title: Shilling

text: The Somaliland shilling is the official currency of Somaliland, a self-declared republic that is internationally recognised as an autonomous region of Somalia. The currency is not recognised as legal tender by the international community, and it currently has no official exchange rate. It is regulated by the Bank of Somaliland, Somaliland's central bank. Although the authorities in Somaliland have attempted to bar usage of the Somali shilling, Somalia's official currency is still in circulation in some regions.


title: Shilling

text: In Vanuatu and Solomon Islands, "selen" is used in Bislama and Pijin to mean "money"; in Malaysia, "syiling" (pronounced like "shilling") means "coin". In Egypt and Jordan the "shillin" () is equal to 1/20 (five "qirshes" — , ) of the Egyptian pound or the Jordanian dinar. In Belize, the term "shilling" is commonly used to refer to twenty-five cents.


title: Sergei Pavlovich

text: Sergei Vladimirovich Pavlovich (born 13 May 1992) is a Russian professional mixed martial artist. He was the former Fight Nights Global heavyweight champion and currently competes in the Heavyweight division in the Ultimate Fighting Championship (UFC). As of December 6, 2022, he is #3 in the UFC heavyweight rankings.


title: Sergei Pavlovich

text: Sergei was born in 1992 in the village of Orlovsky, Rostov Oblast. At the age of 5, Pavlovich began to engage in Greco-Roman wrestling under the guidance of coach Alexander Fedorovich Aloyan. He was engaged in wrestling until the 11th grade. After serving in the army, he began to engage in army hand-to-hand fighting and combat sambo.


title: Sergei Pavlovich

text: Pavlovich started his professional MMA career in 2014 under the Fight Nights Global promotion, under which he won 12 fights without suffering a single defeat. On June 2, 2017, in a fight against Mikhail Mokhnatkin, he won the heavyweight title by unanimous decision. On November 19, 2017, he defended his heavyweight title in a fight against Kirill Sidelnikov.


title: Sergei Pavlovich

text: Pavlovich made his UFC debut on 24 November 2018 at UFC Fight Night 141 against Alistair Overeem. He lost the fight via TKO in the first round.


title: Sergei Pavlovich

text: Pavlovich faced Marcelo Golm on April 20, 2019, at . He won the fight via knockout. This win earned "Performance of the Night" award.


title: Sergei Pavlovich

text: Pavlovich faced Maurice Greene on October 26, 2019, at UFC Fight Night 162. He won the fight via knockout in the first round.


title: Sergei Pavlovich

text: Pavlovich was expected to face Ciryl Gane on August 8, 2020, at UFC Fight Night 174. Pavlovich however had to pull out because of an injury.


title: Sergei Pavlovich

text: Pavlovich was expected to face Tom Aspinall on September 4, 2021, at UFC Fight Night 191. However, Pavlovich pulled out a week before the contest due to visa issues and was replaced by Sergey Spivak.


title: Sergei Pavlovich

text: Pavlovich was scheduled to face Tanner Boser on December 4, 2021 at UFC on ESPN 31. However due to travel issues, the bout was scrapped.


title: Sergei Pavlovich

text: Pavlovich faced Shamil Abdurakhimov on March 19, 2022 at UFC Fight Night 204. He won the fight via technical knockout in round one. With this win, he received the "Performance of the Night" award.


title: Sergei Pavlovich

text: Pavlovich fought Derrick Lewis on July 30, 2022 at UFC 277. He won the fight via TKO under a minute into the first round, though controversy arose as the stoppage by the referee was considered premature by fighters and fans alike.


title: Sergei Pavlovich

text: Pavlovich faced Tai Tuivasa on December 3, 2022, at UFC on ESPN 42. He won the fight via KO under a minute into the first round. With this win, he received the "Performance of the Night" award.


title: Mary Ellen Trainor

text: Mary Ellen Trainor (July 8, 1952 – May 20, 2015) was an American character actress best known for her roles as LAPD psychiatrist Dr. Stephanie Woods in the "Lethal Weapon" films, newscaster Gail Wallens in "Die Hard" and "Ricochet", and working mother Irene Walsh in "The Goonies". She also appeared in numerous other well-known films including "Romancing the Stone", "The Monster Squad", "Death Becomes Her", "Forrest Gump", and "Freaky Friday" (2003).


title: Mary Ellen Trainor

text: Trainor started her career working at radio stations KSDO as well as KCBS. Her first television appearance came in the 1983 "Cheers" episode "Father Knows Last", and her big-screen debut came the following year in "Romancing the Stone". She frequently appeared in the films of Richard Donner and her ex-husband Robert Zemeckis.


title: Mary Ellen Trainor

text: In addition to her film work she had recurring television roles as Judy Lewis in "Parker Lewis Can't Lose" (1989–1991), as Eve Lukens in "Relativity" (1996–1997), and as Diane Evans in "Roswell" (1999–2002).


title: Mary Ellen Trainor

text: She has appeared in three films that have been selected for the National Film Registry by the Library of Congress as being "culturally, historically or aesthetically" significant: "The Goonies" (1985), "Die Hard" (1988) and "Forrest Gump" (1994).


title: Mary Ellen Trainor

text: Trainor was married to director Robert Zemeckis for 20 years, with whom she had a son, Alexander. She was good friends with producer Kathleen Kennedy, who worked with Steven Spielberg extensively and serves as President of Lucasfilm. Trainor introduced the two.


title: Mary Ellen Trainor

text: Trainor died on May 20, 2015, at her home in Montecito, California, from complications of pancreatic cancer. She was 62 years old.


title: Joey Travolta

text: Joseph Allen Travolta (born October 14, 1950) is an American actor, singer, producer, director and screenwriter. He is the older brother of actor John Travolta.


title: Joey Travolta

text: Travolta was born and raised in Englewood, New Jersey, a nearby suburb of New York City, where he attended Dwight Morrow High School. His father, Salvatore Travolta, was a semi-professional football player turned tire salesman and partner in a tire company. His mother, Helen Cecilia (née Burke; 1912–1978), was an actress and singer who had appeared in "The Sunshine Sisters", a radio vocal group, and acted and directed before becoming a high school drama and English teacher. His father was a second-generation Italian American and his mother was Irish American. He is one of six children including actors John Travolta, Ellen Travolta and Margaret Travolta.


title: Joey Travolta

text: Travolta began a singing career in 1978 as a recording artist on Casablanca Records, releasing his eponymous album. The following year he made his acting debut starring in the feature film "Sunnyside" for Filmways Productions. He then became a guest star in the 1980s television show "Simon & Simon" (episode: "The Hottest Ticket in Town").


title: Joey Travolta

text: Additional acting credits include work with director John Landis on multiple feature film projects: "Amazon Women on the Moon" (1987), "Beverly Hills Cop III" (1994), "Oscar" (1991), and "Susan's Plan" (1998). He was also a series regular on the WB television hit "Movie Stars" (1999).


title: Joey Travolta

text: Stage performances include starring roles in "Bye Bye Birdie", "Guys and Dolls", and "West Side Story". He wrote and directed "Diva Las Vegas" in 1989, which went on to win the Italian Funny Film Festival.


title: Joey Travolta

text: In 1991, Joey Travolta produced and starred in "Da Vinci's War". He later produced and starred in the sequel, "To the Limit" (1995). He made directing his main priority in 1994. He directed the action thrillers "Hard Vice" (1994) and "Navajo Blues" (1996). Subsequent titles include "Earth Minus Zero" (1996), "Laws of Deception" (1997), "Detour" (1999), "Mel" (1996), "Partners" (2000), "Enemies of Laughter" (2000), and "Waiting to Live" (2002).


title: Joey Travolta

text: For television audiences he directed the police drama "L.A. Heat" (1999), "Friday Night After the Movies" (2010), and the syndicated Disney series "" (2007). He has directed music videos as well such as Aqua's "Doctor Jones" and Latvia's entry, in Eurovision Song Contest 2008, "Pirates of the Sea".


title: Joey Travolta

text: Travolta has worked as a special education teacher in New Jersey. In 2005, he produced a documentary film called Normal People Scare Me, directed by a 15 old boy with autism whom he mentored. Around this time, he founded Inclusion Films, which involve individuals with special needs in the process of making films.


title: Joey Travolta

text: He has collaborated with a non-profit organization called HEAL to form a Jacksonville, Florida based "HEAL Film Camp with Joey Travolta".


title: Joey Travolta

text: In 2019, Travolta directed "Carol of the Bells" for Inclusion Films starring R.J. Mitte as an adoptee who discovers his biological mother has Down Syndrome. 70% of the crew had developmental disabilities. The film won the Audience Award for Best Feature at the 2019 San Diego International Film Festival. His next feature film titled "Let's Work" premiered at SDIFF in the documentary competition in October 2020.


title: Joey Travolta

text: Travolta is married to Wendy Shawn (daughter of comedian Dick Shawn) and they have one daughter, Rachel.


title: Change management

text: Change management (sometimes abbreviated as CM) is a collective term for all approaches to prepare, support, and help individuals, teams, and organizations in making organizational change. It includes methods that redirect or redefine the use of resources, business process, budget allocations, or other modes of operation that significantly change a company or organization.


title: Change management

text: Organizational change management (OCM) considers the full organization and what needs to change, while change management may be used solely to refer to how people and teams are affected by such organizational transition. It deals with many different disciplines, from behavioral and social sciences to information technology and business solutions.


title: Change management

text: As change management becomes more necessary in the business cycle of organizations, it is beginning to be taught as its own academic discipline at universities. There are a growing number of universities with research units dedicated to the study of organizational change. One common type of organizational change may be aimed at reducing outgoing costs while maintaining financial performance, in an attempt to secure future profit margins.


title: Change management

text: In a project-management context, the term "change management" may be used as an alternative to change control processes wherein changes to the scope of a project are formally introduced and approved.


title: Change management

text: Drivers of change may include the ongoing evolution of technology, internal reviews of processes, crisis response, customer demand changes, competitive pressure, acquisitions and mergers, and organizational restructuring.


