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167-596: The deciphered text fragment is identical to what was to become, during the Middle Ages , the standard text of the Hebrew Bible , known as the Masoretic Text , which it precedes by several centuries. Damaged by a fire in approximately 600 CE, the scroll is badly charred and fragmented and required noninvasive scientific and computational techniques to virtually unwrap and read, which was completed in 2015 by

334-458: A lookup table ), and the perspective correctness was about 16 times more expensive. The Doom engine restricted the world to vertical walls and horizontal floors/ceilings, with a camera that could only rotate about the vertical axis. This meant the walls would be a constant depth coordinate along a vertical line and the floors/ceilings would have a constant depth along a horizontal line. After performing one perspective correction calculation for

501-436: A clearly cylindrical geometry. Instead, some portions may look planar, some conical, some triangular, etc. Therefore, the most efficient way to assign a geometry to the layer is to do so in a piecewise fashion. Rather than modeling the complex geometry of the entire layer of the scroll, the piecewise model breaks each layer into more regular shapes that are easy to work with. This makes it easy to virtually lift off each piece of

668-640: A data source, as the point of view nears the objects. As an optimization, it is possible to render detail from a complex, high-resolution model or expensive process (such as global illumination ) into a surface texture (possibly on a low-resolution model). Baking is also known as render mapping . This technique is most commonly used for light maps , but may also be used to generate normal maps and displacement maps . Some computer games (e.g. Messiah ) have used this technique. The original Quake software engine used on-the-fly baking to combine light maps and colour maps (" surface caching "). Baking can be used as

835-421: A few families and still others lived on isolated farms spread over the countryside. There were also areas where the pattern was a mix of two or more of those systems. Unlike in the late Roman period, there was no sharp break between the legal status of the free peasant and the aristocrat, and it was possible for a free peasant's family to rise into the aristocracy over several generations through military service to

1002-657: A form of level of detail generation, where a complex scene with many different elements and materials may be approximated by a single element with a single texture, which is then algorithmically reduced for lower rendering cost and fewer drawcalls . It is also used to take high-detail models from 3D sculpting software and point cloud scanning and approximate them with meshes more suitable for realtime rendering. Various techniques have evolved in software and hardware implementations. Each offers different trade-offs in precision, versatility and performance. Affine texture mapping linearly interpolates texture coordinates across

1169-601: A king to rule over them all. By the late sixth century, this arrangement had been replaced by a permanent monarchy, the Kingdom of the Lombards . The invasions brought new ethnic groups to Europe, although some regions received a larger influx of new peoples than others. In Gaul for instance, the invaders settled much more extensively in the north-east than in the south-west. Slavs settled in Central and Eastern Europe and

1336-450: A line of pixels to simplify the set-up (compared to 2d affine interpolation) and thus again the overhead (also affine texture-mapping does not fit into the low number of registers of the x86 CPU; the 68000 or any RISC is much more suited). A different approach was taken for Quake , which would calculate perspective correct coordinates only once every 16 pixels of a scanline and linearly interpolate between them, effectively running at

1503-420: A modern evolution of tile map graphics ). Modern hardware often supports cube map textures with multiple faces for environment mapping. Texture maps may be acquired by scanning / digital photography , designed in image manipulation software such as GIMP , Photoshop , or painted onto 3D surfaces directly in a 3D paint tool such as Mudbox or ZBrush . This process is akin to applying patterned paper to

1670-408: A period from which textual evidence is almost non-existent. Gary A. Rendsburg noted that the researchers have concluded that by the fourth century CE, there was no halakhic rule prescribing that scrolls used for liturgical purposes must contain the entire Pentateuch, while other statements regarding when this rule came to be observed cannot be made with any degree of certainty. The En-Gedi Scroll

1837-500: A perspective correct texture mapping. To do this, we first calculate the reciprocals at each vertex of our geometry (3 points for a triangle). For vertex n {\displaystyle n} we have u n z n , v n z n , 1 z n {\displaystyle {\frac {u_{n}}{z_{n}}},{\frac {v_{n}}{z_{n}}},{\frac {1}{z_{n}}}} . Then, we linearly interpolate these reciprocals between

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2004-511: A place on the screen, a forward texture mapping renderer iterates through each texel on the texture, splatting each one onto a pixel of the frame buffer . This was used by some hardware, such as the 3DO , the Sega Saturn and the NV1 . The primary advantage is that the texture will be accessed in a simple linear order, allowing very efficient caching of the texture data. However, this benefit

2171-536: A plain white box. Every vertex in a polygon is assigned a texture coordinate (which in the 2d case is also known as UV coordinates ). This may be done through explicit assignment of vertex attributes , manually edited in a 3D modelling package through UV unwrapping tools . It is also possible to associate a procedural transformation from 3D space to texture space with the material . This might be accomplished via planar projection or, alternatively, cylindrical or spherical mapping. More complex mappings may consider

2338-567: A powerful lord. Roman city life and culture changed greatly in the early Middle Ages. Although Italian cities remained inhabited, they contracted significantly in size. Rome, for instance, shrank from a population of hundreds of thousands to around 30,000 by the end of the 6th century. Roman temples were converted into Christian churches and city walls remained in use. In Northern Europe, cities also shrank, while civic monuments and other public buildings were raided for building materials. The establishment of new kingdoms often meant some growth for

2505-466: A practical skill rather than a sign of elite status. In the 4th century, Jerome (d. 420) dreamed that God rebuked him for spending more time reading Cicero than the Bible . By the 6th century, Gregory of Tours (d. 594) had a similar dream, but instead of being chastised for reading Cicero, he was chastised for learning shorthand . By the late 6th century, the principal means of religious instruction in

2672-474: A small foothold in southern Spain. Justinian's reconquests have been criticised by historians for overextending his realm and setting the stage for the early Muslim conquests , but many of the difficulties faced by Justinian's successors were due not just to over-taxation to pay for his wars but to the essentially civilian nature of the empire, which made raising troops difficult. In the Eastern Empire

2839-533: A surface, and so is the fastest form of texture mapping. Some software and hardware (such as the original PlayStation ) project vertices in 3D space onto the screen during rendering and linearly interpolate the texture coordinates in screen space between them. This may be done by incrementing fixed point UV coordinates , or by an incremental error algorithm akin to Bresenham's line algorithm . In contrast to perpendicular polygons, this leads to noticeable distortion with perspective transformations (see figure:

3006-542: A team led by Brent Seales of the University of Kentucky. Radiocarbon dating at the Weizmann Institute of a charred fragment presumed to be from the scroll gave a C age of 1754±40 years. The radiocarbon calibration curve of the time placed this in 235–340 CE with 68% probability and 210–390 CE with 89% probability. This dating was challenged by Ada Yardeni, who proposed on the basis of letter shapes that

3173-430: A texture to the screen: Inverse texture mapping is the method which has become standard in modern hardware. With this method, a pixel on the screen is mapped to a point on the texture. Each vertex of a rendering primitive is projected to a point on the screen, and each of these points is mapped to a u,v texel coordinate on the texture. A rasterizer will interpolate between these points to fill in each pixel covered by

3340-510: A time on a polygon. For instance, a light map texture may be used to light a surface as an alternative to recalculating that lighting every time the surface is rendered. Microtextures or detail textures are used to add higher frequency details, and dirt maps may add weathering and variation; this can greatly reduce the apparent periodicity of repeating textures. Modern graphics may use more than 10 layers, which are combined using shaders , for greater fidelity. Another multitexture technique

3507-403: A traditional CT scan . Researchers used a high energy x-ray beam to pass through the depth of the scroll. Each material will absorb the x-ray radiation differently, whereby the scroll will absorb it minimally but more than the empty space around it, and the ink will absorb it significantly more than the unwritten scroll areas around it. This creates the sharp contrast we see between the text and

