{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 "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 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 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Dark Red Emphasis" -1 261 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Green Emphasis" -1 262 "Times" 1 12 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Red Emphasis" -1 263 "Times " 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" 261 264 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 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 "T imes" 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 66 "Enhancing Maple's colours I - the RGB, HSV and HLS colour systems " }}{PARA 0 "" 0 "" {TEXT -1 37 "by P eter Stone, Nanaimo, B.C., Canada" }}{PARA 0 "" 0 "" {TEXT -1 19 "Vers ion: 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 51 "load extra colours a nd utility routines for colours" }}{PARA 0 "" 0 "" {TEXT -1 111 "The e xtra colours and utility routines for colours considered in this works heet 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, where 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 32 "RGB, HSV and HLS colour syst ems " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "C olor for Maple plots may be specified in various ways. " }}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 259 23 "RGB color specification" }{TEXT -1 159 " requires three numbers for each color. The three values must \+ each be between 0 and 1 and specify the amount of red, green, and blue light in the final color. " }}{PARA 0 "" 0 "" {TEXT 264 8 "Examples" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 82 "COLOUR(RGB, 1, 0, 0) is a pure red color (maximum red) with no green, and no blue," }}{PARA 0 "" 0 "" {TEXT -1 84 "COLOUR(RGB, 0, 1, 0) is a pure green color (max imum green) with no red, and no blue," }}{PARA 0 "" 0 "" {TEXT -1 83 " COLOUR(RGB, 0, 0, 1) is a pure blue color (maximum blue) with no red, \+ and no green," }}{PARA 0 "" 0 "" {TEXT -1 99 "COLOUR(RGB, 1, 1, 0) is \+ yellow, COLOUR(RGB, 0, 1, 1) is cyan and COLOUR(RGB, 1, 0, 1) is mage nta. 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38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "Curve 43" "C urve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55" "Curve 56 " "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "Curve 62" "C urve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74" "Curve 75 " "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "Curve 81" "C urve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93" "Curve 94 " "Curve 95" "Curve 96" "Curve 97" "Curve 98" "Curve 99" "Curve 100" " Curve 101" "Curve 102" "Curve 103" "Curve 104" "Curve 105" "Curve 106 " "Curve 107" "Curve 108" "Curve 109" "Curve 110" "Curve 111" "Curve 1 12" "Curve 113" "Curve 114" }}{TEXT -1 1 " " }}{PARA 258 "" 0 "" {TEXT -1 56 "When S = 1 and V = 0.8 we obtain the following picture. \+ " }}{PARA 257 "" 0 "" {TEXT 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56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "C urve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74 " "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "C urve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93 " "Curve 94" "Curve 95" "Curve 96" "Curve 97" "Curve 98" "Curve 99" "C urve 100" "Curve 101" "Curve 102" "Curve 103" "Curve 104" "Curve 105" "Curve 106" "Curve 107" "Curve 108" "Curve 109" }}{TEXT -1 5 " " } }{PARA 0 "" 0 "" {TEXT -1 56 "When S = 0.5 and V = 1 we obtain the fol lowing picture. 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GFejlF`aoFcjn7%$!+rU869FejlFeaoFcjn7%$!+!38L>&F^boFjaoFcjnFhin-Fchn6#% %LINEG-Fghn6%7%7%$!\"'F^^o$!#9FejnFcjn7%F3FjaoFcjn7%F[fo$!#8FejnFcjnFh inFdeo-%%TEXTG6%7%$!#:F^^oFgfo$\"#7FejnQ-lightness,~LF)Fhin-Fdfo6%7%$F ^^oFejn$!#;Fejn$\"\"$FejnQ'hue,~HF)Fhin-%+PROJECTIONG6%$!#UF4$\"#kF4Fh s" 1 2 0 1 10 0 2 1 1 1 2 1.000000 67.000000 -41.000000 1 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" }}{TEXT -1 1 " " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 30 "Utility routines for colours: " }{TEXT 0 32 "ShowColour s,convert(..,RGB) etc." }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 135 "Reference: \"Computer Graphics, Prin ciples and Practice\" by Foley, van Dam, Feiner, and Hughes,\n Addis on Wesley, Second Edition, 1990." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "ShowColours: usage" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 265 18 "Calling Sequence:\n" }}{PARA 0 "" 0 "" {TEXT -1 26 " \+ ShowColours( clr, n ) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 " " 0 "" {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }} {PARA 0 "" 0 "" {TEXT -1 98 " clr - a colour, which can be a named colour or be specified in RGB, HSV or HLS format. " }}{PARA 0 " " 0 "" {TEXT -1 76 " This argument may also be a posi tive integer, or \"all\". " }}{PARA 0 "" 0 "" {TEXT -1 98 " n \+ - a positive integer giving the number of colours 'similar' to cl r to be displayed. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 256 "" 0 "" {TEXT -1 12 "Description:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 11 "ShowColours " }{TEXT -1 40 " displays colours available for plots. ." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "lighten,d arken: usage" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 260 18 "Calling Sequence:\n" }}{PARA 0 "" 0 "" {TEXT -1 42 " lighten( clr )\n lighten( clr, t ) " }}{PARA 0 "" 0 "" {TEXT -1 40 " darken( clr )\n darken( clr, t ) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 11 "Parameters:" }} {PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 101 " \+ clr - a colour, which can be a named colour or be specified in RG B, HSV or HLS format. " }}{PARA 0 "" 0 "" {TEXT -1 88 " t \+ - a parameter which evaluates to a floating point number between 0 a nd 1. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 256 "" 0 "" {TEXT -1 12 "Description:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "The procedures " }{TEXT 0 14 "lighten,darken" }{TEXT -1 102 " lighten and darken by an amount which can be controlled using th e 2nd optional parameter if desired. " }}{PARA 0 "" 0 "" {TEXT -1 57 " When the colour is given in terms of its HLS components, " }{TEXT 0 7 "lighten" }{TEXT -1 33 " changes the lightness component " }{TEXT 266 1 "L" }{TEXT -1 4 " to " }{XPPEDIT 18 0 "L*`'`" "6#*&%\"LG\"\"\"%\"'GF %" }{TEXT -1 8 ", where " }{XPPEDIT 18 0 "L*`'` = t +(1-t)*L" "6#/*&% \"LG\"\"\"%\"'GF&,&%\"tGF&*&,&F&F&F)!\"\"F&F%F&F&" }{TEXT -1 8 ", whil e " }{TEXT 0 6 "darken" }{TEXT -1 33 " changes the lightness component " }{TEXT 267 1 "L" }{TEXT -1 4 " to " }{XPPEDIT 18 0 "L*`'`" "6#*&%\" LG\"\"\"%\"'GF%" }{TEXT -1 8 ", where " }{XPPEDIT 18 0 "L*`'` = (1-t)* L" "6#/*&%\"LG\"\"\"%\"'GF&*&,&F&F&%\"tG!\"\"F&F%F&" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 14 "The parameter " }{TEXT 268 1 "t" } {TEXT -1 27 " has the default value of " }{XPPEDIT 18 0 "1/3" "6#*&\" \"\"F$\"\"$!\"\"" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 259 16 "How to a ctivate:" }{TEXT 256 1 "\n" }{TEXT -1 163 "To make procedures active o pen the appropriate subsection, place the cursor anywhere after the pr ompt [ > and press [Enter].\nYou can then close up the subsection." } }{PARA 0 "" 0 "" {TEXT 259 4 "Note" }{TEXT -1 242 ": In order for a pr ocedure in this list to work it may be necessary for a preceding proce dure to be active, that is, if you load selectively, you should be awa re of possible depedencies on preceding procedures as you go down thro ugh the list." }}{PARA 0 "" 0 "" {TEXT -1 27 "For example, the procedu re " }{TEXT 0 11 "ShowColours" }{TEXT -1 36 " requires the conversion \+ procedures " }{TEXT 0 15 "convert(..,RGB)" }{TEXT -1 2 ", " }{TEXT 0 15 "convert(..,HSV)" }{TEXT -1 2 ", " }{TEXT 0 15 "convert(..,HLS)" } {TEXT -1 17 " to be active. " }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 48 "type(..,colour), type(..,color): implementation " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 478 "`type/colou r` := proc(cc)\n if type(cc,function) and member(op(0,cc),\{'COLOR', 'COLOUR'\}) then\n if member(op(1,cc),\{'RGB','HSV','HLS'\}) and \+ nops(cc)=4 \n and type([op(2..4,cc)],list(numeric)) then true\n elif op(1,cc)='HUE' and nops(cc)=2 \n and type(op(2,cc),n umeric) then true\n else false end if;\n else \n try\n \+ `plot/color`(cc);\n true;\n catch: false;\n end try;\n end if;\nend proc:\n`type/color` := eval(`type/colour`):" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 64 "convert(..,RGB), convert(..,HSV),convert(..,HLS): implementation" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6570 "`convert/RGB` := proc()\n local h,s,v,synOK,clr,i,f,p,q,t,l,r, g,b;\n\n clr := args[1];\n if type(clr,function) and member(op(0,c lr),\{'COLOR','COLOUR'\}) then\n if member(op(1,clr),\{'RGB','HSV ','HLS'\}) and nops(clr)=4 \n and type([op(2..4,clr)],list(nume ric)) then synOK := true\n elif op(1,clr)='HUE' and nops(clr)=2 \+ \n and type(op(2,clr),numeric) then synOK := true\n else s ynOK := false end if;\n else\n synOK := false\n end if; \n\n \+ if synOK then\n if op(1,clr)='RGB' then\n\011 r := max(m in(evalf(op(2,clr)),1.),0.);\n\011 g := max(min(evalf(op(3,clr) ),1.),0.);\n \011 b := max(min(evalf(op(4,clr)),1.),0.);\n \+ return COLOR(RGB,r,g,b);\n elif op(1,clr)='HUE' then\n \+ h := evalf(op(2,clr));\n h := h-floor(h);\n clr := CO LOR(HSV,h,0.9,1.0)\n end if;\n end if;\n\n if not synOK then \n try\n clr := `plot/color`(clr);\n return clr; \+ \n catch: error \"unable to convert %1 to an RGB colour\" ,clr;\n end try;\n end if;\n\n Digits := 8;\n if op(1,clr)= 'HSV' then\n\011 h := evalf(op(2,clr));\n h := h-floor(h);\n \011 s := max(min(evalf(op(3,clr)),1.),0.);\n \011 v := max(min (evalf(op(4,clr)),1.),0.);\n h := h*6;\n i := floor(h);\n \011 \011\011f := h-i;\n\011 \011 p := v*(1-s);\n\011 \011 q := \+ v*(1-s*f) ;\n\011 \011 t := v*(1-s*(1-f));\n \n \011\011 if i= 0 then\n COLOR('RGB',v,t,p)\n\011\011\011 elif i=1 then\n \011\011\011 COLOR('RGB',q,v,p)\n elif i=2 then\n CO LOR('RGB',p,v,t)\n elif i=3 then\n COLOR('RGB',p,q,v)\n \+ elif i=4 then\n COLOR('RGB',t,p,v)\n\011\011\011 else # \+ i=5 then\n COLOR('RGB',v,p,q)\n end if;\n else # op(1,c lr)='HLS'\n\011 h := evalf(op(2,clr));\n h := h-floor(h);\n \011 l := max(min(evalf(op(3,clr)),1.),0.);\n \011 s := max(min (evalf(op(4,clr)),1.),0.);\n h := h*6;\n p := `if`(l<=.5,l+l *s,l+s-l*s);\n q := 2*l-p;\n t := p-q;\n if s=0 then\n \+ COLOR('RGB',l,l,l);\n else\n if h<1 then\n \+ COLOR('RGB',p,q+t*h,q)\n elif h<2 then\n COLOR ('RGB',q+t*(2-h),p,q)\n elif h<3 then\n COLOR('RGB' ,q,p,q+t*(h-2))\n elif h<4 then \n COLOR('RGB',q,q+ t*(4-h),p)\n elif h<5 then\n COLOR('RGB',q+t*(h-4), q,p)\n else\n COLOR('RGB',p,q,q+t*(6-h))\n \+ end if;\n end if;\n end if;\nend proc: # `convert/RGB`\n\n`conv ert/HSV` := proc()\n local clr,synOK,r,g,b,h,s,v,d,l,u,t;\n\n clr \+ := args[1];\n if type(clr,function) and member(op(0,clr),\{'COLOR',' COLOUR'\}) then\n if member(op(1,clr),\{'RGB','HSV','HLS'\}) and \+ nops(clr)=4 \n and type([op(2..4,clr)],list(numeric)) then synO K := true\n elif op(1,clr)='HUE' and nops(clr)=2 \n and ty pe(op(2,clr),numeric) then synOK := true\n else synOK := false en d if;\n else\n synOK := false\n end if;\n\n if synOK then\n if op(1,clr)='HSV' then\n\011 h := evalf(op(2,clr));\n \+ h := h-floor(h);\n\011 s := max(min(evalf(op(3,clr)),1.), 0.);\n \011 v := max(min(evalf(op(4,clr)),1.),0.);\n ret urn COLOR('HSV',h,s,v);\n elif op(1,clr)='HUE' then\n\011 \+ h := evalf(op(2,clr));\n h := h-floor(h);\n return COL OR('HSV',h,0.9,1.0);\n end if;\n end if;\n\n if not synOK the n\n try clr := `plot/color`(clr);\n catch: error \"unable to convert %1 to an HSV colour\",clr;\n end try;\n end if;\n\011 \n Digits := 8;\n if op(1,clr)='RGB' then\n\011 r := max(min(e valf(op(2,clr)),1.),0.);\n\011 g := max(min(evalf(op(3,clr)),1.),0 .);\n \011 b := max(min(evalf(op(4,clr)),1.),0.);\n\n v := max (r,g,b); \n d := v-min(r,g,b);\n if d=0 then # r = g = b \n return COLOR('HSV',evalf(2/3),0.,r);\n end if;\n\n \+ s := d/v; \n\011 if v=r then\n\011\011 h := (g-b)/d;\011 # between yellow & magenta\n\011 elif v=g then\n\011\011 h : = 2+(b-r)/d;\011# between cyan & yellow\n\011 else\n\011\011 \+ h := 4+(r-g)/d;\011# between magenta & cyan\n end if;\n h : = h/6;\n\011 if h<0 then h := h+1. end if;\n COLOR('HSV',h,s, v);\n else # op(1,clr)=HLS\n\011 h := evalf(op(2,clr));\n h := h-floor(h);\n\011 l := max(min(evalf(op(3,clr)),1.),0.);\n \+ \011 s := max(min(evalf(op(4,clr)),1.),0.);\n u := 2*l;\n \+ d := `if`(u<1,u*s,(2-u)*s);\n t := u+d;\n v := t/2;\n s := `if`(v<>0,d/v,0.);\n COLOR('HSV',h,s,v);\n end if;\nend pro c: # `convert/HSV`\n\n`convert/HLS` := proc()\n local clr,synOK,r,g, b,h,s,l,d,u,v,m;\n\n clr := args[1];\n if type(clr,function) and m ember(op(0,clr),\{'COLOR','COLOUR'\}) then\n if member(op(1,clr), \{'RGB','HSV','HLS'\}) and nops(clr)=4 \n and type([op(2..4,clr )],list(numeric)) then synOK := true\n elif op(1,clr)='HUE' and n ops(clr)=2 \n and type(op(2,clr),numeric) then synOK := true\n \+ else synOK := false end if;\n else\n synOK := false\n en d if;\n\n if synOK then\n if op(1,clr)='HLS' then\n\011 \+ h := evalf(op(2,clr));\n h := h-floor(h);\n\011 l := ma x(min(evalf(op(3,clr)),1.),0.);\n \011 s := max(min(evalf(op(4,c lr)),1.),0.);\n return COLOR(HSV,h,l,s);\n elif op(1,clr) ='HUE' then\n\011 h := evalf(op(2,clr));\n h := h-floor (h);\n return COLOR('HLS',h,0.55,1.0);\n end if;\n end \+ if;\n\n if not synOK then\n try clr := `plot/color`(clr);\n \+ catch: error \"unable to convert %1 to an HLS colour\",clr;\n e nd try;\n end if;\n\011\n Digits := 8;\n if op(1,clr)='RGB' then \n\011 r := max(min(evalf(op(2,clr)),1.),0.);\n\011 g := max(m in(evalf(op(3,clr)),1.),0.);\n \011 b := max(min(evalf(op(4,clr)),1 .),0.);\n\n # compute the lightness\n v := max(r,g,b);\n \+ m := min(r,g,b);\n u := v+m;\n d := v-m;\n l := u/2; \n\n if d=0 then # r = g = b\n return COLOR('HLS',evalf (2/3),l,0.);\n end if;\n\n # compute the HLS saturation\n \+ s := `if`(l<=.5,d/u,d/(2-u));\n\n # compute the hue\n\011 \+ if v=r then\n\011\011 h := (g-b)/d;\011# between yellow & magent a\n\011 elif v=g then\n\011\011 h := 2+(b-r)/d;\011# between cyan & yellow\n\011 else\n\011\011 h := 4+(r-g)/d;\011# bet ween magenta & cyan\n end if;\n h := h/6;\n if h<0 then h := h+1. end if;\n COLOR('HLS',h,l,s);\n else # op(1,clr)=HSV \n\011 h := evalf(op(2,clr));\n h := h-floor(h);\n\011 s \+ := max(min(evalf(op(3,clr)),1.),0.);\n \011 v := max(min(evalf(op(4 ,clr)),1.),0.);\n d := s*v;\n m := v-d;\n u := v+m;\n \+ l := u/2;\n\n # compute the HLS saturation\n if d=0 then \n s := 0.