title: Change management

text: Kurt Lewin was a social scientist who researched learning and social conflict. Lewin's first venture into change management started with researching field theory in 1921. Five years later, Lewin would begin a series consisting of about 20 articles to explain field theory. He would go on and publish "Principles of Topological Psychology" in 1936, which was Lewin's most in depth look at field theory. Shortly before his death, Lewin would write two articles called "Human Relations" which are the foundation of his three-step model.


title: Change management

text: In 1934, Lewin set up a proposal to create an action research-orientated department of psychology at the Hebrew University of Jerusalem. Shortly after, Lewin moved to America and started up other action research initiatives with children, housewives, religious groups, racial intolerance, and leadership. During this time, Lewin became the first psychologist to study group dynamics. His definition of a "group" from this project is still used today; "It is not the similarity or dissimilarity of individuals that constitutes a group, but interdependence of fate".


title: Change management

text: Many change management models and processes are based with their roots in grief studies. As consultants saw a correlation between grieving from health-related issues and grieving among employees in an organization due to loss of jobs and departments, many early change models captured the full range of human emotions as employees mourned job-related transitions.


title: Change management

text: In his work on diffusion of innovations, Everett Rogers posited that change must be understood in the context of time, communication channels, and its impact on all affected participants. Placing people at the core of change thinking was a fundamental contribution to developing the concept of change management. He proposed the descriptive Adopter groups of how people respond to change: Innovators, Early Adopters, Early Majority, Late Majority and Laggards.


title: Change management

text: McKinsey & Company consultant Julien Phillips published a change management model in 1982 in the journal "Human Resource Management".


title: Change management

text: Robert Marshak has since credited the big six accounting and consulting firms with adopting the work of early organizational change pioneers, such as Daryl Conner and Don Harrison, thereby contributing to the legitimization of a whole "change management industry" when they branded their re-engineering services as "change management" in the 1980s.


title: Change management

text: In his 1993 book, "Managing at the Speed of Change", Daryl Conner coined the term "'burning platform"' based on the 1988 North Sea Piper Alpha oil rig fire. He went on to found Conner Partners in 1994, focusing on the human performance and adoption techniques that would help ensure technology innovations were absorbed and adopted as best as possible. The first "State of the Change Management Industry" report was published in the "Consultants News" in February 1995.


title: Change management

text: Linda Ackerman Anderson states in "Beyond Change Management" that in the late 1980s and early 1990s, top leaders, growing dissatisfied with the failures of creating and implementing changes in a top-down fashion, created the role of the change leader to take responsibility for the human side of change.


title: Change management

text: In response to lack of understanding in how to manage change in large projects and programs of work, Christina Dean (author of RIMER Managing Successful Change Professional Edition), established the Australian Government National Competency Standards at Diploma Level, and RIMER as the Australian National Competency Standard Certification. RIMER is a Project Based approach to managing change, which introduced the concept of Enterprise Change Management. Christina also influenced the Human Resource Management Institute and Project Management Institute Industry Associations to include Change Management in their Academic programmes to Masters Level. By 2016, all Australian Universities offered programs that provided a formal vocational pathway, through a HRM or Project Management.


title: Change management

text: In response to continuing reports of the failure of large-scale top-down plan-driven change programmes, innovative change practitioners have been reporting success with applying Lean and Agile principles to the field of change management.


title: Change management

text: The Lean Change Management Association became the world's first global organization to offer trainings designed to apply Lean Startup, Agile, and Design Thinking principles to change.


title: Change management

text: The Association of Change Management Professionals (ACMP) announced a new certification to enhance the profession: Certified Change Management Professional (CCMP) in 2016.


title: Change management

text: Organizational change management employs a structured approach to ensure that changes are documented and implemented smoothly and successfully to achieve lasting benefits.


title: Change management

text: Globalization and accelerated innovation of technology result in a constantly evolving business environment. Phenomena such as social media and mobile adaptability have revolutionized business and the effect of this is an ever-increasing need for change, and therefore change management. The growth in technology also has a secondary effect of increasing the availability and therefore accountability of knowledge. Easily accessible information has resulted in unprecedented scrutiny from stockholders and the media and pressure on management. With the business environment experiencing so much change, organizations must then learn to become comfortable with change as well. Therefore, the ability to manage and adapt to organizational change is an essential ability required in the workplace today. However, major and rapid organizational change is profoundly difficult because the structure, culture, and routines of organizations often reflect a persistent and difficult-to-remove "imprint" of past periods, which are resistant to radical change even as the current environment of the organization changes rapidly.


title: Change management

text: Due to the growth of technology, modern organizational change is largely motivated by exterior innovations rather than internal factors. When these developments occur, the organizations that adapt quickest create a competitive advantage for themselves, while the companies that refuse to change get left behind. This can result in drastic profit and/or market share losses. Organizational change directly affects all departments and employees. The entire company must learn how to handle changes to the organization. The effectiveness of change management can have a strong positive or negative impact on employee morale.


title: Change management

text: Jason began developing Lean Change Management in 2009 as a response to outdated traditional change management approaches designed in a pre-digital world.


title: Change management

text: John P. Kotter, the Konosuke Matsushita Professor of Leadership, Emeritus, at the Harvard Business School is considered the most influential expert of change management. He invented the 8-Step Process for Leading Change. It consists of eight stages:


title: Change management

text: These steps are very much tied to Lewin's model and build upon his simplistic process of creating change. They follow the same general steps of Lewin's model: Unfreezing, Changing, and Refreezing.


title: Change management

text: The Change Management Foundation is shaped like a pyramid with project management managing technical aspects and people implementing change at the base and leadership setting the direction at the top. The Change Management Model consists of four stages:


title: Change management

text: The Prosci ADKAR Model is an individual change framework created by Jeff Hiatt. ADKAR is an acronym that represents the five building blocks of successful change for an individual:


title: Change management

text: The ADKAR Model is prescriptive and goal-oriented, each milestone must be achieved to define success. It uses a 1–5 scale to determine how strongly an individual meets the requirements of each milestone. If a person scores a three or below, that specific step must be addressed before moving forward, Prosci defines this as a barrier point.


title: Change management

text: The Plan-Do-Check-Act Cycle, created by W. Edwards Deming, is a management method to improve business method for control and continuous improvement of choosing which changes to implement. When determining which of the latest techniques or innovations to adopt, there are four major factors to be considered:


title: Change management

text: Although there are many types of organizational changes, the critical aspect is a company's ability to win the buy-in of their organization's employees on the change. Effectively managing organizational change is a four-step process:


title: Change management

text: As a multi-disciplinary practice that has evolved as a result of scholarly research, organizational change management should begin with a systematic diagnosis of the current situation in order to determine both the need for change and the capability to change. The objectives, content, and process of change should all be specified as part of a change management plan. Change management processes should include creative marketing to enable communication between changing audiences, as well as deep social understanding about leadership styles and group dynamics. As a visible track on transformation projects, organizational change management aligns groups' expectations, integrates teams, and manages employee training. It makes use of performance metrics, such as financial results, operational efficiency, leadership commitment, communication effectiveness, and the perceived need for change in order to design appropriate strategies, resolve troubled change projects, and avoid change failures.


title: Change management

text: Change management is faced with the fundamental difficulties of integration and navigation, and human factors. Change management must also take into account the human aspect where emotions and how they are handled play a significant role in implementing change successfully.


title: Change management

text: Traditionally, organizational development (OD) departments overlooked the role of infrastructure and the possibility of carrying out change through technology. Now, managers almost exclusively focus on the structural and technical components of change. Alignment and integration between strategic, social, and technical components requires collaboration between people with different skill-sets.


title: Change management

text: Managing change over time, referred to as navigation, requires continuous adaptation. It requires managing projects over time against a changing context, from interorganizational factors to marketplace volatility. It also requires a balance in bureaucratic organizations between top-down and bottom-up management, ensuring employee empowerment and flexibility.


title: Change management

text: One of the major factors which hinders the change management process is people's natural tendency for inertia. Just as in Newton's first law of motion, people are resistant to change in organizations because it can be uncomfortable. The notion of doing things this way, because 'this is the way we have always done them', can be particularly hard to overcome. Furthermore, in cases where a company has seen declining fortunes, for a manager or executive to view themselves as a key part of the problem can be very humbling. This issue can be exacerbated in countries where "saving face" plays a large role in inter-personal relations. As mentioned above, there are some groups that prioritize their own benefits above organizations' benefits, and involving such groups into organizational change will naturally create obstacles, and some departments may directly or indirectly resist organizational change due to the conflicts of their interests.


title: Change management

text: To assist with this, a number of models have been developed which help identify their readiness for change and then to recommend the steps through which they could move. A common example is ADKAR, an acronym which stands for Awareness, Desire, Knowledge, Ability and Reinforcement. This model was developed by researcher and entrepreneur Jeff Hiatt in 1996 and first published in a white paper entitled "The Perfect Change" in 1999. Hiatt explained that the process of becoming ready for change is sequential, starting from the current level of each individual, and none of the five steps could be avoided: "they cannot be skipped or reordered".


title: Change management

text: When going through change, many organizations and individuals fail and are faced with challenges when implementing change. There are many measures organizations and individuals can take to avoid failure and overcome challenges.


title: Change management

text: When faced with a resistance to change by individuals, there are many strategies to get individuals to change. Morten T. Hansen proposed the following ten methods to induce personal change.


title: Change management

text: These tactics can be helpful when faced with resistance from individuals with implementing change into a group. The tactics can be helpful with either implementing a behavioral change among the group or a procedural or managerial change in the group.


title: Change management

text: When trying to change at an organizational level, these tactics developed by Irving Calish and Donald Gamache help companies in trying to enter into new markets and with creating new products.


title: Change management

text: These tactics implored on an organizational level aid in overcoming resistance and challenges when it comes to change. These tactics are more optimal for when an organization is trying to implement change at an organizational level or trying to enter into a new product space, but still work for other avenues.


title: Change management

text: Based upon the reasons for failure, there are many actions a leader can take to avoid these failures when it comes to change. They can:


title: Change management

text: The antithesis for this is doing the opposite of what causes failure in the first place. Following these steps in combination with the other suggestions will aid in avoiding failure and overcoming challenges. Additionally to be successful with change it is imperative to follow the change models to get actions right and avoid failure in the first place.