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3674-502: Is bump mapping , which allows a texture to directly control the facing direction of a surface for the purposes of its lighting calculations; it can give a very good appearance of a complex surface (such as tree bark or rough concrete) that takes on lighting detail in addition to the usual detailed coloring. Bump mapping has become popular in recent video games, as graphics hardware has become powerful enough to accommodate it in real-time. The way that samples (e.g. when viewed as pixels on

3841-451: Is a means of using data streams for textures, where each texture is available in two or more different resolutions, as to determine which texture should be loaded into memory and used based on draw distance from the viewer and how much memory is available for textures. Texture streaming allows a rendering engine to use low resolution textures for objects far away from the viewer's camera, and resolve those into more detailed textures, read from

4008-409: Is also its disadvantage: as a primitive gets smaller on screen, it still has to iterate over every texel in the texture, causing many pixels to be overdrawn redundantly. This method is also well suited for rendering quad primitives rather than reducing them to triangles, which provided an advantage when perspective correct texturing was not available in hardware. This is because the affine distortion of

4175-591: Is identical both in consonantal text and paragraph division to the Masoretic text as exemplified by the medieval Leningrad Codex . This places it on equal footing with a handful of earlier manuscripts found in the Judean Desert but distinct from the Dead Sea scrolls found at Qumran . If the radiocarbon date is correct, the scroll provides important evidence of the canonicalising of the masoretic text during

4342-440: Is individually flattened. Therefore, this is the first step in the merging process, used to check if the segmentation, texturing, and flattening processes were done correctly, but does not produce a final result. Mesh merging is more precise and is the final step in visualizing the unwrapped scroll. This type of merging recombines each point on the surface of each segment with the corresponding point on its neighbor segment to remove

4509-672: Is no universally agreed upon end date. Depending on the context, events such as the conquest of Constantinople by the Turks in 1453, Christopher Columbus 's first voyage to the Americas in 1492, or the Protestant Reformation in 1517 are sometimes used. English historians often use the Battle of Bosworth Field in 1485 to mark the end of the period. For Spain, dates commonly used are the death of King Ferdinand II in 1516,

4676-460: Is possible to use the alpha channel (which may be convenient to store in formats parsed by hardware) for other uses such as specularity . Multiple texture maps (or channels ) may be combined for control over specularity , normals , displacement , or subsurface scattering e.g. for skin rendering. Multiple texture images may be combined in texture atlases or array textures to reduce state changes for modern hardware. (They may be considered

4843-588: Is ubiquitous as most SOCs contain a suitable GPU. Some hardware combines texture mapping with hidden-surface determination in tile based deferred rendering or scanline rendering ; such systems only fetch the visible texels at the expense of using greater workspace for transformed vertices. Most systems have settled on the Z-buffering approach, which can still reduce the texture mapping workload with front-to-back sorting . Among earlier graphics hardware, there were two competing paradigms of how to deliver

5010-457: Is used on them. The reason this technique works is that the distortion of affine mapping becomes much less noticeable on smaller polygons. The Sony PlayStation made extensive use of this because it only supported affine mapping in hardware but had a relatively high triangle throughput compared to its peers. Software renderers generally preferred screen subdivision because it has less overhead. Additionally, they try to do linear interpolation along

5177-747: The n {\displaystyle n} vertices (e.g., using barycentric coordinates ), resulting in interpolated values across the surface. At a given point, this yields the interpolated u i , v i {\displaystyle u_{i},v_{i}} , and z R e c i p r o c a l i = 1 z i {\displaystyle zReciprocal_{i}={\frac {1}{z_{i}}}} . Note that this u i , v i {\displaystyle u_{i},v_{i}} cannot be yet used as our texture coordinates as our division by z {\displaystyle z} altered their coordinate system. To correct back to

En-Gedi Scroll - Misplaced Pages Continue

5344-989: The u , v {\displaystyle u,v} space we first calculate the corrected z {\displaystyle z} by again taking the reciprocal z c o r r e c t = 1 z R e c i p r o c a l i = 1 1 z i {\displaystyle z_{correct}={\frac {1}{zReciprocal_{i}}}={\frac {1}{\frac {1}{z_{i}}}}} . Then we use this to correct our u i , v i {\displaystyle u_{i},v_{i}} : u c o r r e c t = u i ⋅ z i {\displaystyle u_{correct}=u_{i}\cdot z_{i}} and v c o r r e c t = v i ⋅ z i {\displaystyle v_{correct}=v_{i}\cdot z_{i}} . This correction makes it so that in parts of

5511-539: The fyrd , which were led by the local elites. In military technology, one of the main changes was the return of the crossbow , which had been known in Roman times and reappeared as a military weapon during the last part of the Early Middle Ages. Another change was the introduction of the stirrup, which increased the effectiveness of cavalry as shock troops. A technological advance that had implications beyond

5678-717: The Alans , Vandals , and Suevi crossed into Gaul ; over the next three years they spread across Gaul and in 409 crossed the Pyrenees Mountains into modern-day Spain. The Migration Period began, when various peoples, initially largely Germanic peoples , moved across Europe. The Franks , Alemanni , and the Burgundians all ended up in northern Gaul while the Angles , Saxons , and Jutes settled in Britain , and

5845-529: The Benedictine Rule for Western monasticism during the 6th century, detailing the administrative and spiritual responsibilities of a community of monks led by an abbot . Monks and monasteries had a deep effect on the religious and political life of the Early Middle Ages, in various cases acting as land trusts for powerful families, centres of propaganda and royal support in newly conquered regions, and bases for missions and proselytisation. They were

6012-697: The Carolingian dynasty , briefly established the Carolingian Empire during the later 8th and early 9th centuries. It covered much of Western Europe but later succumbed to the pressures of internal civil wars combined with external invasions: Vikings from the north, Magyars from the east, and Saracens from the south. During the High Middle Ages, which began after 1000, the population of Europe increased greatly as technological and agricultural innovations allowed trade to flourish and

6179-531: The Desert Fathers of Egypt and Syria . Most European monasteries were of the type that focuses on community experience of the spiritual life, called cenobitism , which was pioneered by Pachomius (d. 348) in the 4th century. Monastic ideals spread from Egypt to Western Europe in the 5th and 6th centuries through hagiographical literature such as the Life of Anthony . Benedict of Nursia (d. 547) wrote

6346-584: The Gregorian chant in liturgical music for the churches. An important activity for scholars during this period was the copying, correcting, and dissemination of basic works on religious and secular topics, with the aim of encouraging learning. New works on religious topics and schoolbooks were also produced. Grammarians of the period modified the Latin language, changing it from the Classical Latin of

6513-714: The Macedonian dynasty . Commerce revived and the emperors oversaw the extension of a uniform administration to all the provinces. The military was reorganised, which allowed the emperors John I (r. 969–976) and Basil II (r. 976–1025) to expand the frontiers of the empire on all fronts. The imperial court was the centre of a revival of classical learning, a process known as the Macedonian Renaissance . Writers such as John Geometres ( fl. early 10th century) composed new hymns, poems, and other works. Missionary efforts by both Eastern and Western clergy resulted in

6680-486: The Medieval Warm Period climate change allowed crop yields to increase. Manorialism , the organisation of peasants into villages that owed rent and labour services to the nobles , and feudalism , the political structure whereby knights and lower-status nobles owed military service to their overlords in return for the right to rent from lands and manors , were two of the ways society was organized in

6847-735: The Migration Period , including various Germanic peoples , formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—once part of the Byzantine Empire —came under the rule of the Umayyad Caliphate , an Islamic empire, after conquest by Muhammad's successors . Although there were substantial changes in society and political structures,

