CN115146490A - Full-color-domain color model for blending multidimensional gridding dye liquor and chromatographic construction thereof - Google Patents
Full-color-domain color model for blending multidimensional gridding dye liquor and chromatographic construction thereof Download PDFInfo
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Abstract
The invention relates to a multi-dimensional gridding dye liquor mixed panchromatic domain color model and a chromatogram construction thereof, which belong to the technical field of color regulation and control in the textile industry, firstly, based on gray dye liquor and each color dye liquor under the concentration of each level of dye liquor, and combining the discretization of the quality of each dye liquor, respectively constructing a multi-primary color dye liquor color mixing mode of hue gradient change, chroma gradient change and concentration gradient change, and respectively obtaining the quality, color mixing ratio and color value of a multi-primary color coupling color mixing sample under each mode; then respectively constructing a multi-primary dye liquor coupling color mixing sub-model under each mode; then respectively constructing a full-color phase color mixing model of the multi-primary color dye solution in each mode; finally, respectively constructing circular geometric models of the full color gamut color space under each mode; therefore, hue control, lightness control and chroma control can be realized in application, digital color matching of the dye liquor can be efficiently realized, and the dyeing color precision of the dye liquor is improved.
Description
Technical Field
The invention relates to a full-color-domain color model prepared by blending multidimensional gridding dye liquor and a color spectrum construction thereof, belonging to the technical field of color regulation and control in the textile industry.
Background
In optical physics, classical color models such as RGB, HSI, lab and the like serving basic theoretical research are constructed and are mainly used for expressing the color distribution rule in a color space. In the industry and the design world, a pagoda-shaped color model and a circular color matching model are constructed and used for explaining the change rule of color hue, lightness and chroma in the color matching process.
In the industries of textile, printing and dyeing, dope dyeing and spinning, etc., dyes of different colors, dye solutions, printing inks, polymer solutions (melts) and other color materials are usually uniformly mixed in different proportions to obtain new colors of products, so that product innovation is driven by color innovation. When the product is designed, if the color of the primary color materials and the mixing ratio of the primary color materials are selected, the color of the product can be obtained through the full-color-domain color model; if the product color is designed, it can be known by the full-gamut color model which base colors and the mixing ratio of the colors of each base color can be used to obtain the set color.
The color models such as RGB, HSI, lab and the like constructed based on the physical optical principle have larger difference with the actual color matching process, and cannot be directly used for analyzing and describing the color mixing and the color change in the color matching process.
The pagoda-shaped color model and the circular color matching model constructed based on the three primary colors principle lack a digital color expression means, are too simple and are not suitable for the current digital color matching requirement.
Disclosure of Invention
The invention aims to solve the technical problem of providing a full-color-domain color model prepared by blending multi-dimensional gridding dye liquor and constructing a color spectrum of the full-color-domain color model.
The invention adopts the following technical scheme for solving the technical problems: the invention designs a full-color-domain color model for multi-dimensional gridding dye liquor mixing and a chromatogram construction thereof, which comprises the following steps:
step A, based on preset division of dye liquor concentration from low to highThe concentration of dye liquor of each grade is presetThe quality of the color dye respectively corresponding to the concentration of each grade of dye liquor isThe quality of each color dye solution and the concentration of each level of dye solution corresponding to the gray dye are configured asThe gray dye solutions are sorted according to the size of the hue angle respectively according to the dye solution concentration of each grade and the color dye solutions under the dye solution concentration of each grade; wherein,,,denotes the firstColor dye corresponds to the firstThe quality of the color dye liquor of the grade dye liquor concentration;indicates that the grey dye corresponds toQuality of the colour dye liquor of the grade dye liquor concentration, andandand C, equaling, and then entering the step B;
step B, respectively measuring the quality of each color dye liquorAccording to preset discrete quantityDiscretization is performed as follows (1):
wherein,(ii) a And the quality of the grey dye liquorAccording to preset discrete quantityDiscretization is performed as follows (2):
c, constructing a multi-primary dye liquor color mixing mode with hue gradient change based on the multi-primary dye liquor to obtain the quality, color mixing ratio and color value of the multi-primary binary coupling color mixing sample;
constructing a multi-primary dye liquor color mixing mode with gradient changes of hue and chroma based on the multi-primary dye liquor, and obtaining the quality, the color mixing ratio and the color value of the multi-primary ternary dual coupling color mixing sample;
constructing a multi-primary dye liquor color mixing mode with changing hue, chroma and concentration gradient based on the multi-primary dye liquor, obtaining the quality, color mixing ratio and color value of the multi-primary ternary dual coupling color mixing sample with different levels of dye liquor concentration, and then entering the step D;
d, constructing a multi-primary dye liquor binary coupling color mixing sub-model based on the quality, the color mixing ratio and the color value of the multi-primary binary coupling color mixing sample;
constructing a multi-primary-color dye-liquor ternary double coupling color mixing sub-model based on the quality, the color mixing ratio and the color value of the multi-primary-color ternary double coupling color mixing sample;
constructing a multi-primary color dye liquor ternary double coupling color mixing sub-model based on different levels of dye liquor concentrations based on the quality, color mixing ratio and color value of the multi-primary color ternary double coupling color mixing sample with different levels of dye liquor concentrations; then entering step E;
e, constructing a one-dimensional full-color phase color mixing model of the multi-primary-color dye liquor according to the multi-primary-color dye liquor binary coupling color mixing sub-model;
constructing a two-dimensional full-color-domain color mixing model of the multi-primary-color dye solution according to the multi-primary-color dye solution ternary double-coupling color mixing sub-model;
constructing a three-dimensional full-color-domain color mixing model based on the multi-primary-color dye liquor with different levels of dye liquor concentrations according to the multi-primary-color dye liquor ternary dual coupling color mixing sub-model based on different levels of dye liquor concentrations, and then entering the step F;
f, constructing a circular geometric model of a one-dimensional panchromatic domain color space according to a one-dimensional panchromatic phase color mixing model of the multi-primary color dye solution;
constructing a circular geometric model of a two-dimensional panchromatic domain color space according to a two-dimensional panchromatic domain color mixing model of the multi-primary color dye solution;
and constructing a cylindrical geometric model of a three-dimensional panchromatic domain color space according to a three-dimensional panchromatic domain color mixing model based on the multi-primary-color dye liquor with different levels of dye liquor concentration.
