Himmat is a women's safety mobile application of Delhi Police. It was launched by Home Minister Rajnath Singh on 1 January 2015. The app is freely available for Android mobile phones and can be downloaded from Delhi Police website. Delhi Police plans to launch app for other platforms in future. Low registrations and other problems resulted in a parliamentary panel calling the app a failure in 2018. Himmat has gone on to be called as one of India's best safety apps for women.
Model compression
Model compression is a machine learning technique for reducing the size of trained models. Large models can achieve high accuracy, but often at the cost of significant resource requirements. Compression techniques aim to compress models without significant performance reduction. Smaller models require less storage space, and consume less memory and compute during inference. Compressed models enable deployment on resource-constrained devices such as smartphones, embedded systems, edge computing devices, and consumer electronics computers. Efficient inference is also valuable for large corporations that serve large model inference over an API, allowing them to reduce computational costs and improve response times for users. Model compression is not to be confused with knowledge distillation, in which a smaller "student" model is trained to imitate the input-output behavior of a larger "teacher" model (as opposed to using the "teacher"'s trained parameters or the "teacher"'s training targets). == Techniques == Several techniques are employed for model compression. === Pruning === Pruning sparsifies a large model by setting some parameters to exactly zero. This effectively reduces the number of parameters. This allows the use of sparse matrix operations, which are faster than dense matrix operations. Pruning criteria can be based on magnitudes of parameters, the statistical pattern of neural activations, Hessian values, etc. === Quantization === Quantization reduces the numerical precision of weights and activations. For example, instead of storing weights as 32-bit floating-point numbers, they can be represented using 8-bit integers. Low-precision parameters take up less space, and takes less compute to perform arithmetic with. It is also possible to quantize some parameters more aggressively than others, so for example, a less important parameter can have 8-bit precision while another, more important parameter, can have 16-bit precision. Inference with such models requires mixed-precision arithmetic. Quantized models can also be used during training (rather than after training). PyTorch implements automatic mixed-precision (AMP), which performs autocasting, gradient scaling, and loss scaling. === Low-rank factorization === Weight matrices can be approximated by low-rank matrices. Let W {\displaystyle W} be a weight matrix of shape m × n {\displaystyle m\times n} . A low-rank approximation is W ≈ U V T {\displaystyle W\approx UV^{T}} , where U {\displaystyle U} and V {\displaystyle V} are matrices of shapes m × k , n × k {\displaystyle m\times k,n\times k} . When k {\displaystyle k} is small, this both reduces the number of parameters needed to represent W {\displaystyle W} approximately, and accelerates matrix multiplication by W {\displaystyle W} . Low-rank approximations can be found by singular value decomposition (SVD). The choice of rank for each weight matrix is a hyperparameter, and jointly optimized as a mixed discrete-continuous optimization problem. The rank of weight matrices may also be pruned after training, taking into account the effect of activation functions like ReLU on the implicit rank of the weight matrices. == Training == Model compression may be decoupled from training, that is, a model is first trained without regard for how it might be compressed, then it is compressed. However, it may also be combined with training. The "train big, then compress" method trains a large model for a small number of training steps (less than it would be if it were trained to convergence), then heavily compress the model. It is found that at the same compute budget, this method results in a better model than lightly compressed, small models. In Deep Compression, the compression has three steps. First loop (pruning): prune all weights lower than a threshold, then finetune the network, then prune again, etc. Second loop (quantization): cluster weights, then enforce weight sharing among all weights in each cluster, then finetune the network, then cluster again, etc. Third step: Use Huffman coding to losslessly compress the model. The SqueezeNet paper reported that Deep Compression achieved a compression ratio of 35 on AlexNet, and a ratio of ~10 on SqueezeNets.