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7014-497: The forward texture mapping used by the Nvidia NV1 , was able to offer efficient quad primitives. With perspective correction (see below) triangles become equivalent and this advantage disappears. For rectangular objects that are at right angles to the viewer, like floors and walls, the perspective only needs to be corrected in one direction across the screen, rather than both. The correct perspective mapping can be calculated at

7181-468: The 17th-century German historian Christoph Cellarius divided history into three periods: ancient, medieval, and modern. The most commonly given starting point for the Middle Ages is around 500, with the date of 476 first used by Bruni. Later starting dates are sometimes used in the outer parts of Europe. For Europe as a whole, 1500 is often considered to be the end of the Middle Ages, but there

7348-478: The 5th and the 7th centuries, going first to England and Scotland and then on to the continent. Under such monks as Columba (d. 597) and Columbanus (d. 615), they founded monasteries, taught in Latin and Greek, and authored secular and religious works. The Early Middle Ages witnessed the rise of monasticism in the West. The shape of European monasticism was determined by traditions and ideas that originated with

7515-731: The 5th century. The Eastern Empire was marked by closer relations between the political state and Christian Church, with doctrinal matters assuming an importance in Eastern politics that they did not have in Western Europe. Legal developments included the codification of Roman law ; the first effort—the Codex Theodosianus —was completed in 438. Under Emperor Justinian (r. 527–565), another compilation took place—the Corpus Juris Civilis . Justinian also oversaw

7682-685: The 6th and 7th centuries, all of them ruled by the Merovingian dynasty, who were descended from Clovis. The 7th century was a tumultuous period of wars between Austrasia and Neustria. Such warfare was exploited by Pippin (d. 640), the Mayor of the Palace for Austrasia who became the power behind the Austrasian throne. Later members of his family inherited the office, acting as advisers and regents. One of his descendants, Charles Martel (d. 741), won

7849-651: The Arabs. The migrations and invasions of the 4th and 5th centuries disrupted trade networks around the Mediterranean. African goods stopped being imported into Europe, first disappearing from the interior and by the 7th century found only in a few cities such as Rome or Naples . By the end of the 7th century, under the impact of the Muslim conquests , African products were no longer found in Western Europe. The replacement of goods from long-range trade with local products

8016-536: The Bald received the western Frankish lands, comprising most of modern-day France. Charlemagne's grandsons and great-grandsons divided their kingdoms between their descendants, eventually causing all internal cohesion to be lost. In 987 the Carolingian dynasty was replaced in the western lands, with the crowning of Hugh Capet (r. 987–996) as king. In the eastern lands the dynasty had died out earlier, in 911, with

8183-551: The Balkan Peninsula. The settlement of peoples was accompanied by changes in languages. Latin , the literary language of the Western Roman Empire, was gradually replaced by vernacular languages which evolved from Latin, but were distinct from it, collectively known as Romance languages . These changes from Latin to the new languages took many centuries. Greek remained the language of the Byzantine Empire, but

8350-643: The Battle of Poitiers in 732, halting the advance of Muslim armies across the Pyrenees. Great Britain was divided into small states dominated by the kingdoms of Northumbria , Mercia , Wessex , and East Anglia which descended from the Anglo-Saxon invaders. Smaller kingdoms in present-day Wales and Scotland were still under the control of the native Britons and Picts . Ireland was divided into even smaller political units, usually known as tribal kingdoms, under

8517-577: The Byzantine Empire, as the assumption of the imperial title by the Carolingians asserted their equivalence to the Byzantine state. There were several differences between the newly established Carolingian Empire and both the older Western Roman Empire and the concurrent Byzantine Empire. The Frankish lands were rural in character, with only a few small cities. Most of the people were peasants settled on small farms. Little trade existed and much of that

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8684-523: The Byzantine Empire, which he sealed with the marriage of his son Otto II (r. 967–983) to Theophanu (d. 991), daughter of an earlier Byzantine Emperor Romanos II (r. 959–963). By the late 10th century Italy had been drawn into the Ottonian sphere after a period of instability; Otto III (r. 996–1002) spent much of his later reign in the kingdom. The western Frankish kingdom was more fragmented, and although kings remained nominally in charge, much of

8851-648: The Christian period as nova (or "new"). Petrarch regarded the post-Roman centuries as " dark " compared to the "light" of classical antiquity . Leonardo Bruni was the first historian to use tripartite periodisation in his History of the Florentine People (1442), with a middle period "between the fall of the Roman Empire and the revival of city life sometime in late eleventh and twelfth centuries". Tripartite periodisation became standard after

9018-660: The Church had widened to the extent that the cultural and religious differences were greater than the similarities. The formal break, known as the East–West Schism , came in 1054, when the papacy and the patriarchy of Constantinople clashed over papal supremacy and excommunicated each other, which led to the division of Christianity into two Churches—the Western branch became the Roman Catholic Church and

9185-499: The Church had become music and art rather than the book. Most intellectual efforts went towards imitating classical scholarship, but some original works were created, along with now-lost oral compositions. The writings of Sidonius Apollinaris (d. 489), Cassiodorus (d. c.  585 ), and Boethius (d. c. 525) were typical of the age. Changes also took place among laymen, as aristocratic culture focused on great feasts held in halls rather than on literary pursuits. Clothing for

9352-704: The Dnieper River in modern Ukraine to the Adriatic Sea. By 1018, the last Bulgarian nobles had surrendered to the Byzantine Empire. Few large stone buildings were constructed between the Constantinian basilicas of the 4th century and the 8th century, although many smaller ones were built during the 6th and 7th centuries. By the beginning of the 8th century, the Carolingian Empire revived the basilica form of architecture. One feature of

9519-585: The Early Middle Ages are mostly illuminated manuscripts and carved ivories , originally made for metalwork that has since been melted down. Objects in precious metals were the most prestigious form of art, but almost all are lost except for a few crosses such as the Cross of Lothair , several reliquaries , and finds such as the Anglo-Saxon burial at Sutton Hoo and the hoards of Gourdon from Merovingian France, Guarrazar from Visigothic Spain and Nagyszentmiklós near Byzantine territory. There are survivals from

9686-530: The Eastern branch the Eastern Orthodox Church . The ecclesiastical structure of the Roman Empire survived the movements and invasions in the west mostly intact, but the papacy was little regarded, and few of the Western bishops looked to the bishop of Rome for religious or political leadership. Many of the popes prior to 750 were more concerned with Byzantine affairs and Eastern theological controversies. The register, or archived copies of

9853-538: The Eastern emperors to pay tribute. They remained a strong power until 796. An additional problem to face the empire came as a result of the involvement of Emperor Maurice (r. 582–602) in Persian politics when he intervened in a succession dispute . This led to a period of peace, but when Maurice was overthrown, the Persians invaded and during the reign of Emperor Heraclius (r. 610–641) controlled large chunks of

10020-492: The European population remained rural peasants. Many were no longer settled in isolated farms but had gathered into small communities, usually known as manors or villages. These peasants were often subject to noble overlords and owed them rents and other services, in a system known as manorialism . There remained a few free peasants throughout this period and beyond, with more of them in the regions of Southern Europe than in

10187-733: The Frankish King Charles the Simple (r. 898–922) to settle in what became Normandy . The eastern parts of the Frankish kingdoms, especially Germany and Italy, were under continual Magyar assault until the invader's defeat at the Battle of Lechfeld in 955. The breakup of the Abbasid dynasty meant that the Islamic world fragmented into smaller political states, some of which began expanding into Italy and Sicily, as well as over

