Expression 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 bracketcrossa,b=a2·b3−a3·b2,a1·b3−a3·b1,a1·b2−a2·b1
1821
Expression 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 bracketconcata,b=i3≤lengtha:ai3,bi3−lengthafori3=1...lengtha+lengthb
1822
Expression 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 parenthesisminindexa=maxai0=minai2>0:ai2,∞fori2=1...lengtha:i0,0fori0=1...lengtha
1823
Expression 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 , EndFractionnormalisea=aa12+a22+a32
1824
Expression 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 braceternary3i,ai,bi,ci,ao,bo,co=i=ai:ao,i=bi:bo,i=ci:co,∞
1825
Expression 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 braceAnda,b=a=1:b=1:1,0,0
1826
Expression 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 braceminposa=a1>0:a2>0:mina,a1,a2>0:a2,00
1827
Expression 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" , EndFractionquadratica,b,c,d=−b+db2−4ac2a
1828
Expression 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 bracketmat3multiplya,b=3∑n1=1an1+3floori0−13bn1−13+modi0−1,3+1fori0=1...9
1829
Expression 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 bracketvecmatrixmultiplya,b=3∑n1=1a3i0−1+n1bn1fori0=1...3
1830
Expression 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 braceremovea1,t,e1,i=t=e1:a11...lengtha1=i:∞,1...lengtha1,a1
1831
Expression 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 parenthesisindexa,b=maxa=b:1...500,0
1832
Expression 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 bracemtvia,b,c=mina<minb:mina<minc:1,mina,indexa,mina,3,minc,indexc,minc,minb<minc:2,minb,indexb,minb,3,minc,indexc,minc
1833
Expression 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 parenthesisminover0a,b,c=mtvia>0.01:a,∞,b>0.01:b,∞,c>0.01:c,∞
1834
Expression 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 parenthesisdrawpxlx,y=polygonx,y,x+1,y,x+1,y+1,x,y+1
1835
Expression 1836:
1836
Main Functions
Hide this folder from students.
1837
The main functions currently used by the engine
1838
Expression 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 parenthesisnormalt,i,p=normaliset=1:normalSpherep,i,t=2:normalquadi,normaltrianglei
1839
Expression 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 parenthesisnormalquadq=crossQp3q−Qp1q,Qp2q−Qp1q
1840
Expression 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 parenthesisnormalSpherep,s=p−Sp1s
1841
Expression 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 parenthesisnormaltrianglet=crossTp3t−Tp1t,Tp2t−Tp1t
1842
Expression 1843:
1843
Expression 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 parenthesislightvecp=normaliselight−p
1844
Expression 1845:
1845
Expression 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 bracegetcolourparameterst,i,p=t=1:rspherei,gspherei,bspherei,ambiencespherei,diffusivityspherei,reflectivityspherei,t=2:concatcolourquadatpointi,p,ambiencequadi,diffusivityquadi,reflectivityquadi,rtrianglei,gtrianglei,btrianglei,ambiencetrianglei,diffusivitytrianglei,reflectivitytrianglei
1846
Expression 1847:
1847
Expression 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 parenthesisrelpointplaneo,p,u,v=ternary3maxu1v2−v1u2,u1v3−v1u3,u2v3−v2u3,u1v2−v1u2,u1v3−v1u3,u2v3−v2u3,p1−o1v2−p2−o2v1u1v2−v1u2,p2−o2u1−p1−o1u2u1v2−v1u2,p1−o1v3−p3−o3v1u1v3−v1u3,p3−o3u1−p1−o1u3u1v3−v1u3,p2−o2v3−p3−o3v2u2v3−v2u3,p3−o3u2−p2−o2u3u2v3−v2u3
1848
Expression 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 bracketplaneequationcoeffecientsP,N=N1,N2,N3,−P1N1−P2N2−P3N3
1849
Expression 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 parenthesispoint2dinsidequadp,x01,x02,y01,y02=AndAndp1≥x01,p1≤x02,Andp2≥y01,p2≤y02
1850
Expression 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 parenthesispoint2dinsidetrianglep,x01,x02,y01,y02=AndAndp1≥x01,p2≥y01,p1x02+p2y02≤1
1851
Expression 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 parenthesispointonquadp,q=point2dinsidequadrelpointplaneQp1q+Qp3q2,p,Qp2q−Qp1q4,Qp4q−Qp1q4,−2,2,−2,2
1852
Expression 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 parenthesispointontrianglep,t=point2dinsidetrianglerelpointplaneTp1t,p,Tp2t−Tp1t,Tp3t−Tp1t,0,1,0,1
1853
