text:
Chaldea

Chaldea was a small country that existed between the late 10th or early 9th and mid-6th centuries BC, after which the country and its people were absorbed and assimilated into the indigenous population of Babylonia. Semitic-speaking, it was located in the marshy land of the far southeastern corner of Mesopotamia and briefly came to rule Babylon. The Hebrew Bible uses the term כשדים (Kaśdim) and this is translated as Chaldaeans in the Greek Old Testament, although there is some dispute as to whether Kasdim in fact means Chaldean or refers to the south Mesopotamian Kaldu.

During a period of weakness in the East Semitic-speaking kingdom of Babylonia, new tribes of West Semitic-speaking migrants arrived in the region from the Levant between the 11th and 9th centuries BC. The earliest waves consisted of Suteans and Arameans, followed a century or so later by the Kaldu, a group who became known later as the Chaldeans or the Chaldees. These migrations did not affect the powerful kingdom and empire of Assyria in Upper Mesopotamia, which repelled these incursions.

These nomadic Chaldeans settled in the far southeastern portion of Babylonia, chiefly on the left bank of the Euphrates. Though for a short time the name commonly referred to the whole of southern Mesopotamia in Hebraic literature, this was a geographical and historical misnomer as Chaldea proper was in fact only the plain in the far southeast formed by the deposits of the Euphrates and the Tigris, extending about 400 mi along the course of these rivers and averaging about 100 mi in width. There were several kings of Chaldean origins who ruled Babylonia. From 626 BC to 539 BC, a ruling family referred to as the Chaldean dynasty, named after their possible Chaldean origin, ruled the kingdom at its height under the Neo-Babylonian Empire, although the final ruler of this empire, Nabonidus (556–539 BC) (and his son and regent Belshazzar) was a usurper of Assyrian ancestry.

Name
The name Chaldaea is a latinization of the Greek ' (Χαλδαία), a hellenization of Akkadian ' or , suggesting an underlying /kaɬdu/. The name appears in Hebrew in the Bible as ' (כשדים) and in Aramaic as ' (כשדי).

The Bible (Book of Genesis 22:22) uses the name Kesed (כשׂד, ancient pronunciation /kaɬd/ ), the singular form of Kasdim(כַּשְׂדִּים), meaning Chaldeans. Kesed is identified as son of Abraham's brother Nahor (and brother of Kemuel the father of Aram), residing in Aram Naharaim. Jewish historian Flavius Josephus (37 – c. 100) also links Arphaxad and Chaldaea, in his Antiquities of the Jews: "Arphaxad named the Arphaxadites, who are now called Chaldeans."

Land
In the early period, between the early 9th century and late 7th century BC, mat Kaldi was the name of a small sporadically independent migrant-founded territory under the domination of the Neo-Assyrian Empire (911–605 BC) in southeastern Babylonia, extending to the western shores of the Persian Gulf.

The expression  mat Bit Yâkin is also used, apparently synonymously. Bit Yâkin was the name of the largest and most powerful of the five tribes of the Chaldeans, or equivalently, their territory. The original extension of Bit Yâkin is not known precisely, but it extended from the lower Tigris into the Arabian Peninsula. Sargon II mentions it as extending as far as Dilmun or "sea-land" (littoral Eastern Arabia). "Chaldea" or mat Kaldi generally referred to the low, marshy, alluvial land around the estuaries of the Tigris and Euphrates, which at the time discharged their waters through separate mouths into the sea.

The tribal capital Dur Yâkin was the original seat of Marduk-Baladan.

The king of Chaldea was also called the king of Bit Yakin, just as the kings of Babylonia and Assyria were regularly styled simply king of Babylon or Assur, the capital city in each case. In the same way, what is now known as the Persian Gulf was sometimes called "the Sea of Bit Yakin", and sometimes "the Sea of the Land of Chaldea".

"Chaldea" came to be used in a wider sense, of Southern Mesopotamia in general, following the brief ascendancy of the Chaldeans during 608–557 BC. This is especially the case in the Hebrew Bible, which was substantially composed during this period (roughly corresponding to the period of Babylonian captivity). The Book of Jeremiah makes frequent reference to the Chaldeans (King James Version Chaldees following LXX Χαλδαίοι; in Biblical Hebrew as Kasdîm כַּשְׂדִּים). Book of Habakkuk 1:6 calls them "that bitter and hasty nation" (הַגֹּוי הַמַּר וְהַנִּמְהָר). Book of Isaiah 23:13 DRB states, “Behold the land of the Chaldeans, there was not such a people, the Assyrians founded it: they have led away the strong ones thereof into captivity, they have destroyed the houses thereof, they have brought it to ruin.”

Ancient Chaldeans
Unlike the East Semitic Akkadian-speaking Akkadians, Assyrians and Babylonians, whose ancestors had been established in Mesopotamia since at least the 30th century BC, the Chaldeans were not a native Mesopotamian people, but were late 10th- or early 9th-century BC West Semitic Levantine migrants to the southeastern corner of the region, who had played no part in the previous three millennia of Sumero-Akkadian and Assyro-Babylonian Mesopotamian civilization and history.

The ancient Chaldeans seem to have migrated into Mesopotamia sometime between c. 940 and 860 BC, a century or so after other new Semitic arrivals, the Arameans and the Suteans, appeared in Babylonia, c. 1100 BC. According to Ran Zadok, they first appear in written record in cylinder inscriptions of the King of Mari Aššur-ketta-lēšir II (late 12th-early 11th century BC), which record them reaching Messopotamia as early as the 11th century BC. They later appear in the annals of the Assyrian king Shalmaneser III during the 850s BC. This was a period of weakness in Babylonia, and its ineffectual native kings were unable to prevent new waves of semi-nomadic foreign peoples from invading and settling in the land.

Though belonging to the same West Semitic speaking ethnic group and migrating from the same Levantine regions as the earlier arriving Aramaeans, they are to be differentiated; the Assyrian king Sennacherib, for example, carefully distinguishes them in his inscriptions.

The Chaldeans were for a time able to keep their identity despite the dominant native Assyro-Babylonian (Sumero-Akkadian-derived) culture although, as was the case for the earlier Amorites, Kassites and Suteans before them, by the time Babylon fell in 539 BC, perhaps before, the Chaldeans ceased to exist as a specific ethnic group.

In the Hebrew Bible, "Ur of the Chaldees" (Ur Kaśdim) is cited as the starting point of the patriarch Abraham's journey to Canaan.

Language
Ancient Chaldeans originally spoke a West Semitic language similar to Old Aramaic. During the Neo-Assyrian Empire, Imperial Aramaic became the lingua franca of the empire under the rule of the Assyrian king Tiglath-Pileser III in the mid-8th century BC. As a result, in late periods both the Babylonian and Assyrian dialects of Akkadian became marginalized, and Aramaic took its place across Mesopotamia, including among the Chaldeans, and later, also the southern Levant. One form of this once widespread Aramaic language was used in some books of the Hebrew Bible (the Book of Daniel and the Book of Ezra). The use of the name "Chaldean" (Chaldaic, Chaldee) to describe it, first introduced by Jerome of Stridon (d. 420), became common in early Aramaic studies, but that misnomer was later corrected, when modern scholars concluded that the Aramaic dialect used in the Hebrew Bible was not related to the ancient Chaldeans and their language.

Religion
Ancient Chaldeans believed in "three heavens".

History
The region that the Chaldeans eventually made their homeland was in relatively poor southeastern Mesopotamia, at the head of the Persian Gulf. They appear to have migrated into southern Babylonia from the Levant at some unknown point between the end of the reign of Ninurta-kudurri-usur II (a contemporary of Tiglath-Pileser II) circa 940 BC, and the start of the reign of Marduk-zakir-shumi I in 855 BC, although there is no historical proof of their existence prior to the late 850s BC.

For perhaps a century or so after settling in the area, these semi-nomadic migrant Chaldean tribes had no impact on the pages of history, seemingly remaining subjugated by the native Akkadian speaking kings of Babylon or by perhaps regionally influential Aramean tribes. The main players in southern Mesopotamia during this period were Babylonia and Assyria, together with Elam to the east and the Aramaeans, who had already settled in the region a century or so prior to the arrival of the Chaldeans.

The very first written historical attestation of the existence of Chaldeans occurs in 852 BC, in the annals of the Assyrian king Shalmaneser III, who mentions invading the southeastern extremes of Babylonia and subjugating one Mushallim-Marduk, the chief of the Amukani tribe and overall leader of the Kaldu tribes, together with capturing the town of Baqani, extracting tribute from Adini, chief of the Bet-Dakkuri, another Chaldean tribe.

Shalmaneser III had invaded Babylonia at the request of its own king, Marduk-zakir-shumi I, who, being threatened by his own rebellious relations, together with powerful Aramean tribes pleaded with the more powerful Assyrian king for help. The subjugation of the Chaldean tribes by the Assyrian king appears to have been an aside, as they were not at that time a powerful force or a threat to the native Babylonian king.

Important Kaldu tribes and their regions in southeastern Babylonia were Bit-Yâkin (the original area the Chaldeans settled in on the Persian Gulf), Bet-Dakuri, Bet-Adini, Bet-Amukkani, and Bet-Shilani.

Chaldean leaders had by this time already adopted Assyro-Babylonian names, religion, language, and customs, indicating that they had become Akkadianized to a great degree.

The Chaldeans remained quietly ruled by the native Babylonians (who were in turn subjugated by their Assyrian relations) for the next seventy-two years, only coming to historical prominence for the first time in Babylonia in 780 BC, when a previously unknown Chaldean named Marduk-apla-usur usurped the throne from the native Babylonian king Marduk-bel-zeri (790–780 BC). The latter was a vassal of the Assyrian king Shalmaneser IV (783–773 BC), who was otherwise occupied quelling a civil war in Assyria at the time.

This was to set a precedent for all future Chaldean aspirations on Babylon during the Neo-Assyrian Empire; always too weak to confront a strong Assyria alone and directly, the Chaldeans awaited periods when Assyrian kings were distracted elsewhere in their vast empire, or engaged in internal conflicts, then, in alliance with other powers stronger than themselves (usually Elam), they made a bid for control over Babylonia.