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10354-578: The Franks and Celtic Britons set up small polities. Francia was centred in northern Gaul, and the first king of whom much is known is Childeric I (d. 481). His grave was discovered in 1653 and is remarkable for its grave goods , which included weapons and a large quantity of gold. Under Childeric's son Clovis I (r. 509–511), the founder of the Merovingian dynasty , the Frankish kingdom expanded and converted to Christianity. The Britons, related to

10521-685: The German tried to annex all of East Francia. Louis the Pious died in 840, with the empire still in chaos. A three-year civil war followed his death. By the Treaty of Verdun (843), a kingdom between the Rhine and Rhone rivers was created for Lothair to go with his lands in Italy, and his imperial title was recognised. Louis the German was in control of Bavaria and the eastern lands in modern-day Germany. Charles

10688-700: The Great (d. 526) and set up a kingdom marked by its co-operation between the Italians and the Ostrogoths, at least until the last years of Theodoric's reign. The Burgundians settled in Gaul, and after an earlier realm was destroyed by the Huns in 436, formed a new kingdom in the 440s. Between today's Geneva and Lyon , it grew to become the realm of Burgundy in the late 5th and early 6th centuries. Elsewhere in Gaul,

10855-438: The High Middle Ages. This period also saw the collapse of the unified Christian church, with the East-West Schism of 1054 . The Crusades , first preached in 1095, were military attempts by Western European Christians to regain control of the Holy Land from Muslims . Kings became the heads of centralised nation-states , reducing crime and violence but making the ideal of a unified Christendom more distant. Intellectual life

11022-403: The Italian peninsula was conquered by the Ostrogoths . The Eastern Roman Empire, often referred to as the Byzantine Empire after the fall of its western counterpart, had little ability to assert control over the lost western territories. The Byzantine emperors maintained a claim over the territory, but while none of the new kings in the west dared to elevate himself to the position of emperor of

11189-619: The Late Middle Ages and beginning the early modern period . The Middle Ages is one of the three major periods in the most enduring scheme for analysing European history : classical civilisation or Antiquity , the Middle Ages and the Modern Period . The "Middle Ages" first appears in Latin in 1469 as media tempestas or "middle season". In early usage, there were many variants, including medium aevum , or "middle age", first recorded in 1604, and media saecula , or "middle centuries", first recorded in 1625. The adjective "medieval" (or sometimes "mediaeval" or "mediæval"), meaning pertaining to

11356-439: The Lombards, which freed the papacy from the fear of Lombard conquest and marked the beginnings of the Papal States . The coronation of Charlemagne as emperor on Christmas Day 800 is regarded as a turning point in medieval history, marking a return of the Western Roman Empire, since the new emperor ruled over much of the area previously controlled by the Western emperors. It also marks a change in Charlemagne's relationship with

11523-405: The Mediterranean, pottery remained prevalent and appears to have been traded over medium-range networks, not just produced locally. The various Germanic states in the west all had coinages that imitated existing Roman and Byzantine forms. Gold continued to be minted until the end of the 7th century in 693-94 when it was replaced by silver in the Merovingian kingdom. The basic Frankish silver coin

11690-411: The Middle Ages, derives from medium aevum . Medieval writers divided history into periods such as the " Six Ages " or the " Four Empires ", and considered their time to be the last before the end of the world. When referring to their own times, they spoke of them as being "modern". In the 1330s, the Italian humanist and poet Petrarch referred to pre-Christian times as antiqua (or "ancient") and to

11857-496: The Middle East than Europe, losing control of sections of the Muslim lands. Umayyad descendants took over the Iberian Peninsula, the Aghlabids controlled North Africa, and the Tulunids became rulers of Egypt. By the middle of the 8th century, new trading patterns were emerging in the Mediterranean; trade between the Franks and the Arabs replaced the old Roman economy . Franks traded timber, furs, swords and slaves in return for silks and other fabrics, spices, and precious metals from

12024-666: The Pyrenees into the southern parts of the Frankish kingdoms. Efforts by local kings to fight the invaders led to the formation of new political entities. In Anglo-Saxon England , King Alfred the Great (r. 871–899) came to an agreement with the Viking invaders in the late 9th century, resulting in Danish settlements in Northumbria, Mercia, and parts of East Anglia. By the middle of the 10th century, Alfred's successors had conquered Northumbria, and restored English control over most of

12191-623: The Rhine and eastwards, leaving Charles West Francia with the empire to the west of the Rhineland and the Alps. Louis the German (d. 876), the middle child, who had been rebellious to the last, was allowed to keep Bavaria under the suzerainty of his elder brother. The division was disputed. Pepin II of Aquitaine (d. after 864), the emperor's grandson, rebelled in a contest for Aquitaine , while Louis

12358-515: The Roman Empire into a more flexible form to fit the needs of the Church and government. By the reign of Charlemagne, the language had so diverged from the classical Latin that it was later called Medieval Latin . Charlemagne planned to continue the Frankish tradition of dividing his kingdom between all his heirs, but was unable to do so as only one son, Louis the Pious (r. 814–840), was still alive by 813. Just before Charlemagne died in 814, he crowned Louis as his successor. Louis's reign of 26 years

12525-496: The Romans and the invaders are often similar, and tribal items were often modelled on Roman objects. Much of the scholarly and written culture of the new kingdoms was also based on Roman intellectual traditions. An important difference was the gradual loss of tax revenue by the new polities. Many of the new political entities no longer supported their armies through taxes, instead relying on granting them land or rents. This meant there

12692-585: The Vandals went on to cross the strait of Gibraltar after which they conquered the province of Africa . In the 430s the Huns began invading the empire; their king Attila (r. 434–453) led invasions into the Balkans in 442 and 447, Gaul in 451, and Italy in 452. The Hunnic threat remained until Attila's death in 453, when the Hunnic confederation he led fell apart. These invasions by the tribes completely changed

12859-455: The West were not uniform; some areas had greatly fragmented landholding patterns, but in other areas large contiguous blocks of land were the norm. These differences allowed for a wide variety of peasant societies, some dominated by aristocratic landholders and others having a great deal of autonomy. Land settlement also varied greatly. Some peasants lived in large settlements that numbered as many as 700 inhabitants. Others lived in small groups of

13026-567: The acceptance of figurative monumental sculpture in Christian art , and by the end of the period near life-sized figures such as the Gero Cross were common in important churches. During the later Roman Empire, the principal military developments were attempts to create an effective cavalry force as well as the continued development of highly specialised types of troops. The creation of heavily armoured cataphract -type soldiers as cavalry

13193-445: The appearance of a texture mapped landscape without the use of traditional geometric primitives. Every triangle can be further subdivided into groups of about 16 pixels in order to achieve two goals. First, keeping the arithmetic mill busy at all times. Second, producing faster arithmetic results. For perspective texture mapping without hardware support, a triangle is broken down into smaller triangles for rendering and affine mapping

13360-417: The basilica is the use of a transept , or the "arms" of a cross-shaped building that are perpendicular to the long nave . Other new features of religious architecture include the crossing tower and a monumental entrance to the church , usually at the west end of the building. Carolingian art was produced for a small group of figures around the court, and the monasteries and churches they supported. It

13527-632: The break with classical antiquity was not complete. The still-sizeable Byzantine Empire, Rome's direct continuation, survived in the Eastern Mediterranean and remained a major power. The empire's law code, the Corpus Juris Civilis or "Code of Justinian", was rediscovered in Northern Italy in the 11th century. In the West, most kingdoms incorporated the few extant Roman institutions. Monasteries were founded as campaigns to Christianise pagan Europe continued. The Franks , under

13694-488: The carbon-based parchment, the ink will appear bright compared to the paper. After virtually peeling off the layers during the segmentation process, the texturing step matches the voxels of each geometric piece to their corresponding brightness value so that an observer is able to see the text written on each piece. In ideal cases, the scanned volume will match perfectly with the surface of each geometric piece and yield perfectly rendered text, but there are often small errors in

