{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "Blue Emphasis" -1 256 "Times" 0 0 0 0 255 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Grey Emphasis" -1 257 "Times" 1 12 96 52 84 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Maroon Emphasis" -1 258 "Times" 1 12 128 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Purple Emphasis" -1 259 "Tim es" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 260 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Green Emph asis" -1 261 "Times" 1 12 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Red \+ Emphasis" -1 262 "Times" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times " 1 18 0 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 3 0 3 0 2 2 0 1 } {PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 128 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 22 "The HLS colour system " }}{PARA 0 "" 0 "" {TEXT -1 37 "by Peter Stone, Nanaimo, B.C., Canada" }}{PARA 0 "" 0 "" {TEXT -1 19 "Version: 27.3.2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 46 "load extra colours, conversion procedures and " }{TEXT 0 11 "ShowColours" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 111 "The extra colours and utility routines for colours considered in this wor ksheet are stored in the Maple m-file " }{TEXT 257 9 "colours.m" } {TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 128 "This file can be read \+ into a Maple session by a command similar to the one that follows, whe re the file path gives its location." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "read \"K:\\\\Maple/procdrs/colours.m\";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 68 "Conversion \+ between the HLS system and the RGB and HSV colour systems" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 185 " The conversion between the HLS system and the RGB and HSV colour syste ms can be be most easily visualised in terms of the correspondence bet ween the HSV cone and the HLS \"double-cone\". " }}{PARA 0 "" 0 "" {TEXT -1 225 "This fixing the hue and considering a transformation bet ween a triangular half-cross-section of the HSV cone and a correspondi ng half-section of the HLS double-cone in the shape of the region unde r a section of a sine curve. 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Fcjn7%$!+'HM\"p6F0$!+')****\\nFejlFcjn7%$!+VH<#4\"F0$!+-45NzFejlFcjn7% $!+:bC.5F0$!+\"=jK.*FejlFcjn7%$!+#>jK.*FejlFg_oFcjn7%$!+845NzFejlF\\`o Fcjn7%$!+4++]nFejlFa`oFcjn7%$!+$pW4\\&Fejl$!+njGL7F0Fcjn7%$!+Q%H<<%Fej lF[aoFcjn7%$!+Ty!o!GFejlF`aoFcjn7%$!+rU869FejlFeaoFcjn7%$!+!38L>&F^boF jaoFcjnFhin-Fchn6#%%LINEG-Fghn6%7%7%$!\"'F^^o$!#9FejnFcjn7%F3FjaoFcjn7 %F[fo$!#8FejnFcjnFhinFdeo-%%TEXTG6%7%$!#:F^^oFgfo$\"#7FejnQ-lightness, ~LF)Fhin-Fdfo6%7%$F^^oFejn$!#;Fejn$\"\"$FejnQ'hue,~HF)Fhin-%+PROJECTIO NG6%$!#UF4$\"#kF4Fhs" 1 2 0 1 10 0 2 1 1 1 2 1.000000 64.000000 -40.000000 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curv e 6" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 205 " The HLS double-cone can also be thought of as being obtained by a tran sformation of the RGB cube in which the six vertices for red, yellow, \+ green, cyan, blue and magenta are made to lie in the same plane. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 57 "A procedure for drawing sections of the HLS double-cone: " }{TEXT 0 12 "HLSsection3d" }{TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1711 "HLSsection3d := proc(t)\n local k,h,l,s,p1,p2;\n \n k := t-floor(t);\n h := k*6; \n if h<1 then\n plot3d( [s*cos(2*Pi*k)*sin(Pi*l),s*sin(2*Pi*k)*sin(Pi*l),l],\n l=0..1,s =0..1,style=patchnogrid,\n color=[`if`(l<.5,l+l*s,l+s-l*s),\n \+ `if`(l<.5,l-l*s+2*l*s*h,l-s+l*s+(2*s-2*l*s)*h),\n `if`(l< .5,l-l*s,l-s+l*s)]);\n elif h<2 then\n plot3d([s*cos(2*Pi*k)*si n(Pi*l),s*sin(2*Pi*k)*sin(Pi*l),l],\n l=0..1,s=0..1,style=patc hnogrid,\n color=[`if`(l<.5,l-l*s+2*l*s*(2-h),l-s+l*s+(2*s-2*l *s)*(2-h)),\n `if`(l<.5,l+l*s,l+s-l*s),`if`(l<.5,l-l*s,l-s+l*s )]);\n elif h<3 then \n