Shalmaneser IV attacked and defeated Marduk-apla-user, retaking northern Babylonia and forcing on him a border treaty in Assyria's favour. The Assyrians allowed him to remain on the throne, although subject to Assyria. Eriba-Marduk, another Chaldean, succeeded him in 769 BC and his son, Nabu-shuma-ishkun in 761 BC, with both being dominated by the new Assyrian king Ashur-Dan III (772–755 BC). Babylonia appears to have been in a state of chaos during this time, with the north occupied by Assyria, its throne occupied by foreign Chaldeans, and continual civil unrest throughout the land.

The Chaldean rule proved short-lived. A native Babylonian king named Nabonassar (748–734 BC) defeated and overthrew the Chaldean usurpers in 748 BC, restored indigenous rule, and successfully stabilised Babylonia. The Chaldeans once more faded into obscurity for the next three decades. During this time both the Babylonians and the Chaldean and Aramean migrant groups who had settled in the land once more fell completely under the yoke of the powerful Assyrian king Tiglath-Pileser III (745–727 BC), a ruler who introduced Imperial Aramaic as the lingua franca of the empire. The Assyrian king at first made Nabonassar and his successor native Babylonian kings Nabu-nadin-zeri, Nabu-suma-ukin II and Nabu-mukin-zeri his subjects, but decided to rule Babylonia directly from 729 BC. He was followed by Shalmaneser V (727–722 BC), who also ruled Babylon in person.

When Sargon II (722–705 BC) ascended the throne of the Assyrian Empire in 722 BC after the death of Shalmaneser V, he was forced to launch a major campaign in his subject states of Persia, Mannea and Media in Ancient Iran to defend his territories there. He defeated and drove out the Scythians and Cimmerians who had attacked Assyria's Persian and Median vassal colonies in the region. At the same time, Egypt began encouraging and supporting the rebellion against Assyria in Israel and Canaan, forcing the Assyrians to send troops to deal with the Egyptians.

These events allowed the Chaldeans to once more attempt to assert themselves. While the Assyrian king was otherwise occupied defending his Iranian colonies from the Scythians and Cimmerians and driving the Egyptians from Canaan, Marduk-apla-iddina II (the Biblical Merodach-Baladan) of Bit-Yâkin, allied himself with the powerful Elamite kingdom and the native Babylonians, briefly seizing control of Babylon between 721 and 710 BC. With the Scythians and Cimmerians vanquished, the Medes and Persians pledging loyalty, and the Egyptians defeated and ejected from southern Canaan, Sargon II was free at last to deal with the Chaldeans, Babylonians, and Elamites. He attacked and deposed Marduk-apla-adding II in 710 BC, also defeating his Elamite allies in the process. After defeat by the Assyrians, Merodach-Baladan fled to his protectors in Elam

In 703, Merodach-Baladan very briefly regained the throne from a native Akkadian-Babylonian ruler Marduk-zakir-shumi II, who was a puppet of the new Assyrian king, Sennacherib (705–681 BC). He was once more soundly defeated at Kish, and once again fled to Elam where he died in exile after one final failed attempt to raise a revolt against Assyria in 700 BC, this time not in Babylon, but in the Chaldean tribal land of Bit-Yâkin. A native Babylonian king named Bel-ibni (703–701 BC) was placed on the throne as a puppet of Assyria.

The next challenge to Assyrian domination came from the Elamites in 694 BC, with Nergal-ushezib deposing and murdering Ashur-nadin-shumi (700–694 BC), the Assyrian prince who was king of Babylon and son of Sennacherib. The Chaldeans and Babylonians again allied with their more powerful Elamite neighbors in this endeavour. This prompted the enraged Assyrian king Sennacherib to invade and subjugate Elam and Chaldea and to sack Babylon, laying waste to and largely destroying the city. Babylon was regarded as a sacred city by all Mesopotamians, including the Assyrians, and this act eventually resulted in Sennacherib's being murdered by his own sons while he was praying to the god Nisroch in Nineveh.

Esarhaddon (681–669 BC) succeeded Sennacherib as ruler of the Assyrian Empire. He completely rebuilt Babylon and brought peace to the region. He conquered Egypt, Nubia and Libya and entrenched his mastery over the Persians, Medes, Parthians, Scythians, Cimmerians, Arameans, Israelites, Phoenicians, Canaanites, Urartians, Pontic Greeks, Cilicians, Phrygians, Lydians, Manneans and Arabs. For the next 60 or so years, Babylon and Chaldea remained peacefully under direct Assyrian control. The Chaldeans remained subjugated and quiet during this period, and the next major revolt in Babylon against the Assyrian empire was fermented not by a Chaldean, Babylonian or Elamite, but by Shamash-shum-ukin, who was an Assyrian king of Babylon, and elder brother of Ashurbanipal (668–627 BC), the new ruler of the Neo-Assyrian Empire.

Shamash-shum-ukin (668–648 BC) had become infused with Babylonian nationalism after sixteen years peacefully subject to his brother, and despite being Assyrian himself, declared that the city of Babylon and not Nineveh or Assur should be the seat of the empire.

In 652 BC, he raised a powerful coalition of peoples resentful of their subjugation to Assyria against his own brother Ashurbanipal. The alliance included the Babylonians, Persians, Chaldeans, Medes, Elamites, Sultans, Arameans, Israelites, Arabs and Canaanites, together with some disaffected elements among the Assyrians themselves. After a bitter struggle lasting five years, the Assyrian king triumphed over his rebellious brother in 648 BC, Elam was utterly destroyed, and the Babylonians, Persians, Medes, Chaldeans, Arabs, and others were savagely punished. An Assyrian governor named Kandalanu was then placed on the throne of Babylon to rule on behalf of Ashurbanipal. The next 22 years were peaceful, and neither the Babylonians nor Chaldeans posed a threat to the dominance of Ashurbanipal.

However, after the death of the mighty Ashurbanipal (and Kandalanu) in 627 BC, the Neo-Assyrian Empire descended into a series of bitter internal dynastic civil wars that were to be the cause of its downfall.

Ashur-etil-ilani (626–623 BC) ascended to the throne of the empire in 626 BC but was immediately engulfed in a torrent of fierce rebellions instigated by rival claimants. He was deposed in 623 BC by an Assyrian general (turtanu) named Sin-shumu-lishir (623–622 BC), who was also declared king of Babylon. Sin-shar-ishkun (622–612 BC), the brother of Ashur-etil-ilani, took back the throne of empire from Sin-shumu-lishir in 622 BC, but was then himself faced with unremitting rebellion against his rule by his own people. Continual conflict among the Assyrians led to a myriad of subject peoples, from Cyprus to Persia and The Caucasus to Egypt, quietly reasserting their independence and ceasing to pay tribute to Assyria.

Nabopolassar, a previously obscure and unknown Chaldean chieftain, followed the opportunistic tactics laid down by previous Chaldean leaders to take advantage of the chaos and anarchy gripping Assyria and Babylonia and seized the city of Babylon in 620 BC with the help of its native Babylonian inhabitants.

Sin-shar-ishkun amassed a powerful army and marched into Babylon to regain control of the region. Nabopolassar was saved from likely destruction because yet another massive Assyrian rebellion broke out in Assyria proper, including the capital Nineveh, which forced the Assyrian king to turn back in order to quell the revolt. Nabopolassar took advantage of this situation, seizing the ancient city of Nippur in 619 BC, a mainstay of pro-Assyrianism in Babylonia, and thus Babylonia as a whole.

However, his position was still far from secure, and bitter fighting continued in the Babylonian heartlands from 620 to 615 BC, with Assyrian forces encamped in Babylonia in an attempt to eject Nabopolassar. Nabopolassar attempted a counterattack, marched his army into Assyria proper in 616 BC, and tried to besiege Assur and Arrapha (modern Kirkuk), but was defeated by Sin-shar-ishkun and chased back into Babylonia after being driven from Idiqlat (modern Tikrit) at the southernmost end of Assyria. A stalemate seemed to have ensued, with Nabopolassar unable to make any inroads into Assyria despite its greatly weakened state, and Sin-shar-ishkun unable to eject Nabopolassar from Babylonia due to constant rebellions and civil war among his own people.

Nabopolassar's position, and the fate of the Assyrian empire, was sealed when he entered into an alliance with another of Assyria's former vassals, the Medes, the now dominant people of what was to become Persia. The Median Cyaxares had also recently taken advantage of the anarchy in the Assyrian Empire, while officially still a vassal of Assyria, he took the opportunity to meld the Iranian peoples; the Medes, Persians, Sagartians and Parthians, into a large and powerful Median-dominated force. The Medes, Persians, Parthians, Chaldeans and Babylonians formed an alliance that also included the Scythians and Cimmerians to the north.

While Sin-shar-ishkun was fighting both the rebels in Assyria and the Chaldeans and Babylonians in southern Mesopotamia, Cyaxares (hitherto a vassal of Assyria), in alliance with the Scythians and Cimmerians launched a surprise attack on civil-war-beleaguered Assyria in 615 BC, sacking Kalhu (the Biblical Calah/Nimrud) and taking Arrapkha (modern Kirkuk). Nabopolassar, still pinned down in southern Mesopotamia, was not involved in this major breakthrough against Assyria. From this point however, the alliance of Medes, Persians, Chaldeans, Babylonians, Sagartians, Scythians and Cimmerians fought in unison against Assyria.

Despite the sorely depleted state of Assyria, bitter fighting ensued. Throughout 614 BC the alliance of powers continued to make inroads into Assyria itself, although in 613 BC the Assyrians somehow rallied to score a number of counterattacking victories over the Medes-Persians, Babylonians-Chaldeans and Scythians-Cimmerians. This led to a coalition of forces ranged against it to unite and launch a massive combined attack in 612 BC, finally besieging and sacking Nineveh in late 612 BC, killing Sin-shar-ishkun in the process.

A new Assyrian king, Ashur-uballit II (612–605 BC), took the crown amidst the house-to-house fighting in Nineveh, and refused a request to bow in vassalage to the rulers of the alliance. He managed to fight his way out of Nineveh and reach the northern Assyrian city of Harran, where he founded a new capital. Assyria resisted for another seven years until 605 BC, when the remnants of the Assyrian army and the army of the Egyptians, whose 26th Dynasty had formed a brief allied coalition with the Assyrians, were defeated at Karchemish. Nabopolassar and his Median, Scythian and Cimmerian allies were now in possession of much of the huge Neo-Assyrian Empire. The Egyptians had belatedly come to the aid of Assyria, which they would have hoped to support as a secure buffer between Egypt and the new powers of Babylon, Medes and Persians, having already been raided by the Scythians.

