Color science is the scientific study of color including lighting and optics; measurement of light and color; the physiology, psychophysics, and modeling of color vision; and color reproduction. It is the modern extension of traditional color theory. == Organizations == International Commission on Illumination (CIE) Illuminating Engineering Society (IES) Inter-Society Color Council (ISCC) Society for Imaging Science and Technology (IS&T) International Colour Association (AIC) Optica, formerly the Optical Society of America (OSA) The Colour Group Society of Dyers and Colourists (SDC) American Association of Textile Chemists and Colorists (AATCC) Association for Research in Vision and Ophthalmology (ARVO) ACM SIGGRAPH Vision Sciences Society (VSS) Council for Optical Radiation Measurements (CORM) == Journals == The preeminent scholarly journal publishing research papers in color science is Color Research and Application, started in 1975 by founding editor-in-chief Fred Billmeyer, along with Gunter Wyszecki, Michael Pointer and Rolf Kuehni, as a successor to the Journal of Colour (1964–1974). Previously most color science work had been split between journals with broader or partially overlapping focus such as the Journal of the Optical Society of America (JOSA), Photographic Science and Engineering (1957–1984), and the Journal of the Society of Dyers and Colourists (renamed Coloration Technology in 2001). Other journals where color science papers are published include the Journal of Imaging Science & Technology, the Journal of Perceptual Imaging, the Journal of the International Colour Association (JAIC), the Journal of the Color Science Association of Japan, Applied Optics, and the Journal of Vision. == Conferences == Congress of the International Color Association IS&T Color and Imaging Conference (CIC) SIGGRAPH International Symposium for Color Science and Art == Selected books == Berns, Roy S. (2019). Billmeyer and Saltzman's Principles of Color Technology (4th ed.). Wiley. doi:10.1002/9781119367314. 3rd ed. (2000). Daw, Nigel (2012). How Vision Works: The Physiological Mechanisms Behind What We See. Oxford. doi:10.1093/acprof:oso/9780199751617.001.0001. Elliot, Andrew J.; Fairchild, Mark D.; Franklin, Anna, eds. (2015). Handbook of Color Psychology. Cambridge. doi:10.1017/CBO9781107337930. Fairchild, Mark D. (2013). Color Appearance Models (3rd ed.). Wiley. doi:10.1002/9781118653128. Author's website. 2nd ed. (2005). Hunt, Robert W. G. (2004). The Reproduction of Colour (6th ed.). Wiley. doi:10.1002/0470024275. Kuehni, Rolf G. (2012). Color: An Introduction to Practice and Principles (3rd ed.). Wiley. doi:10.1002/9781118533567. 1st ed. (1997). Luo, Ming R., ed. (2016). Encyclopedia of Color Science and Technology. Springer. doi:10.1007/978-1-4419-8071-7. MacAdam, David L., ed. (1970). Sources of Color Science. MIT Press. Reinhard, Erik; Khan, Erum Arif; Akyuz, Ahmet Oguz; Johnson, Garrett (2008). Color Imaging: Fundamentals and Applications. CRC Press. doi:10.1201/b10637. Schanda, János, ed. (2007). Colorimetry: Understanding the CIE System. Wiley. doi:10.1002/9780470175637. Shamey, Renzo; Kuehni, Rolf G. (2020). Pioneers of Color Science. Springer. doi:10.1007/978-3-319-30811-1. Wyszecki, Günter; Stiles, Walter S. (1982). Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley.
Kindara
Kindara is a femtech company headquartered in Colorado that develops apps that help women identify their fertile window. The products are used for women trying to get pregnant, or women who want to track their menstrual cycle for overall health. Their latest product, Priya Fertility and Ovulation Monitor, maximizes a woman's chance of getting pregnancy by identifying her most fertile days. == Overview == Kindara was founded in 2011 by husband-and-wife team Will Sacks and Kati Bicknell. The company launched its free mobile application in 2012. Kindara's mobile application allows women to track signs of fertility, such as basal body temperature, cervical fluid, and the position of the cervix to determine when ovulation is occurring. Kindara also sells a thermometer, Wink, which records basal body temperature and syncs automatically to the Kindara fertility application. In 2018, Kindara was acquired by the company Prima-Temp.