13861-448: The checker box texture appears bent), especially as primitives near the camera . Such distortion may be reduced with the subdivision of the polygon into smaller ones. For the case of rectangular objects, using quad primitives can look less incorrect than the same rectangle split into triangles, but because interpolating 4 points adds complexity to the rasterization, most early implementations preferred triangles only. Some hardware, such as

14028-407: The city of Byzantium as the newly renamed eastern capital, Constantinople . Diocletian's reforms strengthened the governmental bureaucracy, reformed taxation, and strengthened the army, which bought the empire time but did not resolve the problems it was facing: excessive taxation, a declining birthrate, and pressures on its frontiers, among others. Civil war between rival emperors became common in

14195-599: The conquest of North Africa sundered maritime connections between those areas. Increasingly, the Byzantine Church differed in language, practices, and liturgy from the Western Church. The Eastern Church used Greek instead of the Western Latin. Theological and political differences emerged, and by the early and middle 8th century issues such as iconoclasm , clerical marriage , and state control of

14362-684: The construction of the Hagia Sophia in Constantinople and the reconquest of North Africa from the Vandals and Italy from the Ostrogoths, under Belisarius (d. 565). The conquest of Italy was not complete, as a deadly outbreak of plague in 542 led to the rest of Justinian's reign concentrating on defensive measures rather than further conquests. At the Emperor's death, the Byzantines had control of most of Italy , North Africa, and

14529-551: The control of kings. There were perhaps as many as 150 local kings in Ireland, of varying importance. The Carolingian dynasty , as the successors to Charles Martel are known, officially took control of the kingdoms of Austrasia and Neustria in a coup of 753 led by Pippin III (r. 752–768). A contemporary chronicle claims that Pippin sought, and gained, authority for this coup from Pope Stephen II (pope 752–757). Pippin's takeover

14696-638: The conversion of the Moravians , Bulgars , Bohemians , Poles , Magyars, and Slavic inhabitants of the Kievan Rus' . These conversions contributed to the founding of political states in the lands of those peoples—the states of Moravia , Bulgaria , Bohemia , Poland , Hungary, and the Kievan Rus'. Bulgaria, which was founded around 680, at its height reached from Budapest to the Black Sea and from

14863-700: The death of Louis the Child , and the selection of the unrelated Conrad I (r. 911–918) as king. The breakup of the Carolingian Empire was accompanied by invasions, migrations, and raids by external foes. The Atlantic and northern shores were harassed by the Vikings , who also raided the British Isles and settled there as well as in Iceland. In 911, the Viking chieftain Rollo (d. c. 931) received permission from

15030-401: The death of Queen Isabella I of Castile in 1504, or the conquest of Granada in 1492. Historians from Romance-speaking countries tend to divide the Middle Ages into two parts: an earlier "High" and later "Low" period. English-speaking historians, following their German counterparts, generally subdivide the Middle Ages into three intervals: "Early", "High", and "Late". In the 19th century,

15197-429: The depth, the rest of the line could use fast affine mapping. Some later renderers of this era simulated a small amount of camera pitch with shearing which allowed the appearance of greater freedom whilst using the same rendering technique. Some engines were able to render texture mapped Heightmaps (e.g. Nova Logic 's Voxel Space , and the engine for Outcast ) via Bresenham -like incremental algorithms, producing

15364-578: The disorder, was killed fighting the Goths at the Battle of Adrianople on 9 August 378. In addition to the threat from such tribal confederacies in the north, internal divisions within the empire, especially within the Christian Church, caused problems. In 400, the Visigoths invaded the Western Roman Empire and, although briefly forced back from Italy, in 410 sacked the city of Rome . In 406

15531-458: The distance along a surface to minimize distortion. These coordinates are interpolated across the faces of polygons to sample the texture map during rendering. Textures may be repeated or mirrored to extend a finite rectangular bitmap over a larger area, or they may have a one-to-one unique " injective " mapping from every piece of a surface (which is important for render mapping and light mapping , also known as baking ). Texture mapping maps

15698-430: The distortions due to individual flattening. This step also re-flattens and re-textures the image to create the final visualization of the unwrapped scroll, and is computationally expensive compared to the texture merging process detailed above. Using each of these steps, the computer is able to transform the voxels from the 3D volumetric scan and their corresponding density brightnesses to a 2D virtually unwrapped image of

15865-442: The early Carolingian period, with a growing dominance of elite heavy cavalry. The use of militia-type levies of the free population declined over the Carolingian period. Although much of the Carolingian armies were mounted, a large proportion during the early period appear to have been mounted infantry , rather than true cavalry. One exception was Anglo-Saxon England, where the armies were still composed of regional levies, known as

16032-531: The elites was richly embellished with jewels and gold. Lords and kings supported entourages of fighters who formed the backbone of the military forces. Family ties within the elites were important, as were the virtues of loyalty, courage, and honour. These ties led to the prevalence of the feud in aristocratic society, examples of which included those related by Gregory of Tours that took place in Merovingian Gaul. Most feuds seem to have ended quickly with

16199-591: The emergence of Islam in Arabia during the lifetime of Muhammad (d. 632). After his death, Islamic forces conquered much of the Eastern Roman Empire and Persia, starting with Syria in 634–635, continuing with Persia between 637 and 642, reaching Egypt in 640–641, North Africa in the later seventh century, and the Iberian Peninsula in 711. By 714, Islamic forces controlled much of

16366-403: The empire than tax-payers. The Emperor Diocletian (r. 284–305) split the empire into separately administered eastern and western halves in 286; the empire was not considered divided by its inhabitants or rulers, as legal and administrative promulgations in one division were considered valid in the other. In 330, after a period of civil war, Constantine the Great (r. 306–337) refounded

16533-573: The empire to Christianity , a gradual process that lasted from the 2nd to the 5th centuries. In 376, the Goths , fleeing from the Huns , received permission from Emperor Valens (r. 364–378) to settle in the Roman province of Thracia in the Balkans . The settlement did not go smoothly, and when Roman officials mishandled the situation, the Goths began to raid and plunder. Valens, attempting to put down

16700-447: The empire, including Egypt, Syria, and Anatolia until Heraclius' successful counterattack. In 628 the empire secured a peace treaty and recovered all of its lost territories. In Western Europe, some of the older Roman elite families died out while others became more involved with ecclesiastical than secular affairs. Values attached to Latin scholarship and education mostly disappeared, and while literacy remained important, it became

16867-486: The empire. Such movements were aided by the refusal of the Western Roman elites to support the army or pay the taxes that would have allowed the military to suppress the migration. The emperors of the 5th century were often controlled by military strongmen such as Stilicho (d. 408), Aetius (d. 454), Aspar (d. 471), Ricimer (d. 472), or Gundobad (d. 516), who were partly or fully of non-Roman background. When

17034-454: The entire Middle Ages were often referred to as the " Dark Ages ", but with the adoption of these subdivisions, use of this term was restricted to the Early Middle Ages, at least among historians. The Roman Empire reached its greatest territorial extent during the 2nd century AD; the following two centuries witnessed the slow decline of Roman control over its outlying territories. Economic issues, including inflation, and external pressure on

17201-635: The frontiers combined to create the Crisis of the Third Century , with emperors coming to the throne only to be rapidly replaced by new usurpers. Military expenses increased steadily during the 3rd century, mainly in response to the war with the Sasanian Empire , which revived in the middle of the 3rd century. The army doubled in size, and cavalry and smaller units replaced the Roman legion as

17368-451: The imperial officials called missi dominici , who served as roving inspectors and troubleshooters. Charlemagne's court in Aachen was the centre of the cultural revival sometimes referred to as the " Carolingian Renaissance ". Literacy increased, as did development in the arts, architecture and jurisprudence, as well as liturgical and scriptural studies. The English monk Alcuin (d. 804)

17535-401: The inside of the scroll, but for the arts and antiquities world, it is often best to convert this to a 2D flat image to demonstrate what the scroll’s parchment would have looked like if they could physically unravel without damage. This requires the virtual unwrapping process to include a step that converts the curved 3D geometric pieces into flat 2D planes. To do so, the virtual unwrapping models

17702-415: The king of the united Austrasia and Neustria. Charles, more often known as Charles the Great or Charlemagne , embarked upon a programme of systematic expansion in 774 that unified a large portion of Europe, eventually controlling modern-day France, northern Italy, and Saxony . In the wars that lasted beyond 800, he rewarded allies with war booty and command over parcels of land. In 774, Charlemagne conquered

17869-679: The large brooches in fibula or penannular form that were a key piece of personal adornment for elites, including the Irish Tara Brooch . Highly decorated books were mostly Gospel Books and these have survived in larger numbers , including the Insular Book of Kells , the Book of Lindisfarne , and the imperial Codex Aureus of St. Emmeram , which is one of the few to retain its " treasure binding " of gold encrusted with jewels. Charlemagne's court seems to have been responsible for

18036-408: The layer one at a time. Because each voxel is ordered, peeling off each layer will preserve the continuity of the scroll structure. The second stage, texturing, focuses on identifying intensity values that correspond with each voxel using texture mapping . From the micro-CT scan, each voxel has an associated brightness value that corresponds to a higher density. Since the metallic ink is denser than

18203-468: The left and right edges of the floor, and then an affine linear interpolation across that horizontal span will look correct, because every pixel along that line is the same distance from the viewer. Perspective correct texturing accounts for the vertices' positions in 3D space, rather than simply interpolating coordinates in 2D screen space. This achieves the correct visual effect but it is more expensive to calculate. To perform perspective correction of

18370-476: The letters, of Pope Gregory the Great (pope 590–604) survived, and of those more than 850 letters, the vast majority were concerned with affairs in Italy or Constantinople. The only part of Western Europe where the papacy had influence was Britain, where Gregory had sent the Gregorian mission in 597 to convert the Anglo-Saxons to Christianity. Irish missionaries were most active in Western Europe between

18537-417: The line of Western emperors ceased, many of the kings who replaced them were from the same background. Intermarriage between the new kings and the Roman elites was common. This led to a fusion of Roman culture with the customs of the invading tribes, including the popular assemblies that allowed free male tribal members more say in political matters than was common in the Roman state. Material artefacts left by

18704-638: The line of constant distance for arbitrary polygons and rendering along it. Texture mapping hardware was originally developed for simulation (e.g. as implemented in the Evans and Sutherland ESIG and Singer-Link Digital Image Generators DIG), and professional graphics workstations such as Silicon Graphics , broadcast digital video effects machines such as the Ampex ADO and later appeared in Arcade cabinets , consumer video game consoles , and PC video cards in

18871-517: The main and sometimes only outposts of education and literacy in a region. Many of the surviving manuscripts of the Latin classics were copied in monasteries in the Early Middle Ages. Monks were also the authors of new works, including history, theology, and other subjects, written by authors such as Bede (d. 735), a native of northern England who wrote in the late 7th and early 8th centuries. The Frankish kingdom in northern Gaul split into kingdoms called Austrasia , Neustria , and Burgundy during

19038-410: The main tactical unit. The need for revenue led to increased taxes and a decline in numbers of the curial , or landowning, class, and decreasing numbers of them willing to shoulder the burdens of holding office in their native towns. More bureaucrats were needed in the central administration to deal with the needs of the army, which led to complaints from civilians that there were more tax-collectors in

19205-718: The mid-1990s. In flight simulation , texture mapping provided important motion and altitude cues necessary for pilot training not available on untextured surfaces. It was also in flight simulation applications, that texture mapping was implemented for real-time processing with prefiltered texture patterns stored in memory for real-time access by the video processor. Modern graphics processing units (GPUs) provide specialised fixed function units called texture samplers , or texture mapping units , to perform texture mapping, usually with trilinear filtering or better multi-tap anisotropic filtering and hardware for decoding specific formats such as DXTn . As of 2016, texture mapping hardware

19372-467: The middle of the 4th century, diverting soldiers from the empire's frontier forces and allowing invaders to encroach. For much of the 4th century, Roman society stabilised in a new form that differed from the earlier classical period , with a widening gulf between the rich and poor, and a decline in the vitality of the smaller towns. Another change was the Christianisation , or conversion of

19539-488: The migrations of the Slavs added Slavic languages to Eastern Europe. As Western Europe witnessed the formation of new kingdoms, the Eastern Roman Empire remained intact and experienced an economic revival that lasted into the early 7th century. There were fewer invasions of the eastern section of the empire; most occurred in the Balkans. Peace with the Sasanian Empire , the traditional enemy of Rome, lasted throughout most of

19706-464: The military was the horseshoe , which allowed horses to be used in rocky terrain. The High Middle Ages was a period of tremendous expansion of population . The estimated population of Europe grew from 35 to 80 million between 1000 and 1347, although the exact causes remain unclear: improved agricultural techniques, the decline of slaveholding, a more clement climate and the lack of invasion have all been suggested. As much as 90 per cent of

19873-430: The model surface (or screen space during rasterization) into texture space ; in this space, the texture map is visible in its undistorted form. UV unwrapping tools typically provide a view in texture space for manual editing of texture coordinates. Some rendering techniques such as subsurface scattering may be performed approximately by texture-space operations. Multitexturing is the use of more than one texture at

20040-786: The natives of Britannia  – modern-day Great Britain – settled in what is now Brittany . Other monarchies were established by the Visigothic Kingdom in the Iberian Peninsula , the Suebi in northwestern Iberia, and the Vandal Kingdom in North Africa . In the sixth century, the Lombards settled in Northern Italy , replacing the Ostrogothic kingdom with a grouping of duchies that occasionally selected

20207-415: The north. The practice of assarting , or bringing new lands into production by offering incentives to the peasants who settled them, also contributed to the expansion of population. Texture mapping Texture mapping is a method for mapping a texture on a computer-generated graphic . "Texture" in this context can be high frequency detail , surface texture , or color . The original technique

20374-545: The payment of some sort of compensation . Women took part in aristocratic society mainly in their roles as wives and mothers of men, with the role of mother of a ruler being especially prominent in Merovingian Gaul. In Anglo-Saxon society the lack of many child rulers meant a lesser role for women as queen mothers, but this was compensated for by the increased role played by abbesses of monasteries. Only in Italy does it appear that women were always considered under

20541-587: The peninsula in a region they called Al-Andalus . The Islamic conquests reached their peak in the mid-eighth century. The defeat of Muslim forces at the Battle of Tours in 732 led to the reconquest of southern France by the Franks, but the main reason for the halt of Islamic growth in Europe was the overthrow of the Umayyad Caliphate and its replacement by the Abbasid Caliphate . The Abbasids moved their capital to Baghdad and were more concerned with

20708-493: The perspective with a faster calculation, such as a polynomial. Still another technique uses 1/z value of the last two drawn pixels to linearly extrapolate the next value. The division is then done starting from those values so that only a small remainder has to be divided but the amount of bookkeeping makes this method too slow on most systems. Finally, the Build engine extended the constant distance trick used for Doom by finding

