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"Fake real" color mixing from RGB values, just something to play with (new revision updated).
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| import math | |
| import matplotlib.pyplot as plot | |
| EPS = 1e-24 | |
| red = (2.0,0.0,0.0) | |
| green = (0.0,2.0,0.0) | |
| blue = (0.0,0.0,2.0) | |
| yellow = (1.0,1.0,0.0) | |
| cyan = (0.0,1.0,1.0) | |
| magenta = (1.0,0.0,1.0) | |
| wl = {"red": 700.0, "orange": 600.0, "yellow": 580.0, "green": 550.0, "cyan": 500.0, "blue": 450.0, "violet": 400.0} | |
| wlr = wl["red"] | |
| wlg = wl["green"] | |
| wlb = wl["blue"] | |
| wly = wl["yellow"] | |
| wlo = wl["orange"] | |
| wlv = wl["violet"] | |
| def interpolate(x,y,f): | |
| t = type(x) | |
| if t in {tuple,list}: | |
| return t(g*(1.-f)+f*h for g,h in zip(x,y)) | |
| else: | |
| return x*(1.-f)+f*y | |
| def wavelength_to_rgb(l, gray=0.0, lum=None): | |
| if l > wlr or l < 0.0: | |
| l = l % wlr | |
| if l <= wlr: | |
| res = None | |
| if l > wlg: | |
| f = (l - wlg)/(wlr - wlg) | |
| res = interpolate(green,red,f) | |
| elif l > wlb: | |
| f = (l - wlb)/(wlg - wlb) | |
| res = interpolate(blue,green,f) | |
| else: | |
| f = l/wlb | |
| res = interpolate(red,blue,f) | |
| if lum is None: | |
| res = add_gray(res, gray) | |
| else: | |
| s = (lum - 3*gray)/sum(res) | |
| res = add_gray(scale(res, s), gray) | |
| return res | |
| raise ValueError | |
| def rgb_to_wavelength(x): | |
| mn = min(x) | |
| lum = sum(x) | |
| i = min(range(len(x)),key=lambda i: x[i]) | |
| x = sub_gray(x, mn) | |
| if i == 0: | |
| if x[1] == 0: | |
| return wlb, mn, lum | |
| elif x[2] == 0: | |
| return wlg, mn, lum | |
| l = 0.5 * (wlb + wlg) | |
| d = 0.5 * (wlg - wlb) | |
| if i == 1: | |
| if x[2] == 0: | |
| return wlr, mn, lum | |
| if x[0] == 0: | |
| return wlb, mn, lum | |
| l = 0.5 * wlb | |
| d = 0.25 * wlb | |
| if i == 2: | |
| if x[0] == 0: | |
| return wlg, mn, lum | |
| if x[1] == 0: | |
| return wlr, mn, lum | |
| l = 0.5 * (wlr + wlg) | |
| d = 0.5 * (wlr - wlg) | |
| while d > EPS: | |
| y = wavelength_to_rgb(l + d, mn, lum) | |
| err = math.sqrt(sum((e-f)**2 for e,f in zip(x,y))) | |
| yl = wavelength_to_rgb(l - d, mn, lum) | |
| lerr = math.sqrt(sum((e-f)**2 for e,f in zip(x,yl))) | |
| if lerr > err: | |
| l += d | |
| elif err > lerr: | |
| l -= d | |
| d *= 0.5 | |
| return l, mn, lum | |
| def inverse(x, unit = 1.0): | |
| t = type(x) | |
| return t(unit - e for e in x) | |
| def sub_gray(x, l = 0.5): | |
| t = type(x) | |
| return t(e - l for e in x) | |
| def add_gray(x, l = 0.5): | |
| t = type(x) | |
| return t(e + l for e in x) | |
| def add(x,y): | |
| t = type(x) | |
| return t(e+f for e,f in zip(x,y)) | |
| def sub(x,y): | |
| t = type(x) | |
| return t(e-f for e,f in zip(x,y)) | |
| def prod(xs): | |
| if not xs: | |