Prompt engineering
Prompt engineering is the process of structuring natural language inputs (known as prompts) to produce specified outputs from a generative artificial intelligence (GenAI) model. Context engineering is the related area of software engineering that focuses on the management of non-prompt contexts supplied to the GenAI model, such as metadata, API tools, and tokens. It can also be defined as the practice of designing and refining input instructions given to a generative AI model to produce more accurate, relevant, or useful outputs. Effective prompt engineering involves understanding how a model interprets language, and may include techniques such as few-shot prompting, chain-of-thought prompting, and role assignment. It is increasingly considered a skill for working with large language models (LLMs) in both research and professional contexts. During the 2020s AI boom, prompt engineering became regarded as a business capability across corporations and industries. Employees with the title prompt engineer were hired to create prompts that would increase productivity and efficacy, although the individual title has since lost traction amid AI models that produce better prompts than humans and corporate training in prompting for general employees. Common prompting techniques include multi-shot, chain-of-thought, and tree-of-thought prompting, as well as the use of assigning roles to the model. Automated prompt generation methods, such as retrieval-augmented generation (RAG), provide for greater accuracy and a wider scope of functions for prompt engineers. Prompt injection is a type of cybersecurity attack that targets machine learning models through malicious prompts. == Terminology == The Oxford English Dictionary defines prompt engineering as "The action or process of formulating and refining prompts for an artificial intelligence program, algorithm, etc., in order to optimize its output or to achieve a desired outcome; the discipline or profession concerned with this." In 2023, prompt ("an instruction given to an artificial intelligence program, algorithm, etc., which determines or influences the content it generates") was the runner-up to Oxford's word of the year. === Prompt === A prompt is some natural language text that describes and prescribes the task that an artificial intelligence (AI) should perform. A prompt for a text-to-text language model can be a query, a command, or a longer statement referencing context, instructions, and conversation history. The process of prompt engineering may involve designing clear queries, refining wording, providing relevant context, specifying the style of output, and assigning a character for the AI to mimic in order to guide the model toward more accurate, useful, and consistent responses. When communicating with a text-to-image or a text-to-audio model, a typical prompt contains a description of a desired output such as "a high-quality photo of an astronaut riding a horse" or "Lo-fi slow BPM electro chill with organic samples". Prompt engineering may be applied to text-to-image models to achieve a desired subject, style, layout, lighting, and aesthetic. === Techniques === Common terms used to describe various specific prompt engineering techniques include chain-of-thought, tree-of-thought, and retrieval-augmented generation (RAG). A 2024 survey of the field identified over 50 distinct text-based prompting techniques, 40 multimodal variants, and a vocabulary of 33 terms used across prompting research, highlighting a present lack of standardised terminology for prompt engineering. Vibe coding is an AI-assisted software development method where a user prompts an LLM with a description of what they want and lets it generate or edit the code. In 2025, "vibe coding" was the Collins Dictionary word of the year. === Context engineering === Context engineering is a related process that focuses on the context elements that accompany user prompts, which include system instructions, retrieved knowledge, tool definitions, conversation summaries, and task metadata. Context engineering is performed to improve reliability, provenance and token efficiency in production LLM systems. The concept emphasises operational practices such as token budgeting, provenance tags, versioning of context artifacts, observability (logging which context was supplied), and context regression tests to ensure that changes to supplied context do not silently alter system behaviour. == Rationale == Research has found that the performance of large language models (LLMs) is highly sensitive to choices such as the ordering of examples, the quality of demonstration labels, and even small variations in phrasing. In some cases, reordering examples in a prompt produced accuracy shifts of more than 40 percent. === In-context learning === A model's ability to temporarily learn from prompts is known as in-context learning. In-context learning is an emergent ability of large language models. It is an emergent property of model scale, meaning that breaks in scaling laws occur, leading to its efficacy increasing at a different rate in larger models than in smaller models. Unlike training and fine-tuning, which produce lasting changes, in-context learning is temporary. Training models to perform in-context learning can be viewed as a form of meta-learning, or "learning to learn". === Prompting to estimate model sensitivity === Research consistently demonstrates that LLMs are highly sensitive to subtle variations in prompt formatting, structure, and linguistic properties. Some studies have shown up to 76 accuracy points