Color Mixing Tools: drop2color
Please, visit the Color Mixing Tools page for download, web version and mobile version information.
This program converts the paint mixture into chromatic coordinates, shows the resulting color on the monitor and also places it in a 3D Munsell Space. Moreover, this system allows experimenting with the effects of various lighting conditions on the paint. In other words, if a particular color mixture is created and painted on a test strip, then placed close to the monitor with the defined lighting condition, the colors on the (calibrated) monitor and those on the paper strip will match and give the same color experience. This system also generates color trajectories between paint mixtures. In addition, various other interesting aspects such as the positioning and orientation of the color wheel, and the color space of both the ideal RGB monitor and the brand of the chosen colors can be visualized.
This program is written as a MATLAB script and for its execution it is necessary to have installed "MATLAB Component Runtime library (MCR)". This is the main interface window of the program version 3.4:
In Area 1 we define the paint recipe to be analyzed. Area 2 shows the color resulting from the recipe, while Area 3 shows the spectra. The position of the mixed color and other relationships can also be visualized in Munsell space 3D in Area 5. Up to 4 spectra may be defined in Area 6 and visualized in Area 3 in order to have additional information on the interaction of the reflectance spectra.
The "About" button (10) provides system information with links to websites of interest and MATLAB licensing information (some parts of the document also apply to systems used through the MCR libraries, like the Color Mixing Tools).
In the version number of the "Color Mixing Tools", the number after the first dot refers to the number of color brands coded in color2drop and drop2color, while the number after the second dot indicates the number of databases defined in rs2color.
By clicking "Exit" (11) or closing the window, several settings get saved such as lighting, selected color brand, etc. In case of unrecoverable errors due to operating system malfunction (with Windows you never know), first the application needs to be closed and then the "drop2color.ini" file canceled from the directory where the program is located: the original configuration will be restored the next time the program starts.
Clicking the "web" (12) button opens the drop2color web page.
Once the color brand is chosen (1), up to 6 color bases may be defined (2). Each color base needs to be selected from the available colors found in the drop-down menu (3) together with the quantity of drops/parts. The quantity can be entered in box (4) or defined by using the cursor (5). A click on the left/right arrow (6) reduces/increases the color drops. The cursor (7) can be moved using the mouse. Moreover, if the cursor is to the far right, a click of the mouse multiplies the increase by ten and moves the cursor to the left in order to further increase the paint quantity.
Since color perception also depends on the lighting of a painting, the illumination spectrum needs to be defined from the list (1). There are 19 preset illumination spectra available:
A: This lighting has a low color temperature and corresponds to indoor light, as for example a regular 100W bulb or a halogen one. This spectrum emphasizes the reds and yellows while depresses the blues, creating a "warm" light and reducing strongly the mixable colors (see the example on the drop2color page).
B: This light is similar to D50, corresponding to outdoor daylight.
C: This light is similar to D65, corresponding to cool outdoor daylight, and is the reference for the Munsell space: so, lacking particular requirements this is the light to choose when mixing paint.
D50, D65, D75: These are lights with color temperatures that go from 5000K to 7500K and correspond to outdoor daylight. Calibrated monitors have the White Point set to 6500K (close to D65), while D50 is the industrial light reference for printed images. These are reasonably "white" lights, in the sense that they do not accentuate any spectrum region significantly. Nevertheless, D65 and, especially D75 lightly reinforce the blues creating "cool" light.
F1 to F12: These are fluorescent lights with significant spikes in the spectrum and they may create some strange color aberration effects, similar to what we experience when looking at the color of cars in underground parking lots. F10 is the spectrum of many energy saver lamps (Energetic FE 20 20W E27, or Osram Deluxstar 21W/860 Daylight) used as painting light because they are reasonably white and do not heat the environment significantly. If one uses this type of lighting, it is recommended to choose F10 as spectrum to mix the paint.
In color swatch (2), the color provided by the recipe appears with the lighting defined by the first spectrum (1). In zone (3), the RGB and Lab coordinates of this color are shown.
It is also possible to define a second illumination spectrum (4). The corresponding color is shown in the lower box (5). If the color cannot be visualized on an ideal monitor (i.e. it is outside of the RGB color space) the "no Gamut" (6) message will appear. The RGB and Lab coordinates of this color will be written in zone (7). The color inconstancy index (C.I.I.) between the two lightings is shown in (8). The C.I.I. is the DE*94 error between the Lab values of zone (3) and zone (7).
"Light Strength" (9) refers to lighting intensity. 100% means that the illumination spectrum has an ideal intensity, while it can be lowered to take into account potential dim light. The percentage values are modified to the non linear response of the human eye: for example, a perfect white color with Munsell value 10, with "Light Strength" 50% will be perceived as value 5. If there are no particular reasons to reduce light strength, it is recommended to use value 100%.
The spectra are shown as values from 0 to 1 in increments of 0.25 (1). The frequency coordinates (2) go from 380nm to 730nm in increments of 10nm. The color spectra (3) were drawn point by point to show the perceived color with a spectrum zero everywhere, except at one specific coordinate point. The color intensity decreases below 420nm and above 670nm because our eyes are less sensitive in these areas of the spectrum.
The spectrum of the mixed color is shown by a thick continuous line (4) with the color perceived with lighting "C". The thinner continuous spectra are the ones with 4 spectra definable in Area 6. The standard observer spectra are colored and dotted (x=red, y=green, z=blue), while the lighting spectra are white and drawn with a dashed line.
This area shows the Munsell space (1) defined for lighting "C". (2) shows the Munsell coordinate for the recipe with thick continuous line in Area 3 (or "???" if the color is too far from the color space visible to the human eye). The Munsell space is shown in three dimensions, but starting from a view from top (the Hue-Chroma plane) where one can see the circles (3) with constant Chroma. The distance between adjacent circles is 2 Chroma. The radial lines refer to constant Hue and the name (4) of each principal sector is shown on the larger outer perimeter. The placement of the hue name is next to number 5 of each hue, following the definition of the main sectors of the Munsell space:
The point in the space defined by the coordinates (2) is shown by a sphere (5) colored with the corresponding true RGB value. The position of the sphere is shown on the Hue-Chroma plane while the Value is shown on the line (6), on the grid scale (7) that covers all 10 values of the Munsell space.
For each color brand all the mixable Munsell chips are precalculated (from a total of about 2700 of the Munsell Renotation Data). These chips are shown (8) with the correct RGB color. This way one can see the space of the mixable colors at a glance. It is possible to choose (9) to see the chips in 10, 20 or 40 sectors, but if none of the boxes is selected, the chips are not shown. If box 10 is selected, the chips will be lined up with each principal hue sector (of number 5: these are the 10 most important sectors that give the color a name). With the selection of box 20, there is also the number 10 (or 0, from the moment that 0 and 10 overlap), while with 40, the ones with 2.5 and 7.5 are also added which complete the available data.
The visualization of the three dimensional Munsell space is shown by a virtual camera. The camera is pointed to the center of the neutral axis (V=5) while the same camera is placed at a certain distance to show the whole space. The camera can orbit horizontally (13-14) and vertically (11) around the Munsell space. The camera can also zoom in (12) by a radial motion. Each of these settings can be activated by keying in a number that represents the angle (13) or using the cursor (14). Moreover, it is possible to face the main planes, like the red-blue/green with the"R-BG" button (15), the yellow-blue/viola with "Y-PB" (16) etc. The "HuCh" (20) button shows the hue/chroma plane from top. Sometimes it is useful to swing around the space to better perceive the position of the colors or the trajectories. This movement can be done by checking box (21). By clicking "Persp" (22), the space is seen in perspective or with orthographic projection (this is the default because this way, from above, the chips are aligned).
Choosing a set of paint in Area 1, the space of mixable colors with these bases is calculated (only if box 10 or 20 is selected). The non mixable color chips become transparent. This can answer questions such as whether to use black paint or not, or, if I can mix all the colors from the primary color bases etc., as it is described in the Application Examples section.
You may choose to expand the Munsell space from the mixable colors of a selected brand to the entire color space of the human eye with the "EyeG" (Eye Gamut) button (24).
In order to see better the relationship between the mixed colors and the color space, you can visualize only one plane crossing the point where the camera is pointing by using the "Slice" button (25) that cuts a slice of the space. This way it is possible to see the classic plane with the Munsell chip that will be completely filled when observing the principal sectors or the planes where the chips are shown. The color of each chip is calculated directly from the Munsell Renotation Data coordinates. If the camera is above or below the plane HC (angle with a vertical range of -90 or + 90), the cursor (26) gets activated to move the target of the camera. The neutral axis value of where the camera is pointing is indicated in (27). Changing the value from 1 to 9, you can see the set of mixable colors in sequence with varying values. It can be noticed that colors with low or very high lightness exist only with reduced chroma.
In order to see better the mixable colors there is the "Pnt S" (28) button, Paint Surface, that enables you to see the contour of the mixable colors as a surface. The "rgb S", RGB Surface button (29), on the other hand shows the set of visible colors on an ideal monitor with the white point at 6500K. These surfaces are shown in opaque/semitransparent colors, by selecting/deselecting box "sld" (30), solid, individually or just as gray surface by selecting "gry" (31), gray, for better view in certain cases. Selecting the box "inters" (32), intersection, with "rgb S" (29) deselected, black points are added when the chips do not belong to the color gamut of the monitor. In other words, they are the chips that are outside the color solid defined by all the RGB colors. The box "union" (33), however, adds gray chips to the ones of the color space of the chosen brand to complete also the RGB color space. This way one knows which colors are visible on the monitor, but cannot be mixed, or which colors can be mixed, but not correctly seen on the monitor.
If in Area 6 at least two colors are selected, the buttons of the trajectories are activated "T…" (34) in order to be able to draw them. Each trajectory is white with a starting/ending sphere of the starting/ending color corresponding to the group it belongs to. This is extremely useful in seeing how a color changes perceptually when it is mixed with other colors. The trajectories are red in areas which do not belong to the color gamut of the human eye. The button "del all" (37), deletes all the trajectories (that are canceled anyhow every time when the chips are redrawn).
Even if the Munsell space is defined for lighting "C", there are many curiosities connected to how the perception changes with varying lightness. Only if the brand Polycolor is selected can we see the "illum1" (38) button activated that forces the first chosen lighting. For each color coordinate the XYZ tristimulus response is calculated using the first illumination spectrum and this gets transferred into Munsell space using illumination "C", keeping the XYZ values fixed. If the coordinate cannot be located, it is indicated somehow: for instance, the trajectories become red in the indefinite zone, or their terminal sphere gets filled up with red points, etc.
A possible color wheel for each brand has been defined and can be seen by selecting the "Cweel" (39), Color Wheel, button. The wheel is placed on the plane that better approximates the single colors of the wheel. This way one can see well that the neutral axis never leaves the wheel perpendicularly, as it is often shown, but that the plane of the wheel is tilted: the yellows, in fact, have a high value (lightness), while the values of reds and blues are much lower. From here derives a well known fact that when mixing colors, not only the hue changes, but the value as well. Otherwise, sometimes a color can be brightened also with yellow/orange/etc. without necessarily using white paint, etc.
Button "ShowP" (40), Show Position, indicates where all colors of a certain brand can be found. This is useful, for example, to identify the complementary color of a given paint base or its saturation level.
Finally, the "detach" (41) button allows you to move the Munsell space into an external window. The advantage is that you can resize this window, save it in jpeg or tiff formats, have a complete control of the camera and the positioning of the light to see the surface well:
By moving the mouse pointer over symbols, the function of each button appears. Upon opening the window, the default selection lets you turn the camera around the Munsell space. This is much more efficient than using preset commands of the main page, but the exact position cannot be determined or repeated easily. Moreover, if the mouse moves while releasing the left button, the space starts to rotate continuously. The positioning buttons on the main page readjust the camera any time. Nevertheless, it is a good idea to stop the motion before canceling or adding data to the image because unpredictable errors may occur.
In this area you may choose to draw additional spectra, such as the distribution of the x, y, z tristimulus functions of the Standard Observers (1), lighting spectra (2) of the selected illuminations and the reflectance spectra of 4 possible paint mixes. For each paint base (4) there are four possible options (5), one for each group. In the example the first color belongs to the first group, while the second color to the second group. If there are several selections in the vertical boxes, the recipe obtained from the selected colors will be used taking into account the paint quantity defined for each base. For each group the color is computed (6) and the spectrum is also shown in Area 3.
Example 1: Color placement analysis of a mixed paint
I choose to analyze the paint mixed by two Polycolor bases: "116- Primary Yellow": 11 parts + "256-Primary Red-Magenta": 1 part. Area 5, point (2) indicates that with light spectrum "C" the Munsell coordinates are 4.4YR 6.1/9.1. Using the "detach" button (41) in Area 5, this window shows up:
I can see all the coordinates (Hue, Value and Chroma).
Now, I want to see the position of this color with respect to other mixable colors of the same brand. Using the button "Pnt S" (28) of Area 5, I draw the shell around the mixable colors (i.e. the color gamut) of the Polycolor primaries:
With "vertical orbit" (11) in Area 5, I set the vertical position of the camera at 35 degrees.
I notice that the color I have mixed is on the outer shell regarding both saturation and value, that is, I cannot have a brighter color than this one or a darker one without loosing chroma. Now I check my color to see if it can be shown correctly on an ideal monitor by activating the RGB surface with the "rgb S" (29) button in Area 5, both in side and top views:
I can see that my color is far from the visualization limits of an ideal monitor. In order to see how these color gamuts are positioned compared to my eyes, I activate the "EyeG" (24), Eye Gamut, button in Area 5.
Since the control of the camera is in the detached window, I have to move the camera farther away or zoom to see the borders of the eye gamut. With the sixth control button (from the left) of the camera I activate the Zoom function and upon moving the mouse I get:
Now I can see the strange form of the color gamut of an ideal RGB monitor in the Munsell space.
In order to see the color trajectory resulting from mixing "116-Primary Yellow" and "256-Primary Red -Magenta" paints, I check the yellow paint as group 1 and the magenta as group 2, as shown in the picture of Area 6. Now I deselect the Paint and RGB surfaces and press the already activated "T1-2" button (among the buttons (34)) in Area 5.
I can see in white the trajectory I get by mixing Yellow and Magenta in different ratios. It is curved, as almost all color trajectories in the Munsell space. In order to see how lightness (Value) varies, I notice that the trajectory is almost aligned with the principle direction P-GY. Therefore, I press the "P-GY" button (19) in Area 5.
I notice that the value variation has also a non linear behavior. In order to see the trajectory better, I select "Slice" (point (25) in Area 5) to remove all the chips except those along the direction P-GY forming a plane:
Example 2: positioning of paint colors of a brand and the color wheel in Munsell space
If I want to see how paint colors are positioned, for example those of EFX500, and the respective color wheel, I click on "ShowP" (40) and "CWeel" (39) in Area 5:
I can see, for example, that there are no paint bases in sector GY. At this point, I want to see how the wheel is positioned compared to the gray scale. I deactivate the color positioning display, and set a 200 degree horizontal angle (then 60 degrees in the second image), 20 degrees vertical and an 82 radial motion:
It is clear that the wheel is tilted: therefore, usually mixing with yellow will lead to a brighter color, while violet will darken the color. Obviously, what matters is the relative value with respect to the color to which other paints are added. If the colors are in the complementary sectors, the effect will be even stronger.
Example 3: how does the space of mixable colors change with light?
I choose Polycolor, key in 90 for vertical angle and 270 for horizontal. At this point, I can use the cursor (26) in Area 5 to define the Value where to slice the color space. In order to see the sliced space better, I activate both the RGB space display (button "rgb S" (29) in Area 5 and the paint gamut (button "Pnt S" (28) in Area 5). I select to see the RGB space in gray (click "gry" (31) in Area 5) and the mixable colors in solid (click "sld" (30) in Area 5). Now, with the cursor (26) in Area 5 I can adjust the value to 5, 6, 7 and 8 and slice the space by pressing the "Slice" (25) button in Area 5:
As it shows, the colors have different maximum saturation depending on lightness: yellow appears saturated with higher lightness, while violet only with lower values.
Example 4: color trajectories in the mixable color spaces
Selecting Polycolor primaries and choosing white, yellow, magenta and cyan blue as the first four colors, it is possible to control the trajectories resulting from mixing the paint bases pair wise. To calculate the trajectories, it is necessary to activate also the single colors as a group according to the following map:
This way each group is formed by just one color each. By setting the quantity to 0, you can avoid seeing the sphere showing the mixed paint color and the gray scale reference.
Now all the trajectory related buttons are active, "T…" (34) in Area 5. By clicking on one after the other, the trajectories can be calculated. In the first two images I also selected the 40 sectors to draw the Munsell chips, while in the last two I chose only the surfaces of mixable colors.
It is apparent that the trajectories are definitely non-linear, and the saturation of cyan blue and magenta increases when titanium white is added. The general belief among most artists that adding white to colors makes them less saturated is actually wrong, just like the idea that the more saturated color is the one directly from the tube when paint is applied opaque. These two beliefs are usually correct only when the paint is applied transparent.
These images also show that the space of the mixable colors is formed by surfaces connecting the set of trajectories between paint base pairs. More bases are available and less of these surfaces are clearly visible, and the space tends to become smoother and round. For example, the 24 colors of Pen Color offer a wider and steadier space (with the surface being drawn solid and in color this time):
Example 5: how does the mixable color space change with varying lighting?
Choosing Polycolor (the selection of this brand is mandatory for this analysis) I can also analyze how colors that we actually perceive change with varying lighting. The following image shows the mixable color space with Polycolor primaries through the Munsell chips surrounded by semitransparent surfaces with visible contour:
By pressing the "illum1' (38) button in Area 5 and selecting lighting 'F10' (left image) or 'A' (right image) as the first illumination spectrum, the following images can be obtained:
In both cases the semitransparent surface is the color space contour with lighting "C". However, the Munsell chips are calculated with lighting 'F10' or 'A', and you can see how the first changes the eye's tristimulus value toward the warm colors a bit, while lighting "A" changes them drastically. This way we can really see that the blues of a picture are physically invisible if the lighting source is an incandescent lamp. The grays also become colored and are not neutrals anymore. Our vision system, however, is able to counterbalance this effect and make us believe to see also the true blue color with artificial warm light, even if the physical stimulation of our eyes is only by warm colors.
When drawing the trajectories among the individual color bases the following pictures can be obtained. For lighting "C" the first, for lighting "F10" the second shows well the movement toward warm colors:
Example 6: how does the mixable color space change with varying light intensity?
When choosing Polycolor, for example, I can also analyze how the colors that we actually perceive change with varying light intensity. I choose to draw Munsell chips and use lighting "C". The picture that I get is the first of the two shown below.
Then, I lower the light intensity to 80%, which means that the pure white color will be seen as value 8 and not more 10 as it is with ideal light intensity. In order to see how the color gamut changes, I have to select all the paint bases one by one in Area 1 and click on "Gamut" (23) in Area 5. The first image shows the result:
The image shows very well that when reducing lighting to 80%, the entire color space gets squeezed under value 8 as expected. Moreover, the more saturated colors are also lost and this is less obvious. From this the importance of adequate lighting is evident not only regarding color temperature but also intensity.
Example 7: Do primary colors of a brand let me mix all the colors of the color gamut?
In order to see if that is the case, I use the brand Pen Color because here I have a clear identification of primary colors among the paint bases. In the picture on the left I see the space of mixable colors using the available colors, i.e. the paint gamut. Then, I choose the three primary colors, plus white and black, and I click on "Gamut" (23) in Area 5. The second image shows the result:
It is evident that primaries allow me to mix all the hues, but I do not get the color saturation that I get with all the available bases. On the other hand, if color manufacturers provide us with a large variety of pigments, there has to be a reason! They also say that there are also base colors such as light or dark gray, etc., that do not help increase the mixable color space but only make life easier. Black, in fact, is a very strong color and needs to be dosed with caution. Having grays at your disposal it is easier to dose the color black. Furthermore, some brands like Holbein, carry grays that correspond to various Munsell values and this is important in order to be able to desaturate the colors (better illustrated by some of the examples on the color2drop page).
Example 8: How does the space of mixable colors change if I do not use black color?
The explanation is very similar to the previous case. In fact, if one decides not to use black, the space of mixable colors will be reduced because black and white are subject to the same rules as other colors. It is their position with low chroma that tells us that they are special, but in reality they are not. Nevertheless, the reduction caused by the absence of black is quite insignificant and often unimportant, if among the colors I have some bases that when mixed together let me absorb incident light sufficiently. Black color, among others, is a special color because it plays up the reflection of the paint film more than others creating a mirror effect (by brightening up the color) when shiny objects are around the painting. The image below shows the color gamut of Polycolor primaries on plane Hue/Chroma with section at Value=4. The same section is shown on the right, but there only white and three primaries are chosen and the mixable colors together are calculated with the "Gamut" (23) button of Area 5. Just a pair of chips are missing, but nothing more.
Example 9: Why do we obtain green by mixing yellow and black?
It has to do with one of the properties of the yellow pigments. In order to see what this is about, let me observe what happens when I mix yellow and blue together. Obviously, I get green, but let me examine closely what the spectra do. When I take one part Polycolor yellow and one part cyan blue, the result is as follows in Area 3:
The thicker curve has the resulting green color. If I now analyze how the spectral values are distributed, I notice that up to about 520nm, yellow is the dominant color, that is, the reflectance spectrum of the mixed paint superimposes the yellow! The color blue starts to dominate only over 580nm. This means that the coloring power of a paint base is not a global property, but dependent on the wavelength. In this case, yellow has very strong coloring power below 520nm, while blue becomes strong over 580nm. In order to get a numeric sense, I raise the blue all the way until the mixed color is positioned between yellow and blue below 520nm.When I reach 15 parts of blue per one part of yellow, here is the result:
This means that spectrum wise 15 parts of blue weigh exactly one part of yellow! It is true that our eyes respond to spectra in a non linear way, but this does not change the concept. Now I do the same (checking the wavelength above 580nm) with yellow and when I reach 80 parts of yellow per one part of blue, this is what I see:
It is clear that the yellow is very strong in the high frequency area (shorter wavelength: indigo, blue and green), a lot weaker in the low frequency range above 580nm (longer wavelength: yellows and reds).
Coloring power is not an absolute propriety, but something relative depending on the bases that are mixed together. However, if a base has this strong coloring effect in some frequency ranges when mixed with some paint bases, it is reasonable to assume that it will maintain a similar behavior even with other bases. One consequence of this behavior is that black mixed with yellow turns green, because in the zone around 520nm (green), yellow has a much stronger coloring power than in the longer wavelengths:
This is the complete trajectory we have by mixing yellow and black at varying ratios, where the shift toward green is clearly seen:
However, by mixing ideal primaries, the shift toward green doesn't occur:
Therefore, the green color resulting by mixing black and yellow is a consequence of the physical pigments having coloring strength dependent on the wavelength and it doesn't occur with ideal primaries.
A different aspect of the same phenomenon is the variation of value that we see when we desaturate, for example, a yellow with a neutral gray of the same value. Since neutral gray has weaker coloring power in the shorter wavelengths, while stronger in the second half of the visible spectrum compared to yellow, the trajectory from yellow to gray tends to go down in value (and change also tonality) because yellow depresses gray in the blue-green zone at once, just as gray depresses yellow in the yellow-red zone, bringing it to a lower value with respect to both yellow and gray. The fact that coloring power depends both on the pigment and the wavelength explains a lot of strange color phenomena in the world of paint mixing.