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Bresenham's line algorithm

Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form a close approximation to a straight line between two points. It is used to draw line primitives in a bitmap image, as it uses only integer addition and bit shifting, all of which are cheap operations in standard computer architectures, it is an incremental error algorithm. It is one of the earliest algorithms developed in the field of computer graphics. An extension to the original algorithm may be used for drawing circles. While algorithms such as Wu's algorithm are frequently used in modern computer graphics because they can support antialiasing, the speed and simplicity of Bresenham's line algorithm means that it is still important; the algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards. It can be found in many software graphics libraries; because the algorithm is simple, it is implemented in either the firmware or the graphics hardware of modern graphics cards.

The label "Bresenham" is used today for a family of algorithms extending or modifying Bresenham's original algorithm. Bresenham's line algorithm is named after Jack Elton Bresenham who developed it in 1962 at IBM. In 2001 Bresenham wrote: I was working in the computation lab at IBM's San Jose development lab. A Calcomp plotter had been attached to an IBM 1401 via the 1407 typewriter console. was in production use by summer 1962 a month or so earlier. Programs in those days were exchanged among corporations so Calcomp had copies; when I returned to Stanford in Fall 1962, I put a copy in the Stanford comp center library. A description of the line drawing routine was accepted for presentation at the 1963 ACM national convention in Denver, Colorado, it was a year in which no proceedings were published, only the agenda of speakers and topics in an issue of Communications of the ACM. A person from the IBM Systems Journal asked me after I made my presentation if they could publish the paper. I agreed, they printed it in 1965.

Bresenham's algorithm has been extended to produce circles, ellipses and quadratic bezier curves, as well as native anti-aliased versions of those.. The following conventions will be used: the top-left is such that pixel coordinates increase in the right and down directions, the pixel centers have integer coordinates; the endpoints of the line are the pixels at and, where the first coordinate of the pair is the column and the second is the row. The algorithm will be presented only for the octant in which the segment goes down and to the right, its horizontal projection x 1 − x 0 is longer than the vertical projection y 1 − y 0. In this octant, for each column x between x 0 and x 1, there is one row y containing a pixel of the line, while each row between y 0 and y 1 may contain multiple rasterized pixels. Bresenham's algorithm chooses the integer y corresponding to the pixel center, closest to the ideal y for the same x; the general equation of the line through the endpoints is given by: y − y 0 y 1 − y 0 = x − x 0 x 1 − x 0.

Since we know the column, x, the pixel's row, y, is given by rounding this quantity to the nearest integer: y = y 1 − y 0 x 1 − x 0 + y 0. The slope / depends on the endpoint coordinates only and can be precomputed, the ideal y for successive integer values of x can be computed starting from y 0 and adding the slope. In practice, the algorithm does not keep track of the y coordinate, which increases by m = ∆y/∆x each time the x increases by one.

Qualified Flying Instructor

The UK's military aviation forces train Qualified Flying Instructors to teach flying training to new pilots. The QFI Course can vary from a few weeks to a few months, depending on the complexity of the aircraft involved. Royal Air Force QFIs are entitled to the post nominals'QFI'. Rotary wing aviators QHIs. QFIs assigned to squadrons are rostered to fly with Squadron pilots, ensuring that updated techniques and standardisation is carried out at frontline units as well as training ones; the QFI accreditation is analogous to the Qualified Weapons Instructor qualification, but focused much more on basic flying skills of the aircraft as opposed to tactics and operational usage that the QWI course focuses on. Qualified Flying Instructor is a term used for pilots of Air Force, Army and Coast Guard who have passed the appropriate course before being allowed to instruct flying an aircraft; the pilots are trained at Flying Instructors School of the Air Force. QFI instructional categories is awarded by the Flying Instructors School of the Indian Air Force.