title: Change management

text: There are many situations in which we have seen the change models being implemented and ultimately result success. Two of the following case studies below highlight these examples.


title: Change management

text: At a Vietnamese University there was a desire to use Lewin's change theory to create a more "effective working environment where lecturers collaborate in a constructive spirit to improve their teaching practices and learning outcomes." To start this process of implementing change, they began by observing how the teachers at this university taught their class, and by giving questionnaires and interviews about how the teachers conducted their jobs. After receiving the feedback about how the teachers conducted their lectures and where they needed to improve, the administration communicated to the teachers how to fix these problems. They began by offering professional seminars as a way for the teachers to improve and refine their knowledge. Additionally the university also brought in professionals that introduced them to alternative ways of teaching. After the teachers had learned this new information they then implemented this into the classes they teach. To monitor the transition and the implementation of these new tactics, the classes were once again observed and feedback was provided through questionnaires and interviews. This data was sent to the administration after the second review and later was organized to show the feedback before and after the changes were implemented in the class room. The data ultimately revealed that after this change was conducted, satisfaction among the students was far greatly improved. This university followed Lewin's model when trying to implement change at their university and the end result was a success.


title: Change management

text: The CDC conducted an analysis at a federally qualified health center in Kentucky and looked to "improve its delivery of preventive care services, close care gaps, and reduce health disparities among its patient population." With understanding the goal in mind, they utilized Kotter's change theory as a model to attain this goal and implement the change needed at this facility. They began this process to change, by creating a climate for change within the health center. To do this they interviewed employees on how well this facility implemented certain protocols, how high these standards were held, and how well these standards were being enforced. This was done to gain insight on where the organization currently is and where it should be going. Once this knowledge was attained, the organization then implemented the change into the care facility with higher quality standards. After this was complete, the employees were interviewed again and this time the questions shifted to how leadership engaged and enabled the whole organization. This was done to look at how well the organization was implementing the new standards at the care facility. The final phase of questioning was about how the implementation of these standards could have gone better and if there were any unanticipated challenges that came with implementing these standards. These interviews gave the CDC a read on how well the implementation of new health standards at this care facility went well and where they could have improved. This example is one of many of how organizations can use Kotter's change model to correctly implement change.


title: Hellraiser III: Hell on Earth

text: Hellraiser III: Hell on Earth is a 1992 American supernatural horror film and third installment in the "Hellraiser" series. It was directed by Anthony Hickox and stars Doug Bradley, Terry Farrell, Paula Marshall, and Kevin Bernhardt. Ashley Laurence, who starred in the previous two films, has a cameo. Following the events of "", in which the demon Pinhead (Bradley) is imprisoned in a statue, he resurrects himself by absorbing the life force of unlucky humans. After converting several power-hungry youths (Marshall and Bernhardt) into new Cenobites, Pinhead goes on a rampage, opposed by a reporter (Farrell) and the spiritual manifestation of his good half (also Bradley).


title: Hellraiser III: Hell on Earth

text: Series creator Clive Barker reprised his role as executive producer, though he was largely uninvolved until post-production. It was the first "Hellraiser" film to be filmed outside the United Kingdom and the first Miramax release under its Dimension Films banner. The film's reception on release was better than the previous film, and it grossed $12.5 million in the US. In 1996, it was followed by "", which was the last film in the series to be theatrically released.


title: Hellraiser III: Hell on Earth

text: The revelation of his own former humanity in "" causes Pinhead, a demon called a Cenobite, to be split into two entities: his former self, World War I British Army Captain Elliot Spencer, and a manifestation of Spencer's id, which takes on the form of Pinhead. While Spencer ends up in limbo, Pinhead is trapped, along with the puzzle box, among the writhing figures and distorted faces etched into the surface of an intricately carved pillar — the Pillar of Souls.


title: Hellraiser III: Hell on Earth

text: J. P. Monroe, the womanizing owner of a popular nightclub called The Boiler Room, buys the pillar. An ambitious young television reporter, Joanne "Joey" Summerskill, sees hooked chains embedded in a teenage clubgoer in a hospital emergency room. They come to life and tear the clubgoer to pieces. A young homeless woman, Terri, who came in with the clubgoer, explains that the chains sprang from the puzzle box, which she pried from the pillar. Terri gives the puzzle box to Joey. While investigating the box's background with the help of her cameraman, "Doc", Joey invites Terri to stay with her. Joey uncovers a video tape from one of Pinhead's former victims, Kirsty Cotton, that explains the puzzle box is the only means of returning Pinhead to Hell. Pinhead remains dormant until Monroe has rough sex with a clubgoer, Sandy. Afterward, hooked chains drag Sandy to the pillar and Pinhead absorbs her body. Pinhead points out that they have both used Sandy for their own purposes. Although initially horrified, Monroe agrees to bring Pinhead more club members so he can feed on them and be freed. In return, Pinhead promises Monroe power and unnatural delights.


title: Hellraiser III: Hell on Earth

text: Joey has recurring nightmares about how she presumes her father died in Vietnam. During one such dream, Spencer contacts Joey. He explains that his experiences in WWI caused him to lose faith in humanity, and he sought out the forbidden pleasures promised by the puzzle box. Spencer tells her that without his humanity to act as a balancing influence, Pinhead is completely evil and will indiscriminately wreak havoc on Earth for his own pleasure, in violation of the Cenobite's laws. To defeat him, Joey must reunite Spencer's spirit with Pinhead and use the puzzle box to return him to Hell. A misunderstanding leads Terri to believe that Joey has abandoned her, and she returns to the arms of her ex-boyfriend, Monroe. Monroe attempts to feed her to Pinhead, but she overpowers him. Before she can flee, Pinhead talks her into feeding Monroe to him, promising to turn her into a demon in return. Now free, Pinhead massacres the club's patrons. Hearing the news reports, Joey goes to the club to investigate.


title: Hellraiser III: Hell on Earth

text: Pinhead orders Joey to give him the box, but she escapes him. Pinhead resurrects several of his victims as demonic Cenobites, including Terri, Monroe, the barman, the DJ, and "Doc", who also left to investigate the club. Joey flees through the quiet streets, pursued by the new Cenobites. The Cenobites kill local police as Joey enters a church and begs the priest to help her. Lacking in faith that demons could exist, the priest is appalled by the appearance of Pinhead. Pinhead defiles the church and almost kills the priest until Joey regains his attention to the puzzle box she holds and gets him to chase her. The Cenobites trap Joey on a construction site and prepare to torture her. She solves the puzzle box, and they are sent to Hell. The box transports Joey into limbo, where she comes face to face with an apparition who appears to be her dead father. The apparition tells Joey to give him the puzzle box, only to be revealed as Pinhead in disguise.


title: Hellraiser III: Hell on Earth

text: Pinhead ensnares her in machinery and prepares to transform her into a Cenobite. Spencer's limbo-bound spirit confronts Pinhead and forcibly fuses himself into Pinhead. Joey breaks free and uses the puzzle box, which has transformed into a dagger, to stab Pinhead through the heart, sending him back to Hell. With Pinhead's humanity restored, the box returns Joey to Earth. She buries it in a pool of concrete at the construction site. Later, the finished product of the same site is revealed: a building whose interior design is .


title: Hellraiser III: Hell on Earth

text: Heavy metal band Armored Saint cameo as themselves, performing their song "Hanging Judge" at The Boiler Room nightclub. Actress Ashley Laurence, who played the female lead character Kirsty Cotton in the previous two films, has a cameo appearance via an in-universe videotape.


title: Hellraiser III: Hell on Earth

text: New World Pictures and Film Futures, a production company owned by Clive Barker and Chris Figg, held meetings about a third "Hellraiser" film before "" was released. Barker had originally intended for the "Hellraiser" sequels to focus on Clare Higgins' character Julia, but Higgins declined to reprise her role in a third film, and her character was killed off in later drafts of "Hellbound". Other ideas included a story set in ancient Egypt, a followup to "Hellbound" in which Pinhead attempted to resurrect himself, and a building that functioned as a Lament Configuration. Aspects from the latter two would make it into the final script.


title: Hellraiser III: Hell on Earth

text: During these talks, 20th Century Fox demanded extensive cuts to Barker's latest film, "Nightbreed", an adaptation of his novella "Cabal". Following a misleading marketing campaign from Fox that promoted it as a slasher film, "Nightbreed" underperformed at the box office and caused Film Futures to go out of business. With New World's own bankruptcy troubles, "Hellraiser III" went into development hell. Former New World executives, including Lawrence Kuppin, established Trans-Atlantic Pictures, and the rights were transferred to them. Following disagreements with Trans-Atlantic, Barker had no official involvement in the project until much later, during post-production; he said the studio balked at his fee, as they wanted a "cheap and nasty" film.


title: Hellraiser III: Hell on Earth

text: Tony Randel, who directed "Hellbound", co-wrote the story with Peter Atkins. Atkins completed the first draft of the screenplay in 1991. Many major elements remain unchanged from the shooting script, but the Barbie and CD Cenobites do not exist. The end of the screenplay has Pinhead and Elliott merge into one being, but, following this, Joey makes a deal with him to be his willing bride in return for a successful life. Subsequent rewrites introduced the CD and Barbie Cenobites, Pinhead's deception as Joey's father, and a happier ending. The setting was made unambiguously American, ending the first two films' tradition of mixing British and American elements.


title: Hellraiser III: Hell on Earth

text: Randel was attached to direct, but the producers removed him after they became worried that his vision for the film was too bleak. Anthony Hickox replaced Randel after a mutual friend, whom Hickox had cast in "", suggested him. Barker, who disliked Hickox's prior work, believed him a poor fit for the "Hellraiser" series, as Hickox was known for horror comedy films. When Hickox met with him, Barker stressed that he expected Hickox to take the material seriously. Hickox, a fan of the series, agreed and used the first two films as a guide for the proper tone.