20875-423: The points on the surface of each 3D piece as masses connected by springs where the springs will come to rest only when the 3D pieces are perfectly flat. This technique is inspired by the mass-spring systems traditionally used to model deformation. After segmenting, textualizing, and flattening the scroll to obtain 2D text fragments, the last step is a merge step meant to reconcile each individual segment to visualize

21042-408: The political and demographic nature of what had been the Western Roman Empire. By the end of the 5th century the western section of the empire was divided into smaller political units, ruled by the tribes that had invaded in the early part of the century. The deposition of the last emperor of the west, Romulus Augustulus , in 476 has traditionally marked the end of the Western Roman Empire. By 493

21209-532: The political power devolved to the local lords. Missionary efforts to Scandinavia during the 9th and 10th centuries helped strengthen the growth of kingdoms such as Sweden , Denmark , and Norway , which gained power and territory. Some kings converted to Christianity, although not all by 1000. Scandinavians also expanded and colonised throughout Europe. Besides the settlements in Ireland, England, and Normandy, further settlement took place in what became Russia and Iceland . Swedish traders and raiders ranged down

21376-616: The polygon that are closer to the viewer the difference from pixel to pixel between texture coordinates is smaller (stretching the texture wider) and in parts that are farther away this difference is larger (compressing the texture). 3D graphics hardware typically supports perspective correct texturing. Various techniques have evolved for rendering texture mapped geometry into images with different quality/precision tradeoffs, which can be applied to both software and hardware. Classic software texture mappers generally did only simple mapping with at most one lighting effect (typically applied through

21543-414: The primitive. The primary advantage is that each pixel covered by a primitive will be traversed exactly once. Once a primitive's vertices are transformed, the amount of remaining work scales directly with how many pixels it covers on the screen. The main disadvantage versus forward texture mapping is that the memory access pattern in the texture space will not be linear if the texture is at an angle to

21710-419: The protection and control of a male relative. Peasant society is much less documented than the nobility. Most of the surviving information available to historians comes from archaeology ; few detailed written records documenting peasant life remain from before the 9th century. Most of the descriptions of the lower classes come from either law codes or writers from the upper classes. Landholding patterns in

21877-525: The rivers of the Russian steppe, and even attempted to seize Constantinople in 860 and 907 . Christian Spain, initially driven into a small section of the peninsula in the north, expanded slowly south during the 9th and 10th centuries, establishing the kingdoms of Asturias and León . In Eastern Europe, Byzantium revived its fortunes under Emperor Basil I (r. 867–886) and his successors Leo VI (r. 886–912) and Constantine VII (r. 913–959), members of

22044-551: The screen) are calculated from the texels (texture pixels) is governed by texture filtering . The cheapest method is to use the nearest-neighbour interpolation , but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies . In the event of a texture coordinate being outside the texture, it is either clamped or wrapped . Anisotropic filtering better eliminates directional artefacts when viewing textures from oblique viewing angles. Texture streaming

22211-415: The screen. This disadvantage is often addressed by texture caching techniques, such as the swizzled texture memory arrangement. The linear interpolation can be used directly for simple and efficient affine texture mapping, but can also be adapted for perspective correctness . Forward texture mapping maps each texel of the texture to a pixel on the screen. After transforming a rectangular primitive to

22378-481: The scroll appeared as burned, crushed chunks of charcoal. Each disturbance caused the scroll to disintegrate, leaving few options for conservation or restoration. The scroll fragments were preserved by the IAA, although for decades after their discovery the scroll remains remained in storage due to their severely damaged condition. The scroll's fragility led scientists to search for non-traditional techniques to reconstruct

22545-418: The scroll in the final images. When the scroll completes a full rotation in regard to the x-ray source, the computer generates a 2D slice of the cross-section, and performing this iteratively allows the computer to build up a 3D volumetric scan describing the density as a function of the position inside the scroll. The only data needed for the virtual unwrapping process is this volumetric scan, so after this point

22712-402: The scroll should be dated to the second half of the first century CE or the beginning of the second. Drew Longacre disputed Yardeni's analysis, arguing that it was misled by the paucity of comparative material from later centuries. In Longacre's analysis, the paleographical evidence supported the radiocarbon date. The innermost portion of the scroll contains a large blank area typically placed at

22879-402: The scroll was safely returned to its protective archive. The density distribution is stored by the computer with corresponding positions, called voxels or volume-pixels. The goal of the virtual unwrapping process is to determine the layered structure of the scroll and try to peel back each layer while keeping track of which voxel is being peeled and what density it corresponds to. By transforming

23046-417: The segmentation process that generate noise in the texturing process. Because of this, the texturing process usually includes nearest-neighbor interpolation texture filtering to reduce the noise and sharpen the lettering. After segmentation and texturing, each piece of the virtually deconstructed scroll is ordered and has its corresponding text visualized on its surface. This is, in practice, enough to ‘read’

23213-668: The slow infiltration of the Balkans by the Slavs added a further difficulty for Justinian's successors. It began gradually, but by the late 540s Slavic tribes were in Thrace and Illyrium , and had defeated an imperial army near Adrianople in 551. In the 560s the Avars began to expand from their base on the north bank of the Danube ; by the end of the 6th-century, they were the dominant power in Central Europe and routinely able to force

23380-697: The southern part of Great Britain. In northern Britain, Kenneth MacAlpin (d. c. 860) united the Picts and the Scots into the Kingdom of Alba . In the early 10th century, the Ottonian dynasty had established itself in Germany , and was engaged in driving back the Magyars. Its efforts culminated in the coronation in 962 of Otto I (r. 936–973) as Holy Roman Emperor . In 972, he secured recognition of his title by

23547-402: The speed of linear interpolation because the perspective correct calculation runs in parallel on the co-processor. The polygons are rendered independently, hence it may be possible to switch between spans and columns or diagonal directions depending on the orientation of the polygon normal to achieve a more constant z but the effort seems not to be worth it. Another technique was approximating

23714-466: The start of a scroll in order to protect it. For this reason, the researchers concluded that Leviticus was the first book on the scroll and that at most three books of the Torah were originally present. However, most of the scroll has been burnt away and only two columns of Leviticus were found. The text recovered consists of 18 complete lines and 17 partial lines of the first two chapters of Leviticus . It

23881-400: The surface being textured. In contrast, the original z {\displaystyle z} , u {\displaystyle u} and v {\displaystyle v} , before the division, are not linear across the surface in screen space. We can therefore linearly interpolate these reciprocals across the surface, computing corrected values at each pixel, to result in

24048-1296: The technique (controlled by a materials system ) have made it possible to simulate near- photorealism in real time by vastly reducing the number of polygons and lighting calculations needed to construct a realistic and functional 3D scene. A texture map is an image applied (mapped) to the surface of a shape or polygon . This may be a bitmap image or a procedural texture . They may be stored in common image file formats , referenced by 3D model formats or material definitions , and assembled into resource bundles . They may have one to three dimensions, although two dimensions are most common for visible surfaces. For use with modern hardware, texture map data may be stored in swizzled or tiled orderings to improve cache coherency . Rendering APIs typically manage texture map resources (which may be located in device memory ) as buffers or surfaces, and may allow ' render to texture ' for additional effects such as post processing or environment mapping . They usually contain RGB color data (either stored as direct color , compressed formats , or indexed color ), and sometimes an additional channel for alpha blending ( RGBA ) especially for billboards and decal overlay textures. It

24215-569: The text inside. Middle Ages In the history of Europe , the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the Post-classical period of global history . It began with the fall of the Western Roman Empire and transitioned into the Renaissance and the Age of Discovery . The Middle Ages is the middle period of