\n else\n s := `if`(l<=.5,d/u,d/(2-u)); \n end if;\n COLOR('HLS',h,l,s); \n end if;\nend proc: # ` convert/HLS`" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 27 "ShowColours: implementation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2853 "ShowColour s := proc(ff)\n local i,clrs,clrnames,cc,ci,t,h,pp,rect,txt,start,fi nish,\n jF,jS,jM,n,c1,k,j,under,over,ord;\n\n clrnames := map(o p,[indices(`plot/colortable`)]);\n cc := [];\n for i to nops(clrna mes) do\n ci := clrnames[i];\n if not StringTools[IsUpper](c i) then\n t := COLOR(RGB,op(`plot/colortable`[ci]));\n \+ h := convert(t,HSV);\n cc := [op(cc),[op(2..4,h),ci,t]]\n \+ end if;\n end do;\n ord := proc(_u,_v)\n if op(1,_u)1 do\n jM := trunc((jF+jS)/2);\n if \+ not ord(h,cc[jM]) then jF := jM \n else jS := jM end if;\n \+ end do;\n end if;\n\n if nargs>=2 and type(args[2],p osint) then \n k := iquo(min(args[2],n),2);\n else\n \+ k := 5;\n end if;\n under := min(n+jF-k,n);\n start := max(jF-k,1);\n finish := min(jF+k,n);\n over := max(jF+k -n,1);\n end if;\n\n pp := NULL;\n j := 1;\n if under1 then\n for i from 1 to over do\n re ct := plots[polygonplot]([[0,1-j],[1,1-j],[1,-j],[0,-j]],\n \+ style=patchnogrid,color=op(4,cc[i]));\n txt := plots[textpl ot]([1.2,0.5-j,op(4,cc[i])],color=black,align=RIGHT);\n pp := \+ pp,plots[display]([rect,txt]);\n j := j+1;\n end do;\n \+ end if;\n plots[display]([pp],axes=NONE);\nend proc: # ShowColours" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 31 "lighten, darken: implementati on" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2543 "lighten := proc(cc::color)\n local c,r,c2,drw,opt n,p1,p2;\n\n if op(1,cc)='HLS' then\n c := cc;\n else\n \+ c := convert(cc,'HLS'); \n end if; \n\n Digits := 8;\n if na rgs>1 and type(args[2],numeric) then\n r := evalf(args[2]);\n \+ if r>1 or r<0 then\n error \"expecting the 2nd argument to e valuate to a floating point number between 0 and 1, but received %1\", args[2];\n end if;\n else\n r := evalf(1/3);\n end if;\n \n if nargs=2 and not type(args[2],numeric) then\n optn := args [2]\n elif nargs=3 then\n optn := args[3]\n end if;\n\n drw := false;\n if assigned(optn) then\n if type(optn,`=`) then \n if op(1,optn)=draw then drw := op(2,optn) end if;\n i f drw<>true then drw := false end if;\n elif optn=draw then drw : = true;\n end if;\n end if; \n \n # increase the 'L' compo nent towards 1\n c2 := COLOR(HLS,op(2,c),r+(1-r)*op(3,c),op(4,c));\n if drw then\n p1 := plots[polygonplot]([[0,0],[1,0],[1,1],[0,1 ]],color=c);\n p2 := plots[polygonplot]([[0,0],[1,0],[1,-1],[0,-1 ]],color=c2);\n print(plots[display]([p1,p2],axes=NONE));\n end if;\n if op(1,cc)='RGB' then\n convert(c2,'RGB')\n elif op(1 ,cc)='HSV' then\n convert(c2,HSV)\n else c2 end if;\nend proc: \+ # of lighten\n\ndarken := proc(cc::color)\n local c,r,c2,drw,optn,p1 ,p2;\n\n if op(1,cc)='HLS' then\n c := cc;\n else\n c := convert(cc,'HLS'); \n end if; \n\n Digits := 8;\n if nargs> 1 and type(args[2],numeric) then\n r := evalf(args[2]);\n if r>1 or r<0 then\n error \"expecting the 2nd argument to evalu ate to a floating point number between 0 and 1, but received %1\",args [2];\n end if;\n else\n r := evalf(1/3);\n end if;\n\n \+ if nargs=2 and not type(args[2],numeric) then\n optn := args[2] \n elif nargs=3 then\n optn := args[3]\n end if;\n\n drw := false;\n if assigned(optn) then\n if type(optn,`=`) then \n \+ if op(1,optn)=draw then drw := op(2,optn) end if;\n if d rw<>true then drw := false end if;\n elif optn=draw then drw := t rue;\n end if;\n end if;\n\n # decrease the 'L' component tow ards 0\n c2 := COLOR(HLS,op(2,c),(1-r)*op(3,c),op(4,c));\n if drw \+ then\n p1 := plots[polygonplot]([[0,0],[1,0],[1,1],[0,1]],color=c );\n p2 := plots[polygonplot]([[0,0],[1,0],[1,-1],[0,-1]],color=c 2);\n print(plots[display]([p1,p2],axes=NONE));\n end if;\n i f op(1,cc)='RGB' then\n convert(c2,'RGB')\n elif op(1,cc)='HSV' then\n convert(c2,HSV)\n else c2 end if;\nend proc: # of darke n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{SECT 1 {PARA 4 "" 0 "" {TEXT -1 63 "`plot/color`: implementation (re placement for default version) " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1197 "`plot/color` := proc(t)\n \+ local h,l,s,u,d,w,v;\n if type(t,function) and (op(0,t)='COLOUR' o r op(0,t)='COLOR') then\n if member(op(1,t),\{'HLS','HSV'\}) then \n if nops(t)=4 and type([op(2..4,t)],list(numeric)) then\n \+ h := op(2,t);\n h := h-floor(h);\n if \+ op(1,t)='HSV' then\n COLOUR('HSV',h,op(3..4,t))\n \+ else # convert