title: Hellraiser III: Hell on Earth

text: Only two actors returned from the prior films: Doug Bradley as the Cenobite Pinhead and, in a cameo, Ashley Laurence as Kirsty. Hickox said he found the casting process for a "Hellraiser" film both exciting and frightening. The first to be cast was Terry Farrell, who was returning to a career in acting after a break. Hickox had previously sought her for a role in "Waxwork II", but, when that became impossible because of a scheduling clash, he promised to cast her in his next project. Kevin Bernhardt, who had appeared as a series regular on "General Hospital", was cast as J. P. Munroe. The role of Monroe's girlfriend, Terri, went to Paula Marshall, who Hickox said was a critical casting choice, as the film rested on the performances of Marshall, Ferrell, and Bradley.


title: Hellraiser III: Hell on Earth

text: For Joey's cameraman, Ken Carpenter, an actor friend of studio executive Kuppin, was cast, as he had the look they wanted: practical and hard-working. Atkins himself took the role of the barman and the subsequent Barbie Cenobite, and several other crew members, including Kuppin and producer Lawrence Mortorff, took cameo roles. Smaller roles were filled with friends-of-friends, local actors, and people who had appeared in prior genre films, including Hickox's "Waxwork" series.


title: Hellraiser III: Hell on Earth

text: Most of the crew were new to the series, too. Hickox brought many crew members from his previous films, including cinematographer Gerry Lively, who worked with Hickox on "Waxwork II". Bob Keen from special effects company Image Animation was one of the few returning crew members from previous "Hellraiser" films. Keen had also previously worked on "Nightbreed" and the "Waxwork" films. Gary J. Tunnicliffe, who would become a writer and director in later "Hellraiser" films, joined the film's make-up crew and created the Lament Configuration boxes. Paul Jones replaced Geoff Portass as make-up coordinator.


title: Hellraiser III: Hell on Earth

text: "Hellraiser III" was the first film in the series shot in the United States. Laurence's scene, a recorded interview in which Kirsty explains the series' mythology, was shot separately prior to the rest of the film. Principal photography began in late 1991 in Greensboro, North Carolina, which stood in for New York City. J. P.'s club was set in a furniture factory in neighboring High Point.


title: Hellraiser III: Hell on Earth

text: Trans-Atlantic gave Hickox six weeks to shoot the film. Hickox had previously established a very fast shooting schedule that used long hours, which meant the "Hellraiser III" cast had to adjust to his unorthodox style and the studio's demands. Bradley said that he worked for seventeen hours straight one day, and the large number of scenes shot daily meant they had little time to perfect them. Hickox's preference for in-camera editing sped up production but limited the actors' view of how the completed film would look. They instead had to depend on storyboards. Unlike previous "Hellraiser" films, the stages used were all very close to each other and shared a single sound stage, which made shooting simultaneously with multiple crews difficult.


title: Hellraiser III: Hell on Earth

text: Though Bradley said he enjoyed the production and working with Hickox, he experienced discomfort in some of his scenes. Early on, Bradley had to act from within the uncomfortable Pillar of Souls prop, where Pinhead is trapped. This restricted Bradley's acting to just his face and voice. Bradley also said that the make-up from "Hellraiser III" was his least favorite. Jones had changed Pinhead's make-up to make it faster to apply and remove, but this had the side-effect of making it more uncomfortable to wear. However, Bradley was able to find an optician that allowed him to wear a prescription version of Pinhead's black lenses, allowing him to stay in-character for much longer periods.


title: Hellraiser III: Hell on Earth

text: During the sex scene between Aimée Leigh and Burnhardt, Leigh protested at having to appear topless. This was resolved by having Burnhardt place his hands on her breasts, obscuring them. The cast and crew reportedly got along well, and during an on-set visit by "Fangoria" magazine, the only complaint reported was that Marshall found her outfit too light to shoot during a cold winter night. The scene where Elliott and Pinhead confront each other was difficult to shoot, necessitating a stand-in for Pinhead. Bradley remarked that he felt "jealously protective" of the character when he saw his stand-in, as this was the first time anyone else had ever appeared in-character as Pinhead on a "Hellraiser" set.


title: Hellraiser III: Hell on Earth

text: The biggest issue was the Black Mass scene, which caused controversy in socially-conservative North Carolina. Hickox had been refused permission to shoot in a real church, so he used a matte painting as a background to the altar. When the crew complained of sacrilege, Hickox told them it was no different than the countless Hammer horror films in which Christopher Lee, as Dracula, rampaged in churches. Besides that, Hickox reported only a healthy rivalry between Marshall and Farrell, which he welcomed, as it encouraged them to up the ante in their shared scenes.


title: Hellraiser III: Hell on Earth

text: Keen's effects crew of "Hellraiser III" included coordinator Paul Jones; supervisors Steve Painter, Mark Coulier, and Bob's brother Dave; head sculptor Paul Catlin, and mechanical effects coordinator Ray Bivins.


title: Hellraiser III: Hell on Earth

text: For "Hellraiser III", Keen used a two-piece prosthetic where small plates in the makeup stood up the pins. It took only three hours to apply the make-up, around two hours less than it took to apply the six-to-seven-piece Pinhead makeup in the past two films. A "motor with an off-centered cam" was also built into the right hand side of J.P.'s makeup, where moved around the head and pushed a piston to the left hand side. The actors for both Barbie and CD Head wore prosthetic mask for their roles, with a dummy replication for both characters for shots showing when they used their weapons.


title: Hellraiser III: Hell on Earth

text: Barbie's transformation was done through "reverse shots", where silver-sprayed barbed wire was wrapped around by different strings in each shot. Real barbed wire was used on dummies, while the fake barbed wire was used on the human actors.


title: Hellraiser III: Hell on Earth

text: Producing Barbie's flamethrowers involved putting gas and a 40-foot flamethrower in a fiberglass head; the gas would build up inside a fake torso before fire blasted through the top head.


title: Hellraiser III: Hell on Earth

text: Kuppin suggested that Hickox use the non-linear editing system Ediflex, which was made by a company he owned. This was quickly abandoned after the software turned out to be too time-consuming. Miramax soon became interested in distributing the film in the US, but what happened next is contentious. According to Hickox, Bob Weinstein loved the rough cut he saw and offered Hickox money for additional effects work and to redo the ending. This resulted in an early use of computer-generated imagery – the first in a horror film – to add several gory scenes.


title: Hellraiser III: Hell on Earth

text: Barker disputes this account and says that Kuppin showed him a work print. Unimpressed, Barker declined an executive producer credit, criticizing the film's ending and low-budget effects work. After Miramax become involved, Barker says Weinstein asked for his honest evaluation of the film. Barker reiterated his criticisms, and, at Weinstein's urging, came in to fix the film. In Barker's account, he was the one responsible for Farrell's bondage scene, additional scenes of extended gore in the nightclub massacre, and the CGI when Leigh's character is skinned. Regardless of the extent of Barker's involvement in post-production, it was now enough for him to accept an executive producer credit, and the film was given a "Clive Barker Presents" banner. Additionally, Barker promoted the film alongside "Candyman".


title: Hellraiser III: Hell on Earth

text: Writing in "The Hellraiser Films and Their Legacy", author Paul Kane identifies several themes in the film. The first, the horrors of war, Kane identifies as the strongest and most pervasive. "Hellraiser III" homages war films like "Apocalypse Now", "Platoon", and "Born on the Fourth of July". Kane says both Joey and Elliott are depicted as seeking answers following traumatic experiences with war. Joey wants to understand her father's death in Vietnam, and Elliott searches for meaning after losing his faith in both God and mankind. After Elliott's transformation into Pinhead, he commands Hell's forces, and later is shown directing the newly created Cenobites. Hickox said this is a direct allusion to Elliott's war experiences.


title: Hellraiser III: Hell on Earth

text: Kane identifies dreams as another common theme, often in terms of how they relate to desire. According to Kane, Joey's nightmares reflect her frustrated ambition to be recognized in her career and beat the glass ceiling. Though her dreams of getting the story of her life come true, she is left no better off, as there is no evidence. Likewise, Pinhead appeals to J. P.'s and Terri's dreams, promising to make their ambitions come true. For Terri, this is more literal, as she desires the ability to dream. Kane says that although the film never explicitly states this, it is clear that Elliott wishes to regain his humanity; more immediately, he seeks to control Pinhead, who, in turn, desires unrestrained freedom.


title: Hellraiser III: Hell on Earth

text: In Kane's analysis, technology and, specifically, communication devices figure prominently: unplugged radios and televisions transmit warnings from Elliott, Kirsty's warning comes in the form of a videotape, and Joey works in the television industry. The transformed Cenobites are fused with technology, which Kane compares to "". These transformations also illustrate another theme: duality. Many of the characters have an alter ego, such as Elliott and Pinhead. Kane says that although Joey does not have a physical alter ego, her dream-self regresses to that of a young child similar to Lewis Carroll's Alice.


title: Hellraiser III: Hell on Earth

text: Kane says many of the characters and their relationships in "Hellraiser III" match to those of the first two films. Like Kirsty, Joey has lost her father, and she finds a new father figure in Elliott. Kane identifies Elliott as a vaguely-hinted-at love interest for her, as he shares a psychic intimacy with her that no living man can. Joey and Terri initially have a relationship similar to Kirsty and Tiffany in "Hellbound", then an antagonistic one similar to Kirsty and Julia in "Hellraiser". According to Kane, both J. P. and, to some extent, Pinhead mirror Frank's insatiable lust. Kane describes the Cenobites as reflections of the ones from the first two films.


title: Hellraiser III: Hell on Earth

text: The film features a heavy metal-rock soundtrack. Initially, the score was also meant to be rock music, but this went over poorly in test screenings. Randy Miller was brought in to compose a more traditional, orchestral score within three weeks. Given a restricted budget, the Mosfilm State Orchestra and Choir in Russia was chosen to perform the score. The Russian orchestra, unaccustomed to Hollywood demands, felt they did not have enough time to rehearse, but Miller said they eventually welcomed the challenge. Barker directed the Motörhead video for "Hellraiser", featuring Lemmy and Pinhead playing a game of cards and varied clips of the film.


title: Hellraiser III: Hell on Earth

text: Armored Saint, who contributed to the song "Hanging Judge", make a brief appearance in the film. The single "Hellraiser", which Motörhead's Lemmy Kilmister had helped write, was originally recorded by Ozzy Osbourne on "No More Tears".


title: Hellraiser III: Hell on Earth

text: "Hellraiser III" required several cuts before the Motion Picture Association of America was willing to grant it an "R" rating. Barker ascribed their increased scrutiny to his outspokenness on social issues and the growing popularity of the "Hellraiser" films, which he said they initially saw as too obscure to care about. It premiered at the Dylan Dog Horror Fest in May 1992. Miramax released the film theatrically in the United States on September 11 the same year. It was the first Dimension film to be distributed by Miramax. The film debuted in third place, grossing $3.2 million, which the "Los Angeles Times" characterized as "tepid business". The film grossed $12.5 million in 898 theaters across the United States and Canada, making it second-highest-grossing film in the "Hellraiser" series. It was released on home video in May 1993 via Paramount Pictures and debuted the next month on "Billboard" video rental charts at #19. An R-rated version of the film was released on DVD in the US on August 8, 2006. It includes a documentary short about Barker's inspiration from 1992.


title: Hellraiser III: Hell on Earth

text: On release, reviews of "Hellraiser III" were overall more positive than "Hellbound". Kane attributes this to the film's more commercial aspirations than the previous two films. "Variety"s review echoed this, calling it "highly commercial", and Jack Yeovil of "Empire" said it is "a good horror sequel" that succeeds in its simple goal: to appeal to mainstream American teenagers. Nigel Floyd of "Time Out London" called it "adult horror to die for". Marc Savlov, film critic for "The Austin Chronicle", instead called the film "about as traumatic as a de-clawed Cerebus". In a retrospective review from 2006, Steve Barton of Dread Central called it "just plain goofy" and a low point in the series. Rotten Tomatoes, a review aggregator that collects both contemporary and modern reviews, reports that 40% of 20 surveyed critics gave the film a positive review; the average rating is 4.4/10.


title: Hellraiser III: Hell on Earth

text: Writing for "The Washington Post", Richard Harrington described the plot and themes as faithful to the previous films. Pinhead, he said, is "more ambitious, and more dangerous, than ever", and there is "never a dull moment". Compared to the first film, which he dubbed "deliciously original", Savlov said "Hellraiser III" is a "tepid and wholly uninspired retread of various genre conventions". Yeovil praised Atkins' script for its "surprisingly careful characterisations" and abandoning the "waffling metaphysics" of the previous film, but said that Pinhead remains "a sub-Freddy goon" and the film has been purged of some of Barker's perversity and ambiguity. Owen Gleiberman of "Entertainment Weekly" rated it a letter grade of C− and wrote that the film, though it has a provocative theme, is more oriented toward vulgar depictions of gore than "the thin line separating pleasure and pain". Janet Maslin of "The New York Times" wrote that the series' mythology had become too complex by this point for newcomers to understand despite its popularity with horror fans. At the "Los Angeles Times", Kevin Thomas described the plot as "quite imaginative and even poignant" but said the violence numbs audiences looking for more than just gory special effects, unlike the first film. "Chicago Tribune" critic Johanna Steinmetz said that Joey and Pinhead do not have chemistry, and their back stories fail to mesh with the rest of the plot.


title: Hellraiser III: Hell on Earth

text: Commenting on the film's acting, "Variety"s review identified Farrell as a "strong heroine" and Bradley as "a commanding presence". Harrington said it was "hardly a surprise that Bradley steals the film" and called Farrell "solid". Maslin said that Pinhead's portrayal makes him of interest to "a more discerning audience", and the film "unfolds as intelligently as it can, under the circumstances". Bradley was also highlighted by Thomas, who called him "a fine actor of much resonance"; Thomas wrote that none of the other cast members are as good, describing them as "callow". In a retrospective of the entire series for "The A.V. Club", Katie Rife wrote that "everyone is acting as hard as they possibly can", but the campy scenes make the more serious ones difficult to accept. She also criticized the dialogue as "rejected first drafts of a "True Detective" episode".


title: Hellraiser III: Hell on Earth

text: "Variety" called the film "an effective combination of imaginative special effects with the strangeness of author Clive Barker's original conception". In a pun on special effects supervisor Bob Keen' s name, Harrington called the effects "peachy Keen" and said Pinhead is Keen's masterpiece. Maslin's review described the special effects as "commendable" for bringing sophistication and "helping to usher in the age of high-tech horror". Thomas wrote that the effects are "too obviously synthetic to scare adults" but could be nightmarish for children. Writing for the "Deseret News", Chris Hicks said the film is "one of the most gruesome and unpleasant horror movies", enjoyable only by fans of splatter films. Barton criticized the new Cenobites as "lame" and said the special effects have not aged well, now seeming to be "sickeningly amaturish". According to Barton, this makes the film "pretty tedious viewing". Rife said the design of the new Cenobites bears "the distinct stamp of the early '90s".


title: Attica

text: Attica (, "Attikḗ" or , or ), or the Attic Peninsula, is a historical region that encompasses the city of Athens, the capital of Greece and its countryside. It is a peninsula projecting into the Aegean Sea, bordering on Boeotia to the north and Megaris to the west. The southern tip of the peninsula, known as Laurion, was an important mining region.


title: Attica

text: The history of Attica is tightly linked with that of Athens, and specifically the Golden Age of Athens during the classical period. Ancient Attica (Athens city-state) was divided into demoi or municipalities from the reform of Cleisthenes in 508/7 BC, grouped into three zones: urban ("astu") in the region of Athens main city and Piraeus (port of Athens), coastal ("paralia") along the coastline and inland ("mesogeia") in the interior.


title: Attica

text: The modern administrative region of Attica is more extensive than the historical region and includes Megaris as part of the regional unit West Attica, and the Saronic Islands and Cythera, as well as the municipality of Troizinia on the Peloponnesian mainland, as the regional unit Islands.


title: Attica

text: According to the Roman geographer Pausanias, the place was originally named Actaea, but was later renamed in the honour of Atthis, daughter of king Cranaus of Athens.


title: Attica

text: Attica is a triangular peninsula jutting into the Aegean Sea. It is naturally divided to the north from Boeotia by the long Cithaeron and Parnes mountain ranges.


title: Attica

text: To the west of Eleusis, the Greek mainland narrows into Megaris, connecting to the Peloponnese at the Isthmus of Corinth. The western coast of Attica, also known as the Athens Riviera, forms the eastern coastline of the Saronic Gulf. Mountains separate the peninsula into the plains of Pedias, Mesogeia, and the Thriasian Plain. The mountains of Attica are the Hymettus, the eastern portion of the Geraneia, Parnitha (the highest mountain of Attica), Aigaleo and Penteli. Four mountains — Aigaleo, Parnitha, Penteli and Hymettus (clockwise from the southwest) — delineate the hilly plain on which the Athens urban area now spreads. The plain is pockmarked by a plethora of semi-continuous hills, the most notable ones being the Tourkovounia, Lykavittos, the Acropolis of Athens itself and Philopappou. Mesogeia lies to the east of Mount Hymettus and is bound to the north by the foothills of Mount Penteli, to the east by the Euboean Gulf and Mount Myrrhinous, and to the south by the mountains of Lavrio (modern Lavreotiki), Paneio (Πάνειον Όρος), and Laureotic Olympus (Λαυρεωτικός Όλυμπος). The Lavrio region terminates in Cape Sounion, forming the southeastern tip of the Attic peninsula.


title: Attica

text: Athens' water reservoir, Lake Marathon, is an artificial reservoir created by damming in 1920. Pine and fir forests cover the area around Parnitha. Hymettus, Penteli, Myrrhinous and Lavrio are forested with pine trees, whereas the rest are covered by shrubbery. Parts of the sprawling forests of mount Penteli and Parnitha have been lost to forest fires, while the Synngrou Estate on the foothills of the former (intersecting the border between the neighborhoods of Kifisia, Melissia and Marousi is home to the sole remaining natural forest in the Athenian plain.


title: Attica

text: The Kifisos is the longest river in Attica, which starts from the foothills of mount Parnitha near Varibobi, crosses the Athenian plain and empties into the delta of Faliro east of the port of Piraeus.


title: Attica

text: According to Plato, Attica's ancient boundaries were fixed by the Isthmus, and, toward the continent, they extended as far as the heights of Cithaeron and Parnes. The boundary line came down toward the sea, bounded by the district of Oropus on the right and by the river Asopus on the left.


title: Attica

text: During antiquity, the Athenians boasted about being 'autochthonic', which is to say that they were the original inhabitants of the area and had not moved to Attica from another place. The traditions current in the classical period recounted that, during the Greek Dark Ages, Attica had become the refuge of the Ionians, who belonged to a tribe from the northern Peloponnese. Supposedly, the Ionians had been forced out of their homeland by the Achaeans, who in turn had been forced out of their homeland by the Dorian invasion. Supposedly, the Ionians integrated with the ancient Atticans, who, afterward, considered themselves part of the Ionian tribe and spoke the Ionian dialect of Ancient Greek. Many Ionians later left Attica to colonize the Aegean coast of Asia Minor and to create the twelve cities of Ionia.


title: Attica

text: During the Mycenaean period, the inhabitants of Attica lived in autonomous agricultural societies. The main places where prehistoric remains were found are Marathon, Rafina, Nea Makri, Brauron, Thorikos, Agios Kosmas, Elefsina, Menidi, Markopoulo, Spata, Aphidnae and Athens. All of these settlements flourished during the Mycenaean period.


title: Attica

text: According to tradition, Attica comprised twelve small communities during the reign of Cecrops, the legendary Ionian king of Athens. Strabo assigns these the names of Cecropia, Tetrapolis, Epacria, Decelea, Eleusis, Aphidna, Thoricus, Brauron, Cytherus, Sphettus, Cephisia, and possibly Phaleron. These were said to have been later incorporated in an Athenian state during the reign of Theseus, the mythical king of Athens. Modern historians consider it more likely that the communities were progressively incorporated into an Athenian state during the 8th and the 7th centuries BC.


title: Attica

text: Until the 6th century BC, aristocratic families lived independent lives in the suburbs of Athens, such as Hippios Kolonos. Only after Peisistratos's tyranny and the reforms implemented by Cleisthenes did the local communities lose their independence and succumb to the central government in Athens. As a result of these reforms, Attica was divided into approximately a hundred municipalities, the demes ("dēmoi", δῆμοι), and also into three large sectors: the city (ἄστυ), which comprised the areas of central Athens, Ymittos, Aegaleo and the foot of Mount Parnes, the coast (παράλια), that included the area between Eleusis and Cape Sounion and the area around the city (ἐσωτερικό-μεσογαία), inhabited by people living on the north of Mount Parnitha, Penteliko and the area east of the mountain of Hymettus on the plain of Mesogeia. Principally, each civic unit would include equal parts of townspeople, seamen, and farmers. A “trittýs” ("third") of each sector constituted a tribe. Consequently, Attica comprised ten tribes.


title: Attica

text: During the Peloponnesian war, Attica was invaded and raided several times by the Lacedaemonians, while in the war's third phase the fortress of Decelea was captured and fortified by Lacedaemon.


title: Attica

text: During the classical period, Athens was fortified to the north by the fortress of Eleutherae, which is preserved well. Other fortresses are those of Oenoe, Decelea, Phyle and Aphidnae. To protect the mines at Laurium, on the coast, Athens was protected by the walls at Rhamnus, Thoricus, Sounion, Anavyssos, Piraeus, and Elefsina. Although these forts and walls had been constructed, Attica did not establish a fortification system until later, in the 4th century BC. Attica's warfare is displayed by piles of rubble from fortresses from the Chremonidean war.


title: Attica

text: Even though archaeological ruins of religious importance are found in nearly the whole area of Attica, the most important are those found in Eleusis. The worship of the goddesses Demeter and Cora, beginning in the Mycenaean period, continued until the late years of antiquity.


title: Attica

text: Many other types of worship can be traced to the prehistory. For example, the worship of Pan and the Nymphs was common in many areas of Attica such as Marathon, Parnes and Ymittos. The god of wine, Dionysus, was worshipped mainly in the area of Icaria, now the suburb of Dionysus. Iphigeneia and Artemis were worshipped in Brauron, Artemis in Rafina, Athena on Sounion, Aphrodite on Iera Odos, and Apollo in Daphne.


title: Attica

text: The festival of Chalceia was celebrated every autumn in Attica. The festival honored the gods Hephaestus and Athena Ergane. In the deme of Athmonon, in modern-day Marousi, the Athmoneia games were also celebrated.


title: Attica

text: After the period of antiquity, Attica came under Roman, Byzantine, Venetian, and Ottoman rule. In the Roman period, the Scandinavian Heruli tribe raided Athens and Attica in 267 AD, destroying most of the city and laying waste to the countryside. During the Byzantine period, Attica was invaded by the Goths under the command of Alaric in 396. Attica's population diminished in comparison to the neighboring area of Boeotia.


title: Attica

text: The sites of historical interest date to the 11th and 12th centuries, when Attica was under the rule of the Franks. The great monastery of Dafni, that was built under Justinian I's rule, is an isolated case that does not signify a widespread development of Attica during the Byzantine period. On the other hand, the buildings built during the 11th and 12th centuries show a greater development that continued during the rule of the Franks, who did not impose strict rule.


title: Attica

text: From the 14th century onwards, the Arvanites came to Attica from what is today southern Albania. They were mostly invited as mercenaries by the local Greek lords.


title: Attica

text: During the Ottoman rule, Athens enjoyed some rights. However, that was not the case for the villages of Attica. Great areas were possessed by the Turks, who terrorized the population with the help of sipahis. The monasteries of Attica played a crucial role in preserving the Greek element of the villages.


title: Attica

text: In spite of its conquerors, Attica managed to maintain its traditions. This fact is proved by the preservation of ancient toponyms such as Oropos, Dionysus, Eleusis, and Marathon.


title: Attica

text: During the Greek War of Independence in the 1820s, the peasants of Attica were the first to revolt (April 1821), occupying Athens and seizing the Acropolis that was handed over to the Greek revolutionaries in June, 1822.


title: Attica

text: Attica belonged to the newly-founded Greek state from its founding. From 1834, Athens was refounded and made the new Greek capital (moved from Nafplio in Argolis), which caused the gradual repopulation of Attica by other people around Greece. The most dramatic surge came with Greek refugees from Anatolia following the population exchanges between Greece and Turkey under the Treaty of Lausanne. Today, much of Attica is occupied by urban Athens, encompassing the entirety of the Athenian plain. The modern Greek region of Attica includes classical Attica as well as the Saronic Islands, a small part of the Peloponnese around Troezen, and the Ionian Island of Kythira.


title: Attica

text: Attica enjoys a typical Mediterranean climate. It has a distinct, long, dry period in the summer and a short, wet period in the winter. The highest precipitation is experienced during the winter months. The southern part of the peninsula has a hot, semi-arid climate.


title: Attica

text: According to the World Meteorological Organisation, the official European record for highest temperature was 48.0 °C (118.4 °F) was recorded in the areas of Eleusina and Tatoi in 1977, by the use of minimum-maximum thermometers.


title: Progressive house

text: Progressive house is a subgenre of house music. The progressive house style emerged in the early 1990s. It initially developed in the United Kingdom as a natural progression of American and European house music of the late 1980s.


title: Progressive house

text: In the context of popular music the word "progressive" was first used widely in the 1970s to differentiate experimental forms of rock music from mainstream styles. Such music attempted to explore alternate approaches to rock music production. Some acts also attempted to elevate the aesthetic values of rock music by incorporating features associated with classical instrumental music. This led to a style of music called progressive rock, which has been described as "the most self-consciously arty branch of rock."


title: Progressive house

text: In disco music, and later house music, a similar desire to separate more exploratory styles from standard approaches saw DJs and producers adopting the word "progressive" to make a distinction. According to the DJ and producer Carl Craig, the term "progressive" was used in Detroit in the early 1980s in reference to Italo disco. The music was dubbed "progressive" because it drew upon the influence of Giorgio Moroder's Euro disco rather than the disco inspired by the symphonic sound of Philadelphia soul. In Detroit, prior to the emergence of techno, artists like Alexander Robotnick, Klein + M.B.O. and Capricorn filled a vacancy left after disco's demise in America. In the late 1980s, UK music journalist Simon Reynolds introduced the term "progressive dance" to describe acts such as 808 State, The Orb, Bomb the Bass and The Shamen. Between 1990 and 1992, the term "progressive" referred to the short-form buzz word for the house music subgenre "progressive house".


title: Progressive house

text: Progressive house emerged after the first wave of house music. The roots of progressive house can be traced back to the early 1990s rave and club scenes in the United Kingdom. In 1992, "Mixmag" described it at the time as a "new breed of hard but tuneful, banging but thoughtful, uplifting and trancey British house." A combination of US house, UK house, Italian house, Polish house, German house, and techno largely influenced one another during this era. The term was used mainly as a marketing label to differentiate new rave house from traditional American house. Progressive house was a departure from the Chicago acid house sound. The buzz word emerged from the rave scene around 1990 to 1992, describing a new sound of house that broke away from its American roots. Progressive house was viewed by some as anti-rave as its popularity rose in English clubs while breakbeat hardcore flourished at raves. According to DJ Dave Seaman, the sound faced a backlash in the early 1990s because "it had gone the same way as progressive rock before it. Pompous, po-faced and full of its own self importance. But basically was really quite boring." The label progressive house was often used interchangeably with trance in the early years. The record label Bedrock Records released a series of "Bedrock’s ‘Compiled and Mixed’" albums featuring artists like Chris Fortier, John Creamer & Stephane K. Australian artist, Luke Chable has been known for his 2003 seminal remix release PQM’s "You Are Sleeping", titled "You Are Sleeping (Luke Chable Vocal Pass)".


title: Progressive house

text: AllMusic says that progressive house "led the increasingly mainstream-sounding house from the charts back to the dance floors".


title: Progressive house

text: According to American DJ/producer duo Gabriel & Dresden, Leftfield's October 1990 release "Not Forgotten" was possibly the first progressive house production. The record label Guerilla Records, set up by William Orbit & Dick O'Dell, is thought to have been pivotal in the growth of a scene around the genre. "" in 1994 and "Northern Exposure" in 1996 have both been credited with establishing the genre on mixed compilation albums. As well as Guerilla Records, the labels Deconstruction Records, Hooj Choons and Soma Records contributed to the scene's development in the early to mid-1990s.


title: Progressive house

text: In June 1992, "Mixmag" published a list that contained what the magazine viewed as the top progressive house tracks at that time.


title: Progressive house

text: According to Dave Seaman, house DJs who had originally played what was known as Eurodance borrowed from that the genre. This led to a commercial sound that people associate with progressive house today. Seaman notes that with the various lines between genres having become so blurred that true progressive house is often found "masquerading" as techno, tech house or even deep house. As such, the music can feature elements derived from styles such as dub, deep house and Italo house.


title: Progressive house

text: The progressive sound can be distinct from the later uplifting trance and vocal trance. It tends to lack anthemic choruses, crescendos and drum rolling, but holds an emphasis on rhythmic layers. Intensity is added by the regular addition and subtraction of layers of sound. Phrases are typically a power of two number of bars and often begin with a new or different melody or rhythm.


title: Progressive house

text: Later progressive house tunes often featured a build-up section which can last up to four minutes. This is followed by a breakdown and then a climax. "Strobe" by Deadmau5 is a good example. Elements drawn from the progressive rock genre include the use of extended or linked-movement tracks, more complexity and reflection but almost always within the four on the floor rhythm pattern.


title: Quaternions and spatial rotation

text: Unit quaternions, known as "versors", provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis.


title: Quaternions and spatial rotation

text: When used to represent rotation, unit quaternions are also called rotation quaternions as they represent the 3D rotation group. When used to represent an orientation (rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions. A spatial rotation around a fixed point of formula_1 radians about a unit axis formula_2 that denotes the "Euler axis" is given by the quaternion formula_3, where formula_4 and formula_5.


title: Quaternions and spatial rotation

text: Compared to rotation matrices, quaternions are more compact, efficient, and numerically stable. Compared to Euler angles, they are simpler to compose. However, they are not as intuitive and easy to understand and, due to the periodic nature of sine and cosine, rotation angles differing precisely by the natural period will be encoded into identical quaternions and recovered angles in radians will be limited to formula_6.


title: Quaternions and spatial rotation

text: In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle formula_1 about a fixed axis (called the "Euler axis") that runs through the fixed point. The Euler axis is typically represented by a unit vector  (formula_8 in the picture). Therefore, any rotation in three dimensions can be represented as a combination of a vector  and a scalar formula_1.


title: Quaternions and spatial rotation

text: Quaternions give a simple way to encode this axis–angle representation in four numbers, and can be used to apply (calculate) the corresponding rotation to a position vector , representing a point relative to the origin in R.


title: Quaternions and spatial rotation

text: Euclidean vectors such as or can be rewritten as or , where , , are unit vectors representing the three Cartesian axes (traditionally , , ), and also obey the multiplication rules of the fundamental quaternion units.


title: Quaternions and spatial rotation

text: It can be shown that the desired rotation can be applied to an ordinary vector formula_13 in 3-dimensional space, considered as a quaternion with a real coordinate equal to zero, by evaluating the conjugation of  by :


title: Quaternions and spatial rotation

text: using the Hamilton product, where is the new position vector of the point after the rotation. In a programmatic implementation, the conjugation is achieved by constructing a quaternion whose vector part is and real part equals zero, and then performing the quaternion multiplication. The vector part of the resulting quaternion is the desired vector .


title: Quaternions and spatial rotation

text: A geometric fact independent of quaternions is the existence of a two-to-one mapping from physical rotations to rotational transformation matrices. If 0 ⩽ formula_1 ⩽ formula_16, a physical rotation about formula_17 by formula_1 and a physical rotation about formula_19 by formula_20 both achieve the same final orientation by disjoint paths through intermediate orientations. By inserting those vectors and angles into the formula for above, one finds that if represents the first rotation, represents the second rotation. This is a geometric proof that conjugation by and by must produce the same rotational transformation matrix. That fact is confirmed algebraically by noting that the conjugation is quadratic in , so the sign of cancels, and does not affect the result. (See 2:1 mapping of SU(2) to SO(3)) If both rotations are a half-turn formula_21, both and will have a real coordinate equal to zero. Otherwise, one will have a positive real part, representing a rotation by an angle less than formula_22, and the other will have a negative real part, representing a rotation by an angle greater than formula_22.


title: Quaternions and spatial rotation

text: Mathematically, this operation carries the "set" of all "pure" quaternions (those with real part equal to zero)—which constitute a 3-dimensional space among the quaternions—into itself, by the desired rotation about the axis u, by the angle θ. (Each real quaternion is carried into itself by this operation. But for the purpose of rotations in 3-dimensional space, we ignore the real quaternions.)


title: Quaternions and spatial rotation

text: It follows that conjugation by the product of two quaternions is the composition of conjugations by these quaternions: If and are unit quaternions, then rotation (conjugation) by  is


title: Quaternions and spatial rotation

text: which is the same as rotating (conjugating) by  and then by . The scalar component of the result is necessarily zero.


title: Quaternions and spatial rotation

text: The quaternion inverse of a rotation is the opposite rotation, since formula_26. The square of a quaternion rotation is a rotation by twice the angle around the same axis. More generally is a rotation by  times the angle around the same axis as . This can be extended to arbitrary real , allowing for smooth interpolation between spatial orientations; see Slerp.


title: Quaternions and spatial rotation

text: in which corresponds to the rotation followed by the rotation . Thus, an arbitrary number of rotations can be composed together and then applied as a single rotation. (Note that quaternion multiplication is not commutative.)


title: Quaternions and spatial rotation

text: The length of is , the half angle is (60°) with cosine , () and sine , (). We are therefore dealing with a conjugation by the unit quaternion


title: Quaternions and spatial rotation

text: It can be proven that the inverse of a unit quaternion is obtained simply by changing the sign of its imaginary components. As a consequence,


title: Quaternions and spatial rotation

text: As expected, the rotation corresponds to keeping a cube held fixed at one point, and rotating it 120° about the long diagonal through the fixed point (observe how the three axes are permuted cyclically).


title: Quaternions and spatial rotation

text: A quaternion rotation formula_14 (with formula_36) can be algebraically manipulated into a matrix rotation formula_37, where formula_38 is the rotation matrix given by:


title: Quaternions and spatial rotation

text: This can be obtained by using vector calculus and linear algebra if we express formula_42 and formula_43 as scalar and vector parts and use the formula for the multiplication operation in the equation formula_14. If we write formula_42 as formula_46, formula_47 as formula_48 and formula_43 as formula_50, where formula_51, our equation turns into formula_52. By using the formula for multiplication of two quaternions that are expressed as scalar and vector parts,


title: Quaternions and spatial rotation

text: where formula_55 denotes the outer product, formula_56 is the identity matrix and formula_57 is the transformation matrix that when multiplied from the right with a vector formula_58 gives the cross product formula_59.


title: Quaternions and spatial rotation

text: Since formula_60, we can identify formula_38 as formula_62, which upon expansion should result in the expression written in matrix form above.


title: Quaternions and spatial rotation

text: The expression formula_63 rotates any vector quaternion formula_64 around an axis given by the vector formula_65 by the angle formula_1, where formula_65 and formula_1 depends on the quaternion formula_36.


title: Quaternions and spatial rotation

text: Care should be taken when the quaternion approaches a scalar, since due to degeneracy the axis of an identity rotation is not well-defined.


title: Quaternions and spatial rotation

text: A benefit of the quaternion formulation of the composition of two rotations "R" and "R" is that it yields directly the rotation axis and angle of the composite rotation "R" = "R""R".


title: Quaternions and spatial rotation

text: Let the quaternion associated with a spatial rotation "R" be constructed from its rotation axis S with the rotation angle formula_74 around this axis. The associated quaternion is given by


title: Quaternions and spatial rotation

text: Then the composition of the rotation "R" with "R" is the rotation "R" = "R""R" with rotation axis and angle defined by the product of the quaternions


title: Quaternions and spatial rotation

text: This is Rodrigues' formula for the axis of a composite rotation defined in terms of the axes of the two rotations. He derived this formula in 1840 (see page 408).


title: Quaternions and spatial rotation

text: The three rotation axes A, B, and C form a spherical triangle and the dihedral angles between the planes formed by the sides of this triangle are defined by the rotation angles. Hamilton presented the component form of these equations showing that the quaternion product computes the third vertex of a spherical triangle from two given vertices and their associated arc-lengths, which is also defines an algebra for points in Elliptic geometry.


title: Quaternions and spatial rotation

text: The normalized rotation axis, removing the formula_81 from the expanded product, leaves the vector which is the rotation axis, times some constant. Care should be taken normalizing the axis vector when formula_82 is formula_83 or formula_84 where the vector is near formula_83; which is identity, or 0 rotation around any axis.


title: Quaternions and spatial rotation

text: The rotated quaternion needs to be differentiated with respect to the rotating quaternion , when the rotation is estimated from numerical optimization. The estimation of rotation angle is an essential procedure in 3D object registration or camera calibration. For unitary and pure imaginary , that is for a rotation in 3D space, the derivatives of the rotated quaternion can be represented using matrix calculus notation as


title: Quaternions and spatial rotation

text: The complex numbers can be defined by introducing an abstract symbol which satisfies the usual rules of algebra and additionally the rule . This is sufficient to reproduce all of the rules of complex number arithmetic: for example:


title: Quaternions and spatial rotation

text: In the same way the quaternions can be defined by introducing abstract symbols , , which satisfy the rules and the usual algebraic rules "except" the commutative law of multiplication (a familiar example of such a noncommutative multiplication is matrix multiplication). From this all of the rules of quaternion arithmetic follow, such as the rules on multiplication of quaternion basis elements. Using these rules, one can show that:


title: Quaternions and spatial rotation

text: The imaginary part formula_93 of a quaternion behaves like a vector formula_94 in three-dimensional vector space, and the real part behaves like a scalar in . When quaternions are used in geometry, it is more convenient to define them as a scalar plus a vector:


title: Quaternions and spatial rotation

text: Some might find it strange to add a "number" to a "vector", as they are objects of very different natures, or to "multiply" two vectors together, as this operation is usually undefined. However, if one remembers that it is a mere notation for the real and imaginary parts of a quaternion, it becomes more legitimate. In other words, the correct reasoning is the addition of two quaternions, one with zero vector/imaginary part, and another one with zero scalar/real part:


title: Quaternions and spatial rotation

text: We can express quaternion multiplication in the modern language of vector cross and dot products (which were actually inspired by the quaternions in the first place). When multiplying the vector/imaginary parts, in place of the rules we have the quaternion multiplication rule:


title: Quaternions and spatial rotation

text: Quaternion multiplication is noncommutative (because of the cross product, which anti-commutes), while scalar–scalar and scalar–vector multiplications commute. From these rules it follows immediately that (see details):


title: Quaternions and spatial rotation

text: The (left and right) multiplicative inverse or reciprocal of a nonzero quaternion is given by the conjugate-to-norm ratio (see details):


title: Quaternions and spatial rotation

text: as can be verified by direct calculation (note the similarity to the multiplicative inverse of complex numbers).


title: Quaternions and spatial rotation

text: yields the vector formula_106 rotated by an angle formula_107 around the axis formula_17. Expanding out (and bearing in mind that formula_109), we have


title: Quaternions and spatial rotation

text: where formula_112 and formula_113 are the components of (perpendicular and parallel to respectively). This is the formula of a rotation by formula_107 around the axis.


title: Quaternions and spatial rotation

text: Unit quaternions represent the group of Euclidean rotations in three dimensions in a very straightforward way. The correspondence between rotations and quaternions can be understood by first visualizing the space of rotations itself.


title: Quaternions and spatial rotation

text: In order to visualize the space of rotations, it helps to consider a simpler case. Any rotation in three dimensions can be described by a rotation by some angle about some axis; for our purposes, we will use an axis "vector" to establish handedness for our angle. Consider the special case in which the axis of rotation lies in the "xy" plane. We can then specify the axis of one of these rotations by a point on a circle through which the vector crosses, and we can select the radius of the circle to denote the angle of rotation.


title: Quaternions and spatial rotation

text: Similarly, a rotation whose axis of rotation lies in the "xy" plane can be described as a point on a sphere of "fixed" radius in "three" dimensions. Beginning at the north pole of a sphere in three-dimensional space, we specify the point at the north pole to be the identity rotation (a zero angle rotation). Just as in the case of the identity rotation, no axis of rotation is defined, and the angle of rotation (zero) is irrelevant. A rotation having a very small rotation angle can be specified by a slice through the sphere parallel to the "xy" plane and very near the north pole. The circle defined by this slice will be very small, corresponding to the small angle of the rotation. As the rotation angles become larger, the slice moves in the negative "z" direction, and the circles become larger until the equator of the sphere is reached, which will correspond to a rotation angle of 180 degrees. Continuing southward, the radii of the circles now become smaller (corresponding to the absolute value of the angle of the rotation considered as a negative number). Finally, as the south pole is reached, the circles shrink once more to the identity rotation, which is also specified as the point at the south pole.


title: Quaternions and spatial rotation

text: Notice that a number of characteristics of such rotations and their representations can be seen by this visualization. The space of rotations is continuous, each rotation has a neighborhood of rotations which are nearly the same, and this neighborhood becomes flat as the neighborhood shrinks. Also, each rotation is actually represented by two antipodal points on the sphere, which are at opposite ends of a line through the center of the sphere. This reflects the fact that each rotation can be represented as a rotation about some axis, or, equivalently, as a negative rotation about an axis pointing in the opposite direction (a so-called double cover). The "latitude" of a circle representing a particular rotation angle will be half of the angle represented by that rotation, since as the point is moved from the north to south pole, the latitude ranges from zero to 180 degrees, while the angle of rotation ranges from 0 to 360 degrees. (the "longitude" of a point then represents a particular axis of rotation.) Note however that this set of rotations is not closed under composition. Two successive rotations with axes in the "xy" plane will not necessarily give a rotation whose axis lies in the "xy" plane, and thus cannot be represented as a point on the sphere. This will not be the case with a general rotation in 3-space, in which rotations do form a closed set under composition.


title: Quaternions and spatial rotation

text: This visualization can be extended to a general rotation in 3-dimensional space. The identity rotation is a point, and a small angle of rotation about some axis can be represented as a point on a sphere with a small radius. As the angle of rotation grows, the sphere grows, until the angle of rotation reaches 180 degrees, at which point the sphere begins to shrink, becoming a point as the angle approaches 360 degrees (or zero degrees from the negative direction). This set of expanding and contracting spheres represents a hypersphere in four dimensional space (a 3-sphere). Just as in the simpler example above, each rotation represented as a point on the hypersphere is matched by its antipodal point on that hypersphere. The "latitude" on the hypersphere will be half of the corresponding angle of rotation, and the neighborhood of any point will become "flatter" (i.e. be represented by a 3-D Euclidean space of points) as the neighborhood shrinks. This behavior is matched by the set of unit quaternions: A general quaternion represents a point in a four dimensional space, but constraining it to have unit magnitude yields a three-dimensional space equivalent to the surface of a hypersphere. The magnitude of the unit quaternion will be unity, corresponding to a hypersphere of unit radius. The vector part of a unit quaternion represents the radius of the 2-sphere corresponding to the axis of rotation, and its magnitude is the cosine of half the angle of rotation. Each rotation is represented by two unit quaternions of opposite sign, and, as in the space of rotations in three dimensions, the quaternion product of two unit quaternions will yield a unit quaternion. Also, the space of unit quaternions is "flat" in any infinitesimal neighborhood of a given unit quaternion.


title: Quaternions and spatial rotation

text: We can parameterize the surface of a sphere with two coordinates, such as latitude and longitude. But latitude and longitude are ill-behaved (degenerate) at the north and south poles, though the poles are not intrinsically different from any other points on the sphere. At the poles (latitudes +90° and −90°), the longitude becomes meaningless.


title: Quaternions and spatial rotation

text: It can be shown that no two-parameter coordinate system can avoid such degeneracy. We can avoid such problems by embedding the sphere in three-dimensional space and parameterizing it with three Cartesian coordinates , placing the north pole at , the south pole at , and the equator at , . Points on the sphere satisfy the constraint , so we still have just two degrees of freedom though there are three coordinates. A point on the sphere represents a rotation in the ordinary space around the horizontal axis directed by the vector by an angle formula_115.


title: Quaternions and spatial rotation

text: In the same way the hyperspherical space of 3D rotations can be parameterized by three angles (Euler angles), but any such parameterization is degenerate at some points on the hypersphere, leading to the problem of gimbal lock. We can avoid this by using four Euclidean coordinates , with . The point represents a rotation around the axis directed by the vector by an angle formula_116


title: Quaternions and spatial rotation

text: The multiplication of quaternions is non-commutative. This fact explains how the formula can work at all, having by definition. Since the multiplication of unit quaternions corresponds to the composition of three-dimensional rotations, this property can be made intuitive by showing that three-dimensional rotations are not commutative in general.


title: Quaternions and spatial rotation

text: Set two books next to each other. Rotate one of them 90 degrees clockwise around the "z" axis, then flip it 180 degrees around the "x" axis. Take the other book, flip it 180° around "x" axis first, and 90° clockwise around "z" later. The two books do not end up parallel. This shows that, in general, the composition of two different rotations around two distinct spatial axes will not commute.


title: Quaternions and spatial rotation

text: The vector cross product, used to define the axis–angle representation, does confer an orientation ("handedness") to space: in a three-dimensional vector space, the three vectors in the equation will always form a right-handed set (or a left-handed set, depending on how the cross product is defined), thus fixing an orientation in the vector space. Alternatively, the dependence on orientation is expressed in referring to such that specifies a rotation as to "axial vectors". In quaternionic formalism the choice of an orientation of the space corresponds to order of multiplication: but . If one reverses the orientation, then the formula above becomes , i.e., a unit is replaced with the conjugate quaternion – the same behaviour as of axial vectors.


title: Quaternions and spatial rotation

text: It is reported that the existence and continued usage of an alternative quaternion convention in the aerospace and, to a lesser extent, robotics community is incurring a "significant and ongoing cost". This alternative convention is proposed by Shuster M.D. in and departs from tradition by reversing the definition for multiplying quaternion basis elements such that under Shuster's convention, formula_117 whereas Hamilton's definition is formula_118. This convention is also referred to as "JPL convention" for its use in some parts of NASA's Jet Propulsion Laboratory.


title: Quaternions and spatial rotation

text: To identify the changes under Shuster's convention, see that the sign before the cross product is flipped from plus to minus.


title: Quaternions and spatial rotation

text: While use of either convention does not impact the capability or correctness of applications thus created, the authors of argued that the Shuster convention should be abandoned because it departs from the much older quaternion multiplication convention by Hamilton and may never be adopted by the mathematical or theoretical physics areas.


title: Quaternions and spatial rotation

text: The representation of a rotation as a quaternion (4 numbers) is more compact than the representation as an orthogonal matrix (9 numbers). Furthermore, for a given axis and angle, one can easily construct the corresponding quaternion, and conversely, for a given quaternion one can easily read off the axis and the angle. Both of these are much harder with matrices or Euler angles.


title: Quaternions and spatial rotation

text: In video games and other applications, one is often interested in "smooth rotations", meaning that the scene should slowly rotate and not in a single step. This can be accomplished by choosing a curve such as the spherical linear interpolation in the quaternions, with one endpoint being the identity transformation 1 (or some other initial rotation) and the other being the intended final rotation. This is more problematic with other representations of rotations.


title: Quaternions and spatial rotation

text: When composing several rotations on a computer, rounding errors necessarily accumulate. A quaternion that is slightly off still represents a rotation after being normalized: a matrix that is slightly off may not be orthogonal any more and is harder to convert back to a proper orthogonal matrix.


title: Quaternions and spatial rotation

text: Quaternions also avoid a phenomenon called gimbal lock which can result when, for example in pitch/yaw/roll rotational systems, the pitch is rotated 90° up or down, so that yaw and roll then correspond to the same motion, and a degree of freedom of rotation is lost. In a gimbal-based aerospace inertial navigation system, for instance, this could have disastrous results if the aircraft is in a steep dive or ascent.


title: Quaternions and spatial rotation

text: The orthogonal matrix corresponding to a rotation by the unit quaternion (with ) when post-multiplying with a column vector is given by


title: Quaternions and spatial rotation

text: This rotation matrix is used on vector as formula_123. The quaternion representation of this rotation is given by:


title: Quaternions and spatial rotation

text: Also, quaternion multiplication is defined as (assuming "a" and "b" are quaternions, like "z" above):


title: Quaternions and spatial rotation

text: One must be careful when converting a rotation matrix to a quaternion, as several straightforward methods tend to be unstable when the trace (sum of the diagonal elements) of the rotation matrix is zero or very small. For a stable method of converting an orthogonal matrix to a quaternion, see the Rotation matrix#Quaternion.


title: Quaternions and spatial rotation

text: The above section described how to recover a quaternion from a 3 × 3 rotation matrix . Suppose, however, that we have some matrix that is not a pure rotation—due to round-off errors, for example—and we wish to find the quaternion that most accurately represents . In that case we construct a symmetric 4 × 4 matrix


title: Quaternions and spatial rotation

text: and find the eigenvector corresponding to the largest eigenvalue (that value will be 1 if and only if is a pure rotation). The quaternion so obtained will correspond to the rotation closest to the original matrix .


title: Quaternions and spatial rotation

text: This section discusses the performance implications of using quaternions versus other methods (axis/angle or rotation matrices) to perform rotations in 3D.