NSynth

NSynth (a portmanteau of "Neural Synthesis") is a WaveNet-based autoencoder for synthesizing audio, outlined in a paper in April 2017. == Overview == The model generates sounds through a neural network based synthesis, employing a WaveNet-style autoencoder to learn its own temporal embeddings from four different sounds. Google then released an open source hardware interface for the algorithm called NSynth Super, used by notable musicians such as Grimes and YACHT to generate experimental music using artificial intelligence. The research and development of the algorithm was part of a collaboration between Google Brain, Magenta and DeepMind. == Technology == === Dataset === The NSynth dataset is composed of 305,979 one-shot instrumental notes featuring a unique pitch, timbre, and envelope, sampled from 1,006 instruments from commercial sample libraries. For each instrument the dataset contains four-second 16 kHz audio snippets by ranging over every pitch of a standard MIDI piano, as well as five different velocities. The dataset is made available under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. === Machine learning model === A spectral autoencoder model and a WaveNet autoencoder model are publicly available on GitHub. The baseline model uses a spectrogram with fft_size 1024 and hop_size 256, MSE loss on the magnitudes, and the Griffin-Lim algorithm for reconstruction. The WaveNet model trains on mu-law encoded waveform chunks of size 6144. It learns embeddings with 16 dimensions that are downsampled by 512 in time. == NSynth Super == In 2018 Google released a hardware interface for the NSynth algorithm, called NSynth Super, designed to provide an accessible physical interface to the algorithm for musicians to use in their artistic production. Design files, source code and internal components are released under an open source Apache License 2.0, enabling hobbyists and musicians to freely build and use the instrument. At the core of the NSynth Super there is a Raspberry Pi, extended with a custom printed circuit board to accommodate the interface elements. == Influence == Despite not being publicly available as a commercial product, NSynth Super has been used by notable artists, including Grimes and YACHT. Grimes reported using the instrument in her 2020 studio album Miss Anthropocene. YACHT announced an extensive use of NSynth Super in their album Chain Tripping. Claire L. Evans compared the potential influence of the instrument to the Roland TR-808. The NSynth Super design was honored with a D&AD Yellow Pencil award in 2018.

Knowledge graph embedding

In representation learning, knowledge graph embedding (KGE), also called knowledge representation learning (KRL), or multi-relation learning, is a machine learning task of learning a low-dimensional representation of a knowledge graph's entities and relations while preserving their semantic meaning. Leveraging their embedded representation, knowledge graphs can be used for various applications such as link prediction, triple classification, entity recognition, clustering, and relation extraction. == Definition == A knowledge graph G = { E , R , F } {\displaystyle {\mathcal {G}}=\{E,R,F\}} is a collection of entities E {\displaystyle E} , relations R {\displaystyle R} , and facts F {\displaystyle F} . A fact is a triple ( h , r , t ) ∈ F {\displaystyle (h,r,t)\in F} that denotes a link r ∈ R {\displaystyle r\in R} between the head h ∈ E {\displaystyle h\in E} and the tail t ∈ E {\displaystyle t\in E} of the triple. Another notation that is often used in the literature to represent a triple (or fact) is ⟨ head , relation , tail ⟩ {\displaystyle \langle {\text{head}},{\text{relation}},{\text{tail}}\rangle } . This notation is called the Resource Description Framework (RDF). A knowledge graph represents the knowledge related to a specific domain; leveraging this structured representation, it is possible to infer a piece of new knowledge from it after some refinement steps. However, nowadays, people have to deal with the sparsity of data and the computational inefficiency to use them in a real-world application. The embedding of a knowledge graph is a function that translates each entity and each relation into a vector of a given dimension d {\displaystyle d} , called embedding dimension. It is even possible to embed the entities and relations with different dimensions. The embedding vectors can then be used for other tasks. A knowledge graph embedding is characterized by four aspects: Representation space: The low-dimensional space in which the entities and relations are represented. Scoring function: A measure of the goodness of a triple-embedded representation. Encoding models: The modality in which the embedded representation of the entities and relations interact with each other. Additional information: Any additional information coming from the knowledge graph that can enrich the embedded representation. Usually, an ad hoc scoring function is integrated into the general scoring function for each additional piece of information. == Embedding procedure == All algorithms for creating a knowledge graph embedding follow the same approach. First, the embedding vectors are initialized to random values. Then, they are iteratively optimized using a training set of triples. In each iteration, a batch of size b {\displaystyle b} triples is sampled from the training set, and a triple from it is sampled and corrupted—i.e., a triple that does not represent a true fact in the knowledge graph. The corruption of a triple involves substituting the head or the tail (or both) of the triple with another entity that makes the fact false. The original triple and the corrupted triple are added in the training batch, and then the embeddings are updated, optimizing a scoring function. Iteration stops when a stop condition is reached. Usually, the stop condition depends on the overfitting of the training set. At the end, the learned embeddings should have extracted semantic meaning from the training triples and should correctly predict unseen true facts in the knowledge graph. === Pseudocode === The following is the pseudocode for the general embedding procedure. algorithm Compute entity and relation embeddings input: The training set S = { ( h , r , t ) } {\displaystyle S=\{(h,r,t)\}} , entity set E {\displaystyle E} , relation set R {\displaystyle R} , embedding dimension k {\displaystyle k} output: Entity and relation embeddings initialization: the entities e {\displaystyle e} and relations r {\displaystyle r} embeddings (vectors) are randomly initialized while stop condition do S b a t c h ← s a m p l e ( S , b ) {\displaystyle S_{batch}\leftarrow sample(S,b)} // Sample a batch from the training set for each ( h , r , t ) {\displaystyle (h,r,t)} in S b a t c h {\displaystyle S_{batch}} do ( h ′ , r , t ′ ) ← s a m p l e ( S ′ ) {\displaystyle (h',r,t')\leftarrow sample(S')} // Sample a corrupted fact T b a t c h ← T b a t c h ∪ { ( ( h , r , t ) , ( h ′ , r , t ′ ) ) } {\displaystyle T_{batch}\leftarrow T_{batch}\cup \{((h,r,t),(h',r,t'))\}} end for Update embeddings by minimizing the loss function end while == Performance indicators == These indexes are often used to measure the embedding quality of a model. The simplicity of the indexes makes them very suitable for evaluating the performance of an embedding algorithm even on a large scale. Given Q {\displaystyle {\ce {Q}}} as the set of all ranked predictions of a model, it is possible to define three different performance indexes: Hits@K, MR, and MRR. === Hits@K === Hits@K or in short, H@K, is a performance index that measures the probability to find the correct prediction in the first top K model predictions. Usually, it is used k = 10 {\displaystyle k=10} . Hits@K reflects the accuracy of an embedding model to predict the relation between two given triples correctly. Hits@K = | { q ∈ Q : q < k } | | Q | ∈ [ 0 , 1 ] {\displaystyle ={\frac {|\{q\in Q:q

CrocBITE

CrocBITE (currently CrocAttack) was an online database of wild crocodilian attacks reported on humans in the world. The non-profit online research tool helped to scientifically analyze crocodilian behavior via complex models. Users were encouraged to feed information in a crowdsourcing manner. This website excludes captive crocodilian attacks, as well as non-fatal bites on professional handlers, rangers, staff, or researchers, and crocodilian attacks on pets and livestock, because its primary goal is to analyze natural human-crocodilian conflict in the wild for conservation and management purposes, and that these incidents do are not considered indicative of natural species behavior or typical human-wildlife conflict, as well as not providing enough useful data and helping researchers understand wild population behavior or typical human-wildlife conflict dynamics and helps create safety strategies for people living or working near wild crocodilians, rather than tracking workplace accidents in zoos or farms. While fatal incidents involving handlers are sometimes included on the website, typical captive incidents (such as handlers being bitten by them in zoos) are excluded because they are considered manageable professional risks rather than general public safety threats. == About == The online database was established in 2013 (2013) by Dr Adam Britton, a researcher at Charles Darwin University, his student Brandon Sideleau and Erin Britton. It was a compilation of government records, individual reports, registered contributors and historical data. Dr Simon Pooley, Junior Research fellow, Imperial College London joined hands to further the studies. The collaboration culminated when Dr Pooley met Dr Britton at the IUCN Crocodile Specialist Group, in Louisiana in 2014. The program received funds from Economic and Social Research Council, United Kingdom to the tune of A$30,000 and unspecified resourced plus amount from Big Gecko Crocodilian Research, Crocodillian.com and Charles Darwin University. The research yielded pertinent observations that provide inside into crocodile attacks. It was observed that most attacks on humans occur from bites of Saltwater crocodile as against the popular understanding of Nile crocodiles taking the top spot. This is not, however, believed to be the actual case, as most attacks by the Nile crocodile are believed to go unreported or only reported on a local level. The broad category of Nile crocodile attacks were segmented into West African crocodile and Crocodylus niloticus (the Nile Crocodile) species to get a clear understanding of their respective attack zones. The objective was that the information would be used by communities and conservation managers to help inform and educate people about how to keep safe. The information was vital for Australia and Africa where such attacks are more likely than in other parts of the world. This was the only database of its kind with such comprehensive collection of information made available online. The database is no longer online, and its founder Adam Britton is in custody having pleaded guilty to charges of bestiality on September 25, 2023. It has been rebranded and renamed CrocAttack, and serves as a updated database focusing on human-crocodilian conflict and records over 8,500 incidents from the past decades.

Ciscogate

Ciscogate, also known as the Black Hat Bug, is the name given to a legal incident that occurred at the Black Hat Briefings security conference in Las Vegas, Nevada, on July 27, 2005. On the morning of the first day of the conference, July 26, 2005, some attendees noticed that 30 pages of text had been physically ripped out of the extensive conference presentation booklet the night before at the request of Cisco Systems and the CD-ROM with presentation slides was not included. It was determined the pages covered a talk to be given by Michael Lynn, a security researcher with Atlanta-based IBM Internet Security Systems (ISS). Instead of the pages with the details, attendees found a photographed copy of a notice from Black Hat saying "Due to some last minute changes beyond Black Hat's control, and at the request of the presenter, the included materials aren't up to the standards Black Hat tries to meet. Black Hat will be the first to apologize. We hope the vendors involved will follow suit." According to Lynn's lawyer, his employer had approved of the talk leading up to the conference but changed their minds two days before the scheduled talk, forbidding him from presenting. Lynn's original presentation was to cover a vulnerability in Cisco routers. The presentation was one of four scheduled to follow Jeff Moss' keynote address on the first day of the conference, titled "Cisco IOS Security Architecture". After being told by his employer that he could not present on the topic, Lynn chose an alternate topic. Cisco and ISS had offered to give new joint presentation but this was turned down by Black Hat because the original speaking slot was given to Lynn, not Cisco. Lynn's presentation began by covering security issues in services that allow users to make Voice over IP telephone calls. Shortly after beginning the presentation Lynn changed back to his original topic and began disclosing some technical details of the vulnerability he found in Cisco routers stating that he would rather resign from his job at ISS than keep the details private. == Lawsuit == Shortly after Lynn concluded his talk he met Jennifer Granick, who would soon become his lawyer. During their initial meeting Lynn told Granick that he expected to be sued. Later in the evening Lynn had heard that Cisco and ISS had filed a lawsuit and requested a temporary restraining order against Black Hat but not himself. A public relations representative from Black Hat told Granick that the lawsuit was against both Black Hat and Lynn and that the companies had scheduled an Ex parte hearing in San Francisco the next morning to request the restraining order. That night, Andrew Valentine, an attorney for ISS and Cisco called Lynn who directed them to Granick. During the conversation Valentine explained the claims and accusations against Lynn, which included three things: 1) ISS claimed copyright over the presentation that Lynn gave, 2) Cisco claimed copyright over the decompiled machine code obtained from the router which was included in the presentation, and 3) Cisco claimed the presentation contained trade secrets. These complaints were outlined in a civil complaint at the U.S. Northern District of California and filed against both Lynn and Black Hat. According to Granick, she and Valentine were able agree to an injunction to settle the case without court proceedings. This deal was almost called off due to an inadvertent mistake by Black Hat in which they had restored Lynn's presentation on their web server. Black Hat, Granick, and the plaintiff's lawyers were able to resolve this problem and the deal stood. One condition of the settlement required Lynn to provide an image of all computer data he used in his research to be provided to a third party for forensic analysis before erasing his research and any Cisco data from his systems. The settlement also stipulated that Lynn was prohibited from talking about the vulnerability in the future. == FBI Investigation == Shortly after lawyers for Lynn and ISS / Cisco filed settlement papers, FBI agents from the Las Vegas office arrived at the conference to begin asking questions. According to Granick, they were there at the request of the Atlanta FBI office and Lynn was not of interest. Granick asserted the Fifth and Sixth amendment rights on behalf of her client, Lynn. Granick asserted his rights for the Atlanta office and asked if an arrest warrant had been issued for Lynn. Over the next 24 hours Granick was not able to ascertain the status of a warrant but ultimately determined no warrant was issued. When the FBI was asked about the case by a journalist, spokesman Paul Bresson declined to discuss the case saying "Our policy is to not make any comment on anything that is ongoing. That's not to confirm that something is, because I really don't know". Granick would only confirm to journalists that the "investigation has to do with the presentation". == Response == === Attendees === Attendees of Black Hat Briefings, as well as many that also attended DEF CON, were not happy with vendors threatening legal action over vulnerability disclosure. The term "Ciscogate" was coined quickly by an unknown person, but some attendees were quick to create shirts to commemorate the incident. === Cisco === Mojgan Khalili, a senior manager for corporate PR at Cisco, issued a statement to the press saying "It is important to note that the information Mr. Lynn presented was not a disclosure of a new vulnerability or a flaw with Cisco IOS software. Mr. Lynn's research explores possible ways to expand exploitations of existing security vulnerabilities impacting routers." === ISS === Kim Duffy, managing director of ISS Australia, was asked about ISS's response to the incident. Duffy responded that it was "business as usual" as the company handled the incident "strictly by the book". He gave a brief statement to ZDNet UK saying "ISS has published rules for disclosure and that is what we stick to. We didn't care to publish [the disclosure] because we were not ready. We had not completed the research to our satisfaction so it was not ready to be disclosed". ISS spokesperson Roger Fortier confirmed that Lynn was no longer employed with the company and that ISS was still working with Cisco on the matter. He gave a statement to the Washington Post saying "ISS and Cisco have been working on this in the background and didn't feel at this time that the material was ready for publication. The decision was made on Monday to pull the presentation because we wanted to make sure the research was fully baked."

Swap chain

In computer graphics, a swap chain (also swapchain) is a series of virtual framebuffers used by the graphics card and graphics API for frame rate stabilization, stutter reduction, and several other purposes. Because of these benefits, many graphics APIs require the use of a swap chain. The swap chain usually exists in graphics memory, but it can exist in system memory as well. A swap chain with two buffers is a kind of double buffer. == Function == In every swap chain there are at least two buffers. The first framebuffer, the screenbuffer, is the buffer that is rendered to the output of the video card. The remaining buffers are known as backbuffers. Each time a new frame is displayed, the first backbuffer in the swap chain takes the place of the screenbuffer, this is called presentation or swapping. A variety of other actions may be taken on the previous screenbuffer and other backbuffers (if they exist). The screenbuffer may be simply overwritten or returned to the back of the swap chain for further processing. The action taken is decided by the client application and is API dependent. == Direct3D == Microsoft Direct3D implements a SwapChain class. Each host device has at least one swap chain assigned to it, and others may be created by the client application. The API provides three methods of swapping: copy, discard, and flip. When the SwapChain is set to flip, the screenbuffer is copied onto the last backbuffer, then all the existing backbuffers are copied forward in the chain. When copy is set, each backbuffer is copied forward, but the screenbuffer is not wrapped to the last buffer, leaving it unchanged. Flip does not work when there is only one backbuffer, as the screenbuffer is copied over the only backbuffer before it can be presented. In discard mode, the driver selects the best method. == Comparison with triple buffering == Outside the context of Direct3D, triple buffering refers to the technique of allowing an application to draw to whichever back buffer was least recently updated. This allows the application to always proceed with rendering, regardless of the pace at which frames are being drawn by the application or the pace at which frames are being sent to the display. Triple buffering may result in a frame being discarded without being displayed if two or more newer frames are completely rendered in the time it takes for one frame to be sent to the display. By contrast, Direct3D swap chains are a strict first-in, first-out queue, so every frame that is drawn by the application will be displayed even if newer frames are available. Direct3D does not implement a most-recent buffer swapping strategy, and Microsoft's documentation calls a Direct3D swap chain of three buffers "triple buffering". Triple buffering as described above is superior for interactive purposes such as gaming, but Direct3D swap chains of more than three buffers can be better for tasks such as presenting frames of a video where the time taken to decode each frame may be highly variable.

WomanStats Project

The WomanStats Project is a donor-funded research and database project housed at Brigham Young University that "seeks to collect detailed statistical data on the status of women around the world, and to connect that data with data on the security of states." The WomanStats Database aims to provide a comprehensive compilation of information on the status of women in the world. Coders comb the extant literature and conduct expert interviews to find qualitative and quantitative information on over 300 indicators of women's status in 174 countries with populations of at least 200,000. Access to the online database is free. == History and structure == WomanStats began as an outgrowth of a paper Dr. Valerie M. Hudson (of the Brigham Young University Political Science department) and one of her graduate students, Andrea den Boer, published in International Security on the association between national security and the abnormal sex ratio in Asia. After the success and influence of their first article, (later added as one of their top twenty national security articles of that journal of all time), Hudson and den Boer did further research on the connection between the status of women and national security, but found that there was no single database that covered the range of topics that they needed for their research. Consequently, they began compiling information on variables regarding the status of women around the world. The database was officially formed in 2001 and grew exponentially as it later added more variables. The Project went live on the Internet in July 2007. The principal investigators are: Valerie M. Hudson (International Relations), Bonnie Ballif-Spanvill (Psychology, emeritus), and Chad F. Emmett (Geography) all from Brigham Young University, Mary Caprioli from the University of Minnesota, Duluth (International Relations), Rose McDermott from Brown University (International Relations), Andrea Den Boer from the University of Kent at Canterbury in the United Kingdom (International Relations) and S. Matthew Stearmer from the Ohio State University (Sociology; doctoral student). Approximately a dozen undergraduate and graduate students at Brigham Young University and Texas A&M University work at any one time as coders for the project. The coders take the raw quantitative and qualitative data collected in government reports, news articles, research papers, etc. and sort the applicable information on women into categories. They may also implement scales developed by the principal investigators, or that they (the students) themselves have developed. == Database == As of February 2011, the database has 307 variables, covers 174 nations with populations over 200,000, uses 18,015 sources and contains over 111,000 individual data points. All data is referenced to original sources. Not every variable has information for each country; similarly, not all countries have information for each variable: overall, about 70% of country-variable combinations have information. These database coding gaps exist where information is not available or is incomplete, or variables are not collected and reported by governments or international organizations. At times, information from different sources may be contradictory, and the WomanStats Database records this discrepant information for triangulation purposes. == Users and role of the database == The database is meant to help fill a hole in the extant data on the situation of women around the world. WomanStats data and research has been vetted and/or used by the United Nations, the United States Department of Defense, the Central Intelligence Agency, and the World Bank. Their data and research were also used by the United States Senate Committee on Foreign Relations in crafting the International Violence Against Women’s Act. The Inter-Agency Network on Women and Gender Equality (IANWGE) of the United Nations has stated that the WomanStats project "filled a major gap in the availability of data on women" (2007). Victor Asal and Mitchell Brown, researchers not affiliated with WomanStats, stated in an article published in Politics and Policy that "one of the most significant challenges of cross-national empirical studies of the prevalence of interpersonal violence is the paucity of available data, particularly reliable data," and that "WomanStats has allowed for an important first glimpse at analyzing the factors related to interpersonal violence." They conclude by stating that "Our findings suggest that, in the same way that larger disciplinary resources have invested in interstate and intrastate war, disciplinary resources need to be expended in creating a data set exploring interpersonal violence. Until the rights and the lives of women and children are taken as seriously as the survival of states by more proactively collaborating on projects like WomanStats, we will continue to only have a small lens through which to understand problems like this." Princeton University professor Evan S. Liberman wrote, "Although data on political regimes and group conflict have been in far greater demand by political scientists than data on gender politics and policies, two gender-related databases provide...examples of innovative HIRDs. Both the Womanstats database project (Hudson et al. 2009) and the Research Network on Gender Politics and the State (RNGS) project (McBride et al. 2008) are well-integrated presentations of quantitative and qualitative data characterizing the quality of gender relations around the world and, in particular, analytic descriptions of the treatment of women."." == Research == The research component of WomanStats focuses on exploring the relationship between the situation of women and the behavior and security of states. Current research initiatives include: Exploring the relationship between violent instability and inequity and family law. Examining the effect of polygyny and marriage market dislocations on the rise of suicide terrorism. Documenting discrepancies between laws on the books and cultural practices on the ground concerning gender issues. Investigating how well the situation of women predicts the peacefulness of nations-states, compared to their variables such as democracy, wealth, and civilization. The Project has published articles in International Security, International Studies Quarterly, Peace and Conflict, Journal of Peace Research, Political Psychology, Cumberland Law Review, and World Political Review, and has a forthcoming book from Columbia University Press.

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.