Flying Instructors School is based at Air Force Station Tambaram and trains operational pilots of Indian Air Force, Indian Army, Indian Navy, para military forces and friendly foreign countries to be flying instructors. Air Chief Marshal Arup Raha, former Chief of Air Staff of the Indian Air Force is Cat A Qualified Flying Instructor. Squadron Leader Shalija Dhami is the first women QFI of the Indian Air Force

Geranium maculatum

Geranium maculatum, the wild geranium, spotted geranium, or wood geranium, is a perennial plant native to woodland in eastern North America, from southern Manitoba and southwestern Quebec south to Alabama and Georgia and west to Oklahoma and South Dakota. It is known as spotted cranesbill or wild cranesbill in Europe, but the wood cranesbill is another plant, the related G. sylvatium. Colloquial names are alum bloom and old maid's nightcap, it grows in dry to moist woods and is abundant when found. It is a perennial herbaceous plant growing to 60 cm tall, producing upright unbranched stems and flowers in spring to early summer; the leaves are palmately lobed with five or seven cut lobes, 10–12.5 cm broad, with a petiole up to 30 cm long arising from the rootstock. They are parted into three or five divisions, each of, again cleft and toothed; the flowers are 2.5–4 cm in diameter, with five rose-purple, pale or violet-purple petals and ten stamens. In the Northern Hemisphere, they appear from April to June.

They are grouped in loose umbels of two to five at the top of the flower stems. The fruit capsule, which springs open when ripe, consists of five cells each containing one seed joined to a long beak-like column 2–3 cm long produced from the center of the old flower; the rhizome is long, 5 to 10 cm thick, with numerous branches. It is covered with scars; when dry it has a somewhat purplish color internally. The plant is well-known in cultivation, numerous cultivars have been developed; the cultivar'Elizabeth Ann' has gained the Royal Horticultural Society's Award of Garden Merit. The plant has been used in herbal medicine, is grown as a garden plant. Wild geranium is considered an astringent, a substance that causes contraction of the tissues and stops bleeding; the Mesquakie Indians brewed a root tea for toothache and for painful nerves and mashed the roots for treating hemorrhoids

El Horno Creek

El Horno Creek or Horno Creek is a tributary stream of San Juan Creek in Orange County in the U. S. state of California. It is 5.9 miles long and drains an area of 4.3 square miles. The creek joins San Juan Creek on the right bank, only a few hundred yards upstream of the Trabuco Creek confluence, within the city limits of San Juan Capistrano; the creek begins in the foothills of the Santa Ana Mountains, in the residential CDP of Ladera Ranch. The headwaters of the creek were divided into two canyons, but during the development of Ladera Ranch starting in the late 1990s the area was regraded, the headwaters combined into a single 2.4-mile channel. The creek flows southwest through a small flood control dam and into San Juan Capistrano, where it crosses under Interstate 5 and turns south, bisecting San Juan Elementary School. Shortly past the school the creek enters an underground concrete channel passing under the I-5/CA 74 interchange and flows into San Juan Creek at. Although significant stretches of the creek remain above ground, riparian habitat along the creek remains "sporadic" despite its perennial flow due to pollution from stormwater

1989 Swatch Open – Doubles

Guy Forget and Henri Leconte were the defending champions but only Leconte competed that year with Eric Winogradsky. Leconte and Winogradsky lost in the quarterfinals to Balázs Taróczy. Ricki Osterthun and Udo Riglewski won in the final 7–6, 6–7, 6–1 against Günthardt and Taróczy. Champion seeds are indicated in bold text while text in italics indicates the round in which those seeds were eliminated. Claudio Panatta / Tomáš Šmíd Heinz Günthardt / Balázs Taróczy Jan Gunnarsson / Michael Mortensen Mark Koevermans / Tom Nijssen 1989 Swatch Open Doubles Draw

Afonso IV of Portugal

Afonso IV, called the Brave, was King of Portugal from 1325 until his death. He was the only legitimate son of King Denis of Portugal by his wife Elizabeth of Aragon. Afonso, born in Lisbon, was the rightful heir to the Portuguese throne. However, he was not Denis' favourite son, the old king preferring his illegitimate son, Afonso Sanches; the notorious rivalry between the half brothers led to civil war several times. On 7 January 1325, Afonso's father died and he, Afonso IV, became king, whereupon he exiled his rival, Afonso Sanches, to Castile, stripped him of all the lands and fiefdom given by their father, Denis. From Castile, Afonso Sanches orchestrated a series of attempts to usurp the crown. After a few failed attempts at invasion, the brothers signed a peace treaty, arranged by Afonso's mother Queen Elizabeth. In 1309, Afonso IV married Infanta Beatrice of Castile, daughter of King Sancho IV of Castile by his wife María de Molina; the first-born of this union was Infanta Maria of Portugal.