| raise ValueError | |
| r = None | |
| for x in xs: | |
| if r is None: | |
| r = x | |
| else: | |
| r *= x | |
| return r | |
| def spectra(ls, n=800, width=100.0): | |
| xs = list(range(n)) | |
| xs = [e/(n-1) for e in xs] | |
| delta = wlr - wlv | |
| assert(delta == 300.0) | |
| spect = [] | |
| for l in ls: | |
| lw = None | |
| if l >= wlv: | |
| lw = tuple(math.pow(2.0*math.pi, -(((delta*e+wlv - l)/(width))**8)) for e in xs) | |
| else: | |
| lw = tuple(1.0 - math.pow(2.0*math.pi, -(((delta*e-wlv + l)/(width))**8)) for e in xs) | |
| spect.append(lw) | |
| return spect, [delta*x+wlv for x in xs] | |
| def absorb(spect, ws, light): | |
| n = len(spect) | |
| assert(len(ws) == n) | |
| res = list(light) | |
| for s,w in zip(spect,ws): | |
| res = multiply(res, inverse(scale(s, w), unit=1.0)) | |
| return res | |
| def non_negative(x): | |
| t = type(x) | |
| return t(max(0.0, e) for e in x) | |
| def scale(x, f): | |
| t = type(x) | |
| return t(f*e for e in x) | |
| def multiply(x,y): | |
| t = type(x) | |
| return t(e*f for e,f in zip(x,y)) | |
| def trap_integral_tuple(xs, ys): | |
| n = len(xs) | |
| result = [0.0,] * len(ys[0]) | |
| previous_y = None | |
| previous_x = None | |
| for x,y in zip(xs,ys): | |
| if previous_x is not None: | |
| result = add(result, tuple(0.5*(e+f)*(x-previous_x)/n for e,f in zip(previous_y, y))) | |
| previous_x = x | |
| previous_y = y | |
| return tuple(result) | |
| def reflected_to_rgb(reflected, xs): | |
| xs, reflected = list(range(len(xs))), list(scale(wavelength_to_rgb(x), r) for x,r in zip(xs,reflected)) | |
| return trap_integral_tuple(xs, reflected) | |
| def complementary_wavelengths(x): | |
| [s],l = spectra([x], n=N) | |
| s = inverse(s, unit=1.0) | |
| i = min(range(len(s)),key=lambda i: s[i]) | |
| u = rgb_to_wavelength(reflected_to_rgb(s[:i], l[:i]))[0] | |
| v = rgb_to_wavelength(reflected_to_rgb(s[i:], l[i:]))[0] | |
| w = u,v | |
| return w | |
| N = 800 | |
| white = [1.0 for _ in range(N)] | |
| spect, xs = spectra([580.0, 700.0], n=N) | |
| reflected0 = absorb(spect[0:1], [1.0], white) | |
| reflected1 = absorb(spect[1:2], [1.0], white) | |
| reflected = absorb(spect, [0.75, 0.75], white) | |
| inv = inverse(non_negative(reflected_to_rgb(reflected, xs))) | |
| wavel,gray,lum = rgb_to_wavelength(inv) | |
| rwavel,rgray,rlum = rgb_to_wavelength(reflected_to_rgb(reflected, xs)) | |
| reflected2 = absorb(spectra([580.0, 700.0, wavel], n=N)[0], [0.333333, 0.333333, 0.333333], white) | |
| reflected3 = absorb(spectra([300.0], n=N)[0], [1.0], white) | |
| reflected3 = non_negative(reflected3) | |
| reflected2 = non_negative(reflected2) | |
| reflected1 = non_negative(reflected1) | |
| reflected0 = non_negative(reflected0) | |
| reflected = non_negative(reflected) | |
| left = plot.Rectangle((0,0),0.2,1,fc=reflected_to_rgb(reflected0, xs)) | |
