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Pixel Conversion

by: John Dolese 125 Maple 18
array convert adobe
August 09 2014
3  1

Here is an example of manipulating an Array of pixels. I chose the x-rite ColorChecker as a model so there would be published results to check my work. A number of details about color spaces have become clear through this exercise. The color adaptation process was modeled by converting betweenXYZ and LMS. Different black points may be selected depending on how close to zero illuminance one would accept as a good model. 

I look forward to extending this work to verify and improve the color calibration of my photography. Also some experimentation with demosaicing should be possible.

Initialization
 

restart

with(LinearAlgebra):

unprotect(gamma):``

NULL

x-rite Colorchecker xyY Matrix

  CCxyY_D50 := Matrix(4, 6, {(1, 1) = Vector(3, {(1) = .4316, (2) = .3777, (3) = .1008}), (1, 2) = Vector(3, {(1) = .4197, (2) = .3744, (3) = .3495}), (1, 3) = Vector(3, {(1) = .2760, (2) = .3016, (3) = .1836}), (1, 4) = Vector(3, {(1) = .3703, (2) = .4499, (3) = .1325}), (1, 5) = Vector(3, {(1) = .2999, (2) = .2856, (3) = .2304}), (1, 6) = Vector(3, {(1) = .2848, (2) = .3911, (3) = .4178}), (2, 1) = Vector(3, {(1) = .5295, (2) = .4055, (3) = .3118}), (2, 2) = Vector(3, {(1) = .2305, (2) = .2106, (3) = .1126}), (2, 3) = Vector(3, {(1) = .5012, (2) = .3273, (3) = .1938}), (2, 4) = Vector(3, {(1) = .3319, (2) = .2482, (3) = 0.637e-1}), (2, 5) = Vector(3, {(1) = .3984, (2) = .5008, (3) = .4446}), (2, 6) = Vector(3, {(1) = .4957, (2) = .4427, (3) = .4357}), (3, 1) = Vector(3, {(1) = .2018, (2) = .1692, (3) = 0.575e-1}), (3, 2) = Vector(3, {(1) = .3253, (2) = .5032, (3) = .2318}), (3, 3) = Vector(3, {(1) = .5686, (2) = .3303, (3) = .1257}), (3, 4) = Vector(3, {(1) = .4697, (2) = .4734, (3) = .5981}), (3, 5) = Vector(3, {(1) = .4159, (2) = .2688, (3) = .2009}), (3, 6) = Vector(3, {(1) = .2131, (2) = .3023, (3) = .1930}), (4, 1) = Vector(3, {(1) = .3469, (2) = .3608, (3) = .9131}), (4, 2) = Vector(3, {(1) = .3440, (2) = .3584, (3) = .5894}), (4, 3) = Vector(3, {(1) = .3432, (2) = .3581, (3) = .3632}), (4, 4) = Vector(3, {(1) = .3446, (2) = .3579, (3) = .1915}), (4, 5) = Vector(3, {(1) = .3401, (2) = .3548, (3) = 0.883e-1}), (4, 6) = Vector(3, {(1) = .3406, (2) = .3537, (3) = 0.311e-1})})

NULL

NULL

M := RowDimension(CCxyY_D50) = 4NULL

N := ColumnDimension(CCxyY_D50) = 6

NULL

Convert xyY to XYZ
   

NULL

CCXYZ_D50 := C_xyY_to_XYZ(CCxyY_D50):

CCXYZ_D50 = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = .1152, (2) = .1008, (3) = 0.509e-1}), (1, 2) = Vector(3, {(1) = .3918, (2) = .3495, (3) = .1922}), (1, 3) = Vector(3, {(1) = .1680, (2) = .1836, (3) = .2571}), (1, 4) = Vector(3, {(1) = .1091, (2) = .1325, (3) = 0.529e-1}), (1, 5) = Vector(3, {(1) = .2419, (2) = .2304, (3) = .3344}), (1, 6) = Vector(3, {(1) = .3042, (2) = .4178, (3) = .3462}), (2, 1) = Vector(3, {(1) = .4071, (2) = .3118, (3) = 0.500e-1}), (2, 2) = Vector(3, {(1) = .1232, (2) = .1126, (3) = .2988}), (2, 3) = Vector(3, {(1) = .2968, (2) = .1938, (3) = .1015}), (2, 4) = Vector(3, {(1) = 0.852e-1, (2) = 0.637e-1, (3) = .1078}), (2, 5) = Vector(3, {(1) = .3537, (2) = .4446, (3) = 0.895e-1}), (2, 6) = Vector(3, {(1) = .4879, (2) = .4357, (3) = 0.606e-1}), (3, 1) = Vector(3, {(1) = 0.686e-1, (2) = 0.575e-1, (3) = .2138}), (3, 2) = Vector(3, {(1) = .1498, (2) = .2318, (3) = 0.790e-1}), (3, 3) = Vector(3, {(1) = .2164, (2) = .1257, (3) = 0.385e-1}), (3, 4) = Vector(3, {(1) = .5934, (2) = .5981, (3) = 0.719e-1}), (3, 5) = Vector(3, {(1) = .3108, (2) = .2009, (3) = .2356}), (3, 6) = Vector(3, {(1) = .1360, (2) = .1930, (3) = .3094}), (4, 1) = Vector(3, {(1) = .8779, (2) = .9131, (3) = .7397}), (4, 2) = Vector(3, {(1) = .5657, (2) = .5894, (3) = .4894}), (4, 3) = Vector(3, {(1) = .3481, (2) = .3632, (3) = .3029}), (4, 4) = Vector(3, {(1) = .1844, (2) = .1915, (3) = .1592}), (4, 5) = Vector(3, {(1) = 0.846e-1, (2) = 0.883e-1, (3) = 0.759e-1}), (4, 6) = Vector(3, {(1) = 0.299e-1, (2) = 0.311e-1, (3) = 0.269e-1})})NULL