Expression 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 parenthesiscolourquadatpointq,p=colourquaditerq,itermandelbrotrelpointplaneQp1q+Qp3q2,p,Qp2q−Qp1q4,Qp4q−Qp1q4
1854
Expression 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 bracecolourquaditerq,i=i=mandelbrotiterations:mandelbrotbasecolour,r1quadq+r2quadq−r1quadqimandelbrotiterations,g1quadq+g2quadq−g1quadqimandelbrotiterations,b1quadq+b2quadq−b1quadqimandelbrotiterations
1855
Expression 1856:
1856
Expression 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 parenthesislinesphereintersectiono,v,Sc,rad=minpos1quadraticv12+v22+v32,−2v1Sc1−o1+v2Sc2−o2+v3Sc3−o3,Sc1−o12+Sc2−o22+Sc3−o32−r2ad,1,quadraticv12+v22+v32,−2v1Sc1−o1+v2Sc2−o2+v3Sc3−o3,Sc1−o12+Sc2−o22+Sc3−o32−r2ad,−1
1857
Expression 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 , EndFractionlineplaneintersectiono,v,P=−P1o1+P2o2+P3o3+P4P1v1+P2v2+P3v3
1858
Expression 1859:
1859
Expression 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 parenthesisintercepto,v=minover0interceptsphereo,v,interceptquado,v,intercepttriangleo,v
1860
Expression 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 parenthesisinterceptexcludeo,v,t,i=minover0removeinterceptsphereo,v,t,1,i,removeinterceptquado,v,t,2,i,removeintercepttriangleo,v,t,3,i
1861
Expression 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 bracketinterceptsphereo,v=linesphereintersectiono,v,Sp1i1,radspherei1fori1=1...ls
1862
Expression 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 bracketinterceptquado,v=pointinterceptandonquado,v,lineplaneintersectiono,v,planeequationcoeffecientsQp1i1,normalquadi1,i1fori1=1...lq
1863
Expression 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 bracketintercepttriangleo,v=pointinterceptandontriangleo,v,lineplaneintersectiono,v,planeequationcoeffecientsTp1i1,normaltrianglei1,i1fori1=1...lt
1864
Expression 1865:
1865
Expression 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" , Baselinepointinterceptandonquado,v,lineplaneint,q=pointonquado+v·lineplaneint,qlineplaneint
1866
Expression 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" , Baselinepointinterceptandontriangleo,v,lineplaneint,q=pointontriangleo+v·lineplaneint,qlineplaneint
1867
Expression 1868:
1868
Expression 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 bracereflectionvectorp,v,i=i2=1:reflectionv,normalSpherep,i1,i2=2:reflectionv,normalquadi1,reflectionv,normaltrianglei1
1869
Expression 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 bracereflectionv,n=v−2dotv,nndotv,n<0:1,1
1870
Expression 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 bracecolourfromvecv,t,n,p,c,typeofentity,indexofentity=t<100:c4·c1...3+c5·dotlightvecp,dotv,n<0:1,−1n·c1...3·interceptexcludep,light−p,typeofentity,indexofentity2<1=1:0.5,1,220,245,255
1871
Expression 1872:
1872
Point Readability Functions
Hide this folder from students.
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
Expression 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 bracketSp1s=xspheres,yspheres,zspheres
1875
Expression 1876:
1876
Expression 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 bracketQp1q=x1quadq,y1quadq,z1quadq
1877
Expression 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 bracketQp2q=x2quadq,y2quadq,z2quadq
1878
Expression 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 bracketQp3q=x3quadq,y3quadq,z3quadq
1879
Expression 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 bracketQp4q=x4quadq,y4quadq,z4quadq
1880
Expression 1881:
1881
Expression 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 bracketTp1t=x1trianglet,y1trianglet,z1trianglet
1882
Expression 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 bracketTp2t=x2trianglet,y2trianglet,z2trianglet
1883
Expression 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 bracketTp3t=x3trianglet,y3trianglet,z3trianglet
1884
Expression 1885:
1885
Archive (Please read note)
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1886
Expression 1944:
1944
Alternative way to compute rotations
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1945
Expression 1978:
1978
Random Vector in unit sphere spanning R3 (Discarded lambert lighting model)