across formatting changes in few-shot settings. Linguistic features significantly influence prompt effectiveness—such as morphology, syntax, and lexico-semantic changes—which meaningfully enhance task performance across a variety of tasks. Clausal syntax, for example, improves consistency and reduces uncertainty in knowledge retrieval. This sensitivity persists even with larger model sizes, additional few-shot examples, or instruction tuning. To address sensitivity of models and make them more robust, several evaluative methods have been proposed. FormatSpread facilitates systematic analysis by evaluating a range of plausible prompt formats, offering a more comprehensive performance interval. Similarly, PromptEval estimates performance distributions across diverse prompts, enabling robust metrics such as performance quantiles and accurate evaluations under constrained budgets. == Prompting techniques == === Multi-shot === A prompt may include a few examples for a model to learn from in context, an approach called few-shot learning. For example, the prompt may ask the model to complete "maison → house, chat → cat, chien →", with the expected response being dog. === Chain-of-thought === Chain-of-thought (CoT) prompting is a technique that allows large language models (LLMs) to solve a problem as a series of intermediate steps before giving a final answer. In 2022, Google Brain reported that chain-of-thought prompting improves reasoning ability by inducing the model to answer a multi-step problem with steps of reasoning that mimic a train of thought. Chain-of-thought techniques were developed to help LLMs handle multi-step reasoning tasks, such as arithmetic or commonsense reasoning questions. When applied to PaLM, a 540 billion parameter language model, according to Google, CoT prompting significantly aided the model, allowing it to perform comparably with task-specific fine-tuned models on several tasks, achieving state-of-the-art results at the time on the GSM8K mathematical reasoning benchmark. It is possible to fine-tune models on CoT reasoning datasets to enhance this capability further and stimulate better interpretability. As originally proposed by Google, each CoT prompt is accompanied by a set of input/output examples—called exemplars—to demonstrate the desired model output, making it a few-shot prompting technique. However, according to a later paper from researchers at Google and the University of Tokyo, simply appending the words "Let's think step-by-step" was also effective, which allowed for CoT to be employed as a zero-shot technique. ==== Self-consistency ==== Self-consistency performs several chain-of-thought rollouts, then selects the most commonly reached conclusion out of all the rollouts. === Tree-of-thought === Tree-of-thought prompting generalizes chain-of-thought by generating multiple lines of reasoning in parallel, with the ability to backtrack or explore other paths. It can use tree search algorithms like breadth-first, depth-first, or beam. === Text-to-image prompting === In 2022, text-to-image models like DALL-E 2, Stable Diffusion, and Midjourney were released to the public. These models take text prompts as input and use them to generate images. Early text-to-image models typically do not understand negation, grammar and sentence structure in the same way as large language models, and may thus requi
Feature engineering
Feature engineering is a preprocessing step in supervised machine learning and statistical modeling which transforms raw data into a more effective set of inputs. Each input comprises several attributes, known as features. By providing models with relevant information, feature engineering significantly enhances their predictive accuracy and decision-making capability. Beyond machine learning, the principles of feature engineering are applied in various scientific fields, including physics. For example, physicists construct dimensionless numbers such as the Reynolds number in fluid dynamics, the Nusselt number in heat transfer, and the Archimedes number in sedimentation. They also develop first approximations of solutions, such as analytical solutions for the strength of materials in mechanics. == Clustering == One of the applications of feature engineering has been clustering of feature-objects or sample-objects in a dataset. Especially, feature engineering based on matrix decomposition has been extensively used for data clustering under non-negativity constraints on the feature coefficients. These include Non-Negative Matrix Factorization (NMF), Non-Negative Matrix-Tri Factorization (NMTF), Non-Negative Tensor Decomposition/Factorization (NTF/NTD), etc. The non-negativity constraints on coefficients of the feature vectors mined by the above-stated algorithms yields a part-based representation, and different factor matrices exhibit natural clustering properties. Several extensions of the above-stated feature engineering methods have been reported in literature, including orthogonality-constrained factorization for hard clustering, and manifold learning to overcome inherent issues with these algorithms. Other classes of feature engineering algorithms include leveraging a common hidden structure across multiple inter-related datasets to obtain a consensus (common) clustering scheme. An example is Multi-view Classification based on Consensus Matrix Decomposition (MCMD), which mines a common clustering scheme across multiple datasets. MCMD is designed to output two types of class labels (scale-variant and scale-invariant clustering), and: is computationally robust to missing information, can obtain shape- and scale-based outliers, and can handle high-dimensional data effectively. Coupled matrix and tensor decompositions are popular in multi-view feature engineering. == Predictive modelling == Feature engineering in machine learning and statistical modeling involves selecting, creating, transforming, and extracting data features. Key components include feature creation from existing data, transforming and imputing missing or invalid features, reducing data dimensionality through methods like Principal Components Analysis (PCA), Independent Component Analysis (ICA), and Linear Discriminant Analysis (LDA), and selecting the most relevant features for model training based on importance scores and correlation matrices. Features vary in significance. Even relatively insignificant features may contribute to a model. Feature selection can reduce the number of features to prevent a model from becoming too specific to the training data set (overfitting). Feature explosion occurs when the number of identified features is too large for effective model estimation or optimization. Common causes include: Feature templates - implementing feature templates instead of coding new features Feature combinations - combinations that cannot be represented by a linear system Feature explosion can be limited via techniques such as regularization, kernel methods, and feature selection. == Automation == Automation of feature engineering is a research topic that dates back to the 1990s. Machine learning software that incorporates automated feature engineering has been commercially available since 2016. Related academic literature can be roughly separated into two types: Multi-relational Decision Tree Learning (MRDTL) uses a supervised algorithm that is similar to a decision tree. Deep Feature Synthesis uses simpler methods. === Multi-relational Decision Tree Learning (MRDTL) === Multi-relational Decision Tree Learning (MRDTL) extends traditional decision tree methods to relational databases, handling complex data relationships across tables. It innovatively uses selection graphs as decision nodes, refined systematically until a specific termination criterion is reached. Most MRDTL studies base implementations on relational databases, which results in many redundant operations. These redundancies can be reduced by using techniques such as tuple id propagation. === Open-source implementations === There are a number of open-source libraries and tools that automate feature engineering on relational data and time series: featuretools is a Python library for transforming time series and relational data into feature matrices for machine learning. MCMD: An open-source feature engineering algorithm for joint clustering of multiple datasets. OneBM or One-Button Machine combines feature transformations and feature selection on relational data with feature selection techniques. OneBM helps data scientists reduce data exploration time allowing them to try and error many ideas in short time. On the other hand, it enables non-experts, who are not familiar with data science, to quickly extract value from their data with a little effort, time, and cost. getML community is an open source tool for automated feature engineering on time series and relational data. It is implemented in C/C++ with a Python interface. It has been shown to be at least 60 times faster than tsflex, tsfresh, tsfel, featuretools or kats. tsfresh is a Python library for feature extraction on time series data. It evaluates the quality of the features using hypothesis testing. tsflex is an open source Python library for extracting features from time series data. Despite being 100% written in Python, it has been shown to be faster and more memory efficient than tsfresh, seglearn or tsfel. seglearn is an extension for multivariate, sequential time series data to the scikit-learn Python library. tsfel is a Python package for feature extraction on time series data. kats is a Python toolkit for analyzing time series data. === Deep feature synthesis === The deep feature synthesis (DFS) algorithm beat 615 of 906 human teams in a competition. == Feature stores == The feature store is where the features are stored and organized for the explicit purpose of being used to either train models (by data scientists) or make predictions (by applications that have a trained model). It is a central location where you can either create or update groups of features created from multiple different data sources, or create and update new datasets from those feature groups for training models or for use in applications that do not want to compute the features but just retrieve them when it needs them to make predictions. A feature store includes the ability to store code used to generate features, apply the code to raw data, and serve those features to models upon request. Useful capabilities include feature versioning and policies governing the circumstances under which features can be used. Feature stores can be standalone software tools or built into machine learning platforms. == Alternatives == Feature engineering can be a time-consuming and error-prone process, as it requires domain expertise and often involves trial and error. Deep learning algorithms may be used to process a large raw dataset without having to resort to feature engineering. However, deep learning algorithms still require careful preprocessing and cleaning of the input data. In addition, choosing the right architecture, hyperparameters, and optimization algorithm for a deep neural network can be a challenging and iterative process.