HLS to HSV\n\011 l := max(min(op(3,t) ,1),0);\n \011 s := max(min(op(4,t),1),0);\n \+ u := 2*l;\n d := `if`(u<1,u*s,(2-u)*s);\n \+ w := u+d;\n v := w/2;\n s := `if`(v<>0,d/ v,0.);\n COLOUR('HSV',h,s,v);\n end if\n \+ else error \"invalid HSV or HLS COLOUR data\"\n end if\n \+ elif op(1,t)='HUE' then\n if nops(t)=2 and type(op(2,t),nu meric) then\n h := op(2,t);\n h := h-floor(h);\n COLOUR('HUE',h);\n else error \"invalid HUE COLOUR data\"\n end if;\n else t end if;\n elif member(t,map(op, \{indices(`plot/colortable`)\})) then\n COLOUR('RGB',op(`plot/col ortable`[t]))\n else error \"invalid color specification\"\n end i f\nend proc: # of `plot/color`" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 52 "`plot/colortable`: replacement fo r default version " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7389 "`plot/colortable` := \n table(\n # co lours retained from default table\n [gold=[.800,.498,.196],\n blue =[0.,0.,1.], \n magenta=[1.,0.,1.],\n white=[1.,1.,1.],\n pink= [1.,.753,.796],\n cyan=[0.,1.,1.],\n sienna=[.557,.42,.137],\n a quamarine=[.439,.859,.576],\n maroon=[.557,.137,.42],\n yellow=[1. ,1.,0.],\n green=[0.,1.,0.],\n navy=[.137,.137,.557],\n khaki=[. 624,.624,.373],\n grey=[.753,.753,.753],\n gray=[.753,.753,.753], \n red=[1.,0.,0.],\n plum=[.918,.678,.918],\n black=[0,0,0],\n \+ turquoise=[.678,.918,.918],\n brown=[.647,.165,.165],\n tan=[.859 ,.576,.439],\n wheat=[.961,.871,.702],\n coral=[1.,.498,0.],\n\n \+ GOLD=[.800,.498,.196],\n BLUE=[0.,0.,1.], \n MAGENTA=[1.,0.,1.], \n WHITE=[1.,1.,1.],\n PINK=[1.,.753,.796],\n CYAN=[0.,1.,1.],\n SIENNA=[.557,.42,.137],\n AQUAMARINE=[.439,.859,.576],\n MAROON =[.557,.137,.42],\n YELLOW=[1.,1.,0.],\n GREEN=[0.,1.,0.],\n NAV Y=[.137,.137,.557],\n KHAKI=[.624,.624,.373],\n GREY=[.753,.753,.7 53],\n GRAY=[.753,.753,.753],\n RED=[1.,0.,0.],\n PLUM=[.918,.67 8,.918],\n BLACK=[0,0,0],\n TURQUOISE=[.678,.918,.918],\n BROWN= [.647,.165,.165],\n TAN=[.859,.576,.439],\n WHEAT=[.961,.871,.702] ,\n CORAL=[1.,.498,0.],\n\n # more colours\n bright_gold=[.851,. 851,.098],\n brass=[.710,.651,.259],\n grey_bronze=[.549,.471,.325 ],\n cool_copper=[.851,.529,.098],\n bronze=[.651,.490,.239],\n \+ spicy_pink=[1.,.11,.682],\n dark_chocolate=[.42,.259,.149],\n scar let=[.549,.0902,.0902],\n light_tan=[.922,.78,.62],\n silver=[.902 ,.91,.98],\n light_grey=[.804,.804,.804],\n old_gold=[.812,.710,.2 31],\n mandarin_orange=[.894,.471,.2],\n neon_pink=[1.,.431,.78], \n neon_blue=[.302,.302,1.],\n copper=[.722,.451,.2],\n light_gr een=[.565,.933,.565],\n very_dark_brown=[.361,.251,.200],\n\n # ev en more colours\n alice_blue=[.941,.973,1.],\n alizarin_crimson=[. 889,.15,.21],\n antique=[.981,.922,.845],\n cyan_aquamarine=[.47, \+ .93, .65],\n medium_aquamarine=[.4,.804,.667],\n aureoline_yellow= [1.,.66,.14],\n azure=[.942,1.,1.],\n banana=[.89,.81,.34],\n be ige=[.64,.58,.5],\n bisque=[1.,.898,.772],\n blanched_almond=[1.,. 923,.804],\n light_blue=[0,.45,1.],\n pale_blue=[.678,.847,.902], \n medium_blue=[0.,0.,.804],\n blue_violet=[.541,.169,.886],\n b rick=[.61,.4,.12],\n brown=[.5,.165,.165],\n brown_oadder=[.86,.16 ,.16],\n brown_ochre=[.53,.26,.12],\n burlywood=[.871,.722,.529], \n burnt_sienna=[.54,.21,.06],\n burnt_umber=[.54,.2,.14],\n cad et=[.372,.62,.628],\n cadmium_lemon=[1.,.89,.01],\n cadmium_orange =[1.,.38,.01],\n deep_cadmium_red=[.89,.09,.05],\n light_cadmium_r ed=[1.,.01,.05],\n cadmium_yellow=[1.,.6,.07],\n light_cadmium_yel low=[1.,.69,.06],\n carrot=[.93,.57,.13],\n cerulean=[.02,.72,.8], \n chartreuse=[.498,1.,0.],\n chocolate=[.823,.412,.118],\n chro me_oxide_green=[.4,.5,.08],\n cinnabar_green=[.38,.7,.16],\n cobal t=[.24,.35,.67],\n cobalt_green=[.24,.57,.25],\n deep_cobalt_viole t=[.57,.13,.62],\n cold_grey=[.5,.54,.53],\n pinkish_coral=[1.,.49 8,.314],\n coral_pink=[.941,.502,.502],\n cornflower_blue=[.392,.5 84,.929],\n cornsilk=[1.,.973,.863],\n light_cyan=[.333,1.,1.],\n \+ orange=[1.,.549,0.],\n deep_pink=[1.,.0784,.576],\n deep_ochre=[ .45,.24,.1],\n dim_grey=[.333333,.333333,.333333],\n dodger_blue=[ .118,.565,1.],\n eggshell=[.99,.9,.79],\n emerald_green=[0.,.79,.3 4],\n english_red=[.83,.24,.1],\n firebrick=[.698,.133,.133],\n \+ flesh=[1.,.49,.25],\n flesh_ochre=[1.,.34,.13],\n floral=[1.,.98,. 941],\n forest_green=[.133,.545,.133],\n gainsboro=[.863,.863,.863 ],\n geranium_lake=[.89,.07,.19],\n gold_yellow=[1.,.843,0.],\n \+ gold_ochre=[.78,.47,.15],\n goldenrod=[.855,.647,.126],\n dark_gol denrod=[.722,.525,.043],\n light_goldenrod=[.98,.98,.823],\n pale_ goldenrod=[.933,.91,.667],\n dark_green=[0.,.3927,0.],\n pale_gree n=[.596,.984,.596],\n green_yellow=[.678,1.,.184],\n redish_umber= [1.,.24,.05],\n honeydew=[.941,1.,.941],\n hot_pink=[1.,.412,.706] ,\n indian_red=[.69,.09,.12],\n indigo=[.03,.18,.33],\n ivory_bl ack=[.16,.14,.13],\n pale_khaki=[.941,.902,.549],\n light_khaki=[. 