3ur Colors are enchanting and elusive. A multitude of color systems has been proposed over a three-digits number of years - maybe more than the number of purposes that they serve... - Everyone knows the additive RGB color system – we usually serve light-emitting IT components like monitors with colors in that system. Here, we use c = (r, g, b) RGB with r, g, bЄ [0,1] to describe a color c. = T For printing, however, we usually use the subtractive CMY color system. The same color c becomes c = (c, m, y) CMY (1-c, 1-m, 1-y) RGB Note how we use subscripts to indicate with coordinate system the coordinates correspond to. Explain, why it is not possible to find a linear transformation between RGB and CMY coordinates. Farbenlehr c von Goethe Erster Band. Roſt einen Defte mit fergen up Tübingen, is et 3. Cotta'fden Babarblung. ISIO Homogeneous coordinates give us a work-around: If we specify colors in 4D, instead, with the 4th coordinate being the homogeneous coordinate h so that every actual color has h=1, then matrices TRGB→CMY and TCMY→RGB can be found, so that (c, m, y, 1) TMY TRGB⇒CMY · (r, g, b, 1) AGB and vice versa. and TCMY→RGB = Find TRGB-CMY and show that they work correctly by transforming at least one color from a known RGB representation into CMY and then back, again. Many printers have a separate supply of black and colors are provided in CMYK form c = (c, m, y, k) CMYK Provide the matrix TCMYK→CMY that converts colors from CMYK to CMY according to (c, m, y) CMY = TCMYK →CMY (c, m, y, k) TCMYK . Obviously, the more interesting (and relevant) question is how to convert from CMY to CMYK. Explain in which way this is insufficiently defined (without the usual assumption). For the particular example color of c₁ = ½-½ (3, 1, 2) CMY (shown on the right) provide at least two possible CMYK representations. Which one is usually used? Why? = A certain individual with initials D.T. has a printer, which has a separate supply of gold (instead of black) and colors are accordingly provided in CMKG format: c = (c, m, y, Y) CMYG and the separately supplied gold color has the following specification: Y (34, 28, 13) RGB For the above specified example color c₁ provide its CMYG representation that is using as much of gold as possible. Explain your calculation. 51

3ur Colors are enchanting and elusive. A multitude of color systems has been proposed over a three-digits number of years - maybe more than the number of purposes that they serve... - Everyone knows the additive RGB color system – we usually serve light-emitting IT components like monitors with colors in that system. Here, we use c = (r, g, b) RGB with r, g, bЄ [0,1] to describe a color c. = T For printing, however, we usually use the subtractive CMY color system. The same color c becomes c = (c, m, y) CMY (1-c, 1-m, 1-y) RGB Note how we use subscripts to indicate with coordinate system the coordinates correspond to. Explain, why it is not possible to find a linear transformation between RGB and CMY coordinates. Farbenlehr c von Goethe Erster Band. Roſt einen Defte mit fergen up Tübingen, is et 3. Cotta'fden Babarblung. ISIO Homogeneous coordinates give us a work-around: If we specify colors in 4D, instead, with the 4th coordinate being the homogeneous coordinate h so that every actual color has h=1, then matrices TRGB→CMY and TCMY→RGB can be found, so that (c, m, y, 1) TMY TRGB⇒CMY · (r, g, b, 1) AGB and vice versa. and TCMY→RGB = Find TRGB-CMY and show that they work correctly by transforming at least one color from a known RGB representation into CMY and then back, again. Many printers have a separate supply of black and colors are provided in CMYK form c = (c, m, y, k) CMYK Provide the matrix TCMYK→CMY that converts colors from CMYK to CMY according to (c, m, y) CMY = TCMYK →CMY (c, m, y, k) TCMYK . Obviously, the more interesting (and relevant) question is how to convert from CMY to CMYK. Explain in which way this is insufficiently defined (without the usual assumption). For the particular example color of c₁ = ½-½ (3, 1, 2) CMY (shown on the right) provide at least two possible CMYK representations. Which one is usually used? Why? = A certain individual with initials D.T. has a printer, which has a separate supply of gold (instead of black) and colors are accordingly provided in CMKG format: c = (c, m, y, Y) CMYG and the separately supplied gold color has the following specification: Y (34, 28, 13) RGB For the above specified example color c₁ provide its CMYG representation that is using as much of gold as possible. Explain your calculation. 51

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.2: Points, Lines, And Their Graphs

Problem 5WE

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