Automated medical scribe
Automated medical scribes (also called artificial intelligence scribes, AI scribes, digital scribes, virtual scribes, ambient AI scribes, AI documentation assistants, and digital/virtual/smart clinical assistants) are tools for transcribing medical speech, such as patient consultations and dictated medical notes. Many also produce summaries of consultations. Automated medical scribes based on large language models (LLMs, commonly called "AI", short for "artificial intelligence") increased drastically in popularity in 2024. There are privacy and antitrust concerns. Accuracy concerns also exist, and intensify in situations in which tools try to go beyond transcribing and summarizing, and are asked to format information by its meaning, since LLMs do not deal well with meaning (see weak artificial intelligence). Medics using these scribes are generally expected to understand the ethical and legal considerations, and supervise the outputs. The privacy protections of automated medical scribes vary widely. While it is possible to do all the transcription and summarizing locally, with no connection to the internet, most closed-source providers require that data be sent to their own servers over the internet, processed there, and the results sent back (as with digital voice assistants). Some retailers say their tools use zero-knowledge encryption (meaning that the service provider can't access the data). Others explicitly say that they use patient data to train their AIs, or rent or resell it to third parties; the nature of privacy protections used in such situations is unclear, and they are likely not to be fully effective. Most providers have not published any safety or utility data in academic journals, and are not responsive to requests from medical researchers studying their products. == Privacy == Some providers unclear about what happens to user data. Some may sell data to third parties. Some explicitly send user data to for-profit tech companies for secondary purposes, which may not be specified. Some require users to sign consents to such reuse of their data. Some ingest user data to train the software, promising to anonymize it; however, deanonymization may be possible (that is, it may become obvious who the patient is). It is intrinsically impossible to prevent an LLM from correlating its inputs; they work by finding similar patterns across very large data sets. Some information on the patient will be known from other sources (for instance, information that they were injured in an incident on a certain day might be available from the news media; information that they attended specific appointment locations at specific times is probably available to their cellphone provider/apps/data brokers; information about when they had a baby is probably implied by their online shopping records; and they might mention lifestyle changes to their doctor and on a forum or blog). The software may correlate such information with the "anonymized" clinical consultation record, and, asked about the named patient, provide information which they only told their doctor privately. Because a patient's record is all about the same patient, it is all unavoidably linked; in very many cases, medical histories are intrinsically identifiable. Depending on how common a condition and what other data is available, K-anonymity may be useless. Differential privacy could theoretically preserve privacy. Data broker companies like Google, Amazon, Apple and Microsoft have produced or bought up medical scribes, some of which use user data for secondary purposes, which has led to antitrust concerns. Transfer of patient records for AI training has, in the past, prompted legal action. Open-source programs typically do all the transcription locally, on the doctor's own computer. Open-source software is widely used in healthcare, with some national public healthcare bodies holding hack days. === Data resale and commercialization === Several AI medical scribe providers include terms in their service agreements that allow the reuse, sale, or commercialization of de-identified or user-submitted data. Although such data are generally described as anonymized or aggregated, these practices have raised ethical concerns among clinicians and privacy advocates regarding secondary uses of medical information beyond clinical documentation. Freed, an AI transcription and scribe platform, states in its Terms of Use that it may "collect, use, publish, disseminate, sell, transfer, and otherwise exploit" de-identified and aggregated data derived from user inputs. OpenEvidence similarly states that it may "collect, use, transfer, sell, and disclose non-personal information and customer usage data for any purpose including commercial uses." Doximity, which offers an AI-enabled medical scribe as part of its physician platform, grants itself a "nonexclusive, irrevocable, worldwide, perpetual, unlimited, assignable, sublicensable, royalty-free" license to "copy, prepare derivative works from, improve, distribute, publish, ... analyze, index, tag, [and] commercialize" content submitted by users, subject to its privacy policy. Because these terms allow broad secondary use—including sale, licensing, model-training, derivative works, and commercial exploitation of de-identified or user-submitted data—some commentators have recommended that clinicians review data-handling provisions carefully when adopting AI-scribe tools, particularly in clinical environments where patient privacy and regulatory compliance are critical. === Encryption === Multifactor authentication for access to the data is expected practice. Typically, Diffie–Hellman