24382-470: The text of the document virtually. This search led to the development of a virtual unwrapping technique developed by Prof. Seales of the University of Kentucky , which in 2015 allowed scientists to reveal the text contained in the scroll. The virtual unwrapping process begins with using X-ray microtomography (micro-CT) to scan the damaged scroll. This scan is non-invasive and uses the same technology as

24549-536: The texture coordinates u {\displaystyle u} and v {\displaystyle v} , with z {\displaystyle z} being the depth component from the viewer's point of view, we can take advantage of the fact that the values 1 z {\displaystyle {\frac {1}{z}}} , u z {\displaystyle {\frac {u}{z}}} , and v z {\displaystyle {\frac {v}{z}}} are linear in screen space across

24716-559: The three traditional divisions of Western history: classical antiquity , the medieval period, and the modern period . The medieval period is itself subdivided into the Early , High , and Late Middle Ages . Population decline , counterurbanisation , the collapse of centralized authority, invasions, and mass migrations of tribes , which had begun in Late Antiquity , continued into the Early Middle Ages. The large-scale movements of

24883-497: The towns chosen as capitals. Although there had been Jewish communities in many Roman cities , the Jews suffered periods of persecution after the conversion of the empire to Christianity. Officially they were tolerated, if subject to conversion efforts, and at times were even encouraged to settle in new areas. Religious beliefs in the Eastern Roman Empire and Iran were in flux during the late sixth and early seventh centuries. Judaism

25050-418: The unwrapped parchment as a whole. This involves two parts: texture merging and mesh merging. Texture merging aligns the textures from each segment to create a composite. This process is fast and gives feedback on the quality of the segmentation and alignment of each piece. While this is good enough to create a basic image of what the scroll looks like, there are some distortions which arise because each segment

25217-430: The voxels from a 3D volumetric scan to a 2D image, the writing on this inside is revealed to the viewer. This process happens in three steps: segmentation, texturing and flattening. The first stage of the virtual unwrapping process, segmentation, involves identifying geometric models for the structures within the virtual scan of the scroll. Because of the extensive damage, the parchment has become deformed and no longer has

25384-645: The west, Byzantine control of most of the Western Empire could not be sustained; the reconquest of the Mediterranean periphery and the Italian Peninsula ( Gothic War ) in the reign of Justinian (r. 527–565) was the sole, and temporary, exception. The political structure of Western Europe changed with the end of the united Roman Empire. Although the movements of peoples during this period are usually described as "invasions", they were not just military expeditions but migrations of entire peoples into

25551-438: Was a trend throughout the old Roman lands that happened in the Early Middle Ages. This was especially marked in the lands that did not lie on the Mediterranean, such as northern Gaul or Britain. Non-local goods appearing in the archaeological record are usually luxury goods. In the northern parts of Europe, not only were the trade networks local, but the goods carried were simple, with little pottery or other complex products. Around

25718-469: Was an active proselytising faith, and at least one Arab political leader converted to it. In addition Jewish theologians wrote polemics defending their religion against Christian and Islamic influences. Christianity had active missions competing with the Persians' Zoroastrianism in seeking converts, especially among residents of the Arabian Peninsula . All these strands came together with

25885-438: Was an important feature of the 5th-century Roman military. The various invading tribes had differing emphases on types of soldiers—ranging from the primarily infantry Anglo-Saxon invaders of Britain to the Vandals and Visigoths who had a high proportion of cavalry in their armies. During the early invasion period, the stirrup had not been introduced into warfare, which limited the usefulness of cavalry as shock troops because it

26052-648: Was discovered in a 1970 excavation headed by Dan Barag and Ehud Netzer of the Institute of Archaeology at Hebrew University, and Yosef Porath of the Israel Antiquities Authority (IAA) at the ancient synagogue in Ein Gedi in Israel , the site of an ancient Jewish community. It was found in the burned remains of the ancient synagogue's Torah Ark . Severely damaged by a fire around 600 CE,

26219-474: Was dominated by efforts to regain the dignity and classicism of imperial Roman and Byzantine art , but was also influenced by the Insular art of the British Isles. Insular art integrated the energy of Irish Celtic and Anglo-Saxon Germanic styles of ornament with Mediterranean forms such as the book, and established many characteristics of art for the rest of the medieval period. Surviving religious works from

26386-408: Was invited to Aachen and brought the education available in the monasteries of Northumbria. Charlemagne's chancery —or writing office—made use of a new script today known as Carolingian minuscule , allowing a common writing style that advanced communication across much of Europe. Charlemagne sponsored changes in church liturgy , imposing the Roman form of church service on his domains, as well as

26553-493: Was less need for large tax revenues and so the taxation systems decayed. Warfare was common between and within the kingdoms. Slavery declined as the supply weakened, and society became more rural. Between the 5th and 8th centuries, new peoples and individuals filled the political void left by Roman centralised government. The Ostrogoths , a Gothic tribe, settled in Roman Italy in the late fifth century under Theoderic

26720-555: Was marked by scholasticism , a philosophy that emphasised joining faith to reason, and by the founding of universities . The theology of Thomas Aquinas , the paintings of Giotto , the poetry of Dante and Chaucer , the travels of Marco Polo , and the Gothic architecture of cathedrals such as Chartres are among the outstanding achievements toward the end of this period and into the Late Middle Ages. The Late Middle Ages

26887-656: Was marked by difficulties and calamities including famine, plague, and war, which significantly diminished the population of Europe; between 1347 and 1350, the Black Death killed about a third of Europeans. Controversy, heresy , and the Western Schism within the Catholic Church paralleled the interstate conflict, civil strife, and peasant revolts that occurred in the kingdoms. Cultural and technological developments transformed European society, concluding

27054-439: Was marked by numerous divisions of the empire among his sons and, after 829, civil wars between various alliances of father and sons over the control of various parts of the empire. Eventually, Louis recognised his eldest son Lothair I (d. 855) as emperor and gave him Italy. Louis divided the rest of the empire between Lothair and Charles the Bald (d. 877), his youngest son. Lothair took East Francia , comprising both banks of

27221-496: Was not possible to put the full force of the horse and rider behind blows struck by the rider. The greatest change in military affairs during the invasion period was the adoption of the Hunnic composite bow in place of the earlier, and weaker, Scythian composite bow. Another development was the increasing use of longswords and the progressive replacement of scale armour by mail armour and lamellar armour . The importance of infantry and light cavalry began to decline during

27388-531: Was pioneered by Edwin Catmull in 1974 as part of his doctoral thesis. Texture mapping originally referred to diffuse mapping , a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object). In recent decades, the advent of multi-pass rendering, multitexturing , mipmaps , and more complex mappings such as height mapping , bump mapping , normal mapping , displacement mapping , reflection mapping , specular mapping , occlusion mapping , and many other variations on

27555-442: Was reinforced with propaganda that portrayed the Merovingians as inept or cruel rulers, exalted the accomplishments of Charles Martel, and circulated stories of the family's great piety. At the time of his death in 768, Pippin left his kingdom in the hands of his two sons, Charles (r. 768–814) and Carloman (r. 768–771). When Carloman died of natural causes, Charles blocked the succession of Carloman's young son and installed himself as

27722-417: Was the denarius or denier , while the Anglo-Saxon version was called a penny . From these areas, the denier or penny spread throughout Europe from 700 to 1000 AD. Copper or bronze coins were not struck, nor were gold except in Southern Europe. No silver coins denominated in multiple units were minted. Christianity was a major unifying factor between Eastern and Western Europe before the Arab conquests, but

27889-409: Was with the British Isles and Scandinavia, in contrast to the older Roman Empire with its trading networks centred on the Mediterranean. The empire was administered by an itinerant court that travelled with the emperor, as well as approximately 300 imperial officials called counts , who administered the counties the empire had been divided into. Clergy and local bishops served as officials, as well as

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