Compared with the prior art, the full-color-domain color model prepared by blending the multidimensional gridding dye liquor and the chromatographic construction thereof have the following technical effects:
firstly, based on gray dye liquor and each color dye liquor under the concentration of each level of dye liquor, respectively constructing a multi-primary color dye liquor color mixing mode with hue gradient change, chroma gradient change and concentration gradient change by combining discretization of the quality of each dye liquor, and respectively obtaining the quality, color mixing ratio and color value of a multi-primary color coupling color mixing sample under each mode; then, respectively constructing a multi-primary color dye liquor coupling color mixing sub-model under each mode; then respectively constructing a full-color phase color mixing model of the multi-primary color dye solution in each mode; finally, respectively constructing circular geometric models of the full color gamut color space under each mode; therefore, hue regulation and control, lightness regulation and control and chroma regulation and control can be realized in application, digital color matching of the dye liquor can be efficiently realized, and the precision and the automation level of color matching of the dye liquor are improved.
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FIG. 1 is a flow chart of a full color domain color model for multi-dimensional gridding dye liquor blending and a chromatogram construction thereof;
FIG. 2 is a schematic diagram of a full color phase mixture model of a six-primary-color dye solution according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a full color gamut color mixing model of a dye solution with three colors, one gray, and four primary colors according to a second embodiment of the present disclosure;
FIG. 4 is a schematic diagram of a six-color one-gray seven-primary color dye-liquor full-color-domain color mixing model according to a third embodiment of the present invention;
fig. 5 is a schematic diagram of a full-color-domain color mixing model of a dye solution with six colors, one gray, and seven primary colors in five concentration planes according to a fourth embodiment of the design of the present invention.
Detailed Description
The following description will explain embodiments of the present invention in further detail with reference to the accompanying drawings.
The invention designs a full-color-domain color model mixed with multi-dimensional gridding dye liquor and a chromatogram construction thereof, and the design concept is as follows:
1. the invention discloses a construction method of a one-dimensional panchromatic gamut color space model and a one-dimensional panchromatic gamut color spectrum with hue gradient change thereof;
2. the invention discloses a method for constructing a two-dimensional panchromatic gamut color space model and a two-dimensional gridding panchromatic gamut color spectrum with gradient change of hue and chroma thereof, which are disclosed by the invention;
3. constructing a ternary dual coupling color mixing mode between different color pigments and different gray pigments, and deducing a weight matrix, a mixing ratio matrix and a color matrix of all mixed samples of the three-dimensional color space model;
4. based on the grid point coordinates and the color conversion matrix of the constructed one-dimensional, two-dimensional and three-dimensional full color gamut color space model, the construction method of the one-dimensional, two-dimensional and three-dimensional full color gamut color space geometric model is invented.
Based on the above design concept, in practical application, as shown in fig. 1, the following steps a to F are specifically performed.
Step A, based on preset division of dye liquor concentration from low to highThe concentration of dye liquor of each grade is presetThe quality of the color dye respectively corresponding to the concentration of each grade of dye liquor isThe quality of the gray dye corresponding to the concentration of each grade dye liquor isThe gray dye solutions are sorted according to the size of the hue angle respectively according to the dye solution concentration of each grade and the color dye solutions under the dye solution concentration of each grade; wherein,,,is shown asThe color dye corresponds toThe quality of the color dye liquor of the grade dye liquor concentration;indicates that the grey dye corresponds toQuality of the colour dye liquor of the grade dye liquor concentration, andandequality, then proceed to step B
Based on the characteristic that the lower the concentration of the dye liquor is, the higher the color brightness value of the dye liquor is, in the multi-primary color dye liquor mixed-color system, the molar concentrations of the dye liquor in which the gray dye liquor and the color dye liquor are distributed in a gradient mannerCorresponding to the lightness value of the dye liquor, when the concentration of the dye liquor is from low concentration to high concentrationAt each level, the lightness of the dye liquor is divided into high lightness and low lightnessAnd (4) grading.
Step B, respectively aligning each quality of colour dyeing liquorAccording to preset discrete quantityDiscretization is carried out as follows (1):
wherein,(ii) a And the quality of the grey dye liquorAccording to preset discrete quantityDiscretization is performed as follows (2):
And C, aiming at the multi-primary dye liquor mixed color system, carrying out binary combination pairing on the multi-primary dye liquor with the same concentration to obtainThe two primary colors are mixed with the dye solution, and then the two primary colors are coupled and mixed with each other based on the discretization weight, so that the dye solution can be obtainedA multi-primary dye liquor color mixing mode with hue gradient change is constructed by the mixed sample;
based on the multi-primary dye solution, a multi-primary dye solution color mixing mode with hue gradient change is constructed, and the quality, the color mixing ratio and the color value of the multi-primary binary coupling color mixing sample are obtained according to the following processing.
Aiming at the concentration of the dye liquor in each grade, two kinds of color dye liquor are sequentially selected from the sequencing of the multi-base color dye liquor represented by the formula (1) for combined color mixing as follows:
wherein,is shown asConcentration of the dye liquor of gradeThe discrete mass of the seed color dye,is shown asUnder the concentration of the graded dye liquorDiscrete masses of the colored dyes.
Performing binary coupling color mixing according to the formula (3) to obtainA mixed color sample corresponding to the binary coupled mixed color, each mixed color sampleThe following were used:
is shown asThe quality of a color mixing sample corresponding to binary coupling color mixing under the concentration of the level dye liquor;
according to formula (4), andcolor mixing ratio of color mixing sample corresponding to binary coupling color mixing under level dye liquor concentrationObtainingThe color mixing ratio of each color dye solution in each color mixing sample is as follows:
is shown asThe quality of the mixed color sample corresponding to the binary coupling mixed color under the concentration of the level dye solution isThe color mixing ratio of the colored dye liquor of (1),is shown asThe quality of the mixed color sample corresponding to the binary coupling mixed color under the concentration of the level dye solution isThe color mixture ratio of the colored dye solution;
according to the colour value of binary colour dyeing liquor、Obtained with respect to formula (4)The color values of the mixed color samples are respectively as follows:
is shown asAnd color values of the color mixing sample corresponding to binary coupling color mixing under the concentration of the graded dye solution.
Aiming at the multi-primary dye liquor mixed color system, the multi-primary dye liquor with the same dye liquor concentration is subjected to ternary combination pairing to obtainAnd (3) grouping the three-primary-color mixed dye solution, and performing ternary dual coupling color mixing based on the discretization weight, thereby constructing a multi-primary-color dye solution color mixing mode with gradient change of color phase and chroma.
Based on the multi-primary dye liquor, a multi-primary dye liquor color mixing mode with gradient changes of hue and chroma is established, and the quality, the color mixing ratio and the color value of the multi-primary ternary dual coupling color mixing sample are obtained according to the following processing.
Respectively aiming at the concentration of each level of dye liquor, sequentially selecting two color dye liquors from the sequence of the multi-base color dye liquor represented by the formula (1), and combining and selecting the gray dye liquors with the same concentration of the dye liquor from the gray dye liquors represented by the formula (2) to perform combined color mixing as follows:
wherein,denotes the firstUnder the concentration of the graded dye liquorThe discrete mass of the seed color dye,is shown asConcentration of the dye liquor of gradeThe discrete mass of the seed color dye,is shown asDiscrete mass of grey dye at the level dye liquor concentration;
performing ternary double coupling color mixing according to the formula (8) to obtainThe quality of each mixed color sample is determined by the quality of the mixed color sample corresponding to the ternary dual coupling mixed colorThe following were used:
denotes the firstThe quality of a color mixing sample corresponding to ternary double coupling color mixing under the concentration of the level dye solution;
according to formula (9), andcolor mixing ratio of color mixing sample corresponding to ternary double coupling color mixing under level dye liquor concentrationObtainingThe color mixing ratio of each dye solution in each color mixing sample is as follows:
is shown asThe quality of the mixed color sample corresponding to ternary double coupling mixed color under the concentration of the level dye solution isThe color mixing ratio of the gray dye liquor,denotes the firstThe quality of the mixed color sample corresponding to ternary double coupling mixed color under the concentration of the level dye solution isThe color mixture ratio of the colored dye solution;denotes the firstThe quality of the mixed color sample corresponding to ternary double coupling mixed color under the concentration of the level dye solution isThe color mixture ratio of the colored dye solution;
according to the colour values of two colour dyeing liquors、And color value of the grey dye liquorObtained with respect to formula (9)The color values of the mixed color samples are respectively as follows:
is shown asAnd (3) color values of color mixing samples corresponding to ternary double coupling color mixing under the concentration of the level dye solution.
And (4) constructing a multi-primary dye liquor color mixing mode with changing hue, chroma and concentration gradient based on the multi-primary dye liquor, processing as follows to obtain the quality, color mixing ratio and color value of the multi-primary ternary dual coupling color mixing sample with different levels of dye liquor concentration, and then entering the step D.
Aiming at the multi-primary color dye liquor color mixing system based onThe multi-primary color dye liquids corresponding to different concentration surfaces are subjected to ternary combination pairing, and each concentration surface can be obtainedAnd (3) grouping three-primary color mixed dye liquor, and carrying out ternary double coupling color mixing based on the discretization weight, thereby constructing a multi-primary color dye liquor color mixing mode with gradient changes of lightness, hue and chroma.
Based on the color dye solutions under the dye solution concentrations of all levels, two color dye solutions are selected from the dye solution concentrations of different levels, and the gray dye solutions are selected from the gray dye solutions represented by the formula (2) to carry out combined color mixing as follows:
wherein,、、,denotes the firstDiscrete mass of grey dye at the level dye liquor concentration,denotes the firstUnder the concentration of the graded dye liquorThe discrete mass of the seed color dye,is shown asConcentration of the dye liquor of gradeA discrete mass of seed color dye;
performing ternary double coupling color mixing according to formula (12) to obtainThe quality of each mixed color sample is determined by the quality of the mixed color sample corresponding to the ternary dual coupling mixed colorThe following were used:
representing the quality of a color mixing sample corresponding to ternary double coupling color mixing under different levels of dye liquor concentration; according to the formula (13) and the color mixing ratio of the color mixing sample corresponding to the ternary double coupling color mixing under different levels of dye liquor concentrationObtainingThe color mixing ratio of each dye solution in each color mixing sample is as follows:
the quality of the mixed color sample corresponding to ternary double coupling mixed color under different levels of dye liquor concentration is shown asThe color mixing ratio of the gray dye liquor,the quality of the mixed color sample corresponding to ternary double coupling mixed color under different levels of dye liquor concentration is shown asThe color mixture ratio of the colored dye solution;the quality of the mixed color sample corresponding to ternary double coupling mixed color under different levels of dye liquor concentration is shown asThe color mixing ratio of the colored dye liquor;
according to the colour values of two colour dyeing liquors、And color value of the grey dye liquorObtained with respect to formula (13)The color values of the mixed color samples are respectively as follows:
and the color values of the color mixing samples corresponding to the ternary double coupling color mixing under different levels of dye liquor concentration are represented.
A gridding color mixing system of multi-primary color dye solution is prepared byThe dye liquor molar concentration of each color dye liquor and one gray dye liquor is divided intoAt each level, assumed on each levelEach colour dye liquor has an equal lightness value to 1 grey dye liquor.
If based on the equal concentration surface, willThe color dye solutions are combined pairwise and then subjected to binary coupling color mixing according to the discretization weight, so that the color dye solutions with multiple primary colors on a certain equal concentration surface can be obtainedOne-dimensional color mixing model of grid points andfull color chromatography of individual phase gradients;
if based on isoconcentration planes, fromTwo groups of color dye solutions and a gray dye solution are sequentially selected from the color dye solutions to be combined and then subjected to ternary and dual coupling color mixing according to the discretized weight, so that the multi-primary color dye solution on a certain equal-concentration surface can be obtainedTwo-dimensional color mixture model of individual grid points andgradient panchromatic chromatogram;
from each isoconcentration plane if based on each isoconcentration planeTwo groups of color dye solutions and a gray dye solution are sequentially selected from the color dye solutions to be combined, and then ternary double-coupling color mixing is carried out according to the discretized weight, so that the multi-primary color dye solution on each equal-concentration surface can be obtainedThree-dimensional color mixing model of individual grid points andpanchromatic chromatography of individual gradients.
And D, constructing a multi-primary dye liquor binary coupling color mixing sub-model based on the quality, the color mixing ratio and the color value of the multi-primary binary coupling color mixing sample as follows:
(1) the quality matrix of the multi-primary color dye liquor binary coupling color mixing sub-model is as follows:
denotes the firstThe quality of a color mixing sample corresponding to binary coupling color mixing under the concentration of the level dye liquor;
(2) the color mixing ratio matrix of the multi-primary color dye liquor binary coupling color mixing submodel is as follows:
denotes the firstThe color mixing ratio of the color mixing sample corresponding to binary coupling color mixing under the concentration of the level dye liquor;
(3) the color matrix of the multi-primary color dye liquor binary coupling color mixing submodel is as follows:
is shown asAnd color values of the color mixing sample corresponding to the binary coupling color mixing under the concentration of the graded dye solution.
Based on the quality, the color mixing ratio and the color value of the multi-primary-color ternary double-coupling color mixing sample, the establishment of the multi-primary-color dye solution ternary double-coupling color mixing sub-model comprises the following steps:
(1) the quality matrix of the multi-primary-color dye liquor ternary double-coupling color mixing sub-model is as follows:
denotes the firstThe quality of a color mixing sample corresponding to ternary double coupling color mixing under the concentration of the level dye solution;
(2) the color mixing ratio matrix of the multi-primary color dye liquor ternary double coupling color mixing submodel is as follows:
denotes the firstThe color mixing ratio of the color mixing sample corresponding to the ternary double coupling color mixing under the concentration of the level dye solution;
(3) the color matrix of the multi-primary color dye liquor ternary double coupling color mixing submodel is as follows:
is shown asAnd (3) color values of the color mixing samples corresponding to the ternary double coupling color mixing under the concentration of the graded dye solution.
Based on the quality, the color mixing ratio and the color value of the multi-primary-color ternary double-coupling color mixing sample with different levels of dye liquor concentrations, the multi-primary-color ternary double-coupling color mixing sub-model based on different levels of dye liquor concentrations is constructed as follows:
as can be seen from the formulas (12) and (13), the dye solutions having different concentrations have different concentrations for each concentration levelGroup-element dual-coupling color mixing submodel, each submodel includingA grid point corresponds toOn each concentration plane, can be constructed to includeA two-dimensional submodel, thenLayer oneSub-models of groups includeA plurality of grid points.
(1) The quality matrix of the multi-primary color dye liquor ternary double-coupling color mixing sub-model based on different levels of dye liquor concentrations is as follows:
representing the quality of a color mixing sample corresponding to ternary double coupling color mixing under different levels of dye liquor concentration;
(2) the color mixing ratio matrix of the multi-primary color dye liquor ternary double-coupling color mixing submodel based on different levels of dye liquor concentration is as follows:
representing the color mixing ratio of the color mixing sample corresponding to the ternary double coupling color mixing under different levels of dye liquor concentration;
(3) the color matrix of the multi-primary color dye liquor ternary double coupling color mixing sub-model based on different levels of dye liquor concentrations is as follows:
and the color values of the color mixing samples corresponding to the ternary double coupling color mixing under different levels of dye liquor concentration are represented.
Then step E is entered.
And E, in a multi-primary color dye solution system with the same level of molar concentration, selecting different color dye solutions to carry out binary coupling color mixing, if the hue gradient obtained by all the binary coupling color mixing is changed into one-dimensional color spectrums which are sequentially arranged, equivalently, connecting the color matrixes of all the mixed samples end to carry out merging and expansion, and obtaining the color spectrum with the hue gradient change in the full color domain range. On the basis, a weight matrix, a mixing ratio matrix and a color matrix of all mixed samples are deduced, and a one-dimensional full color gamut color space model and a one-dimensional full color gamut color spectrum with hue gradient change are constructed.
At the same molarity level, selecting molarity of the same levelThe color matching system is composed of multiple base color dye solutions, two dye solutions are sequentially selected from the color matching system to carry out binary coupling color mixing to obtain the productThe group binary coupling color mixing submodel can be obtained by discretizing the weight of the binary dye solution and carrying out binary coupling color mixingA color mixing grid point and a color mixing sample valueIndividual grid point and dither color value, a constructable representationThe multi-primary color dye liquor binary coupling color mixing mode and the mathematical model of the color spectrum thereof can be constructed and expressed at the same timeThe multi-primary color dye solution binary coupling mixed color sample grid point coordinates and the geometric model of the color spectrum thereof are provided.
According to the multi-primary color dye liquor binary coupling color mixing sub-model, a one-dimensional full-color phase color mixing model of the multi-primary color dye liquor is constructed as follows.
Order toIs provided withAll the expressions (16), (17) and (18) correspond toThe quality, color mixing ratio, and color of the binary coupled color mixture sample are measured by 1 lineThe matrix of columns is represented as follows:
the compounds of the formulae (16), (17) and (18)And expanding to obtain a quality matrix of the one-dimensional full-hue gridding color mixing model as follows:
the color mixing ratio matrix of the one-dimensional full-hue gridding color mixing model is obtained as follows:
the color matrix of the one-dimensional full-hue gridding color mixing model is obtained as follows:
namely, a one-dimensional full-color phase color mixing model of the multi-primary color dye solution constructed based on the multi-primary color dye solution binary coupling color mixing is obtained.
Based on the formulas (19), (20) and (21), the dyeing of multiple primary colors is carried outOne-dimensional full color gamut color space constructed by group binary coupling color mixingThe quality matrix, the color mixing ratio matrix and the color matrix of all mixed color samples are given by the grid points, namely the equations (22), (23) and (24), so that a mathematical model of a one-dimensional full-hue color space constructed based on the multi-primary dye liquor binary coupling color mixing is obtained.
According to the multi-primary-color dye liquor ternary double-coupling color mixing sub-model, a two-dimensional full-color-domain color mixing model of the multi-primary-color dye liquor is constructed as follows.
Two color dye liquids and one gray dye liquid are selected from a multi-primary dye liquid system with the same level of molar concentration to carry out ternary double coupling color mixing, if two-dimensional gridding chromatograms with hues and chroma gradient changes, which are obtained by all the ternary double coupling color mixing, are sequentially arranged, namely the color matrixes of all mixed samples are connected end to be merged and expanded, and the chromatograms with hues and chroma gradient changes are obtained in a full color domain range. On the basis, a weight matrix, a mixing ratio matrix and a color matrix of all mixed samples are deduced, and a two-dimensional plane full color gamut color space model and a two-dimensional full color gamut color spectrum with gradient changes of hue and chroma are constructed;
selecting the same order of molarityA color matching system is composed of multi-base color dye liquor and a gray dye liquor, and two dye liquors and the gray dye liquor are sequentially selected from the color dye liquor to carry out ternary double coupling color mixingThe group-element double-coupling color mixing sub-model is obtained by discretizing the weight of the ternary dye solution and performing the ternary double-coupling color mixingA color mixing grid point and a color mixing sample valueIndividual grid point and dither color value, a constructable representationThe method is characterized in that a multi-primary-color dye liquor ternary double-coupling color mixing mode and a mathematical model of the color spectrum thereof are adopted, and meanwhile, expression can be constructedMulti-primary-color dye liquor ternary dual-coupling color mixing sample netGrid point coordinates and geometric models of their chromatograms.
Based on the formulas (13), (14) and (15), it can be seen that the dye solutions of multiple primary colors are respectively used for the dye solution concentrations of each gradeThe group-element dual-coupling color mixing submodel comprisesA grid point of passingLine for mobile communication terminalA matrix representation of the columns, andthe group-ternary dual-coupling color mixing gridding submodel is spliced and combined in sequence from end to end corresponding to each line to obtain the grey dye solutionAnd color dye liquorForming a multi-primary color panchromatic domain gridding color mixing model;
When the temperature is higher than the set temperatureWhen the temperature of the water is higher than the set temperature,,and is and;
based on the aboveObtained by double coupling and color mixing of group-three dye solutionsColor mixture sample, and constructionLine for mobile communication terminalA gridding matrix of columns, thereby constructing a full color gamut gridding color mixing model, and developing the formula (27) to obtain the full color gamut gridding color mixing modelLine for mobile communication terminalThe column quality matrix is as follows, namely the quality matrix of the two-dimensional panchromatic range color mixing model of the multi-primary color dye solution;
and (3) obtaining a color mixing ratio matrix of a two-dimensional full-color-domain color mixing model of the multi-primary-color dye solution corresponding to the formula (28):
corresponding to equation (29), a color matrix of a two-dimensional full-color-domain color mixture model of the multi-primary-color dye solution is obtained:
namely, a two-dimensional full-color-domain color mixing model of the multi-primary dye solution constructed based on the multi-primary dye solution ternary dual coupling color mixing sub-model is obtained.
As can be seen from the formula (30), the panchromatic gamut gridding color mixing model constructed by the multi-primary colors has the same structureAnd (4) obtaining the mixing proportion of the dye liquor of the mixed sample corresponding to the grid points through the coordinates of the grid points (mixed sample). Thus, expression of hue, lightness, and chroma of all mixed samples (grid points) in the full color gamut is realized by equation (16).
According to the multi-primary color dye liquor ternary double coupling color mixing sub-model based on different levels of dye liquor concentrations, a three-dimensional full-color-domain color mixing model based on the multi-primary color dye liquor with different levels of dye liquor concentrations is constructed as follows.
In the multi-primary color dye liquor color mixing system, aiming at multi-primary color dye liquor under different dye liquor concentrations, the gradient change of the dye liquor concentration is used as a newly added dimension to expand the multi-primary color dye liquor into a three-dimensional full-color-domain color model on the basis of a two-dimensional plane full-color-domain color model under the same dye liquor concentration level, namely two groups of color dye liquor and one group of gray dye liquor are selected to carry out ternary coupling color mixing under each dye liquor concentration level, three-dimensional gridding chromatograms with gradient change obtained by all ternary coupling color mixing are sequentially arranged, namely the color matrixes of all mixed samples are connected end to be merged and expanded, and the three-dimensional chromatograms with gradient changes of hue, chroma and lightness are obtained in a full-color-domain range. On the basis, a weight matrix, a mixing ratio matrix and a color matrix of all mixed samples are deduced, and a three-dimensional panchromatic color model and a three-dimensional panchromatic color spectrum with gradient changes of hue, chroma and lightness are constructed.
The dye liquor concentration of the multi-primary color dye liquor is set asOn the surface of each concentration levelThe color matching system corresponding to the concentration is composed of two kinds of color dye liquor and one kind of grey dye liquor, and three-element double coupling color mixing is performed on the concentration plane of each grade by sequentially selecting two kinds of color dye liquor and one kind of grey dye liquorThe group-element dual-coupling color mixing submodel is the first oneLayer oneThe combination of the three-element double-coupling color mixing submodels can obtain a two-dimensional full color gamut color mixing model on the concentration surface and comprisesA grid of points. On all concentration planesThe two-dimensional panchromatic domain color mixing model is combined to obtain a color mixture model containingA three-dimensional full color domain color model constructed by the grid points is obtainedAnd (3) further constructing a mathematical model and a cylindrical geometric model of the gridding color mixing of the multi-primary dye liquor containing all the dye liquor concentrations on the basis of the color values of the grid points, and giving a three-dimensional full color gamut chromatogram with gradient changes of hue, chroma and lightness.
The first of the multi-primary dyeing solutions at different levels of dye solution concentration based on formula (40)Layer oneGroup-ternary double-coupling color mixing is constructedSub-models, each sub-model comprisingIndividual grid points, should workLayer oneOf group (a)Line for mobile communication terminalMatrix representation of the columns, will allOf a layerThe group-ternary dual-coupling color-mixing gridding submodel is spliced and combined in sequence from head to tail corresponding to each line to obtain gray dye solutionAnd color dye liquorForming a multi-primary color panchromatic domain gridding color mixing model;
based on formula (44), under different levels of dye liquor concentrationLayer(s)Obtained by double coupling and color mixing of group-three dye solutionsColor mixing sample constructionAnLine ofA gridding matrix of columns, thereby constructing a full color gamut gridding color mixing model, and expanding the formula (44) to obtain the full color gamut gridding color mixing modelAnLine ofColumn quality matrix:
corresponding to the formula (44), under different levels of dye liquor concentration, obtaining a color mixing ratio matrix of the three-dimensional full-color-gamut gridding color mixing model as follows:
or:
corresponding to the formula (46), under different levels of dye liquor concentration, the color matrix of the two-dimensional full color gamut gridding color mixing model is obtained as follows:
namely, a three-dimensional full-color-domain color mixing model based on the multi-primary-color dye liquor with different levels of dye liquor concentration is constructed, and then the step F is carried out.
As can be seen from the formula (43), the full-color-domain gridding color mixture model constructed from multiple primary colors has a common structureAnd (4) obtaining the mixing proportion of the dye liquor of the mixed sample corresponding to the grid points through the coordinates of the grid points (mixed sample). In this way, expression of hue, brightness, and chroma of all mixed samples (grid points) in the full color gamut is realized by the formula (49).
And F, constructing a circular geometric model of a one-dimensional panchromatic domain color space according to the one-dimensional panchromatic phase color mixing model of the multi-primary color dye solution by the following operation.
Respectively aiming at the dye liquor concentration of each grade according toRespective mixed color samples of respective grid pointsThe hue angle is arranged in sequence and evenly distributed on the circumference with the radius of 1, and each color value is setPolar angle of grid point ofPolar radius ofThen each color valueThe polar coordinates of the grid points of (a) are:
according toThen, the color values of the grid points are obtained by equations (5) and (6)The following were used:
namely, based on the formulae (25) (26), obtainedThe annular geometric model of one-dimensional full color gamut color space constructed by combining multi-primary color dye liquor binary coupling color mixing is uniformly divided into hue circlesThe polar coordinates of each grid point and its color value can be obtained by equations (25) and (26).
According to a two-dimensional panchromatic color mixing model of the multi-primary color dye solution, a circular geometric model of a two-dimensional panchromatic color space is constructed according to the following operation.
According to the formulas (32), (34) and (36), the two-dimensional full-color-domain color mixing model based on the multi-primary-color dye liquor is a modelLine ofA rectangular color model of the column expressed by equation (36) by coordinate conversion of the grid pointsLine ofThe rectangular color model of the column is converted into a circular color model as follows:
assuming that the radius of the circular color model is 1, based on the characteristics of the rectangular color model expressed by the formula (36), the circular color model is made along the circumference with the radius of 1Is divided equally to obtainA grid point is drawnConnecting lines of the grid points and the circle center; then the radius of the circle is processedIs divided equally to obtainA grid point on the circle radius centered at the center of the circleMaking concentric circles at each grid point, thereby obtainingThe polar coordinates of each grid point in the circular gridding color model are as follows:
the color value of each grid point in the circular gridding color model is as follows:
the color mixing ratio of each grid point in the circular gridding color model is as follows:
according to a three-dimensional panchromatic range color mixing model based on multi-primary-color dye liquor with different levels of dye liquor concentration, a cylindrical geometric model of a three-dimensional panchromatic range color space is constructed as follows.
According to the formulas (45), (47) and (49), the three-dimensional full-color-domain color mixing model based on the multi-primary-color dye liquor with different levels of dye liquor concentration is a modelLayer(s)Line ofA quadrangular prism color model of the columns expressed by the formula (49) by coordinate transformation of the grid pointsLayer(s)Line ofThe column rectangular color model is converted to a cylindrical color model as follows:
setting the cylinder height of the cylindrical color model as 1 and the radius of the circle as 1, and based on the characteristics of the quadrangular color model expressed by the formula (49), making the cylinder height of 1 asEqually dividing the circumference with the radius of 1 intoIs divided equally to obtainA grid point ofA tangent plane of each grid point and the center of the cylinder; then the radius of the cylinder is adjustedIs divided equally to obtainA grid point on the radius of the circle with the center of the cylinder as the centerMaking concentric cylinders at each grid point, thereby obtainingThe polar coordinates of each grid point in the cylindrical gridding color model are as follows:
the color values of each grid point in the cylindrical gridding color model are as follows:
the color mixing ratio of each grid point in the cylindrical gridding color model is as follows:
the full-color domain color model and the color spectrum construction thereof which are designed by multi-dimensional gridding dye liquor mixing are applied to the practice, and the following embodiments are analyzed, wherein in the first embodiment, the one-dimensional full-color phase color mixing model and the full-color phase spectrum thereof which are constructed by the color six-primary-color dye liquor are specifically as follows:
1. a binary coupling color mixing mode of the color six-primary-color dye solution;
the weight of a proper dye (one of reactive dye, acid dye, disperse dye and other dyes) is respectively prepared according to specific molar concentrationAnd taking the dye liquor. Color values of the color dye liquor are obtained by a color measuring instrument and are sequentially arranged according to the magnitude of hue angles:,,,,,and the color difference is。
The quality of the six-primary-color dye solution binary coupling color mixture sample obtained based on the formula (4) is as follows:
the color mixing ratio of the six-primary-color dye solution binary coupling color mixing sample can be obtained based on the formula (6) as follows:
2. Constructing a color six-primary-color dye liquor binary coupling color mixing sub-model;
as shown in the formula (4), 6 groups of binary coupled color mixing submodels can be constructed by the color six-primary-color dye solution, each group of submodels comprises 9 grid points, and the grid points can be arranged into a matrix with 1 row and 9 columns.
(1) A color six-primary-color dye liquor binary coupling color mixing sub-model weight matrix;
(2) A color mixing ratio matrix of the color six-primary-color dye liquor binary coupling color mixing sub-model;
(3) A color matrix of a color six-primary-color dye liquor binary coupling color mixing sub-model;
3. a one-dimensional full-color phase color mixing model and a full-color phase color spectrum of the color six-primary-color dye solution;
under the same molar concentration level, based on the formula (4), 6 groups of binary coupled color mixing sub-models can be constructed by 6 primary color dye solutions, each group of binary coupled color mixing sub-models has 9 color mixing samples, and the 6 groups of binary coupled color mixing sub-models have 54 color mixing sub-samples.
Order to;;. Is provided with. All of the equations (53), (54) and (55) correspond toThe weight of each binary coupled color mixture, the color mixture ratio and the color thereof can be represented by a matrix of 1 row and 48 columns (removing the color mixture).
If in the formulas (53), (54) and (55)And expanding to obtain a weight matrix, a color mixing ratio matrix and a color matrix of the full color gamut subsample:
based on the expressions (56), (57) and (58), it can be known that a one-dimensional full color gamut color space constructed by 6 groups of binary coupling color mixing of the color six-primary dye liquor comprises 48 grid points, and the expressions (56), (57) and (58) give a quality matrix, a color mixing ratio matrix and a color matrix of all color mixing samples, so that a mathematical model of the one-dimensional full color gamut color space constructed by the multi-primary dye liquor binary coupling color mixing is obtained.
4. Constructing a circular geometric model of a color space of a full color domain of a color six-primary-color dye solution;
at the same molar concentration level, six primary colors are dyed in order to construct colorThe coordinates of the grid points of the liquid binary coupled color mixing sample and the geometric model of the chromatogram thereof are determined according to 48 grid points (; ) Are arranged in sequence according to the size of the hue angle and are uniformly distributed on a circle with the radius of 2, as shown in figure 2.
Setting color values of each grid pointPolar angle ofPolar radius ofThen each grid pointThe polar coordinates are:
based on the formula (69 (70)A geometric model of a one-dimensional full color gamut color space constructed by grouping multi-primary color dye liquor binary coupling color mixing is uniformly divided into hue circlesThe polar coordinates of each grid point and its color value can be obtained by the equations (69) (70).
In the second embodiment, a full-color-domain color mixing model and a full-color-domain color spectrum thereof constructed by using the dye solutions with three colors, one gray and four primary colors are specifically as follows:
1. a ternary double coupling color mixing mode of a three-color one-gray four-primary-color dye solution;
setting the grey dye liquor in the three-color one-grey four-primary-color dye liquor asThe color dye solution is,Based on the formula (9), the quality of the three-group ternary dye solution double-coupling color mixing sample of the four-primary-color dye solution is as follows:
the color mixture of the three-color-one-gray-four-primary-color dye liquor ternary double-coupling color mixture sample can be obtained based on the formula (71) as follows:
2. Constructing a three-color one-gray four-primary-color dye liquor ternary double-coupling color mixing sub-model;
as can be seen from equations (8) and (9), each submodel includes 54 grid points, which can be arranged in a matrix of 6 rows and 9 columns, based on 3 sets of ternary dual-coupled color mixing submodels.
(1) A weight matrix of a three-color one-gray four-primary-color dye liquor ternary double coupling color mixing sub-model;
when in useObtained by formula (9)First, theAll of the module modelsQuality matrix of mixed color samples:
(2) A color mixing ratio matrix of a three-color one-gray four-primary-color dye liquor ternary double coupling color mixing sub-model;
when in useObtained from the formula (9)All of the module modelsColor mixing ratio matrix of color mixing samples:
(3) A color matrix of a three-color one-gray four-primary-color dye liquor ternary double coupling color mixing sub-model;
when in useObtained from the formula (9)All of the module modelsColor matrix of mixed color samples:
3. A full-color-domain color mixing model and a full-color-domain color spectrum of the dye liquor with three colors, one gray and four primary colors;
(1) A grid point quality matrix of a full-color domain color mixing model of a three-color one-gray four-primary-color dye solution;
the grid point quality matrix of the full-color-domain color mixing model of the dye liquor with three colors, one gray and four primary colors can be obtained based on the formula (75) as follows:
(2) A grid point color mixing ratio matrix of a full-color domain color mixing model of a three-color one-gray four-primary-color dye liquor;
based on the formula (76), a grid point color mixing ratio matrix of a three-color-one-gray-four-primary-color dye liquor full-color-domain color mixing model can be obtained as follows:
(3) A grid point color matrix of a full-color domain color mixing model of the dye liquor with three colors, one gray and four primary colors;
the grid point color matrix of the full-color domain color mixing model of the dye liquor with the three-color-gray four-component primary colors can be obtained based on the formula (77) as follows:
4. constructing a full-color-gamut geometric model of the dye liquor with three colors, one gray and four primary colors;
(1) Coordinates of grid points of the circular color model;
from the equations (79), (80) and (81), the full-color gamut color mixing model of the three-color-gray-four-primary-color dye solution is a rectangular color model with 6 rows and 24 columns, and is visually different from the color matching circular ring model. The rectangular color model of 6 rows and 24 columns expressed by equation (81) can be converted into a circular ring-shaped color model by coordinate transformation of the grid points. The method comprises the following specific steps:
setting the radius of the circular color model to be 1, based on the characteristics of the rectangular color model expressed by the formula (81), dividing 24 equally along the circumference with the radius of 1 to obtain 24 grid points, and drawing a connecting line between the 24 grid points and the circle center; then 5 equal divisions are carried out on the circle radius to obtain 6 grid points, and the 6 grid points pass through the circle radius by taking the circle center as the center6 grid points are made into concentric circles, thereby obtainingGrid points, as shown in fig. 3:
the polar coordinates of each grid point in the circular gridding color model are as follows:
(2) grid point color values of the circular color mixing model;
the color values corresponding to the grid points are:
(3) the grid point color mixing ratio of the annular color mixing model;
the color mixing ratio corresponding to each grid point is:
in the third embodiment, a full-color-domain color mixing model and a full-color-domain color spectrum thereof constructed by a six-color-one-gray-seven-primary-color dye solution are specifically as follows:
1. a ternary double coupling color mixing mode of six-color one-gray seven-primary-color dye liquor;
the gray dye liquor in the six-color one-gray seven-element primary color dye liquor is set asThe color dye solution is,;;The quality of the ternary dye solution double-coupling color mixing sample of the six-color one-gray seven-primary-color dye solution can be obtained based on the formula (3) is as follows:
the color mixing of the six-color-one-gray-seven-primary-color dye liquor ternary dual coupling color mixing sample can be obtained based on the formula (85) as follows:
2. Constructing a six-color one-gray seven-primary-color dye liquor ternary double-coupling color mixing sub-model;
as can be seen from equations (8) and (9), each submodel contains 54 grid points based on 6 sets of ternary dual-coupled color mixing submodels, which can be arranged into a matrix of 6 rows and 9 columns.