key exchange is used for encryption; this is the standard method commonly used for things like online banking. This encryption is expensive but not impossible to break; it is not generally considered safe against eavesdroppers with the resources of a nation-state. If content is encrypted between the client and the service provider's remote server (transport cryptography), then the server has an unencrypted copy. This is necessary if the data is used by the service provider (for instance, to train the software). Zero-knowledge encryption implies that the only unencrypted copy is at the client, and the server cannot decrypt the data any more easily than a monster-in-the-middle attacker. == Platforms == Scribes may operate on desktops, laptop, or mobile computers, under a variety of operating systems. These vary in their risks; for instance, mobiles can be lost. The underlying mobile or desktop operating systems are also part of the trusted computing base, and if they are not secure, the software relying on them cannot be secure either. Some AI medical scribe platforms are designed to operate as cloud-based applications that generate structured clinical documentation from clinician–patient conversations. These systems may offer features such as real-time transcription, document generation, and integration with electronic health record (EHR) systems. == Confabulation, omissions, and other errors == Like other LLMs, medical-scribe LLMs are prone to hallucinations, where they make up content based on statistically associations between their training data and the transcription audio. LLMs do not distinguish between trying to transcribe the audio and guessing what words will come next, but perform both processes mixed together. They are especially likely to take short silences or non-speech noises and invent some sort of speech to transcribe them as. LLM medical scribes have been known to confabulate racist and otherwise prejudiced content; this is partly because the training datasets of many LLMs contain pseudoscientific texts about medical racism. They may misgender patients. A survey found that most doctors preferred, in principle, that scribes be trained on data reviewed by medical subject experts. Relevant, accurate training data increases the probability of an accurate transcription, but does not guarantee accuracy. Software trained on thousands of real clinical conversations generated transcripts with lower word error rates. Software trained on manually-transcribed training data did better than software trained with automatically transcribed training data such as YouTube captions. Autoscribes omit parts of the conversation classes as irrelevant. The may wrongly classify pertinent information as irrelevant and omit it. They may also confuse historic and current symptoms, or otherwise misclassify information. They may also simply wrongly transcribe the speech, writing something incorrect instead. If clinicians do not carefully check the recording, such mistakes could make their way into their medical records and cause patient harms. == Patient consent == Professional organizations generally require that scribes be used only with patient consent; some bodies may require written consent. Medics must also abide by local surveillance laws, which may criminalize recording pri
Geometric primitive
In vector computer graphics, CAD systems, and geographic information systems, a geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (draw, store). Sometimes the subroutines that draw the corresponding objects are called "geometric primitives" as well. The most "primitive" primitives are point and straight line segments, which were all that early vector graphics systems had. In constructive solid geometry, primitives are simple geometric shapes such as a cube, cylinder, sphere, cone, pyramid, torus. Modern 2D computer graphics systems may operate with primitives which are curves (segments of straight lines, circles and more complicated curves), as well as shapes (boxes, arbitrary polygons, circles). A common set of two-dimensional primitives includes lines, points, and polygons, although some people prefer to consider triangles primitives, because every polygon can be constructed from triangles (polygon triangulation). All other graphic elements are built up from these primitives. In three dimensions, triangles or polygons positioned in three-dimensional space can be used as primitives to model more complex 3D forms. In some cases, curves (such as Bézier curves, circles, etc.) may be considered primitives; in other cases, curves are complex forms created from many straight, primitive shapes. == Common primitives == The set of geometric primitives is based on the dimension of the region being represented: Point (0-dimensional), a single location with no height, width, or depth. Line or curve (1-dimensional), having length but no width, although a linear feature may curve through a higher-dimensional space. Planar surface or curved surface (2-dimensional), having length and width. Volumetric region or solid (3-dimensional), having length, width, and depth. In GIS, the terrain surface is often spoken of colloquially as "2 1/2 dimensional," because only the upper surface needs to be represented. Thus, elevation can be conceptualized as a scalar field property or function of two-dimensional space, affording it a number of data modeling efficiencies over true 3-dimensional objects. A shape of any of these dimensions greater than zero consists of an infinite number of distinct points. Because digital systems are finite, only a sample set of the points in a shape can be stored. Thus, vector data