, Indiana.Septic Tank Pumping in Rockville, Indiana.the larger the family members, the even more water made use of, the more frequently your septic tank will need to be pumped). Have your septic tank cleaned up each to three years to stay clear of unnecessary drainpipe field damages or back-flow into your house (the regularity will depend upon the size of your family and how much water you use. it might cost a $100 or more, but you will more than offset that throughout the years with reduced pumping prices). Install a septic riser (you can do this on your own or you could have the septic tank pumper do this for you. See to it you recognize where your septic apparatus is Tips to Minimize Septic Tank Pumping Cost The bottom line is that the simpler it is for the septic tank pumper to locate and also access your septic container the reduced your sewage-disposal tank pumping expense will be. If either of those devices is called for to discover your septic mechanism then you could wager that your septic tank cleansing expense will certainly more than $250. After that the contractor goes out and utilizes a radio receiver to establish where completion of the plumbing snake is and voila! There is your septic container.Ī more sophisticated tool is ground permeating radar (GPR), which could find a septic system a lot more promptly and also with a great deal less initiative. The plumbing system snake is fed via the house water pipes and also into your septic container. One is a straightforward plumbing system snake, with a not-so-simple radio transceiver affixed to the end. The good news is, there are septic system service firms that have special devices utilized to situate septic containers. Some individuals in Kokomo, Indiana do not even know where their septic system is let alone where to locate the access lid. If there is digging included you will certainly be checking out closer to $250 for your septic tank pumping cost. A backbreaking task, no doubt, and also the contractor will certainly intend to be compensated. If you do not have a septic riser installed, then you or the septic system man will have to dig a hole down to the septic container lid. As you might know, the majority of septic tanks are meant to be hidden under ground. Right here is another guideline, the more difficult it is for the septic cleaning person to access your septic system, the much more it will cost you to have it pumped. Sewage-disposal tank cleaning is part of that correct upkeep as well as many individuals ask yourself just how much does septic system pumping in fact set you back? That is a fair question, but it has a somewhat unreasonable answer.Ī good rule of thumb (I enjoy rules of thumb!) is that it will certainly cost between $125 as well as $250 (or more) to have a septic system cleaned in Kokomo, IN. 3/20/2023 0 Comments Star war jedi knight jedi academyNaturally cool because… well… it’s Star Wars. You’ll also get to make some decisions throughout these missions that are associated with the dark and light side of the force – the choices you make will actually affect how the ending of the game plays out, which doesn’t only add weight behind your decisions but also gives players an incentive to play through a second time.Ĭombat in Star Wars Jedi Knight – Jedi Academy is The bulk of gameplay sees you working through a variety of levels, each of which brings with it an assortment of platforming challenges and enemies to kill. You can even customise your lightsaber, with different colours and hilts to choose between to make your perfect weapon. Whilst Star Wars Jedi Knight – Jedi Academy gives you a name, it does allow you to create your own force-wielding hero, with multiple races to choose between and plenty of outfit options on offer for you to give yourself your own unique look. It’s a decent little story that brings some familiar faces into the fray, so fans of the Star Wars universe will certainly enjoy seeing it play out to its conclusion. That doesn’t mean that you’re in a world of complete peace though, and after an encounter with a Dark Jedi you soon learn that a threat to the Jedi Academy isn’t far away. This all takes place after the events of Return of the Jedi, so you don’t have any Order 66 to be worried about – in fact, there’s a real sense of hope with the future of the Jedi (which is something that was erased in the recent movies, so consider this non-canon). Star Wars Jedi Knight – Jedi Academy puts players in the role of Jaden Korr, a Jedi Padawan that is part of the titular Jedi Academy. 3/19/2023 0 Comments Draken us floridaNo one is guaranteed to wake up tomorrow and still have a job by evening. It can happen to anyone, anytime, anywhere. Just because something bad hasn't happened yet, doesn't mean it won't. There are no guarantees in life or promises for a bright future. There will always be a tomorrow, no matter how much you may try to ignore it. 5 min read A Douglas A-4 Skyhawk is on display at the Draken International headquarters on Lakeland Linder International airport in Lakeland, Fla.Lakeland employees are scheduled for May 20, 2022.Ĭhange is coming. The scheduled separation date for Nevada employees is June 4, 2022. Air Force declined to renew Draken International’s ADAIR II contract to provide adversary air services at Nellis Air Force Base in Nevada. The layoffs will include aircraft mechanics, avionics specialists, hydraulics technicians, and support personnel. The reduction in force will impact 247 employees, including 147 in Nevada and 100 headquarters employees in Florida. Jason Dinant at KTNV first reported this story.Lakeland, Florida-based Draken International, pilots for the United States Armed Forces and operates one of the world's largest fleets of privately owned fighter jets providing contract air services to military and defense industry customers, has announced the closure of its facility at Nellis Air Force base in Nevadaa and a major major reduction in force at its Lakeland, Florida headquarters. 2020, "We've contracted with multiple companies around the United States to provide additional services, training platforms to train against." Draken has locations in Fort Worth and San Antonio, Texas, and Kinston, N.C. Cardano (ADA) Yearly rewards 4-6 Cosmos (ATOM) Yearly rewards 12-15 Ethereum 2. Get started with Kraken STAKING CRYPTO Earn crypto rewards Earn up to 23 in rewards annually by staking your assets with Kraken. Such training may take the shape of engaging in DACT (Dissimilar Air Combat Training. Or reach us 24/7/365 on Live Chat or by email. Front line pilots in any air force need to train in air-to-air combat. The National Transportation Safety Board is investigating the crash.Īccording to Retired Brigadier General Robert Novotny, who was Commander of the 57th Wing at Nellis Air Force Base until Nov. Draken International based in Lakeland, Florida has acquired 20 former Ejército del Aire Mirage F1M fighters, as Roberto Yañez and Alex Rodriguez report. Multiple federal and local first responders are on the scene. The pilot’s identity has not yet been released at this time, and no one else was aboard the aircraft. Draken US is also cooperating with investigating agencies to determine what led to this tragic accident,” said Draken US. We are doing everything in our power to assist them in this time of need, and we are working closely with federal, state and local authorities. Our thoughts and prayers go out to the people and families affected by this event. “Draken has received news of a downed aircraft out of Nellis AFB and the tragic loss of one of our pilots. Nellis Air Force Base is a training base that uses both military-owned and contractor-owned aircraft for simulations and training.ĭraken's website says they provide, "Instructors with recent front-line experience provide high-speed, realistic training for the defense of land-based and sea-based assets." today and crashed shortly after.Īccording to authorities, the aircraft was owned, operated, and piloted by Draken US, a Florida-based company contracted to provide adversary air support to Nellis Air Force Base. The aircraft, which National Transportation Safety Board officials have identified as a Dassault Aviation Mirage F-1, took off from the base around 2:30 p.m. LAS VEGAS (KTNV) - Nellis Air Force Base officials confirm that a contractor-operated aircraft from the base has crashed near Cheyenne Avenue and Nellis Boulevard in Las Vegas, killing the pilot. 3/19/2023 0 Comments Outlast 2 game downloadLangermann possesses only a camcorder, which has night vision capabilities, though the camcorder's batteries are also drained when night vision is used. He has a limited stamina meter and the player must manage how long he runs, lest he becomes exhausted and move more slowly. The player can crouch, run, jump, walk, vault, slide and climb much like the first game and can hide in lockers, barrels, wardrobes, beds, pools of water, tall grass, cornfields, and inside of houses. He also wears glasses, which limit the player's vision if they fall off. Langermann cannot fight except in scripted scenes, but must run and hide from the numerous hostile members of Temple Gate. The player controls the investigative journalist Blake Langermann, who investigates a dilapidated rural area in Supai, near the western edge of the Colorado Plateau. The game continues the found footage characteristics from the first game. Outlast 2 is a first-person survival horror game that, like its predecessors Outlast and Outlast: Whistleblower, is a single-player campaign. Criticisms were reserved for the gameplay design and perceived difficulty. The game was met with generally positive reviews upon release, with praise going towards the graphics, sound design, and atmosphere. The Nintendo Switch version released on Maon the Nintendo eShop. Due to development delays, the game was ultimately released on Apfor Microsoft Windows, PlayStation 4, and Xbox One. A gameplay demo was then released at both PAX East and E3 2016 on April 22 and June 15 respectively, with a release originally slated for Autumn 2016. Shortly after the release and popularity of Outlast, Red Barrels announced the sequel. Blake and Lynn get separated in a helicopter crash, and Blake has to find his wife while traveling through a village inhabited by a deranged sect that believes the end of days are upon them. It is the sequel to the 2013 video game Outlast, and features a journalist named Blake Langermann, along with his wife Lynn, roaming the Arizona desert to explore the murder of a pregnant woman only known as Jane Doe. Outlast 2 (stylized as OU ⸸ LASTII) is a first-person survival horror video game developed and published by Red Barrels. 3/19/2023 0 Comments Difficult equation makerThis will definitely take her more than a second to figure out. so you could have instead of +9, have -9e i*pi or something. So you would change it to, instead of -11ln(e), to +11e i*Pi, or add tht to the last linear term. If you wanna add something to this, i recommend you change ln(e) to -e i*Pi which is -(-1) which comes out to 1. the 4/3 and 289/3 cancel each other's trailing. Where 10C3 is the binomial coeficient 10 choose 3 = 120 11*ln(e) = 11 * 1 = 11 because ln is log base e and log base x of x is always 1 289/3 is irreductible, but can also be shown as 96 and 1/3 (integral from pi/6 to pi/3 of sec 2 x dx) 2 comes out to 4/3 and well.7 is a 7.įollowing that the linear combination is basic arithmetic. they are mostly just identities or mathematical oddities taht become things like 1 or 0 or etc.Įach term on the card comes down to this: Let me know if you want to expand on the rest of the terms. So you can change 7 to 9 and get your 23 :) You have several components in a linear combination using plus or minuses. The National Science Foundation, Defense Advanced Research Projects Agency, the Sloan Foundation, Microsoft Research and the Packard Foundation supported this research.Actually in this case if you change 7 to a 9 itll work. "Our vision is to be able to dust off an old math textbook from the library, drop it into the computer and get a beautifully illustrated book - that way more people understand," Crane said, noting that Penrose is a first step toward this goal. In addition to Ye and Crane, the team included Nimo Ni and Jenna Wise, both Ph.D students in CMU's Institute for Software Research (ISR) Jonathan Aldrich, a professor in ISR Joshua Sunshine, an ISR senior research fellow cognitive science undergraduate Max Krieger and Dor Ma'ayan, a former master's student at the Technion-Israel Institute of Technology. "We let them define whatever notation they want, so they can express themselves naturally." An interdisciplinary team developed Penrose. "Mathematicians can get very picky about notation," he explained. The research team developed a special programming language for this purpose that mathematicians should have no trouble learning, Crane said. The user can then select and edit the diagrams they want from a gallery of possibilities. "The secret sauce of our system is to empower people to easily 'explain' this translation process to the computer, so the computer can do all the hard work of actually making the picture." Once the computer learns how the user wants to see mathematical objects visualized - a vector represented by a little arrow, for instance, or a point represented as a dot - it uses these rules to draw several candidate diagrams. student in the Computer Science Department. "We started off by asking: 'How do people translate mathematical ideas into pictures in their head?'" said Katherine Ye, a Ph.D. The researchers will present Penrose at the SIGGRAPH 2020 Conference on Computer Graphics and Interactive Techniques, which will be held virtually this July because of the COVID-19 pandemic. Other users can then access this capability using familiar mathematical language, leaving the computer to do most of the grunt work. Penrose addresses these challenges by enabling diagram-drawing experts to encode how they would do it in the system. "We want to make this expressive power available to anyone." Diagrams are often underused in technical communication, since producing high-quality, digital illustrations is beyond the skill of many researchers and requires a lot of tedious work. "Some mathematicians have a talent for drawing beautiful diagrams by hand, but they vanish as soon as the chalkboard is erased," said Keenan Crane, an assistant professor of computer science and robotics. The researchers named it Penrose after the noted mathematician and physicist Roger Penrose, who is famous for using diagrams and other drawings to communicate complicated mathematical and scientific ideas. Unlike a graphing calculator, these expressions aren't limited to basic functions, but can be complex relationships from any area of mathematics. The tool enables users to create diagrams simply by typing an ordinary mathematical expression and letting the software do the drawing. Thanks to a new tool created at Carnegie Mellon University, anyone can now translate the abstractions of mathematics into beautiful and instructive illustrations. Some people look at an equation and see a bunch of numbers and symbols others see beauty. |
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