XYZ D50 to XYZ D65

   

NULL

CCXYZ_D65 := XYZ_D50_to_D65(CCXYZ_D50):

CCXYZ_D65 = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = .1110, (2) = 0.996e-1, (3) = 0.670e-1}), (1, 2) = Vector(3, {(1) = .3785, (2) = .3459, (3) = .2533}), (1, 3) = Vector(3, {(1) = .1726, (2) = .1861, (3) = .3403}), (1, 4) = Vector(3, {(1) = .1045, (2) = .1318, (3) = 0.690e-1}), (1, 5) = Vector(3, {(1) = .2470, (2) = .2329, (3) = .4430}), (1, 6) = Vector(3, {(1) = .3030, (2) = .4206, (3) = .4556}), (2, 1) = Vector(3, {(1) = .3850, (2) = .3044, (3) = 0.651e-1}), (2, 2) = Vector(3, {(1) = .1340, (2) = .1165, (3) = .3966}), (2, 3) = Vector(3, {(1) = .2855, (2) = .1895, (3) = .1347}), (2, 4) = Vector(3, {(1) = 0.867e-1, (2) = 0.642e-1, (3) = .1431}), (2, 5) = Vector(3, {(1) = .3334, (2) = .4409, (3) = .1142}), (2, 6) = Vector(3, {(1) = .4600, (2) = .4275, (3) = 0.777e-1}), (3, 1) = Vector(3, {(1) = 0.777e-1, (2) = 0.606e-1, (3) = .2839}), (3, 2) = Vector(3, {(1) = .1428, (2) = .2315, (3) = .1022}), (3, 3) = Vector(3, {(1) = .2063, (2) = .1216, (3) = 0.512e-1}), (3, 4) = Vector(3, {(1) = .5578, (2) = .5888, (3) = 0.906e-1}), (3, 5) = Vector(3, {(1) = .3073, (2) = .1990, (3) = .3131}), (3, 6) = Vector(3, {(1) = .1451, (2) = .1976, (3) = .4092}), (4, 1) = Vector(3, {(1) = .8646, (2) = .9129, (3) = .9759}), (4, 2) = Vector(3, {(1) = .5579, (2) = .5895, (3) = .6458}), (4, 3) = Vector(3, {(1) = .3434, (2) = .3633, (3) = .3997}), (4, 4) = Vector(3, {(1) = .1818, (2) = .1915, (3) = .2100}), (4, 5) = Vector(3, {(1) = 0.836e-1, (2) = 0.884e-1, (3) = .1002}), (4, 6) = Vector(3, {(1) = 0.296e-1, (2) = 0.311e-1, (3) = 0.355e-1})})

NULL

NULLConvert XYZ to Lab (D50 or D65 White Point)
 

NULLNULL

Reference White Point for D50

NULL

X_D50wht := XYZ_D50wht[1] = .96422NULL

Y_D50wht := XYZ_D50wht[2] = 1NULL

Z_D50wht := XYZ_D50wht[3] = .82521

NULL

Lab Conversion Constants;

`ε` := 216/24389:

kappa := 24389/27:

NULL

fx_D50 := proc (XYZ) options operator, arrow; piecewise(`&epsilon;` < XYZ[1]/X_D50wht, (XYZ[1]/X_D50wht)^(1/3), XYZ[1]/X_D50wht <= `&epsilon;`, (1/116)*kappa*XYZ[1]/X_D50wht+4/29) end proc
                

NULLNULL

NULL

 
fy_D50 := proc (XYZ) options operator, arrow; piecewise(`&epsilon;` < XYZ[2]/Y_D50wht, (XYZ[2]/Y_D50wht)^(1/3), XYZ[2]/Y_D50wht <= `&epsilon;`, (1/116)*kappa*XYZ[2]/Y_D50wht+4/29) end proc
NULLNULL

NULLNULL

fz_D50 := proc (XYZ) options operator, arrow; piecewise(`&epsilon;` < XYZ[3]/Z_D50wht, (XYZ[3]/Z_D50wht)^(1/3), XYZ[3]/Z_D50wht <= `&epsilon;`, (1/116)*kappa*XYZ[3]/Z_D50wht+4/29) end proc
NULL

XYZ_to_Lab_D50 := proc (XYZ) options operator, arrow; `<,>`(116*fy_D50(XYZ)-16, 500*fx_D50(XYZ)-500*fy_D50(XYZ), 200*fy_D50(XYZ)-200*fz_D50(XYZ)) end proc:

NULL

Reference White Point for D65

NULL

X_D65wht := XYZ_D65wht[1] = .95047NULL

Y_D65wht := XYZ_D65wht[2] = 1NULL

Z_D65wht := XYZ_D65wht[3] = 1.08883 

NULL

NULL

NULL

NULL

NULL

NULL

NULL

fx_D65 := proc (XYZ) options operator, arrow; piecewise(`&epsilon;` < XYZ[1]/X_D65wht, (XYZ[1]/X_D65wht)^(1/3), XYZ[1]/X_D65wht <= `&epsilon;`, (1/116)*kappa*XYZ[1]/X_D65wht+4/29) end proc
                