structures typically represent geometric primitives using a strategic sample, organized in structures that facilitate the software interpolating the remainder of the shape at the time of analysis or display, using the algorithms of Computational geometry. A Point is a single coordinate in a Cartesian coordinate system. Some data models allow for Multipoint features consisting of several disconnected points. A Polygonal chain or Polyline is an ordered list of points (termed vertices in this context). The software is expected to interpolate the intervening shape of the line between adjacent points in the list as a parametric curve, most commonly a straight line, but other types of curves are frequently available, including circular arcs, cubic splines, and Bézier curves. Some of these curves require additional points to be defined that are not on the line itself, but are used for parametric control. A Polygon is a polyline that closes at its endpoints, representing the boundary of a two-dimensional region. The software is expected to use this boundary to partition 2-dimensional space into an interior and exterior. Some data models allow for a single feature to consist of multiple polylines, which could collectively connect to form a single closed boundary, could represent a set of disjoint regions (e.g., the state of Hawaii), or could represent a region with holes (e.g., a lake with an island). A Parametric shape is a standardized two-dimensional or three-dimensional shape defined by a minimal set of parameters, such as an ellipse defined by two points at its foci, or three points at its center, vertex, and co-vertex. A Polyhedron or Polygon mesh is a set of polygon faces in three-dimensional space that are connected at their edges to completely enclose a volumetric region. In some applications, closure may not be required or may be implied, such as modeling terrain. The software is expected to use this surface to partition 3-dimensional space into an interior and exterior. A triangle mesh is a subtype of polyhedron in which all faces must be triangles, the only polygon that will always be planar, including the Triangulated irregular network (TIN) commonly used in GIS. A parametric mesh represents a three-dimensional surface by a connected set of parametric functions, similar to a spline or Bézier curve in two dimensions. The most common structure is the Non-uniform rational B-spline (NURBS), supported by most CAD and animation software. == Application in GIS == A wide variety of vector data structures and formats have been developed during the history of Geographic information systems, but they share a fundamental basis of storing a core set of geometric primitives to represent the location and extent of geographic phenomena. Locations of points are almost always measured within a standard Earth-based coordinate system, whether the spherical Geographic coordinate system (latitude/longitude), or a planar coordinate system, such as the Universal Transverse Mercator. They also share the need to store a set of attributes of each geographic feature alongside its shape; traditionally, this has been accomplished using the data models, data formats, and even software of relational databases. Early vector formats, such as POLYVRT, the ARC/INFO Coverage, and the Esri shapefile support a basic set of geometric primitives: points, polylines, and polygons, only in two dimensional space and the latter two with only straight line interpolation. TIN data structures for representing terrain surfaces as triangle meshes were also added. Since the mid 1990s, new formats have been developed that extend the range of available primitives, generally standardized by the Open Geospatial Consortium's Simple Features specification. Common geometric primitive extensions include: three-dimensional coordinates for points, lines, and polygons; a fourth "dimension" to represent a measured attribute or time; curved segments in lines and polygons; text annotation as a form of geometry; and polygon meshes for three-dimensional objects. Frequently, a representation of the shape of a real-world phenomenon may have a different (usually lower) dimension than the phenomenon being represented. For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes a conceptual model of the cities as points, while giving directions involving travel "up," "down," or "along" a road imply a one-dimensional conceptual model. This is frequently done for purposes of data efficiency, visual simplicity, or cognitive efficiency, and is acceptable if the distinction between the representation and the represented is understood, but can cause confusion if information users assume that the digital shape is a perfect representation of reality (i.e., believing that roads really are lines). == In 3D modelling == In CAD software or 3D modelling, the interface may present the user with the ability to create primitives which may be further modified by edits. For example, in the practice of box modelling the user will start with a cuboid, then use extrusion and other operations to create the model. In this use the primitive is just a convenient starting point, rather than the fundamental unit of modelling. A 3D package may also include a list of extended primitives which are more complex shapes that come with the package. For example, a teapot is listed as a primitive in 3D Studio Max. == In graphics hardware == Various graphics accelerators exist with hardware acceleration for rendering specific primitives such as lines or triangles, frequently with texture mapping and shaders. Modern 3D accelerators typically accept sequences of triangles as triangle strips.