741,.718,.42],\n lamp_black=[.18,.28,.23],\n lavender=[.93,.902,.9 8],\n lawn_green=[.486,.988,0.],\n lemon_chiffon=[1.,.98,.804],\n \+ light_beige=[.961,.961,.863],\n light_goldenrod=[.933,.867,.51],\n medium_grey=[.667,.667,.667],\n dark_grey=[.58,.58,.58],\n ligh t_salmon=[1.,.628,.478],\n lime_green=[.196,.804,.196],\n linen=[. 98,.941,.902],\n deep_madder_lake=[.89,.18,.19],\n manganese_blue= [.01,.66,.62],\n maroon_red=[.69,.188,.377],\n mars_orange=[.59,.2 7,.08],\n mars_yellow=[.89,.44,.1],\n melon=[.89,.66,.41],\n mid night_blue=[.098,.098,.439],\n mint=[.74,.99,.79],\n misty_rose=[1 .,.894,.882],\n moccasin=[1.,.894,.71],\n deep_naples_yellow=[1.,. 66,.07],\n navajo=[1.,.871,.678],\n navy_blue=[0.,0.,.502],\n ol d_lace=[.992,.961,.902],\n olive=[.23,.37,.17],\n drab_olive=[.42, .557,.137],\n dark_olive_green=[.333,.42,.184],\n orange_red=[1.,. 271,0.],\n orchid=[.855,.439,.839],\n dark_orchid=[.6,.196,.8],\n \+ medium_orchid=[.729,.333,.827],\n papaya_whip=[1.,.937,.835],\n \+ peach=[.44,.26,.26],\n peach_puff=[1.,.855,.726],\n peacock=[.2,.6 3,.79],\n permanent_green=[.04,.79,.17],\n permanent_red_violet=[. 86,.15,.27],\n peru=[.804,.522,.247],\n light_pink=[1.,.804,.871], \n plum=[.867,.628,.867],\n light_plum=[.918,.678,.918],\n powde r_blue=[.69,.878,.902],\n prussian_blue=[.18,.18,.31],\n purple=[. 4,0,.9],\n medium_purple=[.628,.126,.941],\n slate_blue_purple=[.5 76,.439,.859],\n raspberry=[.53,.15,.34],\n raw_sienna=[.78,.38,.0 8],\n raw_umber=[.45,.29,.07],\n red_brick=[.8,.196,.196],\n ros e_madder=[.89,.21,.22],\n rosy_brown=[.737,.561,.561],\n royal_blu e=[.255,.412,.882],\n saddle_brown=[.545,.271,.0745],\n salmon=[.9 8,.502,.447],\n sandy_brown=[.957,.643,.377],\n sap_green=[.19,.5, .089],\n sea_green=[.180,.545,.341],\n dark_sea_green=[.561,.737,. 561],\n light_sea_green=[.126,.698,.667],\n medium_sea_green=[.235 ,.702,.443],\n seashell=[1.,.961,.933],\n sepia=[.37,.15,.07],\n \+ rich_sienna=[.628,.322,.177],\n sky_blue=[.529,.808,.922],\n deep _sky_blue=[0.,.749,1.],\n light_sky_blue=[.529,.808,.98],\n slate_ blue=[.416,.353,.804],\n dark_slate_blue=[.282,.239,.545],\n light _slate_blue=[.518,.439,1.],\n medium_slate_blue=[.482,.408,.933],\n \+ slate_grey=[.439,.502,.565],\n dark_slate_grey=[.184,.31,.31],\n \+ light_slate_grey=[.467,.533,.6],\n smoke=[.961,.961,.961],\n spri ng_green=[0.,1.,.498],\n medium_spring_green=[0.,.98,.604],\n stee l_blue=[.274,.51,.706],\n light_steel_blue=[.69,.769,.871],\n terr e_verte=[.22,.37,.06],\n thistle=[.847,.749,.847],\n titanium=[.99 ,1.,.94],\n tomato=[1.,.388,.278],\n turquoise=[.251,.878,.816],\n turquoise_blue=[0.,.78,.55],\n dark_turquoise=[0.,.808,.82],\n \+ medium_turquoise=[.282,.82,.8],\n pale_turquoise=[.686,.933,.933],\n ultramarine=[.07,.04,.56],\n ultramarine_violet=[.36,.14,.43],\n \+ dark_brown=[.37,.15,.02],\n venetian_red=[.83,.1,.12],\n violet= [.56,.37,.6],\n dark_violet=[.58,0.,.827],\n violet_red=[.816,.126 ,.565],\n medium_violet_red=[.78,.0824,.522],\n pale_violet_red=[. 859,.439,.577],\n light_viridian=[.43,1.,.44],\n warm_grey=[.5,.5, .41],\n yellow_brown=[.86,.58,.44],\n yellow_green=[.604,.804,.196 ],\n light_yellow=[1.,1.,.878],\n yellow_ochre=[.89,.51,.09],\n \+ zinc=[.87,.84,.89]]): # of `plot/colortable`" }}}{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 15 "For reference: \+ " }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "`plot/color`: default version " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 353 "`plot/color` := proc(t) \noption `Copyright (c) 1992 by the University of Waterloo. All rights reserved.`;\n if type(t, function) and (op(0, t) = 'COLOUR' or op( 0, t) = 'COLOR') then t\n elif member(t, map(op, \{indices(`plot/co lortable`)\})) then COLOUR('RGB', op(`plot/colortable`[t]))\n else \+ error \"invalid color specification\"\n end if\nend proc:" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 18 "c ode for pictures " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} {SECT 1 {PARA 0 "" 0 "" {TEXT -1 12 "RGB colours " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1253 "p1 := plot s[polygonplot]([[0,0],[1,0],[1,-1],[0,-1]],\n color=COLOR(RGB,1,0, 0)):\np2 := plots[polygonplot]([[0,-1],[1,-1],[1,-2],[0,-2]],\n co lor=COLOR(RGB,0,1,0)):\np3 := plots[polygonplot]([[0,-2],[1,-2],[1,-3] ,[0,-3]],\n color=COLOR(RGB,0,0,1)):\np4 := plots[polygonplot]([[0 ,-3],[1,-3],[1,-4],[0,-4]],\n color=COLOR(RGB,1,1,0)):\np5 := plot s[polygonplot]([[0,-4],[1,-4],[1,-5],[0,-5]],\n color=COLOR(RGB,0, 1,1)):\np6 := plots[polygonplot]([[0,-5],[1,-5],[1,-6],[0,-6]],\n \+ color=COLOR(RGB,1,0,1)):\np7 := plots[polygonplot]([[0,-6],[1,-6],[1,- 7],[0,-7]],\n color=COLOR(RGB,1,.5,0)):\np8 := plots[polygonplot]( [[0,-7],[1,-7],[1,-8],[0,-8]],\n color=COLOR(RGB,.5,1,0)):\np9 := \+ plots[polygonplot]([[0,-8],[1,-8],[1,-9],[0,-9]],\n color=COLOR(RG B,.5,0,1)):\nt1 := plots[textplot]([[1.2,-.5,`COLOUR(RGB,1,0,0) = red` ],\n[1.2,-1.5,`COLOUR(RGB,0,1,0) = green`],\n[1.2,-2.5,`COLOUR(RGB,0,0 ,1) = blue`],\n[1.2,-3.5,`COLOUR(RGB,1,1,0) = yellow`],\n[1.2,-4.5,`CO LOUR(RGB,0,1,1) = cyan`],\n[1.2,-5.5,`COLOUR(RGB,1,0,1) = magenta`],\n [1.2,-6.5,`COLOUR(RGB,1,.5,0) = orange`],\n[1.2,-7.5,`COLOUR(RGB,.5,1, 0) = chartreuse`],\n[1.2,-8.5,`COLOUR(RGB,.5,0,1) = purple`]],color=bl ack,align=RIGHT):\nplots[display]([p1,p2,p2,p3,p4,p5,p6,p7,p8,p9,t1],a xes=none);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 15 "RGB colo ur cube" }}{PARA 0 "" 0 "" {TEXT -1 15 "external faces " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1236 "p1 := plot3d(0,x=0..1,y=0..1,styl e=patchnogrid,color=[x,y,0]):\np2 := plot3d(1,x=0..1,y=0..1,style=patc hnogrid,color=[x,y,1]):\np3 := plot3d([0,y,z],y=0..1,z=0..1,style=patc hnogrid,color=[0,y,z]):\np4 := plot3d([1,y,z],y=0..1,z=0..1,style=patc hnogrid,color=[1,y,z]):\np5 := plot3d([x,0,z],x=0..1,z=0..1,style=patc hnogrid,color=[x,0,z]):\np6 := plot3d([x,1,z],x=0..1,z=0..1,style=patc hnogrid,color=[x,1,z]):\np7 := plots[pointplot3d]([[0,1,0],[1,1,0],[1, 0,0],[1,0,1],[0,0,1],\n [0,1,1],[0,1,0]],style=line,color=black): \np8 := plots[pointplot3d]([[0,1,1],[1,1,1],[1,0,1]],style=line,color= black):\np9 := plots[pointplot3d]([[1,1,1],[1,1,0]],style=line,color=b lack):\np10 := plottools[arrow]([0,0,0],[0,0,1.3],.1,.05,.06,arrow,col or=black):\np11 := plottools[arrow]([0,0,0],[0,1.3,0],.1,.05,.06,arrow ,color=black):\np12 := plottools[arrow]([0,0,0],[1.3,0,0],.1,.05,.06,a rrow,color=black):\nt1 := plots[textplot3d]([[1.3,0,-.15,`red, R`],[0, 1.3,-.15,`green, G`],\n [0,0,1.35,`blue, B`],[1.1,1.1,0,`yellow`] ,\n [1.1,0,1.1,`magenta`],[0,1.1,1.1,`cyan`],\n [1.1,1.1,1.1 ,`white`],[-.1,-.1,-.1,`black`]],\n font=[HELVETICA,9],color=bl ack):\nplots[display]([p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,t1],\n \+ orientation=[45,56],axes=none);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 15 "diagonal faces " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1261 "p1 := plot3d([x,y,1-y],x=0..1,y=0..1,style=patch nogrid,color=[x,y,1-y]):\np2 := plot3d([x,y,y],x=0..1,y=0..1,style=pat chnogrid,color=[x,y,y]):\np3 := plot3d([x,y,1-x],x=0..1,y=0..1,style=p atchnogrid,color=[x,y,1-x]):\np4 := plot3d([x,y,x],x=0..1,y=0..1,style =patchnogrid,color=[x,y,x]):\np5 := plot3d([x,1-x,z],x=0..1,z=0..1,sty le=patchnogrid,color=[x,1-x,z]):\np6 := plot3d([x,x,z],x=0..1,z=0..1,s tyle=patchnogrid,color=[x,x,z]):\np7 := plots[pointplot3d]([[0,1,0],[1 ,1,0],[1,0,0],[1,0,1],[0,0,1],\n [0,1,1],[0,1,0]],style=line,colo r=black):\np8 := plots[pointplot3d]([[0,1,1],[1,1,1],[1,0,1]],style=li ne,color=black):\np9 := plots[pointplot3d]([[1,1,1],[1,1,0]],style=lin e,color=black):\np10 := plottools[arrow]([0,0,0],[0,0,1.3],.1,.05,.06, arrow,color=black):\np11 := plottools[arrow]([0,0,0],[0,1.3,0],.1,.05, .06,arrow,color=black):\np12 := plottools[arrow]([0,0,0],[1.3,0,0],.1, .05,.06,arrow,color=black):\nt1 := plots[textplot3d]([[1.3,0,-.15,`red , R`],[0,1.3,-.15,`green, G`],\n [0,0,1.35,`blue, B`],[1.1,1.1,0, `yellow`],\n [1.1,0,1.1,`magenta`],[0,1.1,1.1,`cyan`],\n [1. 1,1.1,1.1,`white`],[-.1,-.1,-.1,`black`]],\n font=[HELVETICA,9] ,color=black):\nplots[display]([p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12 ,t1],\n orientation=[45,56],axes=none);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 21 "code for hue \"wheel\" " }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 803 "ss := 1: \nvv := 1:\nd := evalf(Pi/50):\nv := 0.13:\nr1 := .4: r2 := 1.34:\ns : = evalf(sqrt(3)/2): c := .5:\npp := seq(plots[polygonplot]([[r1*cos(d* i),r1*sin(d*i)],\n[r1*cos(d*(i+1)),r1*sin(d*(i+1))],[cos(d*(i+1)),sin( d*(i+1))],\n[cos(d*i),sin(d*i)]],color=convert(COLOUR(HSV,(i+.5)/100,s s,vv),RGB),\n style=PATCHNOGRID),i=0..99):\np1 := plot([cos(t),sin(t) ,t=0..2*Pi],color=black):\np2 := plot([r1*cos(t),r1*sin(t),t=0..2*Pi], color=black):\nt1 := plots[textplot]([[r2,v/2,`H = 0`],[r2,-v/2,`red`] ,\n[r2*c,r2*s,`H = 0.1667`],[r2*c,r2*s-v,`yellow`],\n[-r2*c,r2*s,`H = \+ 0.3333`],[-r2*c,r2*s-v,`green`],\n[-r2,v/2,`H = 0.5`],[-r2,-v/2,`cyan` ],\n[-r2*c,-r2*s+v,`H = 0.6667`],[-r2*c,-r2*s,`blue`],\n[r2*c,-r2*s+v, `H = 0.8333`],[r2*c,-r2*s,`magenta`]],color=black):\nplots[display]([p p,p1,p2,t1],scaling=constrained,axes=none);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 698 "ss := .5:\nvv := \+ 1:\nd := evalf(Pi/50):\nv := 0.13:\nr1 := .4: r2 := 1.34:\ns := evalf( sqrt(3)/2): c := .5:\npp := seq(plots[polygonplot]([[r1*cos(d*i),r1*si n(d*i)],\n[r1*cos(d*(i+1)),r1*sin(d*(i+1))],[cos(d*(i+1)),sin(d*(i+1)) ],\n[cos(d*i),sin(d*i)]],color=convert(COLOUR(HSV,(i+.5)/100,ss,vv),RG B),\n style=PATCHNOGRID),i=0..99):\np1 := plot([cos(t),sin(t),t=0..2* Pi],color=black):\np2 := plot([r1*cos(t),r1*sin(t),t=0..2*Pi],color=bl ack):\nt1 := plots[textplot]([[r2,v/2,`H = 0`],\n[r2*c,r2*s,`H = 0.166 7`],\n[-r2*c,r2*s,`H = 0.3333`],\n[-r2,v/2,`H = 0.5`],[-r2,-v/2,`cyan` ],\n[-r2*c,-r2*s+v,`H = 0.6667`],\n[r2*c,-r2*s+v,`H = 0.8333`]],color= black):\nplots[display]([pp,p1,p2,t1],scaling=constrained,axes=none); " }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6]r-%)POLYGONS G6%7&7$$\"\"%!