plot3d([s*cos(2*Pi*k)*sin(Pi *l),s*sin(2*Pi*k)*sin(Pi*l),l],\n l=0..1,s=0..1,style=patchnog rid,\n color=[`if`(l<.5,l-l*s,l-s+l*s),\n `if`(l<.5,l+ l*s,l+s-l*s),\n `if`(l<.5,l-l*s+2*l*s*(h-2),l-s+l*s+(2*s-2*l*s )*(h-2))]);\n elif h<4 then \n plot3d([s*cos(2*Pi*k)*sin(Pi*l), s*sin(2*Pi*k)*sin(Pi*l),l],\n l=0..1,s=0..1,style=patchnogrid, \n color=[`if`(l<.5,l-l*s,l-s+l*s),\n `if`(l<.5,l-l*s+ 2*l*s*(4-h),l-s+l*s+(2*s-2*l*s)*(4-h)),\n `if`(l<.5,l+l*s,l+s- l*s)]);\n elif h<5 then\n plot3d([s*cos(2*Pi*k)*sin(Pi*l),s*sin (2*Pi*k)*sin(Pi*l),l],\n l=0..1,s=0..1,style=patchnogrid,\n \+ color=[`if`(l<.5,l-l*s+2*l*s*(h-4),l-s+l*s+(2*s-2*l*s)*(h-4)),\n `if`(l<.5,l-l*s,l-s+l*s),\n `if`(l<.5,l+l*s,l+s-l*s)] );\n else \n plot3d([s*cos(2*Pi*k)*sin(Pi*l),s*sin(2* Pi*k)*sin(Pi*l),l],\n l=0..1,s=0..1,style=patchnogrid,\n \+ color=[`if`(l<.5,l+l*s,l+s-l*s),\n `if`(l<.5,l-l*s,l-s+l*s) ,\n `if`(l<.5,l-l*s+2*l*s*(6-h),l-s+l*s+(2*s-2*l*s)*(6-h))]); \n end if;\nend proc:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 53 "Illustration of half-sections of the HLS double-cone " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 258 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 12 "HLSsection3d" }{TEXT -1 65 " can be used to draw half-cross-sections of the HLS double-cone. 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000000003FEFFFFFFFFFFFFC3CD178832EEC5CFF00000000000000003FEFFFFFFFFFFF FC3CD2900B61DB22CF00000000000000003FEFFFFFFFFFFFFC3CD3A79394C9E89E0000 0000000000003FEFFFFFFFFFFFFC3CD4BF1BC7B8AE6E00000000000000003FEFFFFFFF FFFFFC3CD5D6A3FAA7743E00000000000000003FEFFFFFFFFFFFFC3CD6EE2C2D963A0E 00000000000000003FEFFFFFFFFFFFFC3CD805B46084FFDD00000000000000003FEFFF FFFFFFFFFC3CD91D3C9373C5AD00000000000000003FEFFFFFFFFFFFFC3CDA34C4C662 8B7D00000000000000003FEFFFFFFFFFFFFCF*Fd[r-%+PROJECTIONG6%$!#]F_dn$\"# vF_dn\"\"\"" 1 2 0 1 10 0 2 1 1 1 2 1.000000 75.000000 -50.000000 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 135 "The following \+ code can be executed to construct an animation which displays half-cro ss-sections of the HLS double-cone for varying hue " }{TEXT 263 1 "h" }{TEXT -1 36 ". It requires the special procedure " }{TEXT 0 12 "HLSse ction3d" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 251 "p1 := plots[spacecurve]([cos(t),si n(t),.5],t=0..2*Pi,\n style=line,col or=black):\nd := evalf(1/48):\nplots[display]([seq(plots[display]([HLS section3d(j*d),p1]),\n j=0..47)],orientation=[-50,75],axes=none,insequ ence=true);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 17 "Cod e for pictures" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} {SECT 1 {PARA 0 "" 0 "" {TEXT -1 15 "HLS double-cone" }}{PARA 0 "" 0 " " {TEXT -1 42 " cos(t)*sin(Pi*l),sin(2*Pi*k)*sin(Pi*l),l " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 860 "rf := proc(h,l) op(2,convert(COLOR (HLS,h,l,1),RGB)) end proc:\ngf := proc(h,l) op(3,convert(COLOR(HLS,h, l,1),RGB)) end proc:\nbf := proc(h,l) op(4,convert(COLOR(HLS,h,l,1),RG B)) end proc:\nxf := proc(h,l) sin(Pi*l)*cos(2*Pi*h) end proc:\nyf := \+ proc(h,l) sin(Pi*l)*sin(2*Pi*h) end proc:\nzf := proc(h,l) l end proc: \np1 := plot3d([xf,yf,zf],0..1,0..1,style=patchnogrid,\n grid=[30, 30],color=[rf,gf,bf]):\np2 := plottools[arrow]([0,0,1],[0,0,1.15],0,.1 ,.2,arrow,color=black):\nd1 := evalf(Pi/30): r1 := 1.35:\np3 := plots[ pointplot3d]([seq([r1*cos(d1*i),r1*sin(d1*i),.5],i=2..45)],\n colo r=black,style=line):\np4 := plots[pointplot3d]([[-.06,-1.4,.5],[0,-1.3 5,.5],[-.06,-1.3,.5]],\n color=black,style=line):\nt1 := plots[te xtplot3d]([[-.15,-.15,1.2,`lightness, L`],\n [-.2,-1.6,.3,`hue, H` ]],color=black):\nplots[display]([p1,p2,p3,p4,t1],orientation=[-42,64] );" }}{PARA 13 "" 1 "" {GLPLOT3D 390 389 389 {PLOTDATA 3 "6)-%%MESHG6% X.%)anythingG6\"6\"[gl'!%\"!!$gcu\"?\"?\"$0000000000000000000000000000 000000000000000000003FBBADB02034D9FF00000000000000003FA1A7B9611A7B963F CB8426C12812BC00000000000000003FB1A7B9611A7B963FD46F6FAF5FCB7200000000 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