The Chaldean king of Babylon now ruled all of southern Mesopotamia (Assyria in the north was ruled by the Medes), and the former Assyrian possessions of Aram (Syria), Phoenicia, Israel, Cyprus, Edom, Philistia, and parts of Arabia, while the Medes took control of the former Assyrian colonies in Ancient Iran, Asia Minor and the Caucasus.

Nabopolassar was not able to enjoy his success for long, dying in 604 BC, only one year after the victory at Karchemish. He was succeeded by his son, who took the name Nebuchadnezzar II, after the unrelated 12th century BC native Akkadian-Babylonian king Nebuchadnezzar I, indicating the extent to which the migrant Chaldeans had become infused with native Mesopotamian culture.

Nebuchadnezzar II and his allies may well have been forced to deal with remnants of Assyrian resistance based in and around Dur-Katlimmu, as Assyrian imperial records continue to be dated in this region between 604 and 599 BC. In addition, the Egyptians remained in the region an attempt to revive the Asian colonies of the ancient Egyptian Empire.

Nebuchadnezzar II was to prove himself to be the greatest of the Chaldean rulers, rivaling another non-native ruler, the 18th century BC Amorite king Hammurabi, as the greatest king of Babylon. He was a patron of the cities and a spectacular builder, rebuilding all of Babylonia's major cities on a lavish scale. His building activity at Babylon, expanding on the earlier major and impressive rebuilding of the Assyrian king Esarhaddon, helped to turn it into the immense and beautiful city of legend. Babylon covered more than 3 sqmi, surrounded by moats and ringed by a double circuit of walls. The Euphrates flowed through the center of the city, spanned by a beautiful stone bridge. At the center of the city rose the giant ziggurat called Etemenanki, "House of the Frontier Between Heaven and Earth," which lay next to the Temple of Marduk. He is also believed by many historians to have built The Hanging Gardens of Babylon (although others believe these gardens were built much earlier by an Assyrian king in Nineveh) for his wife, a Median princess from the green mountains, so that she would feel at home.

A capable leader, Nebuchadnezzar II conducted successful military campaigns; cities like Tyre, Sidon and Damascus were subjugated. He also conducted numerous campaigns in Asia Minor against the Scythians, Cimmerians, and Lydians. Like their Assyrian relations, the Babylonians had to campaign yearly in order to control their colonies.

In 601 BC, Nebuchadnezzar II was involved in a major but inconclusive battle against the Egyptians. In 599 BC, he invaded Arabia and routed the Arabs at Qedar. In 597 BC, he invaded Judah, captured Jerusalem after the siege of Jerusalem (597 BC) and deposed its king Jehoiachin, carrying the Israelites into captivity in Babylon. Egyptian and Babylonian armies fought each other for control of the Near East throughout much of Nebuchadnezzar's reign, and this encouraged king Zedekiah of Judah to revolt. After an eighteen-month siege, Jerusalem was captured in 587 BC, thousands of Jews were deported to Babylon, and Solomon's Temple was razed to the ground.

Nebuchadnezzar successfully fought the Pharaohs Psammetichus II and Apries throughout his reign, and during the reign of Pharaoh Amasis in 568 BC it is rumoured that he may have briefly invaded Egypt itself.

By 572, Nebuchadnezzar was in full control of Babylonia, Chaldea, Aramea (Syria), Phonecia, Israel, Judah, Philistia, Samarra, Jordan, northern Arabia, and parts of Asia Minor. Nebuchadnezzar died of illness in 562 BC after a one-year co-reign with his son, Amel-Marduk, who was deposed in 560 BC after a reign of only two years.

End of the Chaldean dynasty
Neriglissar succeeded Amel-Marduk. It is unclear as to whether he was in fact an ethnic Chaldean or a native Babylonian nobleman, as he was not related by blood to Nabopolassar's descendants, having married into the ruling family. He conducted successful military campaigns against the Hellenic inhabitants of Cilicia, which had threatened Babylonian interests. Neriglissar reigned for only four years and was succeeded by the youthful Labashi-Marduk in 556 BC. Again, it is unclear whether he was a Chaldean or a native Babylonian.

Labashi-Marduk reigned only for a matter of months, being deposed by Nabonidus in late 556 BC. Nabonidus was certainly not a Chaldean, but an Assyrian from Harran, the last capital of Assyria, and proved to be the final native Mesopotamian king of Babylon. He and his son, the regent Belshazzar, were deposed by the Persians under Cyrus the Great in 539 BC.

When the Babylonian Empire was absorbed into the Persian Achaemenid Empire, the name "Chaldean" lost its meaning in reference to a particular ethnicity or land, but lingered for a while as a term solely and explicitly used to describe a societal class of astrologers and astronomers in southern Mesopotamia. The original Chaldean tribe had long ago became Akkadianized, adopting Akkadian culture, religion, language and customs, blending into the majority native population, and eventually wholly disappearing as a distinct race of people, as had been the case with other preceding migrant peoples, such as the Amorites, Kassites, Suteans and Arameans of Babylonia.

The Persians considered this Chaldean societal class to be masters of reading and writing, and especially versed in all forms of incantation, sorcery, witchcraft, and the magical arts. They spoke of astrologists and astronomers as Chaldeans, and it is used with this specific meaning in the Book of Daniel (Dan. i. 4, ii. 2 et seq.) and by classical writers, such as Strabo.

The disappearance of the Chaldeans as an ethnicity and Chaldea as a land is evidenced by the fact that the Persian rulers of the Achaemenid Empire (539–330 BC) did not retain a province called "Chaldea", nor did they refer to "Chaldeans" as a race of people in their written annals. This is in contrast to Assyria, and for a time Babylonia also, where the Persians retained the names Assyria and Babylonia as designations for distinct geo-political entities within the Achaemenid Empire. In the case of the Assyrians in particular, Achaemenid records show Assyrians holding important positions within the empire, particularly with regards to military and civil administration.

Legacy
The term Chaldean was still in use at the time of Cicero (106–43 BC) long after the Chaldeans had disappeared. In one of his speeches he mentioned "Chaldean astrologers", and he spoke of them more than once in his De Divinatione. Other classical Latin writers who speak of them as distinguished for their knowledge of astronomy and astrology are Pliny the Elder, Valerius Maximus, Aulus Gellius, Cato the Elder, Lucretius, and Juvenal. Horace in his Carpe diem ode speaks of the "Babylonian calculations" (Babylonii numeri), the horoscopes of astrologers consulted regarding the future.

In the late antiquity, a variant of Aramaic that was used in some books of the Bible was misnamed as Chaldean by Jerome of Stridon. That inaccurate usage continued down the centuries in Western Europe, and it was still customary during the nineteenth century, until the misnomer was corrected by scholars. In West Asian, Greek and Hebraic sources, however, the term for the language spoken in Mesopotamia was commonly "Assyrian" and later also "Syriac". Accordingly, in the earliest recorded "Western" mentions of the Christians of what is now Iraq and nearby countries, "Chaldean" is used with reference to their language. In 1220/1, Jacques de Vitry wrote that "they denied that Mary was the Mother of God and claimed that Christ existed in two persons. They consecrated leavened bread and used the 'Chaldean' (Syriac) language". In the fifteenth century the term "Chaldeans" was first applied specifically to Assyrians living in Cyprus who entered a union with Rome, and no longer merely with reference to their language but the name of a new church.

Impact on Assyrian identity
In the present, Chaldea has been associated with Assyrian separatism through the Chaldean Catholics, and the belief that their descent is based southern Babylonia. While some religious leaders of the Chaldean church and activists in the West have advocated for a separate identity based on this notion, historians and international organizations generally treat Assyrians and Chaldeans as the same group ethnically, owing to genetic, linguistic, geographic, and modern historical factors. However, across the rest of Mesopotamia (particularly the North) after Chaldea fell, the terms "Assyrian", and its derivative Syrian remained the common ethnic term for the Aramaic-speaking inhabitants. These were used by the people themselves and their Persian, Armenian, Arab, Greek, Georgian and Kurdish neighbours both before and after the advent of Christianity in Iraq, Northeast Syria, Southeast Turkey and Northwest Iran. The Assyrian continuity in these regions is well documented.

title: Chaldea


text:
Currying

In mathematics and computer science, currying is the technique of translating a function that takes multiple arguments into a sequence of families of functions, each taking a single argument.

In the prototypical example, one begins with a function $$f:(X\times Y)\to Z$$ that takes two arguments, one from $$X$$ and one from $$Y,$$ and produces objects in $$Z.$$ The curried form of this function treats the first argument as a parameter, so as to create a family of functions $$f_x :Y\to Z.$$ The family is arranged so that for each object $$x$$ in $$X,$$ there is exactly one function $$f_x.$$

In this example, $$\mbox{curry}$$ itself becomes a function, that takes $$f$$ as an argument, and returns a function that maps each $$x$$ to $$f_x.$$ The proper notation for expressing this is verbose. The function $$f$$ belongs to the set of functions $$(X\times Y)\to Z.$$ Meanwhile, $$f_x$$ belongs to the set of functions $$Y\to Z.$$ Thus, something that maps $$x$$ to $$f_x$$ will be of the type $$X\to [Y\to Z].$$ With this notation, $$\mbox{curry}$$ is a function that takes objects from the first set, and returns objects in the second set, and so one writes $$\mbox{curry}:[(X\times Y)\to Z]\to (X\to [Y\to Z]).$$ This is a somewhat informal example; more precise definitions of what is meant by "object" and "function" are given below. These definitions vary from context to context, and take different forms, depending on the theory that one is working in.

Currying is related to, but not the same as, partial application. The example above can be used to illustrate partial application; it is quite similar. Partial application is the function $$\mbox{apply}$$ that takes the pair $$f$$ and $$x$$ together as arguments, and returns $$f_x.$$ Using the same notation as above, partial application has the signature $$\mbox{apply}:([(X\times Y)\to Z] \times X) \to [Y\to Z].$$ Written this way, application can be seen to be adjoint to currying.

The currying of a function with more than two arguments can be defined by induction.

Currying is useful in both practical and theoretical settings. In functional programming languages, and many others, it provides a way of automatically managing how arguments are passed to functions and exceptions. In theoretical computer science, it provides a way to study functions with multiple arguments in simpler theoretical models which provide only one argument. The most general setting for the strict notion of currying and uncurrying is in the closed monoidal categories, which underpins a vast generalization of the Curry–Howard correspondence of proofs and programs to a correspondence with many other structures, including quantum mechanics, cobordisms and string theory.

The concept of currying was introduced by Gottlob Frege, developed by Moses Schönfinkel, and further developed by Haskell Curry.

Uncurrying is the dual transformation to currying, and can be seen as a form of defunctionalization. It takes a function $$f$$ whose return value is another function $$g$$, and yields a new function $$f'$$ that takes as parameters the arguments for both $$f$$ and $$g$$, and returns, as a result, the application of $$f$$ and subsequently, $$g$$, to those arguments. The process can be iterated.

Motivation
Currying provides a way for working with functions that take multiple arguments, and using them in frameworks where functions might take only one argument. For example, some analytical techniques can only be applied to functions with a single argument. Practical functions frequently take more arguments than this. Frege showed that it was sufficient to provide solutions for the single argument case, as it was possible to transform a function with multiple arguments into a chain of single-argument functions instead. This transformation is the process now known as currying. All "ordinary" functions that might typically be encountered in mathematical analysis or in computer programming can be curried. However, there are categories in which currying is not possible; the most general categories which allow currying are the closed monoidal categories.

Some programming languages almost always use curried functions to achieve multiple arguments; notable examples are ML and Haskell, where in both cases all functions have exactly one argument. This property is inherited from lambda calculus, where multi-argument functions are usually represented in curried form.

Currying is related to, but not the same as partial application. In practice, the programming technique of closures can be used to perform partial application and a kind of currying, by hiding arguments in an environment that travels with the curried function.

History
The "Curry" in "Currying" is a reference to logician Haskell Curry, who used the concept extensively, but Moses Schönfinkel had the idea six years before Curry. The alternative name "Schönfinkelisation" has been proposed. In the mathematical context, the principle can be traced back to work in 1893 by Frege.

The originator of the word "currying" is not clear. David Turner says the word was coined by Christopher Strachey in his 1967 lecture notes Fundamental Concepts in Programming Languages, but that source introduces the concept as "a device originated by Schönfinkel", and the term "currying" is not used, while Curry is mentioned later in the context of higher-order functions. John C. Reynolds defined "currying" in a 1972 paper, but did not claim to have coined the term.

Definition
Currying is most easily understood by starting with an informal definition, which can then be molded to fit many different domains. First, there is some notation to be established. The notation $$X \to Y $$ denotes all functions from $$X$$ to $$Y$$. If $$f$$ is such a function, we write $$f \colon X \to Y $$. Let $$X \times Y$$ denote the ordered pairs of the elements of $$X$$ and $$Y$$ respectively, that is, the Cartesian product of $$X$$ and $$Y$$. Here, $$X$$ and $$Y$$ may be sets, or they may be types, or they may be other kinds of objects, as explored below.

Given a function

 * $$f \colon (X \times Y) \to Z $$,

currying constructs a new function

 * $$g \colon X \to (Y \to Z) $$.

That is, $$g$$ takes an argument of type $$X$$ and returns a function of type $$Y\to Z$$. It is defined by

 * $$g(x)(y)=f(x,y)$$

for $$x$$ of type $$X$$ and $$y$$ of type $$Y$$. We then also write

 * $$\text{curry}(f)=g.$$

Uncurrying is the reverse transformation, and is most easily understood in terms of its right adjoint, the function $\operatorname{apply}.$

Set theory
In set theory, the notation $$Y^X$$ is used to denote the set of functions from the set $$X$$ to the set $$Y$$. Currying is the natural bijection between the set $$A^{B\times C}$$ of functions from $$B\times C$$ to $$A$$, and the set $$(A^C)^B$$ of functions from $$B$$ to the set of functions from $$C$$ to $$A$$. In symbols:

 * $$A^{B\times C}\cong (A^C)^B$$

Indeed, it is this natural bijection that justifies the exponential notation for the set of functions. As is the case in all instances of currying, the formula above describes an adjoint pair of functors: for every fixed set $$C$$, the functor $$B\mapsto B\times C$$ is left adjoint to the functor $$A \mapsto A^C$$.

In the category of sets, the object $$Y^X$$ is called the exponential object.

Function spaces
In the theory of function spaces, such as in functional analysis or homotopy theory, one is commonly interested in continuous functions between topological spaces. One writes $$\text{Hom}(X,Y)$$ (the Hom functor) for the set of all functions from $$X$$ to $$Y$$, and uses the notation $$Y^X$$ to denote the subset of continuous functions. Here, $$\text{curry}$$ is the bijection

 * $$\text{curry}:\text{Hom}(X\times Y, Z) \to \text{Hom}(X, \text{Hom}(Y,Z)) ,$$

while uncurrying is the inverse map. If the set $$Y^X$$ of continuous functions from $$X$$ to $$Y$$ is given the compact-open topology, and if the space $$Y$$ is locally compact Hausdorff, then

 * $$\text{curry} : Z^{X\times Y}\to (Z^Y)^X$$

is a homeomorphism. This is also the case when $$X$$, $$Y$$ and $$Y^X$$ are compactly generated, although there are more cases.

One useful corollary is that a function is continuous if and only if its curried form is continuous. Another important result is that the application map, usually called "evaluation" in this context, is continuous (note that eval is a strictly different concept in computer science.) That is,

$$\begin{align} &&\text{eval}:Y^X \times X \to Y \\ && (f,x) \mapsto f(x) \end{align}$$

is continuous when $$Y^X$$ is compact-open and $$Y$$ locally compact Hausdorff. These two results are central for establishing the continuity of homotopy, i.e. when $$X$$ is the unit interval $$I$$, so that $$Z^{I\times Y} \cong (Z^Y)^I$$ can be thought of as either a homotopy of two functions from $$Y$$ to $$Z$$, or, equivalently, a single (continuous) path in $$Z^Y$$.

Algebraic topology
In algebraic topology, currying serves as an example of Eckmann–Hilton duality, and, as such, plays an important role in a variety of different settings. For example, loop space is adjoint to reduced suspensions; this is commonly written as
 * $$[\Sigma X,Z] \approxeq [X, \Omega Z]$$

where $$[A,B]$$ is the set of homotopy classes of maps $$A \rightarrow B$$, and $$\Sigma A$$ is the suspension of A, and $$\Omega A$$ is the loop space of A. In essence, the suspension $$\Sigma X$$ can be seen as the cartesian product of $$X$$ with the unit interval, modulo an equivalence relation to turn the interval into a loop. The curried form then maps the space $$X$$ to the space of functions from loops into $$Z$$, that is, from $$X$$ into $$\Omega Z$$. Then $$\text{curry}$$ is the adjoint functor that maps suspensions to loop spaces, and uncurrying is the dual.

The duality between the mapping cone and the mapping fiber (cofibration and fibration) can be understood as a form of currying, which in turn leads to the duality of the long exact and coexact Puppe sequences.

In homological algebra, the relationship between currying and uncurrying is known as tensor-hom adjunction. Here, an interesting twist arises: the Hom functor and the tensor product functor might not lift to an exact sequence; this leads to the definition of the Ext functor and the Tor functor.

Domain theory
In order theory, that is, the theory of lattices of partially ordered sets, $$\text{curry}$$ is a continuous function when the lattice is given the Scott topology. Scott-continuous functions were first investigated in the attempt to provide a semantics for lambda calculus (as ordinary set theory is inadequate to do this). More generally, Scott-continuous functions are now studied in domain theory, which encompasses the study of denotational semantics of computer algorithms. Note that the Scott topology is quite different than many common topologies one might encounter in the category of topological spaces; the Scott topology is typically finer, and is not sober.

The notion of continuity makes its appearance in homotopy type theory, where, roughly speaking, two computer programs can be considered to be homotopic, i.e. compute the same results, if they can be "continuously" refactored from one to the other.

Lambda calculi
In theoretical computer science, currying provides a way to study functions with multiple arguments in very simple theoretical models, such as the lambda calculus, in which functions only take a single argument. Consider a function $$f(x,y)$$ taking two arguments, and having the type $$(X \times Y)\to Z$$, which should be understood to mean that x must have the type $$X$$, y must have the type $$Y$$, and the function itself returns the type $$Z$$. The curried form of f is defined as

 * $$\text{curry}(f) = \lambda x.(\lambda y.(f(x,y)))$$

where $$\lambda$$ is the abstractor of lambda calculus. Since curry takes, as input, functions with the type $$(X\times Y)\to Z$$, one concludes that the type of curry itself is

 * $$\text{curry}:((X \times Y)\to Z) \to (X \to (Y \to Z))$$

The → operator is often considered right-associative, so the curried function type $$X \to (Y \to Z)$$ is often written as $$X \to Y \to Z$$. Conversely, function application is considered to be left-associative, so that $$f(x, y)$$ is equivalent to

 * $$((\text{curry}(f) \; x) \;y) = \text{curry}(f) \; x \;y$$.

That is, the parenthesis are not required to disambiguate the order of the application.

Curried functions may be used in any programming language that supports closures; however, uncurried functions are generally preferred for efficiency reasons, since the overhead of partial application and closure creation can then be avoided for most function calls.

Type theory
In type theory, the general idea of a type system in computer science is formalized into a specific algebra of types. For example, when writing $$f \colon X \to Y $$, the intent is that $$X$$ and $$Y$$ are types, while the arrow $$\to$$ is a type constructor, specifically, the function type or arrow type. Similarly, the Cartesian product $$X \times Y$$ of types is constructed by the product type constructor $$\times$$.

The type-theoretical approach is expressed in programming languages such as ML and the languages derived from and inspired by it: CaML, Haskell and F#.

The type-theoretical approach provides a natural complement to the language of category theory, as discussed below. This is because categories, and specifically, monoidal categories, have an internal language, with simply-typed lambda calculus being the most prominent example of such a language. It is important in this context, because it can be built from a single type constructor, the arrow type. Currying then endows the language with a natural product type. The correspondence between objects in categories and types then allows programming languages to be re-interpreted as logics (via Curry–Howard correspondence), and as other types of mathematical systems, as explored further, below.

Logic
Under the Curry–Howard correspondence, the existence of currying and uncurrying is equivalent to the logical theorem $$((A \land B) \to C) \Leftrightarrow (A \to (B \to C))$$, as tuples (product type) corresponds to conjunction in logic, and function type corresponds to implication.