Problem solving
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to get from point A to B) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for. Similarly, one may distinguish formal or fact-based problems requiring psychometric intelligence, versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as tactful behavior, fashion, or gift choices. Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a scalable solution. There are many specialized problem-solving techniques and methods in fields such as science, engineering, business, medicine, mathematics, computer science, philosophy, and social organization. The mental techniques to identify, analyze, and solve problems are studied in psychology and cognitive sciences. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include confirmation bias, mental set, and functional fixedness. == Definition == The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems. Solving problems sometimes involves dealing with pragmatics (the way that context contributes to meaning) and semantics (the interpretation of the problem). The ability to understand what the end goal of the problem is, and what rules could be applied, represents the key to solving the problem. Sometimes a problem requires abstract thinking or coming up with a creative solution. Problem solving has two major domains: mathematical problem solving and personal problem solving. Each concerns some difficulty or barrier that is encountered. === Psychology === Problem solving in psychology refers to the process of finding solutions to problems encountered in life. Solutions to these problems are usually situation- or context-specific. The process starts with problem finding and problem shaping, in which the problem is discovered and simplified. The next step is to generate possible solutions and evaluate them. Finally a solution is selected to be implemented and verified. Problems have an end goal to be reached; how you get there depends upon problem orientation (problem-solving coping style and skills) and systematic analysis. Mental health professionals study the human problem-solving processes using methods such as introspection, behaviorism, simulation, computer modeling, and experiment. Social psychologists look into the person-environment relationship aspect of the problem and independent and interdependent problem-solving methods. Problem solving has been defined as a higher-order cognitive process and intellectual function that requires the modulation and control of more routine or fundamental skills. Empirical research shows many different strategies and factors influence everyday problem solving. Rehabilitation psychologists studying people with frontal lobe injuries have found that deficits in emotional control and reasoning can be re-mediated with effective rehabilitation and could improve the capacity of injured persons to resolve everyday problems. Interpersonal everyday problem solving is dependent upon personal motivational and contextual components. One such component is the emotional valence of "real-world" problems, which can either impede or aid problem-solving performance. Researchers have focused on the role of emotions in problem solving, demonstrating that poor emotional control can disrupt focus on the target task, impede problem resolution, and lead to negative outcomes such as fatigue, depression, and inertia. In conceptualization,human problem solving consists of two related processes: problem orientation, and the motivational/attitudinal/affective approach to problematic situations and problem-solving skills. People's strategies cohere with their goals and stem from the process of comparing oneself with others. === Cognitive sciences === Among the first experimental psychologists to study problem solving were the Gestaltists in Germany, such as Karl Duncker in The Psychology of Productive Thinking (1935). Perhaps best known is the work of Allen Newell and Herbert A. Simon. Experiments in the 1960s and early 1970s asked participants to solve relatively simple, well-defined, but not previously seen laboratory tasks. These simple problems, such as the Tower of Hanoi, admitted optimal solutions that could be found quickly, allowing researchers to observe the full problem-solving process. Researchers assumed that these model problems would elicit the characteristic cognitive processes by which more complex "real world" problems are solved. An outstanding problem-solving technique found by this research is the principle of decomposition. === Computer science === Much of computer science and artificial intelligence involves designing automated systems to solve a specified type of problem: to accept input data and calculate a correct or adequate response, reasonably quickly. Algorithms are recipes or instructions that direct such systems, written into computer programs. Steps for designing such systems include problem determination, heuristics, root cause analysis, de-duplication, analysis, diagnosis, and repair. Analytic techniques include linear and nonlinear programming, queuing systems, and simulation. A large, perennial obstacle is to find and fix errors in computer programs: debugging. === Logic === Formal logic concerns issues like validity, truth, inference, argumentation, and proof. In a problem-solving context, it can be used to formally represent a problem as a theorem to be proved, and to represent the knowledge needed to solve the problem as the premises to be used in a proof that the problem has a solution. The use of computers to prove mathematical theorems using formal logic emerged as the field of automated theorem proving in the 1950s. It included the use of heuristic methods designed to simulate human problem solving, as in the Logic Theory Machine, developed by Allen Newell, Herbert A. Simon and J. C. Shaw, as well as algorithmic methods such as the resolution principle developed by John Alan Robinson. In addition to its use for finding proofs of mathematical theorems, automated theorem-proving has also been used for program verification in computer science. In 1958, John McCarthy proposed the advice taker, to represent information in formal logic and to derive answers to questions using automated theorem-proving. An important step in this direction was made by Cordell Green in 1969, who used a resolution theorem prover for question-answering and for such other applications in artificial intelligence as robot planning. The resolution theorem-prover used by Cordell Green bore little resemblance to human problem solving methods. In response to criticism of that approach from researchers at MIT, Robert Kowalski developed logic programming and SLD resolution, which solves problems by problem decomposition. He has advocated logic for both computer and human problem solving and computational logic to improve human thinking. === Engineering === When products or processes fail, problem solving techniques can be used to develop corrective actions that can be taken to prevent further failures. Such techniques can also be applied to a product or process prior to an actual failure event—to predict, analyze, and mitigate a potential problem in advance. Techniques such as failure mode and effects analysis can proactively reduce the likelihood of problems. In either the reactive or the proactive case, it is necessary to build a causal explanation through a process of diagnosis. In deriving an explanation of effects in terms of causes, abduction generates new ideas or hypothes