\"\"$\"\"!F,7$$\"+9p5#*R!#5$\"+#y?;^#!#67$$\"+%Gn-)**F0$ 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"Curve 78" "Curve 79" "Curve 80" "Curve 81" "Curve 82" "C urve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93" "Curve 94" "Curve 95 " "Curve 96" "Curve 97" "Curve 98" "Curve 99" "Curve 100" "Curve 101" "Curve 102" "Curve 103" "Curve 104" "Curve 105" "Curve 106" "Curve 107 " "Curve 108" "Curve 109" }}}}{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 16 "HSV colour cone " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1323 "rf := proc(h,v) op(2,convert(COLOR(HSV,h,1,v),RGB)) end proc:\ngf := proc(h ,v) op(3,convert(COLOR(HSV,h,1,v),RGB)) end proc:\nbf := proc(h,v) op( 4,convert(COLOR(HSV,h,1,v),RGB)) end proc:\nxf := proc(h,v) v*cos(2*Pi *h) end proc:\nyf := proc(h,v) v*sin(2*Pi*h) end proc:\nzf := proc(h,v ) v end proc:\np1 := plot3d([xf,yf,zf],0..1,0..1,style=patchnogrid,\n \+ color=[rf,gf,bf]):\nrf := proc(h,s) op(2,convert(COLOR(HSV,h,s,1), RGB)) end proc:\ngf := proc(h,s) op(3,convert(COLOR(HSV,h,s,1),RGB)) e nd proc:\nbf := proc(h,s) op(4,convert(COLOR(HSV,h,s,1),RGB)) end proc :\nxf := proc(h,s) s*cos(2*Pi*h) end proc:\nyf := proc(h,s) s*sin(2*Pi *h) end proc:\nzf := proc(h,s) 1 end proc:\np2 := plot3d([xf,yf,zf],0. .1,0..1,style=patchnogrid,\n color=[rf,gf,bf]):\np3 := plottools[a rrow]([0,0,0],[0,0,1.3],.1,.1,.06,arrow,color=black):\nd1 := evalf(Pi/ 30): r1 := .75:\np4 := plots[pointplot3d]([seq([r1*cos(d1*i),r1*sin(d1 *i),.5],i=2..45)],\n color=black,style=line):\np5 := plots[pointpl ot3d]([seq([cos(d1*i),sin(d1*i),1],i=0..60)],\n color=black,style= line,color=COLOR(RGB,.6,.6,.6)):\np6 := plots[pointplot3d]([[-.04,-.79 ,.5],[0,-.75,.5],[-.04,-.71,.5]],\n color=black,style=line):\nt1 \+ := plots[textplot3d]([[-.15,-.15,1.4,`value, V`],\n [-.2,-.9,.3,`h ue, H`]],color=black):\nplots[display]([p1,p2,p3,p4,p5,p6,t1],orientat ion=[-42,64]);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "sections of HSV cone " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1589 "HSVsection3d := proc(t)\n local k,h,i,f;\n k := t-floor(t);\n h := k*6;\n i := floor(h);\n \011\011f := h-i; \+ \n \011 if i=0 then\n plot3d([v*s*cos(2*Pi*k),v*s*sin(2*Pi*k),v], v=0..1,s=0..1,\n style=patchnogrid,color=[v,v*(1-s*(1-f)),v*(1- s)]);\n\011\011\011elif i=1 then\n plot3d([v*s*cos(2*Pi*k),v*s*s in(2*Pi*k),v],v=0..1,s=0..1,\n style=patchnogrid,color=[v*(1-s *f),v,v*(1-s)]);\n elif i=2 then\n\011 plot3d([v*s*cos(2*Pi*k), v*s*sin(2*Pi*k),v],v=0..1,s=0..1,\n style=patchnogrid,color=[v *(1-s),v,v*(1-s*(1-f))]);\n elif i=3 then\n\011 plot3d([v*s*cos (2*Pi*k),v*s*sin(2*Pi*k),v],v=0..1,s=0..1,\n style=patchnogrid ,color=[v*(1-s),v*(1-s*f),v]);\n elif i=4 then\n\011 plot3d([v* s*cos(2*Pi*k),v*s*sin(2*Pi*k),v],v=0..1,s=0..1,\n style=patchn ogrid,color=[v*(1-s*(1-f)),v*(1-s),v]);\n\011\011\011else # i=5 then\n \011 plot3d([v*s*cos(2*Pi*k),v*s*sin(2*Pi*k),v],v=0..1,s=0..1,\n \+ style=patchnogrid,color=[v,v*(1-s),v*(1-s*f)]);\n end if;\ne nd proc:\nd := evalf(1/12):\np1 := seq(HSVsection3d(j*d),j=0..11):\np2 := plots[spacecurve]([cos(t),sin(t),1],t=0..2*Pi,\n linestyle=2 ,style=line,color=grey):\np3 := plottools[arrow]([0,0,0],[0,0,1.3],.1, .1,.06,arrow,color=black):\nd1 := evalf(Pi/30): r1 := .75:\np4 := plot s[pointplot3d]([seq([r1*cos(d1*i),r1*sin(d1*i),.5],i=2..45)],\n co lor=black,style=line):\np5 := plots[pointplot3d]([[-.04,-.79,.5],[0,-. 75,.5],[-.04,-.71,.5]],\n color=black,style=line):\nt1 := plots[t extplot3d]([[-.15,-.15,1.4,`value, V`],\n [-.2,-.75,.35,`hue, H` ]],color=black):\nplots[display]([p1,p2,p3,p4,p5,t1],orientation=[-42, 64]);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 18 "HLS \"doub le-cone\" " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{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 p roc:\nbf := proc(h,l) op(4,convert(COLOR(HLS,h,l,1),RGB)) end proc:\nx f := 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]([se q([r1*cos(d1*i),r1*sin(d1*i),.5],i=2..45)],\n color=black,style=li ne):\np4 := plots[pointplot3d]([[-.06,-1.4,.5],[0,-1.35,.5],[-.06,-1.3 ,.5]],\n color=black,style=line):\nt1 := plots[textplot3d]([[-.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 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "4 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }