Raycasting Engine

表达式1821: "c" Subscript, "r" "o" "s" "s" , Baseline left parenthesis, "a" , "b" , right parenthesis equals left bracket, "a" left bracket, 2 , right bracket times "b" left bracket, 3 , right bracket minus "a" left bracket, 3 , right bracket times "b" left bracket, 2 , right bracket , "a" left bracket, 1 , right bracket times "b" left bracket, 3 , right bracket minus "a" left bracket, 3 , right bracket times "b" left bracket, 1 , right bracket , "a" left bracket, 1 , right bracket times "b" left bracket, 2 , right bracket minus "a" left bracket, 2 , right bracket times "b" left bracket, 1 , right bracket , right bracket

1821

表达式1822: "c" Subscript, "o" "n" "c" "a" "t" , Baseline left parenthesis, "a" , "b" , right parenthesis equals left bracket, left brace, "i" Subscript, 3 , Baseline less than or equal to length left parenthesis, "a" , right parenthesis : "a" left bracket, "i" Subscript, 3 , Baseline , right bracket , "b" left bracket, "i" Subscript, 3 , Baseline minus length left parenthesis, "a" , right parenthesis , right bracket , right brace for "i" Subscript, 3 , Baseline equals left bracket, 1...length left parenthesis, "a" , right parenthesis plus length left parenthesis, "b" , right parenthesis , right bracket , right bracket

1822

表达式1823: "m" Subscript, "i" "n" "i" "n" "d" "e" "x" , Baseline left parenthesis, "a" , right parenthesis equals max left parenthesis, left bracket, left brace, "a" left bracket, "i" Subscript, 0 , Baseline , right bracket equals min left parenthesis, left bracket, left brace, "a" left bracket, "i" Subscript, 2 , Baseline , right bracket greater than 0 : "a" left bracket, "i" Subscript, 2 , Baseline , right bracket , infinity , right brace for "i" Subscript, 2 , Baseline equals left bracket, 1...length left parenthesis, "a" , right parenthesis , right bracket , right bracket , right parenthesis : "i" Subscript, 0 , Baseline , 0 , right brace for "i" Subscript, 0 , Baseline equals left bracket, 1...length left parenthesis, "a" , right parenthesis , right bracket , right bracket , right parenthesis

1823

表达式1824: "n" Subscript, "o" "r" "m" "a" "l" "i" "s" "e" , Baseline left parenthesis, "a" , right parenthesis equals StartFraction, "a" Over StartRoot, "a" left bracket, 1 , right bracket squared plus "a" left bracket, 2 , right bracket squared plus "a" left bracket, 3 , right bracket squared , EndRoot , EndFraction

1824

表达式1825: "t" Subscript, "e" "r" "n" "a" "r" "y" 3 , Baseline left parenthesis, "i" , "a" Subscript, "i" , Baseline , "b" Subscript, "i" , Baseline , "c" Subscript, "i" , Baseline , "a" Subscript, "o" , Baseline , "b" Subscript, "o" , Baseline , "c" Subscript, "o" , Baseline , right parenthesis equals left brace, "i" equals "a" Subscript, "i" , Baseline : "a" Subscript, "o" , Baseline , left brace, "i" equals "b" Subscript, "i" , Baseline : "b" Subscript, "o" , Baseline , left brace, "i" equals "c" Subscript, "i" , Baseline : "c" Subscript, "o" , Baseline , infinity , right brace , right brace , right brace

1825

表达式1826: "A" Subscript, "n" "d" , Baseline left parenthesis, "a" , "b" , right parenthesis equals left brace, "a" equals 1 : left brace, "b" equals 1 : 1 , 0 , right brace , 0 , right brace

1826

表达式1827: "m" Subscript, "i" "n" "p" "o" "s" , Baseline left parenthesis, "a" , right parenthesis equals left brace, "a" left bracket, 1 , right bracket greater than 0 : left brace, "a" left bracket, 2 , right bracket greater than 0 : min left parenthesis, "a" , right parenthesis , "a" left bracket, 1 , right bracket , right brace , left brace, "a" left bracket, 2 , right bracket greater than 0 : "a" left bracket, 2 , right bracket , StartFraction, 0 Over 0 , EndFraction , right brace , right brace

1827

表达式1828: "q" Subscript, "u" "a" "d" "r" "a" "t" "i" "c" , Baseline left parenthesis, "a" , "b" , "c" , "d" , right parenthesis equals StartFraction, negative "b" plus "d" StartRoot, "b" squared minus 4 "a" "c" , EndRoot Over 2 "a" , EndFraction

1828

表达式1829: "m" Subscript, "a" "t" 3 "m" "u" "l" "t" "i" "p" "l" "y" , Baseline left parenthesis, "a" , "b" , right parenthesis equals left bracket, left parenthesis, Start sum from "n" Subscript, 1 , Baseline equals 1 to 3, end sum, "a" left bracket, "n" Subscript, 1 , Baseline plus 3floor left parenthesis, StartFraction, "i" Subscript, 0 , Baseline minus 1 Over 3 , EndFraction , right parenthesis , right bracket "b" left bracket, left parenthesis, "n" Subscript, 1 , Baseline minus 1 , right parenthesis left parenthesis, 3 , right parenthesis plus mod left parenthesis, left parenthesis, "i" Subscript, 0 , Baseline minus 1 , right parenthesis , 3 , right parenthesis plus 1 , right bracket , right parenthesis for "i" Subscript, 0 , Baseline equals left bracket, 1...9 , right bracket , right bracket

1829

表达式1830: "v" Subscript, "e" "c" "m" "a" "t" "r" "i" "x" "m" "u" "l" "t" "i" "p" "l" "y" , Baseline left parenthesis, "a" , "b" , right parenthesis equals left bracket, left parenthesis, Start sum from "n" Subscript, 1 , Baseline equals 1 to 3, end sum, "a" left bracket, 3 left parenthesis, "i" Subscript, 0 , Baseline minus 1 , right parenthesis plus "n" Subscript, 1 , Baseline , right bracket "b" left bracket, "n" Subscript, 1 , Baseline , right bracket , right parenthesis for "i" Subscript, 0 , Baseline equals left bracket, 1...3 , right bracket , right bracket

1830

表达式1831: "r" Subscript, "e" "m" "o" "v" "e" , Baseline left parenthesis, "a" Subscript, 1 , Baseline , "t" , "e" Subscript, 1 , Baseline , "i" , right parenthesis equals left brace, "t" equals "e" Subscript, 1 , Baseline : "a" Subscript, 1 , Baseline left bracket, left brace, left bracket, 1...length left parenthesis, "a" Subscript, 1 , Baseline , right parenthesis , right bracket equals "i" : infinity , left bracket, 1...length left parenthesis, "a" Subscript, 1 , Baseline , right parenthesis , right bracket , right brace , right bracket , "a" Subscript, 1 , Baseline , right brace

1831

表达式1832: "i" Subscript, "n" "d" "e" "x" , Baseline left parenthesis, "a" , "b" , right parenthesis equals max left parenthesis, left brace, "a" equals "b" : left bracket, 1...5 0 0 , right bracket , 0 , right brace , right parenthesis

1832

表达式1833: "m" Subscript, "t" "v" "i" , Baseline left parenthesis, "a" , "b" , "c" , right parenthesis equals left brace, min left parenthesis, "a" , right parenthesis less than min left parenthesis, "b" , right parenthesis : left brace, min left parenthesis, "a" , right parenthesis less than min left parenthesis, "c" , right parenthesis : left bracket, 1 , min left parenthesis, "a" , right parenthesis , "i" Subscript, "n" "d" "e" "x" , Baseline left parenthesis, "a" , min left parenthesis, "a" , right parenthesis , right parenthesis , right bracket , left bracket, 3 , min left parenthesis, "c" , right parenthesis , "i" Subscript, "n" "d" "e" "x" , Baseline left parenthesis, "c" , min left parenthesis, "c" , right parenthesis , right parenthesis , right bracket , right brace , left brace, min left parenthesis, "b" , right parenthesis less than min left parenthesis, "c" , right parenthesis : left bracket, 2 , min left parenthesis, "b" , right parenthesis , "i" Subscript, "n" "d" "e" "x" , Baseline left parenthesis, "b" , min left parenthesis, "b" , right parenthesis , right parenthesis , right bracket , left bracket, 3 , min left parenthesis, "c" , right parenthesis , "i" Subscript, "n" "d" "e" "x" , Baseline left parenthesis, "c" , min left parenthesis, "c" , right parenthesis , right parenthesis , right bracket , right brace , right brace

1833

表达式1834: "m" Subscript, "i" "n" "o" "v" "e" "r" 0 , Baseline left parenthesis, "a" , "b" , "c" , right parenthesis equals "m" Subscript, "t" "v" "i" , Baseline left parenthesis, left brace, "a" greater than 0.0 1 : "a" , infinity , right brace , left brace, "b" greater than 0.0 1 : "b" , infinity , right brace , left brace, "c" greater than 0.0 1 : "c" , infinity , right brace , right parenthesis

1834

表达式1835: "d" Subscript, "r" "a" "w" "p" "x" "l" , Baseline left parenthesis, "x" , "y" , right parenthesis equals polygon left parenthesis, left parenthesis, "x" , "y" , right parenthesis , left parenthesis, "x" plus 1 , "y" , right parenthesis , left parenthesis, "x" plus 1 , "y" plus 1 , right parenthesis , left parenthesis, "x" , "y" plus 1 , right parenthesis , right parenthesis

1835

表达式1836:

1836

Main Functions

1837

The main functions currently used by the engine

1838

表达式1839: "n" Subscript, "o" "r" "m" "a" "l" , Baseline left parenthesis, "t" , "i" , "p" , right parenthesis equals "n" Subscript, "o" "r" "m" "a" "l" "i" "s" "e" , Baseline left parenthesis, left brace, "t" equals 1 : "n" Subscript, "o" "r" "m" "a" "l" "S" "p" "h" "e" "r" "e" , Baseline left parenthesis, "p" , "i" , right parenthesis , left brace, "t" equals 2 : "n" Subscript, "o" "r" "m" "a" "l" "q" "u" "a" "d" , Baseline left parenthesis, "i" , right parenthesis , "n" Subscript, "o" "r" "m" "a" "l" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "i" , right parenthesis , right brace , right brace , right parenthesis

1839

表达式1840: "n" Subscript, "o" "r" "m" "a" "l" "q" "u" "a" "d" , Baseline left parenthesis, "q" , right parenthesis equals "c" Subscript, "r" "o" "s" "s" , Baseline left parenthesis, "Q" Subscript, "p" 3 , Baseline left parenthesis, "q" , right parenthesis minus "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis , "Q" Subscript, "p" 2 , Baseline left parenthesis, "q" , right parenthesis minus "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis , right parenthesis

1840

表达式1841: "n" Subscript, "o" "r" "m" "a" "l" "S" "p" "h" "e" "r" "e" , Baseline left parenthesis, "p" , "s" , right parenthesis equals "p" minus "S" Subscript, "p" 1 , Baseline left parenthesis, "s" , right parenthesis

1841

表达式1842: "n" Subscript, "o" "r" "m" "a" "l" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "t" , right parenthesis equals "c" Subscript, "r" "o" "s" "s" , Baseline left parenthesis, "T" Subscript, "p" 3 , Baseline left parenthesis, "t" , right parenthesis minus "T" Subscript, "p" 1 , Baseline left parenthesis, "t" , right parenthesis , "T" Subscript, "p" 2 , Baseline left parenthesis, "t" , right parenthesis minus "T" Subscript, "p" 1 , Baseline left parenthesis, "t" , right parenthesis , right parenthesis

1842

表达式1843:

1843

表达式1844: "l" Subscript, "i" "g" "h" "t" "v" "e" "c" , Baseline left parenthesis, "p" , right parenthesis equals "n" Subscript, "o" "r" "m" "a" "l" "i" "s" "e" , Baseline left parenthesis, "l" Subscript, "i" "g" "h" "t" , Baseline minus "p" , right parenthesis

1844

表达式1845:

1845

表达式1846: "g" Subscript, "e" "t" "c" "o" "l" "o" "u" "r" "p" "a" "r" "a" "m" "e" "t" "e" "r" "s" , Baseline left parenthesis, "t" , "i" , "p" , right parenthesis equals left brace, "t" equals 1 : left bracket, "r" Subscript, "s" "p" "h" "e" "r" "e" , Baseline left bracket, "i" , right bracket , "g" Subscript, "s" "p" "h" "e" "r" "e" , Baseline left bracket, "i" , right bracket , "b" Subscript, "s" "p" "h" "e" "r" "e" , Baseline left bracket, "i" , right bracket , "a" Subscript, "m" "b" "i" "e" "n" "c" "e" "s" "p" "h" "e" "r" "e" , Baseline left bracket, "i" , right bracket , "d" Subscript, "i" "f" "f" "u" "s" "i" "v" "i" "t" "y" "s" "p" "h" "e" "r" "e" , Baseline left bracket, "i" , right bracket , "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "v" "i" "t" "y" "s" "p" "h" "e" "r" "e" , Baseline left bracket, "i" , right bracket , right bracket , left brace, "t" equals 2 : "c" Subscript, "o" "n" "c" "a" "t" , Baseline left parenthesis, "c" Subscript, "o" "l" "o" "u" "r" "q" "u" "a" "d" "a" "t" "p" "o" "i" "n" "t" , Baseline left parenthesis, "i" , "p" , right parenthesis , left bracket, "a" Subscript, "m" "b" "i" "e" "n" "c" "e" "q" "u" "a" "d" , Baseline left bracket, "i" , right bracket , "d" Subscript, "i" "f" "f" "u" "s" "i" "v" "i" "t" "y" "q" "u" "a" "d" , Baseline left bracket, "i" , right bracket , "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "v" "i" "t" "y" "q" "u" "a" "d" , Baseline left bracket, "i" , right bracket , right bracket , right parenthesis , left bracket, "r" Subscript, "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "i" , right bracket , "g" Subscript, "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "i" , right bracket , "b" Subscript, "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "i" , right bracket , "a" Subscript, "m" "b" "i" "e" "n" "c" "e" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "i" , right bracket , "d" Subscript, "i" "f" "f" "u" "s" "i" "v" "i" "t" "y" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "i" , right bracket , "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "v" "i" "t" "y" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "i" , right bracket , right bracket , right brace , right brace

1846

表达式1847:

1847

表达式1848: "r" Subscript, "e" "l" "p" "o" "i" "n" "t" "p" "l" "a" "n" "e" , Baseline left parenthesis, "o" , "p" , "u" , "v" , right parenthesis equals "t" Subscript, "e" "r" "n" "a" "r" "y" 3 , Baseline left parenthesis, max left parenthesis, "u" left bracket, 1 , right bracket "v" left bracket, 2 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 2 , right bracket , "u" left bracket, 1 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 3 , right bracket , "u" left bracket, 2 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 2 , right bracket "u" left bracket, 3 , right bracket , right parenthesis , "u" left bracket, 1 , right bracket "v" left bracket, 2 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 2 , right bracket , "u" left bracket, 1 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 3 , right bracket , "u" left bracket, 2 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 2 , right bracket "u" left bracket, 3 , right bracket , left bracket, StartFraction, left parenthesis, "p" left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis "v" left bracket, 2 , right bracket minus left parenthesis, "p" left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis "v" left bracket, 1 , right bracket Over "u" left bracket, 1 , right bracket "v" left bracket, 2 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 2 , right bracket , EndFraction , StartFraction, left parenthesis, "p" left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis "u" left bracket, 1 , right bracket minus left parenthesis, "p" left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis "u" left bracket, 2 , right bracket Over "u" left bracket, 1 , right bracket "v" left bracket, 2 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 2 , right bracket , EndFraction , right bracket , left bracket, StartFraction, left parenthesis, "p" left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis "v" left bracket, 3 , right bracket minus left parenthesis, "p" left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis "v" left bracket, 1 , right bracket Over "u" left bracket, 1 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 3 , right bracket , EndFraction , StartFraction, left parenthesis, "p" left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis "u" left bracket, 1 , right bracket minus left parenthesis, "p" left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis "u" left bracket, 3 , right bracket Over "u" left bracket, 1 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 1 , right bracket "u" left bracket, 3 , right bracket , EndFraction , right bracket , left bracket, StartFraction, left parenthesis, "p" left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis "v" left bracket, 3 , right bracket minus left parenthesis, "p" left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis "v" left bracket, 2 , right bracket Over "u" left bracket, 2 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 2 , right bracket "u" left bracket, 3 , right bracket , EndFraction , StartFraction, left parenthesis, "p" left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis "u" left bracket, 2 , right bracket minus left parenthesis, "p" left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis "u" left bracket, 3 , right bracket Over "u" left bracket, 2 , right bracket "v" left bracket, 3 , right bracket minus "v" left bracket, 2 , right bracket "u" left bracket, 3 , right bracket , EndFraction , right bracket , right parenthesis

1848

表达式1849: "p" Subscript, "l" "a" "n" "e" "e" "q" "u" "a" "t" "i" "o" "n" "c" "o" "e" "f" "f" "e" "c" "i" "e" "n" "t" "s" , Baseline left parenthesis, "P" , "N" , right parenthesis equals left bracket, "N" left bracket, 1 , right bracket , "N" left bracket, 2 , right bracket , "N" left bracket, 3 , right bracket , negative "P" left bracket, 1 , right bracket "N" left bracket, 1 , right bracket minus "P" left bracket, 2 , right bracket "N" left bracket, 2 , right bracket minus "P" left bracket, 3 , right bracket "N" left bracket, 3 , right bracket , right bracket

1849

表达式1850: "p" Subscript, "o" "i" "n" "t" 2 "d" "i" "n" "s" "i" "d" "e" "q" "u" "a" "d" , Baseline left parenthesis, "p" , "x" Subscript, 01 , Baseline , "x" Subscript, 02 , Baseline , "y" Subscript, 01 , Baseline , "y" Subscript, 02 , Baseline , right parenthesis equals "A" Subscript, "n" "d" , Baseline left parenthesis, "A" Subscript, "n" "d" , Baseline left parenthesis, left brace, "p" left bracket, 1 , right bracket greater than or equal to "x" Subscript, 01 , Baseline , right brace , left brace, "p" left bracket, 1 , right bracket less than or equal to "x" Subscript, 02 , Baseline , right brace , right parenthesis , "A" Subscript, "n" "d" , Baseline left parenthesis, left brace, "p" left bracket, 2 , right bracket greater than or equal to "y" Subscript, 01 , Baseline , right brace , left brace, "p" left bracket, 2 , right bracket less than or equal to "y" Subscript, 02 , Baseline , right brace , right parenthesis , right parenthesis

1850

表达式1851: "p" Subscript, "o" "i" "n" "t" 2 "d" "i" "n" "s" "i" "d" "e" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "p" , "x" Subscript, 01 , Baseline , "x" Subscript, 02 , Baseline , "y" Subscript, 01 , Baseline , "y" Subscript, 02 , Baseline , right parenthesis equals "A" Subscript, "n" "d" , Baseline left parenthesis, "A" Subscript, "n" "d" , Baseline left parenthesis, left brace, "p" left bracket, 1 , right bracket greater than or equal to "x" Subscript, 01 , Baseline , right brace , left brace, "p" left bracket, 2 , right bracket greater than or equal to "y" Subscript, 01 , Baseline , right brace , right parenthesis , left brace, StartFraction, "p" left bracket, 1 , right bracket Over "x" Subscript, 02 , Baseline , EndFraction plus StartFraction, "p" left bracket, 2 , right bracket Over "y" Subscript, 02 , Baseline , EndFraction less than or equal to 1 , right brace , right parenthesis