| center = plot.Rectangle((0.2,0),0.2,1,fc=reflected_to_rgb(reflected, xs)) | |
| center1 = plot.Rectangle((0.4,0),0.2,1,fc=reflected_to_rgb(reflected2, xs)) | |
| center2 = plot.Rectangle((0.6,0),0.2,1,fc=inv) | |
| right = plot.Rectangle((0.8,0),0.2,1,fc=reflected_to_rgb(reflected1, xs)) | |
| figure = plot.figure(figsize=(16,8)) | |
| subfigures = figure.subfigures(1,2) | |
| subfigures[0].gca().add_patch(left) | |
| subfigures[0].gca().add_patch(center) | |
| subfigures[0].gca().add_patch(center1) | |
| subfigures[0].gca().add_patch(center2) | |
| subfigures[0].gca().add_patch(right) | |
| subplot = subfigures[1].subplots(1,1) | |
| subplot.plot(xs, reflected) | |
| subplot.plot(xs, reflected2) | |
| subplot.plot(xs, reflected3) | |
| plot.show() | |
| c = non_negative(inverse(multiply(scale(yellow,1.0),scale(red,1.0)),unit=1.0)) | |
| print(c) | |
| l,g,_ = rgb_to_wavelength(c) | |
| print(l,g) | |
| r,x = spectra([wly,wlr], n=N) | |
| sy,sr = scale(r[0], 1.0), scale(r[1], 2.0) | |
| syr = non_negative(inverse(multiply(sy, sr), unit=1.0)) | |
| yr = reflected_to_rgb(syr, x) | |
| l,g,_ = rgb_to_wavelength(yr) | |
| myr = min(yr) | |
| myr = sub_gray(yr, myr) | |
| myr = scale(myr, 1.0/max(myr)) | |
| print(l,g) | |
| print(yr, myr) | |
| one = plot.Rectangle((0,0),0.2,1,fc=scale(yellow, 0.5)) | |
| two = plot.Rectangle((0.2,0),0.2,1,fc=scale(red, 0.5)) | |
| three = plot.Rectangle((0.4,0),0.2,1,fc=yr) | |
| four = plot.Rectangle((0.6,0),0.2,1,fc=myr) | |
| five = plot.Rectangle((0.8,0),0.2,1,fc=c) | |
| figure = plot.figure(figsize=(16,8)) | |
| subfigures = figure.subfigures(1,2) | |
| subfigures[0].gca().add_patch(one) | |
| subfigures[0].gca().add_patch(two) | |
| subfigures[0].gca().add_patch(three) | |
| subfigures[0].gca().add_patch(four) | |
| subfigures[0].gca().add_patch(five) | |
| subplot = subfigures[1].subplots(1,1) | |
| subplot.plot(x, r[0], color=scale(yellow, 0.5)) | |
| subplot.plot(x, r[1], color=scale(red, 0.5)) | |
| subplot.plot(x, syr, color=yr) | |
| plot.show() | |
| print(l) | |
| print(l, complementary_wavelengths(l)) | |
| print(580.0, complementary_wavelengths(580.0)) | |
| w = complementary_wavelengths(580.0) | |
| s,l = spectra((580.,) + w, n=N) | |
| print(reflected_to_rgb(absorb(s, (1.0,1.0,1.0), white), l)) | |
| print(wavelength_to_rgb(rgb_to_wavelength(red)[0])) | |
| print(wavelength_to_rgb(rgb_to_wavelength(yellow)[0])) | |
| print(wavelength_to_rgb(rgb_to_wavelength(blue)[0])) | |
| print(wavelength_to_rgb(rgb_to_wavelength(cyan)[0])) | |
| print(wavelength_to_rgb(rgb_to_wavelength(magenta)[0])) | |
| c,g,l = rgb_to_wavelength((0.25, 0.5, 0.75)) | |
| d = wavelength_to_rgb(c,g,l) | |
| print(c,g,l) | |
| print(c,d,0.75/0.5,d[2]/d[1]) | |
| f,h,l = rgb_to_wavelength(d) | |
| print(c,f,h,l) |
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