Digital on-screen graphics by country
Digital on-screen graphics by country are the varying logos and differences of digital on-screen graphics in different countries and regions. == Overview == Digital on-screen graphics (DOGs; also called a digitally originated graphic, bug, network bug, on-screen bug, or screenbug) are almost always placed in one of four corners: the top left, the top right, the bottom left, or the bottom right. There are few exceptions to this rule: most notably, Saturday! in Russia, which places their DOG in the top center. Many news broadcasters, as well as a few television networks, also place a clock alongside their bug. In the United States, Canada, Australia, and New Zealand, DOGs may also include the show's parental guideline rating. In Australia, this is known as a Program Return Graphic (PRG). It has become common to place text above the station's logo advertising other programs on the network. In many countries, some TV networks insert the word "live" near the DOG to advise viewers that the program is live, rather than pre-recorded. During televised sports events, a DOG may also display game-related statistics such as the current score. This has led people in Canada and the United States to refer to such a DOG as a score bug. In many countries, DOGs are removed in non-program sections such as commercials and program trailers, but TV channels in some other countries have retained in full color or instead replaced them in either of these sections or in both sections (like Turkey, Indonesia, Italy, the entirety of South Asia, Vietnam, Taiwan, and Russia). == MENA == === Arab world === Arabic TV logos are placed in the top-right and top-left except for Al-Jazeera, whose logo appears on the bottom-right of the screen. Some Arabian TV stations hide their logos during commercial breaks and promos/trailers, such as Dubai TV, Dubai One, Funoon, the Egyptian CBC and Nile TV networks, ART Hekayat, ART Hekayat 2, Iqraa, and Al-Jazeera. Abu Dhabi TV and MBC1 initially had their logos at the bottom-right corner from their launch until the mid-2000s, when they were moved to the top-right corner. === Iran === Iranian broadcaster IRIB introduced DOGs in early 2000s. Unlike other Middle Eastern nations that introduced DOGs on their TV networks in 1990s, Iran was very late in this practice. Almost all Iranian TV channels display DOGs at top-left corner of the screen. The few exception is IRIB-owned channels remove DOGs during news broadcasts. === Israel === In Israel, Television DOGs were first introduced in 1991. Israeli channel watermarks most often appear on the top left or the top right corner since Israeli cable and satellite-based services often have the channel description and programming (OSD) on the bottom of the screen. Most channels have an opaque, full-color watermark, though exceptions exist, for example Channel 9, which displays a blue-tinted semi-transparent logo. In ad breaks, it is required to replace the channel watermark with another symbol – sometimes on the other edge of the screen – indicating there are ads at the moment. The Israel Broadcasting Authority, whose channels placed their logos in the top left corner, ceased broadcasting in May 2017. The new public broadcaster, the Israeli Public Broadcasting Corporation, displays its logos at the top right instead. The erstwhile Channel 2 as well as its successors, Keshet 12 and Reshet 13, also use the top right corner. However, Channel 10 used the top left corner before rebranding to Eser (Literally "Ten") in 2017 and simultaneously moving its logo to the top right (Not long after, in January 2019, it ceased broadcasting as it merged with Reshet 13). Channel 14 as well as its predecessor Channel 20 use the top right corner as well. The Knesset Channel, however, uses the top left corner. === Morocco === The SNRT and 2M And Al-Aoula Uses permanent on-screen DOGs for their TV channels. In contrast, other channels such as Medi 1 TV hide their DOGs during commercial breaks. == Asia == === Brunei === Radio Television Brunei introduced DOGs in 1994. Like TV channels from neighbouring Malaysia, all DOGs are removed during advertisement breaks. === Cambodia === Cambodian TV channels introduced DOGs in 1995. Like Thailand, all logos are full-color and displayed on the top-right corner of the screen. Some channels such as TV5 hide their logos during commercial breaks. Hang Meas HDTV Logo on the top-left corner of the screen, CTN (Cambodian Television Network), MyTV, Bayon TV, PNN, Logo on the top-right corner of the screen. === China === TV stations in mainland China always place their logo (usually semi-transparent and sometimes animated) in the top-left corner of the screen in full-color or grey-scale. Regardless of the content being broadcast (program or advertisements), some channels like Phoenix Television hide their logos during commercial breaks; although in some rare cases, the DOG may be placed elsewhere to avoid covering the score bug during the broadcast of a sporting event. China introduced logos in 1983 on the bottom-left corner of the screen, but they were used only during commercial breaks and clock idents. Later China Central Television (CCTV) introduced permanent DOGs for all programs in 1992, on the top-left corner of the screen. China also displays a clock on top-right corner of the screen for 1 minute between 59:30–00:30 & 29:30–30:30 time in transition between programs. === Hong Kong === Hong Kong TV introduced DOGs in 1994. Hong Kong DOGs can be either of full color or semi-transparent and (except for RTHK 31) always be hidden during commercial breaks. Television Broadcasts Limited (TVB) placed their logos at the top-right corner of the screen while now-defunct Asia Television and other channels placed their logos at the top-left corner of the screen. Sometimes, weather information, date, and time clocks had been used alongside DOGs in news programs, continuity & live broadcasts. === India === The first on-screen logo in India was introduced in 1984 by DD2 Metro (now DD News). It was white and slightly transparent. All Indian TV channels have on-screen logos. They are always full-colors, never transparent, and they are almost never removed during commercial breaks (though the channels of the South Indian Sun TV Network did so until 2015). The great majority of Indian TV channels place their logos in the top right corner of the screen, though there are exceptions. The corner used may be broadcaster-dependent. Among the big national broadcasters: Channels from the Sony network always use the top right corner, without exception. Star channels also use the top right, with the exception of National Geographic and Nat Geo Wild, which use the top left corner in line with their international counterparts. Past exceptions include The History Channel, whose logo was placed in the top left until it rebranded to Fox History & Entertainment in 2008; the now-defunct Channel V, which used the top left between 2013 and 2016; and Nat Geo People, Nat Geo Music and BabyTV, were withdrawn from India in June 2019. TV18 and Viacom18 channels use the top right corner as well, with the exceptions of regional-language movie channels (e.g., Colors Kannada Cinema and Colors Gujarati Cinema) as well as Colors Super, which have shown their logos at the top left corner since 2018; and VH1, which has always used the bottom right corner. Also, CNBC-TV18, CNBC Awaaz and CNBC Bajar use the bottom right. Moreover, MTV showed its logo in the top left corner until 23 April 2018, when it was moved to the top right (its HD version, launched in 2017, has always used the top right). Unlike most other major networks, the Zee Network's non-news channels containing 'Zee' in their name display their logos at the top left corner and not the top right. This has been the case since 15 October 2017, when almost all the Zee-branded TV channels of the Zee network rebranded with a new logo and, in many cases, a new graphics package and look. Before then, the logos were shown at the top right, as with other broadcasters. (News channels' logos—i.e., logos of channels owned by Zee Media Corporation—stayed put at the top right corner, with the exception of WION, which uses the bottom left.) All the major Zee-branded channels—such as Zee TV, Zee Cinema, Zee Café and the regional-language channels like Zee Tamil, Zee Telugu, Zee Marathi and Zee Bangla—show their logos at the top left; moreover, the Odia-language channel Sarthak TV rebranded to Zee Sarthak and moved its logo to the top left. Among the Zee channels not containing the word 'Zee' that moved their logos to the top left during the big rebrand in 2017 was English movie channel Zee Studio; when it was renamed to &flix on 3 June 2018, the logo remained at the top left. Moreover, Hindi movie channel &pictures has always shown its logo at the top left since its launch in 2013. However, &privé HD, Zee's other English movie channel, and Hindi entertainment channel &TV place the
Touch 'n Go eWallet
Touch 'n Go eWallet is a Malaysian digital wallet and online payment platform, established in Kuala Lumpur, Malaysia, in July 2017 as a joint venture between Touch 'n Go and Ant Financial. It allows users to make payments at over 280,000 merchant touch points via QR code, as well as perform peer-to-peer (P2P) money transfers. Since then, the e-wallet further diversified for users to pay for tolls via RFID or PayDirect, street parking and various online payment spanning e-hailing, car-sharing apps or taxis, various overhead bills; top-up for mobile prepaid or in-game currencies; purchases on e-commerce websites; food delivery; renewing motor insurance and other insurance/takaful plans; and even movie, bus, trains or airline tickets. == Background == Prior to the launch of the e-wallet service, Touch 'n Go provided stored-value physical all-in-one contactless card (namely Touch 'n Go cards or "TnG cards") that users can use to pay for toll fares, public transportation and parking lots as well as purchases in some retail stores. In 1999, Touch 'n Go also markets SmartTag devices that allow road users to pass through certain toll booths without the need to unwind the car window. The high entry cost of the device (around RM 100 each) also meant that only few can enjoy the seamless experience. In 2009, Touch 'n Go partnered with Maxis to launch FastTap, a new mobile payment service that utilised Near-Field Communication (NFC). Maxis customers can make payments by placing the phone near the card readers (that also supports physical bank cards and Touch ’N Go cards). However, the venture featured only one phone model, Nokia 6212, which greatly limited the public reach. In July 2012, Touch 'n Go announced another collaboration with CIMB and Maxis to create similar NFC-based online transaction service that runs on compatible smartphones. Touch 'n Go Wallet was launched in February 2017 as an QR code-based e-wallet application, to compete with Samsung Pay that utilizes NFC modules. In the controlled pilot test in Taman Tun Dr Ismail, the correspondents can experience basic functionalities (prepaid mobile service reload, bills payment, movie tickets and flight tickets purchase, transfer of money with another user, and payments at participating stores and restaurants). While the deployed version of the app was generally well-received, the existing process to transfer the balance to the physical TnG card stored value from the app garnered unanimous backlash. Test groups felt that the need to head to a self-service terminal named "Pick Up Device" in person within 24 hours for completion, along with the failure to do so (the balance would be credited back to the wallet after 24 hours), was not divulged clearly and also defeated the purpose of convenience, not to mention there were only 2 such terminals. The feature was eventually suspended. On 15 November 2017, Touch 'n Go was granted permission by the Central Bank of Malaysia to form a joint venture with Ant Financial, a Chinese-based financial company that operates Alipay. The partnership allowed the local e-wallet to learn from and build upon the operational model pioneered by Alipay. In June 2018, it was reported that Touch 'n Go was pilot testing the uses of the Touch 'n Go eWallet in Rapid Transit, as the ticketing system was enabled on the Kelana Jaya line in the Klang Valley. Pilot testing only applied to stations in Kelana Jaya, KL Gateway–Universiti, Kerinchi, KL Sentral, Dang Wangi, KLCC, and Ampang Park. The test was reported to be successful in February 2020 and was planned to be fully deployed on the LRT and MRT. Due to unforeseen circumstances, this feature did not come into fruition, the app merely adds in-app purchase of monthly concession cards called "My50". In August 2018, Touch 'n Go announced that selected drivers may experience first-hand a new RFID-based payment (later rebranded as "myRFID") that serves to replace SmartTag devices on closed toll roads with during pilot testing phase commencing on 3 September 2018. On 2 November 2018, participation in the ongoing pilot programme was expanded, allowing more drivers to sign up ahead of the public rollout of the RFID system. During the same period, Touch 'n Go has discontinued the sales of SmartTAG devices in favor of the RFID-based payment system. Initially, the installation of the RFID chip onto the car could only be done by Touch 'n Go staff at the RFID fitment centers, at no cost. As the pilot testing concluded on 15 February 2020, a self-installation kit are being offered to the public on Lazada and Shopee. Support for taxi-hailing mobile apps was added in November 2018 when Touch 'n Go partnered with EzCab and Public Cab, allowing users to make payments via QR code. This was later expanded to support MULA on 7 January 2020, and later MyCar on 4 April 2020. Touch 'n Go eWallet was also the first eWallet to convert Kuala Lumpur's most famous Ramadan bazaar in Kampong Bahru into "Kampong Kashless", a venue that can accept cashless QR payments. It welcomed more than 250,000 Malaysians including local celebrities and government officials. On 1 October 2019, some e-commerce websites owned by the Alibaba Group (TMall and Taobao) began to support Touch 'n Go eWallet payments, Lazada joined the list on 29 October 2019. Touch 'n Go eWallet was one of the three e-wallet services in Malaysia (the other being Boost and GrabPay) that was eligible for its users to receive an RM 30 credit in conjunction of E-Tunai Rakyat program under the Budget 2020 plan, that further normalizes adoption of cashless and mobile payment among Malaysians. Unlike Boost and GrabPay, whose P2P transfers were completely disabled until users have exhausted the RM 30 first, Touch 'n Go eWallet did not impose such measures. in 2020, Touch 'n Go eWallet joined DuitNow, an electronic transaction ecosystem in Malaysia which allows the funds from Touch 'n Go eWallet to be transferred to other competing services and vice versa, by implementing a standard DuitNow QR code deisgn. Japan become the first country outside Malaysia to support Touch 'n Go eWallet payment via Alipay Connect. During the COVID-19 pandemic and the enforcement of the movement control order, use of eWallets (including Touch 'n Go eWallet) increased tremendously among citizens due to its contactless nature of the payment and increased take-out orders at home; which in turn helped small and medium-sized enterprises to thrive. Touch 'n Go eWallet launched its loyalty programme – The Goal Hunter – in October 2020 where on monthly basis, users collect stamps by paying with the app in exchange for rewards that include lucky draws and other vouchers. == Services == Touch 'n Go eWallet app is available for download on both Google Play and Apple Appstore. It utilizes QR code technology for local in-store payments. The Touch 'n Go eWallet app also diversifies payment types, including but not limited to Utility bills Purchase of motor insurance policy Pay Later facility Prepaid reload and Postpaid payment to telecommunications companies loan repayments for courts, MBSJ payments, zakat and PTPTN payment for car parking P2P transfer airline ticket bookings; movie tickets from TGV Cinemas RFID refuelling at Shell stations (defunct after Shell launched its own payment app in 2024) User can reload the eWallet credit by setting up auto-reload, purchasing reload pins from convenience stores (such as 7-Eleven, KK Super Mart, MyNews, Family Mart etc.), reloading by FPX and credit/debit card. The PayDirect feature allows users to link their physical Touch 'n Go cards into the eWallet, where the toll fare can be debited from the eWallet balance when flashing the card near the sensor. In the circumstance of insufficient balance in the app, the toll fare will be deducted from the physical card's balance instead. This also conveniently allows users to view the card's remaining balance. Touch 'n Go eWallet is the first and only eWallet to offer a money-back guarantee when an unauthorised transaction is made on the user’s eWallet account, subject to Terms & Conditions. Payment via QR code scanning, including Touch 'n Go eWallet, becomes a norm in most of the shops/restaurants across Malaysia, including roadside hawkers/stall owners and automatic vending machines. The merchants usually display their owner's individual QR or Business account that they can apply for in-app. The popularity attributes to the low merchant onboarding cost (Unlike NFC payment and debit/credit card that requires purchase or rental of a payment terminal device at a yearly fee.) The app is also one of the few ewallet that supports bidirectional liquidity (alongside MAE developed by Maybank), where funds can be transferred two-way with bank accounts. This is not possible with the other major ewallets (GrabPay, Boost, ShopeePay etc.) where the money that is reloaded to the wallet cannot be transferred to another bank account, unless through manual req
Data access layer
A data access layer (DAL) is a software architectural layer that provides access to data from one or more sources, such as a relational database, NoSQL database, SQL query engine, file system, or other persistent storage. It separates client code from the details of storage systems, query execution, connection handling, and data retrieval. Data access layers are commonly used to centralize data access logic, reduce coupling between applications and data sources, and provide a consistent interface for retrieving, writing, or querying data. Depending on the system, a data access layer may be implemented as application code, a shared library, an intermediary service, or part of a broader database abstraction layer. == In application architecture == In application software, a data access layer provides a boundary between business logic or application code and the systems used to store or retrieve data. For example, a data access layer may expose methods or interfaces for retrieving, writing, or querying data while hiding details such as connection management, SQL statements, storage APIs, error handling, and result conversion. Depending on the application, the layer may return objects, records, tabular results, documents, streams, or other representations of data. A common implementation is a set of classes, functions, or methods that directly reference database queries, stored procedures, storage APIs, or other data sources. For example, instead of using commands such as insert, delete, and update throughout an application to access a specific table, methods such as registerUser or loginUser may be implemented inside the data access layer. Business logic methods from an application can also be mapped to the data access layer. Instead of making several database queries directly, an application can call a single DAL method that abstracts those database calls. Applications using a data access layer may be either dependent on or independent from a particular database server. If the data access layer supports multiple database systems, the application can use any database system that the DAL can access. In either case, the data access layer provides a centralized location for calls into the underlying data store, which can make it easier to maintain, test, or port the application to other storage systems. == Implementation patterns == A data access layer can be implemented using several patterns and technologies, including data access objects, repositories, stored procedures, query builders, database drivers, or object–relational mapping tools. These mechanisms may implement part or all of a data access layer, but are not always equivalent to the layer itself. Object–relational mapping tools are commonly used in data access layers for object-oriented applications that map records in a relational database to objects in a programming language. Other data access layers may expose lower-level database interfaces, tabular results, document-oriented data, files, streams, or protocol-level interfaces. == Use with multiple underlying data systems == A data access layer may be used to abstract differences between multiple underlying data systems, allowing applications to access them through a more consistent interface. In such designs, applications call the DAL rather than interacting directly with each database or storage system. The layer may then handle connection management, query generation, result mapping, error handling, and other implementation details. A data access layer may be implemented as a shared library or as an intermediary service, such as a proxy or gateway. In this configuration, client applications or services connect to the data access layer, which then communicates with one or more underlying databases or query engines. This can provide a common location for authentication, authorization, logging, routing, and translation between different database interfaces. == Interfaces and protocols == Data access layers may expose or use standardized interfaces and protocols for database access. Examples include Open Database Connectivity (ODBC), Java Database Connectivity (JDBC), database-native wire protocols, and newer interfaces such as Apache Arrow Database Connectivity (ADBC) and Arrow Flight SQL. In systems that support multiple data stores, a data access layer may provide a consistent interface while using different drivers, protocols, or query mechanisms internally. == Distinction from related patterns == A data access layer is related to, but broader than, a data access object, which is usually an object-oriented design pattern for encapsulating access to a persistence mechanism. It is also related to a database abstraction layer, which focuses on hiding differences between database systems. In practice, the terms may overlap.
Caspio
Caspio, Inc. is an American software company providing a low-code platform for building cloud-based business applications. Founded in 2000 by Frank Zamani, the company is headquartered in Sunnyvale, California, with operations in Poland, the Philippines, and Spain. Caspio’s platform allows organizations to create online database applications and workflow tools without extensive coding. == History == Caspio was founded by Frank Zamani in 2000. The company initially focused on simplifying custom cloud applications and reducing development time and cost as compared to traditional software development. Caspio released the first version of its platform, Caspio Bridge, in 2001. In 2014, Caspio released a HIPAA-Compliant Edition of its low-code application development platform. Caspio also released an EU General Data Protection Regulation (GDPR) Compliance Edition of its low-code application development platform in 2016. Caspio's second European Software Development Center opened in Kraków, Poland in 2017. In 2019, Forrester Research listed Caspio and three other platforms in its highest of four ranked tiers of twelve low-code platforms for business developers based on rankings of offerings and strategy at that time. Caspio also opened data centers in Montreal, Canada and India in 2020.