NULLNULL

NULL

 
fy_D65 := proc (XYZ) options operator, arrow; piecewise(`&epsilon;` < XYZ[2]/Y_D65wht, (XYZ[2]/Y_D65wht)^(1/3), XYZ[2]/Y_D65wht <= `&epsilon;`, (1/116)*kappa*XYZ[2]/Y_D65wht+4/29) end proc
NULLNULL

NULLNULL

fz_D65 := proc (XYZ) options operator, arrow; piecewise(`&epsilon;` < XYZ[3]/Z_D65wht, (XYZ[3]/Z_D65wht)^(1/3), XYZ[3]/Z_D65wht <= `&epsilon;`, (1/116)*kappa*XYZ[3]/Z_D65wht+4/29) end proc
NULL

XYZ_to_Lab_D65 := proc (XYZ) options operator, arrow; `<,>`(116*fy_D65(XYZ)-16, 500*fx_D65(XYZ)-500*fy_D65(XYZ), 200*fy_D65(XYZ)-200*fz_D65(XYZ)) end proc:

NULL

NULL
 

NULL

C_XYZ_to_Lab := proc (XYZ, L) options operator, arrow; piecewise(evalb(L = D50), Array([`$`('[`$`('XYZ_to_Lab_D50(XYZ[m, n])', n = 1 .. N)]', m = 1 .. M)]), evalb(L = D65), Array([`$`('[`$`('XYZ_to_Lab_D65(XYZ[m, n])', n = 1 .. N)]', m = 1 .. M)])) end proc
 NULL

NULL

NULLNULL

NULL

CCLab_D50 := C_XYZ_to_Lab(CCXYZ_D50, D50): NULL

CCLab_D50 = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = 37.99, (2) = 13.55, (3) = 14.06}), (1, 2) = Vector(3, {(1) = 65.71, (2) = 18.14, (3) = 17.82}), (1, 3) = Vector(3, {(1) = 49.93, (2) = -4.91, (3) = -21.92}), (1, 4) = Vector(3, {(1) = 43.14, (2) = -13.10, (3) = 21.89}), (1, 5) = Vector(3, {(1) = 55.11, (2) = 8.84, (3) = -25.39}), (1, 6) = Vector(3, {(1) = 70.72, (2) = -33.39, (3) = -.21}), (2, 1) = Vector(3, {(1) = 62.66, (2) = 36.06, (3) = 57.08}), (2, 2) = Vector(3, {(1) = 40.01, (2) = 10.42, (3) = -45.98}), (2, 3) = Vector(3, {(1) = 51.13, (2) = 48.24, (3) = 16.26}), (2, 4) = Vector(3, {(1) = 30.33, (2) = 23.00, (3) = -21.59}), (2, 5) = Vector(3, {(1) = 72.53, (2) = -23.70, (3) = 57.27}), (2, 6) = Vector(3, {(1) = 71.94, (2) = 19.37, (3) = 67.86}), (3, 1) = Vector(3, {(1) = 28.77, (2) = 14.17, (3) = -50.30}), (3, 2) = Vector(3, {(1) = 55.26, (2) = -38.32, (3) = 31.36}), (3, 3) = Vector(3, {(1) = 42.11, (2) = 53.38, (3) = 28.20}), (3, 4) = Vector(3, {(1) = 81.73, (2) = 4.03, (3) = 79.85}), (3, 5) = Vector(3, {(1) = 51.94, (2) = 50.00, (3) = -14.57}), (3, 6) = Vector(3, {(1) = 51.04, (2) = -28.65, (3) = -28.63}), (4, 1) = Vector(3, {(1) = 96.54, (2) = -.46, (3) = 1.19}), (4, 2) = Vector(3, {(1) = 81.26, (2) = -.64, (3) = -.35}), (4, 3) = Vector(3, {(1) = 66.76, (2) = -.72, (3) = -.51}), (4, 4) = Vector(3, {(1) = 50.86, (2) = -.14, (3) = -.28}), (4, 5) = Vector(3, {(1) = 35.65, (2) = -.44, (3) = -1.23}), (4, 6) = Vector(3, {(1) = 20.48, (2) = -0.7e-1, (3) = -.98})})NULL

NULL

Convert XYZ to aRGB (XYZ D50 or D65 to aRGB D65)
 

XYZ Scaling for aRGB Ymax,Ymin (Ref. Adobe RGB (1998) Color Image Encoding Section 4.3.2.2 and 4.3.8)

NULL

White Point (Luminance=160Cd/m^2) D65

Black Point (Luminance=0.5557Cd/m^2) D65

White Point (Luminance=160Cd/m^2) D50

Black Point (Luminance=0.5557Cd/m^2) D50

XW_D65 := 152.07*(1/160) = .9504375000NULL

YW_D65 := 160*(1/160) = 1``

ZW_D65 := 174.25*(1/160) = 1.089062500``

NULL

xXK_D65 := .5282*(1/160) = 0.3301250000e-2``

xYK_D65 := .5557*(1/160) = 0.3473125000e-2``

xZK_D65 := .6025*(1/160) = 0.3765625000e-2``

XK_D65 := 0:

YK_D65 := 0:

ZK_D65 := 0:

``

``

XW_D50 := .9462:NULL

YW_D50 := 1.0000:

ZW_D50 := .8249:

``

NULL

xXK_D50 := 0.33488e-2:

xYK_D50 := 0.34751e-2:

xZK_D50 := 0.28650e-2:

``

XK_D50 := 0:

YK_D50 := 0:

ZK_D50 := 0:

NULL
 

NULL

XYZD65_to_aXYZ := proc (XYZ) options operator, arrow; `<,>`((XYZ[1]-XK_D65)*XW_D65/((XW_D65-XK_D65)*YW_D65), (XYZ[2]-YK_D65)/(YW_D65-YK_D65), (XYZ[3]-ZK_D65)*ZW_D65/((ZW_D65-ZK_D65)*YW_D65)) end proc:

XYZD50_to_aXYZ := proc (XYZ) options operator, arrow; `<,>`((XYZ[1]-XK_D50)*XW_D50/((XW_D50-XK_D50)*YW_D50), (XYZ[2]-YK_D50)/(YW_D50-YK_D50), (XYZ[3]-ZK_D50)*ZW_D50/((ZW_D50-ZK_D50)*YW_D50)) end proc:

 

NULL

(ref. Adobe RGB(1998) section 4.3.6.1, Bradford Matrix includes D50 to D65 adaptation)

M_XYZtoaRGB_D50 := Matrix(3, 3, {(1, 1) = 1.96253, (1, 2) = -.61068, (1, 3) = -.34137, (2, 1) = -.97876, (2, 2) = 1.91615, (2, 3) = 0.3342e-1, (3, 1) = 0.2869e-1, (3, 2) = -.14067, (3, 3) = 1.34926})

  aXYZ_to_RGB_D50 := proc (aXYZ) options operator, arrow; `<,>`(Typesetting:-delayDotProduct(M_XYZtoaRGB_D50, aXYZ)) end proc: NULL

 

(ref. Adobe RBG(1998) section 4.3.4.1, Bradford Matrix assumes XYZ is D65)

M_XYZtoaRGB_D65 := Matrix(3, 3, {(1, 1) = 2.04159, (1, 2) = -.56501, (1, 3) = -.34473, (2, 1) = -.96924, (2, 2) = 1.87597, (2, 3) = 0.4156e-1, (3, 1) = 0.1344e-1, (3, 2) = -.11836, (3, 3) = 1.01517})

  NULL

aXYZ_to_RGB_D65 := proc (aXYZ) options operator, arrow; `<,>`(Typesetting:-delayDotProduct(M_XYZtoaRGB_D65, aXYZ)) end proc:

NULL

  aRGB Expansion for 8bits

 

`&gamma;a` := 2.19921875:

RGB_to_aRGB := proc (RGB) options operator, arrow; `<,>`(round(255*Norm(RGB[1])^(1/`&gamma;a`)), round(255*Norm(RGB[2])^(1/`&gamma;a`)), round(255*Norm(RGB[3])^(1/`&gamma;a`))) end proc:
NULL

 

Combine Steps

NULL

XYZ_to_aRGB := proc (XYZ, L) options operator, arrow; piecewise(evalb(L = D50), Array([`$`('[`$`('RGB_to_aRGB(aXYZ_to_RGB_D50(XYZD50_to_aXYZ(XYZ[m, n])))', n = 1 .. N)]', m = 1 .. M)]), evalb(L = D65), Array([`$`('[`$`('RGB_to_aRGB(aXYZ_to_RGB_D65(XYZD65_to_aXYZ(XYZ[m, n])))', n = 1 .. N)]', m = 1 .. M)])) end proc