1851

表达式1852: "p" Subscript, "o" "i" "n" "t" "o" "n" "q" "u" "a" "d" , Baseline left parenthesis, "p" , "q" , right parenthesis equals "p" Subscript, "o" "i" "n" "t" 2 "d" "i" "n" "s" "i" "d" "e" "q" "u" "a" "d" , Baseline left parenthesis, "r" Subscript, "e" "l" "p" "o" "i" "n" "t" "p" "l" "a" "n" "e" , Baseline left parenthesis, StartFraction, "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis plus "Q" Subscript, "p" 3 , Baseline left parenthesis, "q" , right parenthesis Over 2 , EndFraction , "p" , StartFraction, "Q" Subscript, "p" 2 , Baseline left parenthesis, "q" , right parenthesis minus "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis Over 4 , EndFraction , StartFraction, "Q" Subscript, "p" 4 , Baseline left parenthesis, "q" , right parenthesis minus "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis Over 4 , EndFraction , right parenthesis , negative 2 , 2 , negative 2 , 2 , right parenthesis

1852

表达式1853: "p" Subscript, "o" "i" "n" "t" "o" "n" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "p" , "t" , right parenthesis equals "p" Subscript, "o" "i" "n" "t" 2 "d" "i" "n" "s" "i" "d" "e" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "r" Subscript, "e" "l" "p" "o" "i" "n" "t" "p" "l" "a" "n" "e" , Baseline left parenthesis, "T" Subscript, "p" 1 , Baseline left parenthesis, "t" , right parenthesis , "p" , "T" Subscript, "p" 2 , Baseline left parenthesis, "t" , right parenthesis minus "T" Subscript, "p" 1 , Baseline left parenthesis, "t" , right parenthesis , "T" Subscript, "p" 3 , Baseline left parenthesis, "t" , right parenthesis minus "T" Subscript, "p" 1 , Baseline left parenthesis, "t" , right parenthesis , right parenthesis , 0 , 1 , 0 , 1 , right parenthesis

1853

表达式1854: "c" Subscript, "o" "l" "o" "u" "r" "q" "u" "a" "d" "a" "t" "p" "o" "i" "n" "t" , Baseline left parenthesis, "q" , "p" , right parenthesis equals "c" Subscript, "o" "l" "o" "u" "r" "q" "u" "a" "d" "i" "t" "e" "r" , Baseline left parenthesis, "q" , "i" Subscript, "t" "e" "r" "m" "a" "n" "d" "e" "l" "b" "r" "o" "t" , Baseline left parenthesis, "r" Subscript, "e" "l" "p" "o" "i" "n" "t" "p" "l" "a" "n" "e" , Baseline left parenthesis, StartFraction, "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis plus "Q" Subscript, "p" 3 , Baseline left parenthesis, "q" , right parenthesis Over 2 , EndFraction , "p" , StartFraction, "Q" Subscript, "p" 2 , Baseline left parenthesis, "q" , right parenthesis minus "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis Over 4 , EndFraction , StartFraction, "Q" Subscript, "p" 4 , Baseline left parenthesis, "q" , right parenthesis minus "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis Over 4 , EndFraction , right parenthesis , right parenthesis , right parenthesis

1854

表达式1855: "c" Subscript, "o" "l" "o" "u" "r" "q" "u" "a" "d" "i" "t" "e" "r" , Baseline left parenthesis, "q" , "i" , right parenthesis equals left brace, "i" equals "m" Subscript, "a" "n" "d" "e" "l" "b" "r" "o" "t" "i" "t" "e" "r" "a" "t" "i" "o" "n" "s" , Baseline : "m" Subscript, "a" "n" "d" "e" "l" "b" "r" "o" "t" "b" "a" "s" "e" "c" "o" "l" "o" "u" "r" , Baseline , left bracket, "r" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket plus left parenthesis, "r" Subscript, 2 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket minus "r" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , right parenthesis StartFraction, "i" Over "m" Subscript, "a" "n" "d" "e" "l" "b" "r" "o" "t" "i" "t" "e" "r" "a" "t" "i" "o" "n" "s" , Baseline , EndFraction , "g" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket plus left parenthesis, "g" Subscript, 2 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket minus "g" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , right parenthesis StartFraction, "i" Over "m" Subscript, "a" "n" "d" "e" "l" "b" "r" "o" "t" "i" "t" "e" "r" "a" "t" "i" "o" "n" "s" , Baseline , EndFraction , "b" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket plus left parenthesis, "b" Subscript, 2 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket minus "b" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , right parenthesis StartFraction, "i" Over "m" Subscript, "a" "n" "d" "e" "l" "b" "r" "o" "t" "i" "t" "e" "r" "a" "t" "i" "o" "n" "s" , Baseline , EndFraction , right bracket , right brace

1855

表达式1856:

1856

表达式1857: "l" Subscript, "i" "n" "e" "s" "p" "h" "e" "r" "e" "i" "n" "t" "e" "r" "s" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "o" , "v" , "S" Subscript, "c" , Baseline , "r" Subscript, "a" "d" , Baseline , right parenthesis equals "m" Subscript, "i" "n" "p" "o" "s" 1 , Baseline left parenthesis, "q" Subscript, "u" "a" "d" "r" "a" "t" "i" "c" , Baseline left parenthesis, left parenthesis, "v" left bracket, 1 , right bracket squared plus "v" left bracket, 2 , right bracket squared plus "v" left bracket, 3 , right bracket squared , right parenthesis , left parenthesis, negative 2 left parenthesis, "v" left bracket, 1 , right bracket left parenthesis, "S" Subscript, "c" , Baseline left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis plus "v" left bracket, 2 , right bracket left parenthesis, "S" Subscript, "c" , Baseline left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis plus "v" left bracket, 3 , right bracket left parenthesis, "S" Subscript, "c" , Baseline left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis , right parenthesis , right parenthesis , left parenthesis, left parenthesis, "S" Subscript, "c" , Baseline left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis squared plus left parenthesis, "S" Subscript, "c" , Baseline left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis squared plus left parenthesis, "S" Subscript, "c" , Baseline left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis squared minus "r" squared , right parenthesis , 1 , right parenthesis , "q" Subscript, "u" "a" "d" "r" "a" "t" "i" "c" , Baseline left parenthesis, left parenthesis, "v" left bracket, 1 , right bracket squared plus "v" left bracket, 2 , right bracket squared plus "v" left bracket, 3 , right bracket squared , right parenthesis , left parenthesis, negative 2 left parenthesis, "v" left bracket, 1 , right bracket left parenthesis, "S" Subscript, "c" , Baseline left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis plus "v" left bracket, 2 , right bracket left parenthesis, "S" Subscript, "c" , Baseline left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis plus "v" left bracket, 3 , right bracket left parenthesis, "S" Subscript, "c" , Baseline left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis , right parenthesis , right parenthesis , left parenthesis, left parenthesis, "S" Subscript, "c" , Baseline left bracket, 1 , right bracket minus "o" left bracket, 1 , right bracket , right parenthesis squared plus left parenthesis, "S" Subscript, "c" , Baseline left bracket, 2 , right bracket minus "o" left bracket, 2 , right bracket , right parenthesis squared plus left parenthesis, "S" Subscript, "c" , Baseline left bracket, 3 , right bracket minus "o" left bracket, 3 , right bracket , right parenthesis squared minus "r" squared , right parenthesis , negative 1 , right parenthesis , right parenthesis

1857

表达式1858: "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" "e" "r" "s" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "o" , "v" , "P" , right parenthesis equals negative StartFraction, left parenthesis, "P" left bracket, 1 , right bracket "o" left bracket, 1 , right bracket plus "P" left bracket, 2 , right bracket "o" left bracket, 2 , right bracket plus "P" left bracket, 3 , right bracket "o" left bracket, 3 , right bracket plus "P" left bracket, 4 , right bracket , right parenthesis Over left parenthesis, "P" left bracket, 1 , right bracket "v" left bracket, 1 , right bracket plus "P" left bracket, 2 , right bracket "v" left bracket, 2 , right bracket plus "P" left bracket, 3 , right bracket "v" left bracket, 3 , right bracket , right parenthesis , EndFraction

1858

表达式1859:

1859

表达式1860: "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" , Baseline left parenthesis, "o" , "v" , right parenthesis equals "m" Subscript, "i" "n" "o" "v" "e" "r" 0 , Baseline left parenthesis, "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "s" "p" "h" "e" "r" "e" , Baseline left parenthesis, "o" , "v" , right parenthesis , "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "q" "u" "a" "d" , Baseline left parenthesis, "o" , "v" , right parenthesis , "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "o" , "v" , right parenthesis , right parenthesis

1860

表达式1861: "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "e" "x" "c" "l" "u" "d" "e" , Baseline left parenthesis, "o" , "v" , "t" , "i" , right parenthesis equals "m" Subscript, "i" "n" "o" "v" "e" "r" 0 , Baseline left parenthesis, "r" Subscript, "e" "m" "o" "v" "e" , Baseline left parenthesis, "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "s" "p" "h" "e" "r" "e" , Baseline left parenthesis, "o" , "v" , right parenthesis , "t" , 1 , "i" , right parenthesis , "r" Subscript, "e" "m" "o" "v" "e" , Baseline left parenthesis, "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "q" "u" "a" "d" , Baseline left parenthesis, "o" , "v" , right parenthesis , "t" , 2 , "i" , right parenthesis , "r" Subscript, "e" "m" "o" "v" "e" , Baseline left parenthesis, "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "o" , "v" , right parenthesis , "t" , 3 , "i" , right parenthesis , right parenthesis

1861

表达式1862: "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "s" "p" "h" "e" "r" "e" , Baseline left parenthesis, "o" , "v" , right parenthesis equals left bracket, "l" Subscript, "i" "n" "e" "s" "p" "h" "e" "r" "e" "i" "n" "t" "e" "r" "s" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "o" , "v" , "S" Subscript, "p" 1 , Baseline left parenthesis, "i" Subscript, 1 , Baseline , right parenthesis , "r" Subscript, "a" "d" "s" "p" "h" "e" "r" "e" , Baseline left bracket, "i" Subscript, 1 , Baseline , right bracket , right parenthesis for "i" Subscript, 1 , Baseline equals left bracket, 1... "l" Subscript, "s" , Baseline , right bracket , right bracket

1862

表达式1863: "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "q" "u" "a" "d" , Baseline left parenthesis, "o" , "v" , right parenthesis equals left bracket, "p" Subscript, "o" "i" "n" "t" "i" "n" "t" "e" "r" "c" "e" "p" "t" "a" "n" "d" "o" "n" "q" "u" "a" "d" , Baseline left parenthesis, "o" , "v" , "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" "e" "r" "s" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "o" , "v" , "p" Subscript, "l" "a" "n" "e" "e" "q" "u" "a" "t" "i" "o" "n" "c" "o" "e" "f" "f" "e" "c" "i" "e" "n" "t" "s" , Baseline left parenthesis, "Q" Subscript, "p" 1 , Baseline left parenthesis, "i" Subscript, 1 , Baseline , right parenthesis , "n" Subscript, "o" "r" "m" "a" "l" "q" "u" "a" "d" , Baseline left parenthesis, "i" Subscript, 1 , Baseline , right parenthesis , right parenthesis , right parenthesis , "i" Subscript, 1 , Baseline , right parenthesis for "i" Subscript, 1 , Baseline equals left bracket, 1... "l" Subscript, "q" , Baseline , right bracket , right bracket

1863

表达式1864: "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "o" , "v" , right parenthesis equals left bracket, "p" Subscript, "o" "i" "n" "t" "i" "n" "t" "e" "r" "c" "e" "p" "t" "a" "n" "d" "o" "n" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "o" , "v" , "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" "e" "r" "s" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "o" , "v" , "p" Subscript, "l" "a" "n" "e" "e" "q" "u" "a" "t" "i" "o" "n" "c" "o" "e" "f" "f" "e" "c" "i" "e" "n" "t" "s" , Baseline left parenthesis, "T" Subscript, "p" 1 , Baseline left parenthesis, "i" Subscript, 1 , Baseline , right parenthesis , "n" Subscript, "o" "r" "m" "a" "l" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "i" Subscript, 1 , Baseline , right parenthesis , right parenthesis , right parenthesis , "i" Subscript, 1 , Baseline , right parenthesis for "i" Subscript, 1 , Baseline equals left bracket, 1... "l" Subscript, "t" , Baseline , right bracket , right bracket

1864

表达式1865:

1865

表达式1866: "p" Subscript, "o" "i" "n" "t" "i" "n" "t" "e" "r" "c" "e" "p" "t" "a" "n" "d" "o" "n" "q" "u" "a" "d" , Baseline left parenthesis, "o" , "v" , "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" , Baseline , "q" , right parenthesis equals "p" Subscript, "o" "i" "n" "t" "o" "n" "q" "u" "a" "d" , Baseline left parenthesis, "o" plus "v" times "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" , Baseline , "q" , right parenthesis "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" , Baseline

1866

表达式1867: "p" Subscript, "o" "i" "n" "t" "i" "n" "t" "e" "r" "c" "e" "p" "t" "a" "n" "d" "o" "n" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "o" , "v" , "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" , Baseline , "q" , right parenthesis equals "p" Subscript, "o" "i" "n" "t" "o" "n" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "o" plus "v" times "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" , Baseline , "q" , right parenthesis "l" Subscript, "i" "n" "e" "p" "l" "a" "n" "e" "i" "n" "t" , Baseline

1867

表达式1868:

1868

表达式1869: "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "o" "n" "v" "e" "c" "t" "o" "r" , Baseline left parenthesis, "p" , "v" , "i" , right parenthesis equals left brace, "i" left bracket, 2 , right bracket equals 1 : "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "v" , "n" Subscript, "o" "r" "m" "a" "l" "S" "p" "h" "e" "r" "e" , Baseline left parenthesis, "p" , "i" left bracket, 1 , right bracket , right parenthesis , right parenthesis , left brace, "i" left bracket, 2 , right bracket equals 2 : "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "v" , "n" Subscript, "o" "r" "m" "a" "l" "q" "u" "a" "d" , Baseline left parenthesis, "i" left bracket, 1 , right bracket , right parenthesis , right parenthesis , "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "v" , "n" Subscript, "o" "r" "m" "a" "l" "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left parenthesis, "i" left bracket, 1 , right bracket , right parenthesis , right parenthesis , right brace , right brace

1869

表达式1870: "r" Subscript, "e" "f" "l" "e" "c" "t" "i" "o" "n" , Baseline left parenthesis, "v" , "n" , right parenthesis equals "v" minus 2 "d" Subscript, "o" "t" , Baseline left parenthesis, "v" , "n" , right parenthesis "n" left brace, "d" Subscript, "o" "t" , Baseline left parenthesis, "v" , "n" , right parenthesis less than 0 : 1 , 1 , right brace

1870

表达式1871: "c" Subscript, "o" "l" "o" "u" "r" "f" "r" "o" "m" "v" "e" "c" , Baseline left parenthesis, "v" , "t" , "n" , "p" , "c" , "t" Subscript, "y" "p" "e" "o" "f" "e" "n" "t" "i" "t" "y" , Baseline , "i" Subscript, "n" "d" "e" "x" "o" "f" "e" "n" "t" "i" "t" "y" , Baseline , right parenthesis equals left brace, "t" less than 100 : left parenthesis, "c" left bracket, 4 , right bracket times "c" left bracket, 1...3 , right bracket plus "c" left bracket, 5 , right bracket times "d" Subscript, "o" "t" , Baseline left parenthesis, "l" Subscript, "i" "g" "h" "t" "v" "e" "c" , Baseline left parenthesis, "p" , right parenthesis , left brace, "d" Subscript, "o" "t" , Baseline left parenthesis, "v" , "n" , right parenthesis less than 0 : 1 , negative 1 , right brace "n" , right parenthesis times "c" left bracket, 1...3 , right bracket , right parenthesis times left brace, left brace, "i" Subscript, "n" "t" "e" "r" "c" "e" "p" "t" "e" "x" "c" "l" "u" "d" "e" , Baseline left parenthesis, "p" , "l" Subscript, "i" "g" "h" "t" , Baseline minus "p" , "t" Subscript, "y" "p" "e" "o" "f" "e" "n" "t" "i" "t" "y" , Baseline , "i" Subscript, "n" "d" "e" "x" "o" "f" "e" "n" "t" "i" "t" "y" , Baseline , right parenthesis left bracket, 2 , right bracket less than 1 , right brace equals 1 : 0.5 , 1 , right brace , left bracket, 220 , 245 , 255 , right bracket , right brace

1871

表达式1872:

1872

Point Readability Functions

1873

Functions that return a point in the form of a = [x,y,z]. Purely to improve readability of the main functions which frequently require these values

1874

表达式1875: "S" Subscript, "p" 1 , Baseline left parenthesis, "s" , right parenthesis equals left bracket, "x" Subscript, "s" "p" "h" "e" "r" "e" , Baseline left bracket, "s" , right bracket , "y" Subscript, "s" "p" "h" "e" "r" "e" , Baseline left bracket, "s" , right bracket , "z" Subscript, "s" "p" "h" "e" "r" "e" , Baseline left bracket, "s" , right bracket , right bracket

1875

表达式1876:

1876

表达式1877: "Q" Subscript, "p" 1 , Baseline left parenthesis, "q" , right parenthesis equals left bracket, "x" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "y" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "z" Subscript, 1 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , right bracket

1877

表达式1878: "Q" Subscript, "p" 2 , Baseline left parenthesis, "q" , right parenthesis equals left bracket, "x" Subscript, 2 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "y" Subscript, 2 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "z" Subscript, 2 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , right bracket

1878

表达式1879: "Q" Subscript, "p" 3 , Baseline left parenthesis, "q" , right parenthesis equals left bracket, "x" Subscript, 3 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "y" Subscript, 3 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "z" Subscript, 3 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , right bracket

1879

表达式1880: "Q" Subscript, "p" 4 , Baseline left parenthesis, "q" , right parenthesis equals left bracket, "x" Subscript, 4 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "y" Subscript, 4 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , "z" Subscript, 4 "q" "u" "a" "d" , Baseline left bracket, "q" , right bracket , right bracket

1880

表达式1881:

1881

表达式1882: "T" Subscript, "p" 1 , Baseline left parenthesis, "t" , right parenthesis equals left bracket, "x" Subscript, 1 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , "y" Subscript, 1 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , "z" Subscript, 1 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , right bracket

1882

表达式1883: "T" Subscript, "p" 2 , Baseline left parenthesis, "t" , right parenthesis equals left bracket, "x" Subscript, 2 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , "y" Subscript, 2 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , "z" Subscript, 2 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , right bracket

1883

表达式1884: "T" Subscript, "p" 3 , Baseline left parenthesis, "t" , right parenthesis equals left bracket, "x" Subscript, 3 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , "y" Subscript, 3 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , "z" Subscript, 3 "t" "r" "i" "a" "n" "g" "l" "e" , Baseline left bracket, "t" , right bracket , right bracket

1884

表达式1885:

1885

Archive (Please read note)

1886

表达式1944:

1944

Alternative way to compute rotations

1945

表达式1978:

1978

Random Vector in unit sphere spanning R3 (Discarded lambert lighting model)

1979

表达式1985:

1985

表达式1986:

1986

1987

技术支持