The exponential object $$Q^P$$ in the category of Heyting algebras is normally written as material implication $$P\to Q$$. Distributive Heyting algebras are Boolean algebras, and the exponential object has the explicit form $$\neg P \lor Q$$, thus making it clear that the exponential object really is material implication.

Category theory
The above notions of currying and uncurrying find their most general, abstract statement in category theory. Currying is a universal property of an exponential object, and gives rise to an adjunction in cartesian closed categories. That is, there is a natural isomorphism between the morphisms from a binary product $$f \colon (X \times Y) \to Z $$ and the morphisms to an exponential object $$g \colon X \to Z^Y $$.

This generalizes to a broader result in closed monoidal categories: Currying is the statement that the tensor product and the internal Hom are adjoint functors; that is, for every object $$B$$ there is a natural isomorphism:

 * $$ \mathrm{Hom}(A\otimes B, C) \cong \mathrm{Hom}(A, B\Rightarrow C) .$$

Here, Hom denotes the (external) Hom-functor of all morphisms in the category, while $$B\Rightarrow C$$ denotes the internal hom functor in the closed monoidal category. For the category of sets, the two are the same. When the product is the cartesian product, then the internal hom $$B\Rightarrow C$$ becomes the exponential object $$C^B$$.

Currying can break down in one of two ways. One is if a category is not closed, and thus lacks an internal hom functor (possibly because there is more than one choice for such a functor). Another way is if it is not monoidal, and thus lacks a product (that is, lacks a way of writing down pairs of objects). Categories that do have both products and internal homs are exactly the closed monoidal categories.

The setting of cartesian closed categories is sufficient for the discussion of classical logic; the more general setting of closed monoidal categories is suitable for quantum computation.

The difference between these two is that the product for cartesian categories (such as the category of sets, complete partial orders or Heyting algebras) is just the Cartesian product; it is interpreted as an ordered pair of items (or a list). Simply typed lambda calculus is the internal language of cartesian closed categories; and it is for this reason that pairs and lists are the primary types in the type theory of LISP, Scheme and many functional programming languages.

By contrast, the product for monoidal categories (such as Hilbert space and the vector spaces of functional analysis) is the tensor product. The internal language of such categories is linear logic, a form of quantum logic; the corresponding type system is the linear type system. Such categories are suitable for describing entangled quantum states, and, more generally, allow a vast generalization of the Curry–Howard correspondence to quantum mechanics, to cobordisms in algebraic topology, and to string theory. The linear type system, and linear logic are useful for describing synchronization primitives, such as mutual exclusion locks, and the operation of vending machines.

Contrast with partial function application
Currying and partial function application are often conflated. One of the significant differences between the two is that a call to a partially applied function returns the result right away, not another function down the currying chain; this distinction can be illustrated clearly for functions whose arity is greater than two.

Given a function of type $$f \colon (X \times Y \times Z) \to N $$, currying produces $$\text{curry}(f) \colon X \to (Y \to (Z \to N)) $$. That is, while an evaluation of the first function might be represented as $$f(1, 2, 3)$$, evaluation of the curried function would be represented as $$f_\text{curried}(1)(2)(3)$$, applying each argument in turn to a single-argument function returned by the previous invocation. Note that after calling $$f_\text{curried}(1)$$, we are left with a function that takes a single argument and returns another function, not a function that takes two arguments.

In contrast, partial function application refers to the process of fixing a number of arguments to a function, producing another function of smaller arity. Given the definition of $$f$$ above, we might fix (or 'bind') the first argument, producing a function of type $$\text{partial}(f) \colon (Y \times Z) \to N$$. Evaluation of this function might be represented as $$f_\text{partial}(2, 3)$$. Note that the result of partial function application in this case is a function that takes two arguments.

Intuitively, partial function application says "if you fix the first argument of the function, you get a function of the remaining arguments". For example, if function div stands for the division operation x/y, then div with the parameter x fixed at 1 (i.e., div 1) is another function: the same as the function inv that returns the multiplicative inverse of its argument, defined by inv(y) = 1/y.

The practical motivation for partial application is that very often the functions obtained by supplying some but not all of the arguments to a function are useful; for example, many languages have a function or operator similar to. Partial application makes it easy to define these functions, for example by creating a function that represents the addition operator with 1 bound as its first argument.

Partial application can be seen as evaluating a curried function at a fixed point, e.g. given $$f \colon (X \times Y \times Z) \to N $$ and $$a \in X$$ then $$\text{curry}(\text{partial}(f)_a)(y)(z) = \text{curry}(f)(a)(y)(z) $$ or simply $$\text{partial}(f)_a = \text{curry}_1(f)(a) $$ where $$\text{curry}_1$$ curries f's first parameter.

Thus, partial application is reduced to a curried function at a fixed point. Further, a curried function at a fixed point is (trivially), a partial application. For further evidence, note that, given any function $$f(x,y)$$, a function $$g(y,x)$$ may be defined such that $$g(y,x) = f(x,y)$$. Thus, any partial application may be reduced to a single curry operation. As such, curry is more suitably defined as an operation which, in many theoretical cases, is often applied recursively, but which is theoretically indistinguishable (when considered as an operation) from a partial application.

So, a partial application can be defined as the objective result of a single application of the curry operator on some ordering of the inputs of some function.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Currying


text:
Cyrus

Cyrus (Persian: کوروش) is a male given name. It is the given name of a number of Persian kings. Most notably it refers to Cyrus the Great (c. 600–530 BC). Cyrus is also the name of Cyrus I of Anshan (c. 650 BC), King of Persia and the grandfather of Cyrus the Great; and Cyrus the Younger (died 401 BC), brother to the Persian king Artaxerxes II of Persia.

Etymology
Cyrus, as a word in English, is the Latinized form of the Greek Κῦρος, Kȳros, from Old Persian 𐎤𐎢𐎽𐎢𐏁 Kūruš. According to the inscriptions, the name is reflected in Elamite Kuraš, Babylonian Ku(r)-raš/-ra-áš and Imperial Aramaic kwrš. The modern Persian form of the name is Kūroš.

The etymology of Cyrus has been and continues to be a topic of discussion amongst historians, linguists, and scholars of Iranology. The Old Persian name "kuruš" has been interpreted in various forms such as "the Sun", "like Sun", "young", "hero," and "humiliator of the enemy in verbal contest" and the Elamite "kuraš" has been translated as one "who bestows care".

The name has appeared on many monuments and inscriptions in Old Persian. There is also the record of a small inscription in Morghab (southwestern Iran) on which there is the sentence (adam kūruš xšāyaθiya haxāmanišiya) in Old Persian meaning (I am Cyrus the Achaemenian King). After a questionable proposal by the German linguist F. H. Weissbach that Darius the Great was the first to inscribe in Persian, it had previously been concluded by some scholars that the inscription in Morghab refers to Cyrus the Younger. This proposal resulted from a false interpretation of a passage in paragraph 70 of the Behistun inscription by Darius the Great. Based on many arguments, the accepted theory among modern scholars is that the inscription does belong to Cyrus the Great.

There are interpretations of the name of Cyrus by classical authors identifying with or referring to the Persian word for "Sun". The Historian Plutarch (46–120) states that "the sun, which, in the Persian language, is called Cyrus". Also, the Physician Ctesias who served in the court of the Persian king Artaxerxes II of Persia writes in his book Persica as summarized by Photios that the name Cyrus is from the Persian word "Khur" (the sun). These are, however, not accepted by modern scholars.

Regarding the etymology of Old Persian kuruš, linguists have proposed various etymologies based on Iranian languages as well as non-Indo-European ones. According to Tavernier, the name kuraš, attested in Elamite texts, is likely "the original form" as there is no Elamite or Babylonian spelling ku-ru-uš in the transcriptions of Old Persian ku-u-r(u)-u-š. That is, according to Tavernier, kuraš is an Elamite name and means "to bestow care". Others, such as Schmitt, Hoffmann maintain that the Persian Kuruš, which according to Skalmowsky, may be connected to (or borrowing from) the IE Kúru- from Old Indic can give an etymology of the Elamite kuraš. In this regard, the Old Persian kuruš is considered with the following etymologies: One proposal is discussed by the linguist Janos Harmatta that refers to the common Iranian root "kur-" (be born) of many words in Old, middle, and new Iranian languages (e.g. Kurdish). Accordingly, the name Kūruš means "young, youth...". Other Iranian etymologies have been proposed. The Indian proposal of Skalmowsky goes down to "to do, accomplish". Another theory is the suggestion of Karl Hoffmann that kuruš goes down to a -ru derivation from the IE root *(s)kau meaning "to humiliate" and accordingly "kuruš" (hence "Cyrus") means "humiliator (of the enemy in verbal contest)".

People and fictional characters named Cyrus include:

Ancient world

 * Cyrus I (c. 650 BC), King of Anshan
 * Cyrus the Great (c. 600 BC or 576 BC–530 BC) – also known as Cyrus II – the grandson of Cyrus I, an Achaemenid ruler and founder of the Great Persian Empire
 * Cyrus the Younger (died 401 BC), brother to the Persian King Artaxerxes
 * Cyrus (architect), 1st century Greek architect who worked in Rome
 * Saint Cyrus (see Cyrus and John), 4th century Coptic saint
 * Cyrus I of Edessa, bishop (died 396)
 * Cyrus II of Edessa, bishop (died 498)
 * Cyrus of Alexandria (died 642), Melkite Patriarch and co-founder of Monothelism
 * Cyrus of Panopolis, 5th-century Byzantine writer and official

Modern era

 * Cyrus Leroy Baldridge (1889–1977), American artist, illustrator, author and adventurer
 * Cyrus Townsend Brady (1861–1920), American journalist, historian and adventure writer
 * Cyrus Broacha (born 1971), MTV India VJ
 * Cyrus Ramone Pattinson (born 1994), Team GB Boxer
 * Cyrus Christie (born 1992), professional footballer who plays as right back for Hull City A.F.C
 * Cyrus Chothia (1942–2019), British scientist
 * Cyrus Edwin Dallin (1861–1944), American sculptor
 * Cyrus S. Eaton (1883–1979), Canadian-American banker, investor and philanthropist
 * Cyrus Edwards (1793–1877), American politician and lawyer
 * Cyrus West Field (1819–1892), American businessman who successfully laid the first transatlantic telegraph cable
 * Cyrus Frisch (born 1969), Dutch film director
 * Cyrus Herzl Gordon (1908–2001) was an American scholar of Near Eastern cultures and ancient languages
 * Cyrus Hamlin (general) (1839–1867), Union general during American Civil War, son of Vice President Hannibal Hamlin
 * Cy Hungerford (1889–1983), American editorial cartoonist
 * Cyrus Kabiru (born 1984), Kenyan visual artist
 * Cy Kendall (1898–1953), American actor
 * Cyrus B. Lower (1843–1924), American Civil War Medal of Honor recipient
 * Cyrus McCormick (1809–1884), American inventor who developed the modern mechanical reaper
 * Cyrus Pallonji Mistry (born 1968), Irish-Indian businessman and Chairman of Indian conglomerate Tata Group
 * Cyrus Mistry (writer) (born 1956), Indian author and playwright
 * Cyrus Patell (born 1961), American literary and cultural critic
 * Cyrus Peirce (1790–1860), founder of first public normal school (teachers' college) in the United States
 * Cyrus Poncha (born 1976), national squash coach in India
 * Cyrus S. Poonawalla, Indian businessman
 * Cyrus Rollocks (born 1998), Canadian soccer player
 * Cyrus Sahukar (born 1980), MTV India VJ
 * C. R. Smith (1899–1990), longtime CEO of American Airlines
 * Cyrus Vance Sr. (1917–2002), American politician and lawyer, U.S. Secretary of the Army under Presidents John F. Kennedy and Lyndon B. Johnson, U.S. Secretary of Defense under Lyndon B. Johnson and U.S. Secretary of State under Jimmy Carter
 * Cyrus Vance Jr. (born 1954), American politician and lawyer, son of Cyrus Sr. and former Manhattan District Attorney (2010–2021)
 * Cyrus Villanueva, Australian singer who won The X Factor Australia in 2015

In literature

 * The Garden of Cyrus, a discourse by the English physician-philosopher Thomas Browne

Fictional characters

 * Cyrus, from The Revenge of Magic book series by James Riely
 * Cyrus Beene, from the television series Scandal
 * Cyrus Trask, from John Steinbeck's novel East of Eden
 * Cyrus Spitama, the grandson of Zoroaster and main character of Gore Vidal’s novel, Creation.
 * Cyrus Borg, a character in Ninjago
 * Cyrus Bortel, from the animated TV series Kim Possible
 * Cyrus Goodman, from Andi Mack and Disney Channel's first gay main character
 * Cyrus Lupo, a detective from Law & Order
 * Cyrus Simpson, the brother of Abraham Simpson in The Simpsons
 * Cyrus, from the TV series Trailer Park Boys
 * Cyrus, from the animated series Sonic Underground
 * Cyrus "The Virus" Grissom, in the 1997 film Con Air, played by John Malkovich
 * Cyrus, a gang leader in the 1979 film The Warriors
 * Cyrus, the leader of Team Galactic and the main antagonist of Pokémon Diamond, Pearl, and Platinum
 * Cyrus Gold, the DC Comics character Solomon Grundy
 * Cyrus Smith, the leading character in Jules Verne's novel Mysterious Island
 * Cyrus, a vampaneze from the novel The Vampire Prince by Darren Shan
 * Cyrus (Chrono Trigger), in the video game Chrono Trigger
 * Cyrus, a Redguard pirate and hero in the video game The Elder Scrolls Adventures: Redguard
 * Cyrus Albright, one of the 8 main protagonists of the video game Octopath Traveler
 * Cyrus, an NPC in the video game Genshin Impact
 * Cyrus, an alpaca NPC introduced in Animal Crossing: New Leaf

title: Cyrus


text:
Case

Case or CASE may refer to:

Instances

 * Instantiation (disambiguation), a realization of a concept, theme, or design
 * Special case, an instance that differs in a certain way from others of the type

Containers

 * Case (goods), a package of related merchandise
 * Cartridge case or casing, a firearm cartridge component
 * Bookcase, a piece of furniture used to store books
 * Briefcase or attaché case, a narrow box to carry paperwork
 * Computer case, the enclosure for a PC's main components
 * Keep case, DVD or CD packaging
 * Pencil case
 * Phone case, protective or vanity accessory for mobile phones
 * Battery case
 * Road case or flight case, for fragile equipment in transit
 * Shipping container or packing case
 * Suitcase, a large luggage box
 * Type case, a compartmentalized wooden box for letterpress typesetting

Places

 * Case, Laclede County, Missouri
 * Case, Warren County, Missouri
 * Case River, a Kabika tributary in Ontario, Canada
 * Case Township, Michigan
 * Case del Conte, Italy

People

 * Case (name), people with the surname (or given name)
 * Case (singer), American R&B singer-songwriter and producer (Case Woodard)

Arts, entertainment, and media

 * The Case (1972), a TV movie starring Cliff Richards and Olivia Newton-John
 * The Case (2007), a Chinese film
 * Case (album), a 1996 album by American R&B singer and songwriter Case
 * "Case" (song), a 2018 song by Nigerian singer Teni
 * Réttur, an Icelandic drama series
 * CASE, a fictional robot in Interstellar (film)

Business, finance, and law

 * CASE 30, an index of the Cairo & Alexandria Stock Exchange in Egypt
 * Case Corporation, defunct manufacturer of agricultural equipment, tractors and cars
 * Case Construction Equipment (Case CE), a manufacturer of construction equipment
 * Case IH, a manufacturer of agricultural equipment
 * W. A. Case & Son Manufacturing Co., a defunct American manufacturer of plumbing fixtures
 * W. R. Case & Sons Cutlery Co., an American manufacturer of knives
 * Business case, capturing the reasoning for initiating a project
 * Legal case, a dispute between opposing parties, being resolved by a court proceeding

Education

 * Case (policy debate), in debate competition
 * Case study, a research method involving an up-close, in-depth, and detailed examination of a particular case, in the social and life sciences
 * Case Middle School, part of Punahou School in Oahu, Hawaii
 * Case Western Reserve University, an independent research university in Cleveland, Ohio, US
 * Center for Advanced Studies in Engineering, now Sir Syed CASE Institute of Technology, a private engineering institute in Islamabad, Pakistan
 * Center for Architecture, Science and Ecology, a research facility of the Rensselaer Polytechnic Institute, US
 * Centre for Christian Apologetics, Scholarship and Education, a ministry of New College, University of New South Wales
 * Council for Advancement and Support of Education, a nonprofit association of educational institutions, US

Language and linguistics

 * Conceptually Accurate Signed English, a sign-language variety of Manually Coded English
 * Grammatical case, a common form of morphosyntactic inflection
 * Letter case, a typographical distinction between capital and small letter forms

Computing

 * CASE, a database used by the British Citizens Advice charity
 * Best, worst and average case, in computer science, types of case analysis
 * Computer-aided software engineering, for the software development life cycle
 * Computer-assisted structure elucidation, for molecular geometry
 * Support case (or ticket), in an issue tracking system
 * Switch statement, a control statement, in programming
 * Use case, a description of a system's behaviour in response to requests

Other science, technology and mathematics

 * Calcium selenide (chemical formula: CaSe)
 * Case-hardening, a process of hardening the surface of a metal object
 * Case-shot, a type of anti-personnel canister ammunition similar to a shrapnel shell
 * Case study, a research method involving in-depth examination of an individual
 * Proof by cases (or exhaustion), in mathematics
 * Contribution to ARIEL Spectroscopy of Exoplanets (CASE), an instrument onboard European space telescope ARIEL
 * Limiting case (mathematics), a special case with one or more extreme parameter values
 * Limiting case (philosophy of science), a theory subsumed by another

title: Case


text:
Rendering (computer graphics)

Rendering or image synthesis is the process of generating a photorealistic or non-photorealistic image from a 2D or 3D model by means of a computer program. The resulting image is referred to as a rendering. Multiple models can be defined in a scene file containing objects in a strictly defined language or data structure. The scene file contains geometry, viewpoint, textures, lighting, and shading information describing the virtual scene. The data contained in the scene file is then passed to a rendering program to be processed and output to a digital image or raster graphics image file. The term "rendering" is analogous to the concept of an artist's impression of a scene. The term "rendering" is also used to describe the process of calculating effects in a video editing program to produce the final video output.

A software application or component that performs rendering is called a rendering engine, render engine, rendering system, graphics engine, or simply a renderer.

Rendering is one of the major sub-topics of 3D computer graphics, and in practice it is always connected to the others. It is the last major step in the graphics pipeline, giving models and animation their final appearance. With the increasing sophistication of computer graphics since the 1970s, it has become a more distinct subject.

Rendering has uses in architecture, video games, simulators, movie and TV visual effects, and design visualization, each employing a different balance of features and techniques. A wide variety of renderers are available for use. Some are integrated into larger modeling and animation packages, some are stand-alone, and some are free open-source projects. On the inside, a renderer is a carefully engineered program based on multiple disciplines, including light physics, visual perception, mathematics, and software development.

Though the technical details of rendering methods vary, the general challenges to overcome in producing a 2D image on a screen from a 3D representation stored in a scene file are handled by the graphics pipeline in a rendering device such as a GPU. A GPU is a purpose-built device that assists a CPU in performing complex rendering calculations. If a scene is to look relatively realistic and predictable under virtual lighting, the rendering software must solve the rendering equation. The rendering equation does not account for all lighting phenomena, but instead acts as a general lighting model for computer-generated imagery.

In the case of 3D graphics, scenes can be pre-rendered or generated in realtime. Pre-rendering is a slow, computationally intensive process that is typically used for movie creation, where scenes can be generated ahead of time, while real-time rendering is often done for 3D video games and other applications that must dynamically create scenes. 3D hardware accelerators can improve realtime rendering performance.

Usage
When the pre-image (a wireframe sketch usually) is complete, rendering is used, which adds in bitmap textures or procedural textures, lights, bump mapping and relative position to other objects. The result is a completed image the consumer or intended viewer sees.

For movie animations, several images (frames) must be rendered, and stitched together in a program capable of making an animation of this sort. Most 3D image editing programs can do this.

Features
A rendered image can be understood in terms of a number of visible features. Rendering research and development has been largely motivated by finding ways to simulate these efficiently. Some relate directly to particular algorithms and techniques, while others are produced together.

 * Shading – how the color and brightness of a surface varies with lighting
 * Texture-mapping – a method of applying detail to surfaces
 * Bump-mapping – a method of simulating small-scale bumpiness on surfaces
 * Fogging/participating medium – how light dims when passing through non-clear atmosphere or air
 * Shadows – the effect of obstructing light
 * Soft shadows – varying darkness caused by partially obscured light sources
 * Reflection – mirror-like or highly glossy reflection
 * Transparency (optics), transparency (graphic) or opacity – sharp transmission of light through solid objects
 * Translucency – highly scattered transmission of light through solid objects
 * Refraction – bending of light associated with transparency
 * Diffraction – bending, spreading, and interference of light passing by an object or aperture that disrupts the ray
 * Indirect illumination – surfaces illuminated by light reflected off other surfaces, rather than directly from a light source (also known as global illumination)
 * Caustics (a form of indirect illumination) – reflection of light off a shiny object, or focusing of light through a transparent object, to produce bright highlights on another object
 * Depth of field – objects appear blurry or out of focus when too far in front of or behind the object in focus
 * Motion blur – objects appear blurry due to high-speed motion, or the motion of the camera
 * Non-photorealistic rendering – rendering of scenes in an artistic style, intended to look like a painting or drawing

Assets
CAD libraries can have assets such as 3D models, textures, bump maps, HDRIs, and different Computer graphics lighting sources to be rendered.

Techniques
Many rendering  have been researched, and software used for rendering may employ a number of different techniques to obtain a final image.

Choosing how to render a scene usually involves a trade-off between speed and realism (although realism is not always desired). The techniques developed over the years follow a loose progression, with more advanced methods becoming practical as computing power and memory capacity increased.

An important distinction is between image order algorithms, which iterate over pixels of the image plane, and object order algorithms, which iterate over objects in the scene. For simple scenes, object order is usually more efficient, as there are fewer objects than pixels.

 * Rasterization (including scanline rendering)
 * Geometrically projects objects in the scene to an image plane. Different realistic or stylized effects can be obtained by coloring the pixels covered by the objects in different ways. Surfaces are typically divided into meshes of triangles before being rasterized. Rasterization is usually synonymous with "object order" rendering (as described above).

 * Ray casting
 * Uses geometric formulas to compute the first object that a ray intersects. It can be used to implement "image order" rendering by casting a ray for each pixel, and finding a corresponding point in the scene. Ray casting is a fundamental operation used for both graphical and non-graphical purposes, e.g. determining whether a point is in shadow, or checking what an enemy can see in a game.

 * Ray tracing
 * Simulates the bouncing paths of light caused by specular reflection and refraction, requiring a varying number of ray casting operations for each path. Advanced forms use Monte Carlo techniques to render effects such as area lights, depth of field, blurry reflections, and soft shadows, but computing global illumination is usually in the domain of path tracing.

 * Path tracing
 * Uses Monte Carlo integration with a simplified form of ray tracing, computing the average brightness of a sample of the possible paths that a photon could take when traveling from a light source to the camera (for some images, thousands of paths need to be sampled per pixel). It was introduced as a statistically unbiased way to solve the rendering equation, giving ray tracing a rigorous mathematical foundation.

 * Radiosity
 * A finite element analysis approach that breaks surfaces in the scene into pieces, and estimates the amount of light that each piece receives from light sources, or indirectly from other surfaces. Once the irradiance of each surface is known, the scene can be rendered using rasterization or ray tracing.

Each of the above approaches has many variations, and there is some overlap. Path tracing may be considered either a distinct technique or a particular type of ray tracing. Note that the usage of terminology related to ray tracing and path tracing has changed significantly over time.

Ray marching is a family of algorithms, used by ray casting, for finding intersections between a ray and a complex object, such as a volumetric dataset or a surface defined by a signed distance function. It is not, by itself, a rendering method, but it can be incorporated into ray tracing and path tracing, and is used by rasterization to implement screen-space reflection and other effects.

A technique called photon mapping or photon tracing uses forward ray tracing (also called particle tracing), tracing paths of photons from a light source to an object, rather than backward from the camera. The additional data collected by this process is used together with conventional backward ray tracing or path tracing. Rendering a scene using only forward ray tracing is impractical, even though it corresponds more closely to reality, because a huge number of photons would need to be simulated, only a tiny fraction of which actually hit the camera.

Real-time rendering, including video game graphics, typically uses rasterization, but increasingly combines it with ray tracing and path tracing. To enable realistic global illumination, real-time rendering often relies on pre-rendered ("baked") lighting for stationary objects. For moving objects, it may use a technique called light probes, in which lighting is recorded by rendering omnidirectional views of the scene at chosen points in space (often points on a grid to allow easier interpolation). These are similar to environment maps, but typically use a very low resolution or an approximation such as spherical harmonics. (Note: Blender uses the term 'light probes' for a more general class of pre-recorded lighting data, including reflection maps.)

Scanline rendering and rasterization

A high-level representation of an image necessarily contains elements in a different domain from pixels. These elements are referred to as primitives. In a schematic drawing, for instance, line segments and curves might be primitives. In a graphical user interface, windows and buttons might be the primitives. In rendering of 3D models, triangles and polygons in space might be primitives.

If a pixel-by-pixel (image order) approach to rendering is impractical or too slow for some task, then a primitive-by-primitive (object order) approach to rendering may prove useful. Here, one loop through each of the primitives, determines which pixels in the image it affects, and modifies those pixels accordingly. This is called rasterization, and is the rendering method used by all current graphics cards.

Rasterization is frequently faster than pixel-by-pixel rendering. First, large areas of the image may be empty of primitives; rasterization will ignore these areas, but pixel-by-pixel rendering must pass through them. Second, rasterization can improve cache coherency and reduce redundant work by taking advantage of the fact that the pixels occupied by a single primitive tend to be contiguous in the image. For these reasons, rasterization is usually the approach of choice when interactive rendering is required; however, the pixel-by-pixel approach can often produce higher-quality images and is more versatile because it does not depend on as many assumptions about the image as rasterization.

The older form of rasterization is characterized by rendering an entire face (primitive) as a single color. Alternatively, rasterization can be done in a more complicated manner by first rendering the vertices of a face and then rendering the pixels of that face as a blending of the vertex colors. This version of rasterization has overtaken the old method as it allows the graphics to flow without complicated textures (a rasterized image when used face by face tends to have a very block-like effect if not covered in complex textures; the faces are not smooth because there is no gradual color change from one primitive to the next). This newer method of rasterization utilizes the graphics card's more taxing shading functions and still achieves better performance because the simpler textures stored in memory use less space. Sometimes designers will use one rasterization method on some faces and the other method on others based on the angle at which that face meets other joined faces, thus increasing speed and not hurting the overall effect.

Ray casting
In ray casting the geometry which has been modeled is parsed pixel by pixel, line by line, from the point of view outward, as if casting rays out from the point of view. Where an object is intersected, the color value at the point may be evaluated using several methods. In the simplest, the color value of the object at the point of intersection becomes the value of that pixel. The color may be determined from a texture-map. A more sophisticated method is to modify the color value by an illumination factor, but without calculating the relationship to a simulated light source. To reduce artifacts, a number of rays in slightly different directions may be averaged.

Ray casting involves calculating the "view direction" (from camera position), and incrementally following along that "ray cast" through "solid 3d objects" in the scene, while accumulating the resulting value from each point in 3D space. This is related and similar to "ray tracing" except that the raycast is usually not "bounced" off surfaces (where the "ray tracing" indicates that it is tracing out the lights path including bounces). "Ray casting" implies that the light ray is following a straight path (which may include traveling through semi-transparent objects). The ray cast is a vector that can originate from the camera or from the scene endpoint ("back to front", or "front to back"). Sometimes the final light value is derived from a "transfer function" and sometimes it's used directly.

Rough simulations of optical properties may be additionally employed: a simple calculation of the ray from the object to the point of view is made. Another calculation is made of the angle of incidence of light rays from the light source(s), and from these as well as the specified intensities of the light sources, the value of the pixel is calculated. Another simulation uses illumination plotted from a radiosity algorithm, or a combination of these two.

Ray tracing

Ray tracing aims to simulate the natural flow of light, interpreted as particles. Often, ray tracing methods are utilized to approximate the solution to the rendering equation by applying Monte Carlo methods to it. Some of the most used methods are path tracing, bidirectional path tracing, or Metropolis light transport, but also semi realistic methods are in use, like Whitted Style Ray Tracing, or hybrids. While most implementations let light propagate on straight lines, applications exist to simulate relativistic spacetime effects.

In a final, production quality rendering of a ray traced work, multiple rays are generally shot for each pixel, and traced not just to the first object of intersection, but rather, through a number of sequential 'bounces', using the known laws of optics such as "angle of incidence equals angle of reflection" and more advanced laws that deal with refraction and surface roughness.

Once the ray either encounters a light source, or more probably once a set limiting number of bounces has been evaluated, then the surface illumination at that final point is evaluated using techniques described above, and the changes along the way through the various bounces evaluated to estimate a value observed at the point of view. This is all repeated for each sample, for each pixel.

In distribution ray tracing, at each point of intersection, multiple rays may be spawned. In path tracing, however, only a single ray or none is fired at each intersection, utilizing the statistical nature of Monte Carlo experiments.

As part of the approach known as physically based rendering, path tracing has become the dominant technique for rendering realistic scenes, including effects for movies. For example, the popular open source 3D software Blender uses path tracing in its Cycles renderer. Images produced using path tracing for global illumination are generally noisier than when using radiosity (the main competing algorithm), but radiosity can be difficult to apply to complex scenes and is prone to artifacts that arise from using a tessellated representation of irradiance.

Path tracing's relative simplicity and its nature as a Monte Carlo method (sampling hundreds or thousands of paths per pixel) make it attractive to implement on a GPU, especially on recent GPUs that support ray tracing acceleration technology such as Nvidia's RTX and OptiX. Many techniques have been developed to denoise the output of path tracing, reducing the number of paths required to achieve acceptable quality, at the risk of losing some detail or introducing small-scale artifacts that are more objectionable than noise; neural networks are now widely used for this purpose.

Advances in GPU technology have made real-time ray tracing possible in games, although it is currently almost always used in combination with rasterization. This enables visual effects that are difficult with only rasterization, including reflection from curved surfaces and interreflective objects, and shadows that are accurate over a wide range of distances and surface orientations. Ray tracing support is included in recent versions of the graphics APIs used by games, such as DirectX, Metal, and Vulkan.

Neural rendering
Neural rendering is a rendering method using artificial neural networks. Neural rendering includes image-based rendering methods that are used to reconstruct 3D models from 2-dimensional images. One of these methods are photogrammetry, which is a method in which a collection of images from multiple angles of an object are turned into a 3D model. There have also been recent developments in generating and rendering 3D models from text and coarse paintings by notably Nvidia, Google and various other companies.

Radiosity
Radiosity is a method which attempts to simulate the way in which directly illuminated surfaces act as indirect light sources that illuminate other surfaces. This produces more realistic shading and seems to better capture the 'ambience' of an indoor scene. A classic example is a way that shadows 'hug' the corners of rooms.

The optical basis of the simulation is that some diffused light from a given point on a given surface is reflected in a large spectrum of directions and illuminates the area around it.

The simulation technique may vary in complexity. Many renderings have a very rough estimate of radiosity, simply illuminating an entire scene very slightly with a factor known as ambiance. However, when advanced radiosity estimation is coupled with a high quality ray tracing algorithm, images may exhibit convincing realism, particularly for indoor scenes.

In advanced radiosity simulation, recursive, finite-element algorithms 'bounce' light back and forth between surfaces in the model, until some recursion limit is reached. The colouring of one surface in this way influences the colouring of a neighbouring surface, and vice versa. The resulting values of illumination throughout the model (sometimes including for empty spaces) are stored and used as additional inputs when performing calculations in a ray-casting or ray-tracing model.

Due to the iterative/recursive nature of the technique, complex objects are particularly slow to emulate. Prior to the standardization of rapid radiosity calculation, some digital artists used a technique referred to loosely as false radiosity by darkening areas of texture maps corresponding to corners, joints and recesses, and applying them via self-illumination or diffuse mapping for scanline rendering. Even now, advanced radiosity calculations may be reserved for calculating the ambiance of the room, from the light reflecting off walls, floor and ceiling, without examining the contribution that complex objects make to the radiosity – or complex objects may be replaced in the radiosity calculation with simpler objects of similar size and texture.

Radiosity calculations are viewpoint independent which increases the computations involved, but makes them useful for all viewpoints. If there is little rearrangement of radiosity objects in the scene, the same radiosity data may be reused for a number of frames, making radiosity an effective way to improve on the flatness of ray casting, without seriously impacting the overall rendering time-per-frame.

Because of this, radiosity is a prime component of leading real-time rendering methods, and has been used from beginning-to-end to create a large number of well-known recent feature-length animated 3D-cartoon films.

Sampling and filtering
One problem that any rendering system must deal with, no matter which approach it takes, is the sampling problem. Essentially, the rendering process tries to depict a continuous function from image space to colors by using a finite number of pixels. As a consequence of the Nyquist–Shannon sampling theorem (or Kotelnikov theorem), any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to image resolution. In simpler terms, this expresses the idea that an image cannot display details, peaks or troughs in color or intensity, that are smaller than one pixel.

If a naive rendering algorithm is used without any filtering, high frequencies in the image function will cause ugly aliasing to be present in the final image. Aliasing typically manifests itself as jaggies, or jagged edges on objects where the pixel grid is visible. In order to remove aliasing, all rendering algorithms (if they are to produce good-looking images) must use some kind of low-pass filter on the image function to remove high frequencies, a process called antialiasing.

Optimization
Due to the large number of calculations, a work in progress is usually only rendered in detail appropriate to the portion of the work being developed at a given time, so in the initial stages of modeling, wireframe and ray casting may be used, even where the target output is ray tracing with radiosity. It is also common to render only parts of the scene at high detail, and to remove objects that are not important to what is currently being developed.

For real-time, it is appropriate to simplify one or more common approximations, and tune to the exact parameters of the scenery in question, which is also tuned to the agreed parameters to get the most 'bang for the buck'.

Academic core
The implementation of a realistic renderer always has some basic element of physical simulation or emulation – some computation which resembles or abstracts a real physical process.

The term "physically based" indicates the use of physical models and approximations that are more general and widely accepted outside rendering. A particular set of related techniques have gradually become established in the rendering community.

The basic concepts are moderately straightforward, but intractable to calculate; and a single elegant algorithm or approach has been elusive for more general purpose renderers. In order to meet demands of robustness, accuracy and practicality, an implementation will be a complex combination of different techniques.

Rendering research is concerned with both the adaptation of scientific models and their efficient application.

The rendering equation
This is the key academic/theoretical concept in rendering. It serves as the most abstract formal expression of the non-perceptual aspect of rendering. All more complete algorithms can be seen as solutions to particular formulations of this equation.

 * $$L_o(x, \omega) = L_e(x, \omega) + \int_\Omega L_i(x, \omega') f_r(x, \omega', \omega) (\omega' \cdot n) \, \mathrm d \omega'$$

Meaning: at a particular position and direction, the outgoing light (Lo) is the sum of the emitted light (Le) and the reflected light. The reflected light being the sum of the incoming light (Li) from all directions, multiplied by the surface reflection and incoming angle. By connecting outward light to inward light, via an interaction point, this equation stands for the whole 'light transport' – all the movement of light –  in a scene.

The bidirectional reflectance distribution function
The bidirectional reflectance distribution function (BRDF) expresses a simple model of light interaction with a surface as follows:

 * $$f_r(x, \omega', \omega) = \frac{\mathrm d L_r(x, \omega)}{L_i(x, \omega')(\omega' \cdot \vec n) \mathrm d \omega'}$$

Light interaction is often approximated by the even simpler models: diffuse reflection and specular reflection, although both can ALSO be BRDFs.

Geometric optics
Rendering is practically exclusively concerned with the particle aspect of light physics – known as geometrical optics. Treating light, at its basic level, as particles bouncing around is a simplification, but appropriate: the wave aspects of light are negligible in most scenes, and are significantly more difficult to simulate. Notable wave aspect phenomena include diffraction (as seen in the colours of CDs and DVDs) and polarisation (as seen in LCDs). Both types of effect, if needed, are made by appearance-oriented adjustment of the reflection model.

Visual perception
Though it receives less attention, an understanding of human visual perception is valuable to rendering. This is mainly because image displays and human perception have restricted ranges. A renderer can simulate a wide range of light brightness and color, but current displays – movie screen, computer monitor, etc. –  cannot handle so much, and something must be discarded or compressed. Human perception also has limits, and so does not need to be given large-range images to create realism. This can help solve the problem of fitting images into displays, and, furthermore, suggest what short-cuts could be used in the rendering simulation, since certain subtleties will not be noticeable. This related subject is tone mapping.

Mathematics used in rendering includes: linear algebra, calculus, numerical mathematics, signal processing, and Monte Carlo methods.

Rendering for movies often takes place on a network of tightly connected computers known as a render farm.

The current state of the art in 3-D image description for movie creation is the Mental Ray scene description language designed at Mental Images and RenderMan Shading Language designed at Pixar (compare with simpler 3D fileformats such as VRML or APIs such as OpenGL and DirectX tailored for 3D hardware accelerators).

Other renderers (including proprietary ones) can and are sometimes used, but most other renderers tend to miss one or more of the often needed features like good texture filtering, texture caching, programmable shaders, highend geometry types like hair, subdivision or nurbs surfaces with tesselation on demand, geometry caching, raytracing with geometry caching, high quality shadow mapping, speed or patent-free implementations. Other highly sought features these days may include interactive photorealistic rendering (IPR) and hardware rendering/shading.

Chronology of concepts

 * 1968 - Ray casting
 * 1970 - Scanline rendering
 * 1971 - Gouraud shading
 * 1973 - Phong shading
 * 1973 - Phong reflection
 * 1973 - Diffuse reflection
 * 1973 - Specular highlight
 * 1973 - Specular reflection
 * 1974 - Sprites
 * 1974 - Scrolling
 * 1974 - Texture mapping
 * 1974 - Z-buffering
 * 1976 - Environment mapping
 * 1977 - Blinn shading
 * 1977 - Side-scrolling
 * 1977 - Shadow volumes
 * 1978 - Shadow mapping
 * 1978 - Bump mapping
 * 1979 - Tile map
 * 1980 - BSP trees
 * 1980 - Ray tracing
 * 1981 - Parallax scrolling
 * 1981 - Sprite zooming
 * 1981 Cook shader
 * 1983 - MIP maps
 * 1984 - Octree ray tracing
 * 1984 - Alpha compositing
 * 1984 - Distributed ray tracing
 * 1984 - Radiosity
 * 1985 - Row/column scrolling
 * 1985 - Hemicube radiosity
 * 1986 Light source tracing
 * 1986 - Rendering equation
 * 1987 - Reyes rendering
 * 1988 - Depth cue
 * 1988 - Distance fog
 * 1988 - Tiled rendering
 * 1991 - Xiaolin Wu line anti-aliasing
 * 1991 Hierarchical radiosity
 * 1993 - Texture filtering
 * 1993 - Perspective correction
 * 1993 - Transform, clipping, and lighting
 * 1993 - Directional lighting
 * 1993 - Trilinear interpolation
 * 1993 - Z-culling
 * 1993 - Oren–Nayar reflectance
 * 1993 - Tone mapping
 * 1993 - Subsurface scattering
 * 1994 - Ambient occlusion
 * 1995 - Hidden-surface determination
 * 1995 - Photon mapping
 * 1996 - Multisample anti-aliasing
 * 1997 - Metropolis light transport
 * 1997 Instant Radiosity
 * 1998 - Hidden-surface removal
 * 2000 - Pose space deformation
 * 2002 - Precomputed Radiance Transfer

title: Rendering (computer graphics)


text:
Cartridge

Cartridge may refer to:

Objects

 * Cartridge (firearms), a type of modern ammunition
 * ROM cartridge, a removable component in an electronic device
 * Cartridge (respirator), a type of filter used in respirators
 * Ink cartridge, a component for inkjet printers that contains the ink
 * The liquid storage component of a vaporizer
 * Magnetic cartridge, an electromechanical transducer, commonly called a 'pickup', used to play records on a turntable

Other uses

 * Donald Cartridge (1933–2015), English cricketer and educator
 * Cartridge Creek, a creek near Fresno, California, United States

title: Cartridge