NULLNULL

NULLNULL

Note: The aRGB values published for ColorChecker assume a black point of 0cd/m^2.

````

aRGB_D50in := XYZ_to_aRGB(CCXYZ_D50, D50):

aRGB_D50in = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = 107, (2) = 82, (3) = 70}), (1, 2) = Vector(3, {(1) = 184, (2) = 146, (3) = 128}), (1, 3) = Vector(3, {(1) = 101, (2) = 122, (3) = 153}), (1, 4) = Vector(3, {(1) = 95, (2) = 107, (3) = 69}), (1, 5) = Vector(3, {(1) = 128, (2) = 127, (3) = 173}), (1, 6) = Vector(3, {(1) = 129, (2) = 188, (3) = 171}), (2, 1) = Vector(3, {(1) = 201, (2) = 123, (3) = 56}), (2, 2) = Vector(3, {(1) = 77, (2) = 92, (3) = 166}), (2, 3) = Vector(3, {(1) = 174, (2) = 83, (3) = 97}), (2, 4) = Vector(3, {(1) = 86, (2) = 61, (3) = 104}), (2, 5) = Vector(3, {(1) = 167, (2) = 188, (3) = 75}), (2, 6) = Vector(3, {(1) = 213, (2) = 160, (3) = 55}), (3, 1) = Vector(3, {(1) = 49, (2) = 65, (3) = 143}), (3, 2) = Vector(3, {(1) = 99, (2) = 148, (3) = 80}), (3, 3) = Vector(3, {(1) = 155, (2) = 52, (3) = 59}), (3, 4) = Vector(3, {(1) = 227, (2) = 197, (3) = 52}), (3, 5) = Vector(3, {(1) = 169, (2) = 85, (3) = 147}), (3, 6) = Vector(3, {(1) = 61, (2) = 135, (3) = 167}), (4, 1) = Vector(3, {(1) = 245, (2) = 245, (3) = 242}), (4, 2) = Vector(3, {(1) = 200, (2) = 201, (3) = 201}), (4, 3) = Vector(3, {(1) = 160, (2) = 161, (3) = 162}), (4, 4) = Vector(3, {(1) = 120, (2) = 120, (3) = 121}), (4, 5) = Vector(3, {(1) = 84, (2) = 85, (3) = 86}), (4, 6) = Vector(3, {(1) = 52, (2) = 53, (3) = 54})})NULL

  

NULL

aRGB_D65in := XYZ_to_aRGB(CCXYZ_D65, D65):

aRGB_D65in = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = 107, (2) = 82, (3) = 70}), (1, 2) = Vector(3, {(1) = 184, (2) = 146, (3) = 128}), (1, 3) = Vector(3, {(1) = 101, (2) = 122, (3) = 153}), (1, 4) = Vector(3, {(1) = 95, (2) = 107, (3) = 69}), (1, 5) = Vector(3, {(1) = 128, (2) = 127, (3) = 173}), (1, 6) = Vector(3, {(1) = 129, (2) = 188, (3) = 171}), (2, 1) = Vector(3, {(1) = 201, (2) = 123, (3) = 56}), (2, 2) = Vector(3, {(1) = 77, (2) = 92, (3) = 166}), (2, 3) = Vector(3, {(1) = 174, (2) = 83, (3) = 97}), (2, 4) = Vector(3, {(1) = 86, (2) = 61, (3) = 104}), (2, 5) = Vector(3, {(1) = 167, (2) = 188, (3) = 75}), (2, 6) = Vector(3, {(1) = 213, (2) = 160, (3) = 55}), (3, 1) = Vector(3, {(1) = 49, (2) = 65, (3) = 143}), (3, 2) = Vector(3, {(1) = 99, (2) = 148, (3) = 80}), (3, 3) = Vector(3, {(1) = 155, (2) = 52, (3) = 59}), (3, 4) = Vector(3, {(1) = 227, (2) = 197, (3) = 52}), (3, 5) = Vector(3, {(1) = 169, (2) = 85, (3) = 147}), (3, 6) = Vector(3, {(1) = 61, (2) = 135, (3) = 167}), (4, 1) = Vector(3, {(1) = 245, (2) = 245, (3) = 242}), (4, 2) = Vector(3, {(1) = 200, (2) = 201, (3) = 201}), (4, 3) = Vector(3, {(1) = 160, (2) = 161, (3) = 162}), (4, 4) = Vector(3, {(1) = 120, (2) = 120, (3) = 121}), (4, 5) = Vector(3, {(1) = 84, (2) = 85, (3) = 86}), (4, 6) = Vector(3, {(1) = 52, (2) = 53, (3) = 54})})

Convert XYZ to ProPhoto RGB (D50)
   

NULL

CC_PPhoto := XYZ_to_PPhoto(CCXYZ_D50):

NULL

CC_PPhoto = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = 81, (2) = 67, (3) = 54}), (1, 2) = Vector(3, {(1) = 159, (2) = 135, (3) = 113}), (1, 3) = Vector(3, {(1) = 94, (2) = 102, (3) = 133}), (1, 4) = Vector(3, {(1) = 75, (2) = 86, (3) = 55}), (1, 5) = Vector(3, {(1) = 118, (2) = 111, (3) = 154}), (1, 6) = Vector(3, {(1) = 127, (2) = 168, (3) = 157}), (2, 1) = Vector(3, {(1) = 167, (2) = 118, (3) = 54}), (2, 2) = Vector(3, {(1) = 79, (2) = 74, (3) = 145}), (2, 3) = Vector(3, {(1) = 141, (2) = 83, (3) = 80}), (2, 4) = Vector(3, {(1) = 68, (2) = 49, (3) = 82}), (2, 5) = Vector(3, {(1) = 144, (2) = 170, (3) = 74}), (2, 6) = Vector(3, {(1) = 181, (2) = 152, (3) = 60}), (3, 1) = Vector(3, {(1) = 57, (2) = 50, (3) = 120}), (3, 2) = Vector(3, {(1) = 85, (2) = 123, (3) = 69}), (3, 3) = Vector(3, {(1) = 120, (2) = 59, (3) = 46}), (3, 4) = Vector(3, {(1) = 199, (2) = 188, (3) = 66}), (3, 5) = Vector(3, {(1) = 143, (2) = 85, (3) = 127}), (3, 6) = Vector(3, {(1) = 78, (2) = 111, (3) = 148}), (4, 1) = Vector(3, {(1) = 242, (2) = 243, (3) = 240}), (4, 2) = Vector(3, {(1) = 189, (2) = 190, (3) = 191}), (4, 3) = Vector(3, {(1) = 145, (2) = 146, (3) = 146}), (4, 4) = Vector(3, {(1) = 102, (2) = 102, (3) = 102}), (4, 5) = Vector(3, {(1) = 66, (2) = 66, (3) = 68}), (4, 6) = Vector(3, {(1) = 37, (2) = 37, (3) = 38})})NULL

Convert XYZ to sRGB (XYZ D50 or D65 to sRGB D65)
   

NULL

Note: The sRGB values published for ColorChecker assume a black point of 0cd/m^2.

``

CCsRGB_D65in := XYZ_to_sRGB(CCXYZ_D65, D65):

NULL

CCsRGB_D65in = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = 115, (2) = 81, (3) = 67}), (1, 2) = Vector(3, {(1) = 199, (2) = 147, (3) = 129}), (1, 3) = Vector(3, {(1) = 91, (2) = 122, (3) = 156}), (1, 4) = Vector(3, {(1) = 90, (2) = 108, (3) = 64}), (1, 5) = Vector(3, {(1) = 130, (2) = 128, (3) = 176}), (1, 6) = Vector(3, {(1) = 92, (2) = 190, (3) = 172}), (2, 1) = Vector(3, {(1) = 224, (2) = 124, (3) = 47}), (2, 2) = Vector(3, {(1) = 68, (2) = 91, (3) = 170}), (2, 3) = Vector(3, {(1) = 198, (2) = 82, (3) = 97}), (2, 4) = Vector(3, {(1) = 94, (2) = 58, (3) = 106}), (2, 5) = Vector(3, {(1) = 159, (2) = 189, (3) = 63}), (2, 6) = Vector(3, {(1) = 230, (2) = 162, (3) = 39}), (3, 1) = Vector(3, {(1) = 35, (2) = 63, (3) = 147}), (3, 2) = Vector(3, {(1) = 67, (2) = 149, (3) = 74}), (3, 3) = Vector(3, {(1) = 180, (2) = 49, (3) = 57}), (3, 4) = Vector(3, {(1) = 238, (2) = 198, (3) = 20}), (3, 5) = Vector(3, {(1) = 193, (2) = 84, (3) = 151}), (3, 6) = Vector(3, {(1) = 54, (2) = 136, (3) = 170}), (4, 1) = Vector(3, {(1) = 245, (2) = 245, (3) = 243}), (4, 2) = Vector(3, {(1) = 200, (2) = 202, (3) = 202}), (4, 3) = Vector(3, {(1) = 161, (2) = 163, (3) = 163}), (4, 4) = Vector(3, {(1) = 121, (2) = 121, (3) = 122}), (4, 5) = Vector(3, {(1) = 82, (2) = 84, (3) = 86}), (4, 6) = Vector(3, {(1) = 49, (2) = 49, (3) = 51})})NULL

``

CCsRGB_D50in := XYZ_to_sRGB(CCXYZ_D50, D50):

``

CCsRGB_D50in = Matrix(4, 6, {(1, 1) = Vector(3, {(1) = 115, (2) = 81, (3) = 67}), (1, 2) = Vector(3, {(1) = 199, (2) = 148, (3) = 129}), (1, 3) = Vector(3, {(1) = 91, (2) = 123, (3) = 156}), (1, 4) = Vector(3, {(1) = 90, (2) = 108, (3) = 64}), (1, 5) = Vector(3, {(1) = 130, (2) = 129, (3) = 176}), (1, 6) = Vector(3, {(1) = 92, (2) = 190, (3) = 172}), (2, 1) = Vector(3, {(1) = 224, (2) = 125, (3) = 47}), (2, 2) = Vector(3, {(1) = 68, (2) = 92, (3) = 170}), (2, 3) = Vector(3, {(1) = 198, (2) = 83, (3) = 97}), (2, 4) = Vector(3, {(1) = 94, (2) = 59, (3) = 106}), (2, 5) = Vector(3, {(1) = 159, (2) = 190, (3) = 63}), (2, 6) = Vector(3, {(1) = 230, (2) = 163, (3) = 39}), (3, 1) = Vector(3, {(1) = 35, (2) = 64, (3) = 147}), (3, 2) = Vector(3, {(1) = 67, (2) = 149, (3) = 74}), (3, 3) = Vector(3, {(1) = 180, (2) = 51, (3) = 57}), (3, 4) = Vector(3, {(1) = 238, (2) = 199, (3) = 20}), (3, 5) = Vector(3, {(1) = 193, (2) = 85, (3) = 151}), (3, 6) = Vector(3, {(1) = 54, (2) = 137, (3) = 170}), (4, 1) = Vector(3, {(1) = 245, (2) = 246, (3) = 243}), (4, 2) = Vector(3, {(1) = 200, (2) = 203, (3) = 202}), (4, 3) = Vector(3, {(1) = 161, (2) = 164, (3) = 163}), (4, 4) = Vector(3, {(1) = 121, (2) = 122, (3) = 122}), (4, 5) = Vector(3, {(1) = 82, (2) = 84, (3) = 86}), (4, 6) = Vector(3, {(1) = 49, (2) = 50, (3) = 51})})``

NULL

``

NULL

NULL

``

 

 

 

 

 

 

 

 

``

 

Corrections to the original version of theis document;
• Make the scaling for a nonzero black point the same for all RGB color spaces.
• Clip negative RGB values to zero.
• Remove the redundant Array container from matrix multiplications.
Use map in place of the $ to apply a function to each element of an Array.

Pixel_Conversion_B.mw

 

Interactive Embedded Components in Physics

by: Lenin Araujo Castillo 1790
August 06 2014
2  0

The Interactive Embedded Components in Physics are of great importance today and will be even more in the future. Hereand leave a small tutorial of Embedded Components in Physics applied to physics. I hope that somehow you motives to continue the development of science.

 

  Interactive_Embedded_Components_in_Physics.mw      (in spanish)                 

 Ponencia_CRF.pdf

Atte.

Lenin Araujo Castillo

Physics Pure

Computer Science

 

Stem and Leaf Plot

by: Daniel Skoog 1771 Maple
July 04 2014
2  0

Following @acer 's challenge to create some more examples for the Rosetta Code project, I've put together some code that constructs Stem-And-Leaf plots here.

I've also attached a new mathapp ( StemAndLeafDisplay.mw ) that contains the code as well as an interactive example for Stem-Plots. This MathApp is also viewable online on the MapleCloud here.

This older post may also be of interest for anyone looking to make a stem and leaf plot with decimals.

DEs and Mathematical Functions Updates 2014 (Jan - Jun...

by: ecterrab 14605
physics differential-equations
June 23 2014
3  13

Hi,
The FunctionAdvisor project is currently developing at full speed. During the last two months, a significant amount of new conversion routines and mathematical information for Jacobi elliptic and Jacobi Theta functions, on identities, periodicity, transformations, etc. got added to the conversion network for mathematical functions and to the FunctionAdvisor. The previous months was the turn of the set of complex components, added to the network. Developments regarding the simplification and integration of special functions (e.g SphericalY for computing spherical harmonics or Dirac), as well as fixes to the numerical evaluation of JacobiAM, `assuming` and to differential equation subroutines are also part of the update.

These developments are available to everybody as usual in the Maplesoft R&D Differential Equations and Mathematical Functions webpage. Below there is a list of the latest developments as seen in the worksheet that comes in the zip with the DEsAndMathematicalFunctions update.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Power Group Enumeration (update).

by: Marko Riedel 390
June 19 2014
4  0

Greetings to all.

As some of you may remember I have posted several announcements concerning Power Group Enumeration and the Polya Enumeration Theorem this past year, e.g. at this MaplePrimes link: Power Group Enumeration.

I have continued to work in this field and for those of you who have followed the earlier threads I would like to present some links to my more recent work using the Burnside lemma. Of course all of these are programmed in Maple and include the Maple code and it is with the demonstration of Maple's group theory capabilities in mind that I present them to you (math.stackexchange links).

The third and fourth to last link in particular include advanced Maple code.

The second entry is new as of October 30 2015.

With my best wishes for happy group theory computing with Maple,

Regards,

Marko Riedel

Physics updates 2014 (Jan-Jun)

by: ecterrab 14605
June 19 2014
7  0

Hi,
An interesting sequence of enhancements and new developments happened in the Physics package during this first half of the year. During the last month, improvements happened in the handling of Vectorial expressions and quantum mechanics using Dirac’s notation. During April and part of May it was the turn of general relativity enhancements.

Some of the developments are also interesting beyond Physics. For example: it is now possible to multiply equations. Suppose you have A = B   (1), and C = D   (2), multiplying as in (1) (2) now results in lhs((1)) lhs((2)) = rhs((1)) rhs((2)), saving a lot of typing. You can also perform (1)/(2) or (1)^2. Some enhancements in Physics related simplification, integration, `assuming`, and typesetting - e.g. the simplification and integration of spherical harmonics (SphericalY function) are also part of the update.

These developments are available to everybody as usual in the Maplesoft R&D Physics webpage. Below there is a list of the developments for the last month as seen in the worksheet that comes in the zip with the Physics update.

 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Maple implementation of "24" game

by: Kitonum 21530 Maple 12
June 16 2014
4  1

I learned about this problem from Aser's post   See  page of tasks still without  Maple implementation. 

The procedure  game24  solves the problem. In the procedure Acer's  procedure  MyHandler is  used, which prevents the program to stop in case of 0 in the denominator.

 

game24:=proc(a,b,c,d)

local MyHandler,It, K, M, i, P;

uses StringTools, combinat;

 MyHandler := proc(operator,operands,default_value)

      NumericStatus( division_by_zero = false );

      return infinity;

   end proc;

   NumericEventHandler(division_by_zero=MyHandler); 

It:=proc(L1,L2)

local i, j, L;

L:=[];

for i in L1 do

for j in L2 do

L:=[op(L), op([Substitute(Substitute("( i + j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i - j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i * j )","i",convert(i,string)),"j",convert(j,string)),Substitute(Substitute("( i / j )","i",convert(i,string)),"j",convert(j,string))])];

od; od;

L;

end proc; 

P:=permute([a,b,c,d]); 

K:=[];

for i in P do

K:=[op(K),op(It(It(It([i[1]],[i[2]]),[i[3]]),[i[4]])), op(It(It([i[1]],It([i[2]],[i[3]])),[i[4]])), op(It([i[1]],It(It([i[2]],[i[3]]),[i[4]]))), op(It([i[1]],It([i[2]],It([i[3]],[i[4]])))), op(It(It([i[1]],[i[2]]),It([i[3]],[i[4]])))];

od;

M:=[];

for i in K do

if parse(i)=24 then M:=[op(M), i] fi;

od;

if nops(M)=0 then return `No solutions` else

for i in M do

print(SubString(i,2..length(i)-1));

od; fi; 

end proc:

 

Two examples:

game24(2,3,8,9);

 

game24(2,3,3,4);

        No solutions

 

24.mws

 

 

10-bar linkage spherical mechanism. Animation.

by: one man 1355
animation
June 15 2014
2  4

http://vk.com/doc242471809_295040421

The new method and approach to the calculation of the geometry and kinematics linkages. It is based on the Draghilev method for solving systems of nonlinear equations.

( 10-bar linkage spherical mechanism animation. Program text for professionals only.)

MECHAN123_SPHERE_10.mw

 

convert help of older maple version to 18

by: hacker9130368 65
convert
June 13 2014
4  3

you can change help of older maple version to 18 by this command:

HelpTools:-Database:-ConvertAll():

for example if you download DirectSearch optimization package it's help don't open in maple 18 because in maple 18 .hdb converted to .help and you can do this convert by HelpTools:-Database:-ConvertAll():

DirectSearch version 2 created for maple 13 and i converted it's help to 18.

after i typed this command maple 18 wrote: 

"Converting G:\\Program Files\\Maple 18\\lib\\DirectSearch.hdb to G:\\Program Files\\Maple 18\\lib\\DirectSearch.help"
Warning, .hdb help databases are deprecated, 'G:\Program Files\Maple 18\lib\DirectSearch.hdb' will not be used, see ?HelpTools,Migrate help page for more information.

and when try again it worked properly and DirectSearch help opened.

Maple WWW Net

by: SandraShklyaeva 185
worksheet
June 03 2014
5  7

Maple WWW Net - Maple WWW integration with MapleNet

DigiArea Team is proud to present Maple WWW Net. 

Maple WWW Net is a part of Maple WWW technology that brings integration with MapleNet. Now you can access the power of Maple core directly from your worksheets in the internet. Maple WWW Net allows you to develop Maple worksheets enriched by live computations and interactive controls.

You can read more about the technology here:
http://digi-area.com/light/MapleWWW/

 

 

Useful and interesting link

by: Markiyan Hirnyk 7819 Maple
package
May 30 2014
1  4

Take a look at this link.

Clickable Calculus Study Guide

by: eithne 2072 Maple
May 14 2014
5  0

We have just released an all-new, second edition of the Calculus Study Guide.

This guide has been completely rewritten and greatly expanded and to take full advantage of Maple’s Clickable Math approach.  It covers all of Calculus I and Calculus II and has over 450 worked examples, the vast majority of which are solved using interactive, Clickable Math techniques. 

Not only is this guide useful for students learning calculus, but it can also serve as a guide for instructors interested in pursuing a syntax-free approach to using Maple in their teaching.

See Clickable Calculus Study Guide for more information.  For even more information, you could also attend a live webinar about the new study guide next Wednesday.

 

eithne

May Live Webinars

by: kkoserski 230 Maple , MapleSim , MapleSim Control Design Toolbox
May 09 2014
0  0

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on some upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

 

Hollywood Math (with more new examples!)

Over its storied and intriguing history, Hollywood has entertained us with many mathematical moments in film. John Nash in “A Beautiful Mind,” the brilliant janitor in “Good Will Hunting,” the number theory genius in “Pi,” and even Abbott and Costello are just a few of the Hollywood “mathematicians” that come to mind.

Although the widespread presentation of mathematics on the silver screen is not always entirely accurate, it does serve as a great introduction to the study of mathematics in general. During this webinar Maplesoft will present a number of examples of mathematics in film. See relevant, exciting examples that you can use to engage your students.At the end of the webinar you’ll be given an opportunity to download an application containing all of the Hollywood examples that we demonstrate.

To join us for the live presentation, please click here to register.

 

Applications of Symbolic Computation in Control Design

You may already use Maple and/or MapleSim within your organization to solve various problems, but did you know that they have capabilities for control design as well? In one of our upcoming featured webinars for this month, we will explore the Control Design toolbox including the ability to extract symbolic equations of plant models, perform symbolic linearization, design symbolic controllers, and generate very fast code for HIL testing.

The following examples will be demonstrated:

• PID Control

• LQR, Kalman filter design

• Gain scheduling

• Feedback linearization

To join us for the live presentation, please click here to register.

DEs and Mathematical Functions Updates

by: ecterrab 14605
differential-equations
May 06 2014
2  0

This is the first presentation of updates for the DE and Mathematical Functions programs of Maple 18. It includes several improvements, all in the Mathematical Functions sector, as well as some fixes. The update and instructions for its installation are available on the Maplesoft R&D webpage for DEs and mathematical functions. Some of the items below were mentioned here in Mapleprimes - you are welcome to present suggestions or issues; if possible they will be addressed right away in the next update.

  • Filling gaps in the FunctionAdvisor regarding all the 6 complex components: abs, argument, conjugate, Im, Re, signum, as well as regarding Heaviside (step function), Dirac, min and max.
  • Fix the simplification and differentation rule for doublefactorial
  • Make convert(..., hypergeometric) work the same way as convert(blabla, hypergeom)
  • Implement integral forms for Heaviside(z) and JacobiAM(z, k) via convert(..., Int)
  • Implement appropriate display for the inert %intat function as well as its conversion to the inert Int
  • Make the FunctionAdvisor/DE return not just the PDE system satisfied by f(z, k) = JacobiAM(z, k)and also (new) the ODE satisfied by f(z) = JacobiAM(z, k)
  • Fix conversion rule from Heaviside(z) to Sum
  • Fix unexpected error interruption when differentiating min(...) and max(...) containing more than three arguments
  • Fix issue in simplify/conjugate
  • Improvement in expand/int: factors in disguise are put outside the integration sign
  • Various improvements in the case of multiple integrals involving the Dirac function
  • Make Intat fully inert (before it was evaluating its arguments)
  • Make value of inert indexed objects work

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Maple WWW - Maple Worksheets in the World Wide...

by: SandraShklyaeva 185
May 03 2014
7  19

Maple WWW - Maple Worksheets in the World Wide Web

DigiArea Team is proud to present new modern web technology for Maple Worksheets - Maple WWW. 

Maple WWW is a technology that brings Maple Worksheets to the World Wide Web. The technology provides a web application to view and share interactive scientific documents across the web. Maple WWW allows to open Maple worksheets in your browser without any additional plugins or extensions.

You can read more about the technology here:
http://digi-area.com/light/MapleWWW/

You can see the technology in action right here using the following embedded Maple Worksheet!

 

 

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