In 1325 Alfonso XI of Castile entered a child-marriage with Constanza Manuel of Castile, the daughter of one of his regents. Two years he had the marriage annulled so he could marry Afonso's daughter, Maria of Portugal. Maria became Queen of Castile in 1328 upon her marriage to Alfonso XI, who soon became involved publicly with a mistress. Constanza was imprisoned in a castle in Toro while her father, Juan Manuel, Prince of Villena, waged war against Alfonso XI until 1329; the two reached a peaceful accord after mediation by Juan del Campo, Bishop of Oviedo. The public humiliation of his daughter led Afonso IV to have his son and heir, marry the no less aggrieved Castilian infanta, Constanza. Afonso subsequently started a war against Castile, peace arriving four years through the intervention of the Infanta Maria herself. A year after the peace treaty was signed in Seville, Portuguese troops played an important role in defeating the Moors at the Battle of Río Salado in October 1340. Political intrigue marked the last part of Afonso IV's reign, although Castille was torn by civil war after Alfonso XI died.

Henry of Trastámara challenged the new King Peter of Castile, who sent many Castilian nobles into exile in Portugal. Afonso's heir, fell in love with his new wife's lady-in-waiting, Inês de Castro. Inês was the daughter of an important noble family from Galicia, with links to both the royal houses of Castile and Portugal, her brothers were aligned with the Trastamara faction, became favorites of crown prince Pedro, much to the dismay of others at the Portuguese court, who considered them Castilian upstarts. When Constance of Peñafiel died weeks after giving birth to their third child, Pedro began living with Inês, recognized all her children as his and repudiated the idea of marrying anyone other than Inês herself, his father refused to go to war again against Castile, hoping his heir's infatuation would end, tried to arrange another dynastic marriage for Pedro. The situation became worse as the aging Afonso lost control over his court, his grandson and Pedro's only legitimate son, future king Fernando of Portugal, was a sickly child, while Inês' illegitimate children thrived.

Worried about his legitimate grandson's life, the growing power of Castile within Portugal's borders, Afonso ordered Inês de Castro first imprisoned in his mother's old convent in Coimbra, murdered in 1355. He expected his son to give in and marry a princess, but the heir became enraged upon learning of his lover's decapitation in front of their young children. Pedro put himself at the head of an army and devastated the country between the Douro and the Minho rivers before he was reconciled to his father in early 1357. Afonso died immediately after, in Lisbon in May. Afonso IV's nickname the Brave alludes to his martial exploits. However, his most important accomplishments were the relative peace enjoyed by the country during his long reign and the support he gave to the Portuguese Navy. Afonso granted public funding to raise a proper commercial fleet and ordered the first Portuguese maritime explorations; the conflict with Pedro, the explorations he initiated became the foundation of the Portuguese national epic, Os Lusíadas by Luís de Camões.

The dramatic circumstances of the relationship between father and son and Inês de Castro was used as the basis for the plot of more than twenty operas and ballets. The story with its tragic denouement is immortalized in several plays and poems in Portuguese, such as The Lusíadas by Luís de Camões, in Spanish, including Nise lastimosa and Nise laureada by Jerónimo Bermúdez, Reinar despues de morir by Luís Vélez de Guevara, as well as a play by French playwright Henry de Montherlant called La Reine morte. Mary Russell Mitford wrote a drama based on the story entitled Inez de Castro. Inês de Castro is a novel by Maria Pilar Queralt del Hierro in Portuguese. On 12 September 1309, Afonso married Beatrice of Castile, daughter of Sancho IV of Castile, María de Molina, had four sons and three daughters. Afonso did not have any children out of wedlock. Maria, was the wife of Alfonso XI of Castile, mother of the future king Peter I of Castile. Due to the affair of her husband with his mistress Leonor de Guzmán "it was an unfortunate union from the start, contributing to dampening the relations of both kingdoms".

Buried at the disappeared Convento das Donas of the Dominican Order in Santarém.