Reflection lines
Engineers use reflection lines to judge a surface's quality. Reflection lines reveal surface flaws, particularly discontinuities in normals indicating that the surface is not C 2 {\displaystyle C^{2}} . Reflection lines may be created and examined on physical surfaces or virtual surfaces with the help of computer graphics. For example, the shiny surface of an automobile body is illuminated with reflection lines by surrounding the car with parallel light sources. Virtually, a surface can be rendered with reflection lines by modulating the surfaces point-wise color according to a simple calculation involving the surface normal, viewing direction and a square wave environment map. == Mathematical definition == Consider a point p {\displaystyle p} on a surface M {\displaystyle M} with (normalized) normal n {\displaystyle n} . If an observer views this point from infinity at view direction v {\displaystyle v} then the reflected view direction r {\displaystyle r} is: r = v − 2 ( n ⋅ v ) n . {\displaystyle r=v-2(n\cdot v)n.} (The vector v {\displaystyle v} is decomposed into its normal part v n = ( n ⋅ v ) v {\displaystyle v_{n}=(n\cdot v)v} and tangential part v t = v − v n {\displaystyle v_{t}=v-v_{n}} . Upon reflection, the tangential part is kept and the normal part is negated.) For reflection lines we consider the surface M {\displaystyle M} surrounded by parallel lines with direction a {\displaystyle a} , representing infinite, non-dispersive light sources. For each point p {\displaystyle p} on M {\displaystyle M} we determine which line is seen from direction v {\displaystyle v} . The position on each line is of no interest. Define the vector r p {\displaystyle r_{p}} to be the reflection direction r {\displaystyle r} projected onto a plane P {\displaystyle P} that is orthogonal to a {\displaystyle a} : r p = r − ( r ⋅ a ) a {\displaystyle r_{p}=r-(r\cdot a)a} and similarly let v p {\displaystyle v_{p}} be the viewing direction projected onto P {\displaystyle P} : v p = v − ( v ⋅ a ) a {\displaystyle v_{p}=v-(v\cdot a)a} Finally, define v o {\displaystyle v_{o}} to be the direction lying in P {\displaystyle P} perpendicular to a {\displaystyle a} and v p {\displaystyle v_{p}} : v o = a × v p {\displaystyle v_{o}=a\times v_{p}} Using these vectors, the reflection line function θ ( p ) : M → ( − π , π ] {\displaystyle \theta (p):M\rightarrow (-\pi ,\pi ]} is a scalar function mapping points p {\displaystyle p} on the surface to angles between v p {\displaystyle v_{p}} and r p {\displaystyle r_{p}} : θ = arctan ( r p ⋅ v o , r p ⋅ v p ) {\displaystyle \theta =\arctan {(r_{p}\cdot v_{o},r_{p}\cdot v_{p})}} where a r c t a n ( y , x ) {\displaystyle arctan(y,x)} is the atan2 function producing a number in the range ( − π , π ] {\displaystyle (-\pi ,\pi ]} . ( v p {\displaystyle v_{p}} and v o {\displaystyle v_{o}} can be viewed as a local coordinate system in P {\displaystyle P} with x {\displaystyle x} -axis in direction v p {\displaystyle v_{p}} and y {\displaystyle y} -axis in direction v o {\displaystyle v_{o}} .) Finally, to render the reflection lines positive values θ > 0 {\displaystyle \theta >0} are mapped to a light color and non-positive values to a dark color. == Highlight lines == Highlight lines are a view-independent alternative to reflection lines. Here the projected normal is directly compared against some arbitrary vector x {\displaystyle x} perpendicular to the light source: θ = arctan ( n a ⋅ a ⊥ , n a ⋅ x ) {\displaystyle \theta =\arctan {(n_{a}\cdot a^{\perp },n_{a}\cdot x)}} where n a {\displaystyle n_{a}} is the surface normal projected on the light source plane P {\displaystyle P} : n a ^ / | n a ^ | , n a ^ = n − ( n ⋅ a ) a {\displaystyle {\hat {n_{a}}}/|{\hat {n_{a}}}|,{\hat {n_{a}}}=n-(n\cdot a)a} The relationship between reflection lines and highlight lines is likened to that between specular and diffuse shading.