(1) A six-color one-gray seven-primary-color dyeing ternary double-coupling color mixing sub-model weight matrix;
when the temperature is higher than the set temperatureAll of the 6-module submodels obtained from the equation (85)Quality matrix of mixed color samples:
(2) A color mixing ratio matrix of a six-color one-gray seven-primary-color dye liquor ternary double coupling color mixing sub-model;
when in useAll of the 6-module submodels obtained from the equation (85)Color mixing ratio matrix of color mixing samples:
(3) A color matrix of a six-color one-gray seven-primary-color dye liquor ternary double coupling color mixing sub-model;
when in useAll of the 6-module submodels obtained from the equation (85)Color matrix of mixed color samples:
3. A six-color one-gray seven-primary-color dye liquor three-dimensional full-color-domain color mixing model and a full-color-domain color spectrum;
(1) A grid point quality matrix of a six-color one-gray seven-primary-color dye liquor full color domain color mixing model;
the grid point quality matrix of the six-color-one-gray-seven-primary-color dye liquor full-color-domain color mixing model obtained based on the formula (75) is as follows:
(2) A grid point color mixing ratio matrix of a full-color domain color mixing model of the six-color one-gray seven-primary-color dye liquor;
based on the formula (76), a grid point color mixing ratio matrix of a six-color-one-gray-seven-primary-color dye liquor full color domain color mixing model can be obtained as follows:
(3) A six-color one-gray seven-primary-color dye liquor full-color domain mixed color model grid point color matrix;
the grid point color matrix of the full-color gamut color mixing model of the six-color-one-gray-seven-primary-color dye liquor can be obtained based on the formula (77) as follows:
4. constructing a full-color-gamut geometric model of six-color gray-seven-primary-color dye liquor;
(1) Coordinates of grid points of the circular color model;
from the formulas (91), (92) and (93), the six-color-one-gray-seven-color dye liquor full-color-range color mixing model is a 6-row 48-column rectangular color model, and is visually different from a color matching circular ring model. The rectangular color model of 6 rows and 48 columns expressed by equation (98) can be converted into a circular ring-shaped color model by coordinate transformation of the grid points. The method comprises the following specific steps:
setting the radius of the circular ring-shaped color model to be 1, based on the characteristics of the rectangular color model expressed by the formula (98), performing 48 equal divisions along the circumference with the radius of 1 to obtain 48 grid points, and drawing a connecting line between the 48 grid points and the circle center; then 5 equal divisions are carried out on the circle radius to obtain 6 grid points, and the 6 grid points on the circle radius are crossed by taking the circle center as the center to make concentric circles, thereby obtaining the circular arcIndividual grid points, as shown in fig. 4:
the polar coordinates of each grid point in the circular gridding color model are as follows:
(2) Grid point color values of the circular color mixing model;
the color values corresponding to the grid points are:
in the fourth embodiment, a full-color gamut color mixing model constructed by gridding and color mixing of a six-color one-gray seven-primary color dye solution with five concentration levels is specifically as follows:
1. a six-color one-gray seven-primary-color dye liquor ternary double coupling color mixing mode with five concentration levels;
in a six-color one-gray seven-primary color dye liquor system with five concentration levels, the gray dye liquor isThe color dye solution isSetting:;;;. Then respectively inWith six kinds of color dye liquorThe three-element double-coupling mixed system of the seven-primary-color dye liquor is combined into the following dye liquor color matching systems with different concentrations:
the color mixture of the six-color-one-gray-seven-primary-color dye liquor ternary dual-coupling color mixture sample with five concentration levels can be obtained based on the formula (101) as follows:
2. Constructing a six-color one-gray seven-primary-color dye liquor ternary double-coupling color mixing sub-model based on five concentration surfaces;
as can be seen from the formula (96), for 7-primary-color dye solutions with 5 concentration planes, there are 6 sets of ternary dual-coupling color-mixing submodels corresponding to each concentration plane, and each submodel includesA grid point corresponds toOn each concentration plane, a sub-model containing 6 sets of ternary double coupling color mixing sub-models can be constructed, thenLayer oneSub-models of a group comprisingA grid of points.
(1) A six-color one-gray seven-primary-color dye liquor ternary double coupling color mixing sub-model weight matrix based on five concentration surfaces;
when in use;Obtained by the formula (92) toLayer oneSub-models of a group are allQuality matrix of mixed color samples:
(2) A color mixing ratio matrix of a six-color one-gray seven-primary-color dye liquor ternary double coupling color mixing sub-model based on five concentration planes;
when in use;Obtained from the formula (93)Layer oneSub-models of a group are allColor mixing ratio matrix of color mixing samples:
(3) The color matrix of the six-color one-gray seven-primary-color dye liquor ternary double-coupling color mixing sub-model based on five concentration surfaces;
when in use;Obtained by the formula (94) toLayer oneAll of the submodels of a groupColor matrix of mixed color samples:
3. Constructing a six-color one-gray seven-primary-color dye liquor full-color-domain color mixing model based on five concentration planes;
(1) A six-color one-gray seven-primary-color dye liquor full-color-domain color mixing model grid point quality matrix based on five concentration planes;
the quality matrix of the grid points of the seven-primary-color dye liquid full-color-domain color mixing model with five concentration levels can be obtained based on the formula (108) as follows:
(2) A grid point color mixing ratio matrix of a six-color one-gray seven-primary-color dye liquor full-color-domain color mixing model based on five concentration planes;
the grid point color mixing ratio matrix of the seven-primary color dye liquid color mixing model with five concentration levels can be obtained based on the formula (109) as follows:
(3) A six-color one-gray seven-primary-color dye liquor full-color domain mixed color model grid point color matrix based on five concentration planes;
the mesh point color matrix of the full-color gamut color mixing model of the seven-primary-color dye liquor with five concentration levels can be obtained based on the formula (110) as follows:
4. constructing a six-color one-gray seven-primary color dye liquor full color gamut geometric model based on five concentration surfaces;
(1) Grid point coordinates of the cylindrical color model;
from the equations (112) (113) (114), the full-color gamut color mixing model based on five concentration planes of six colors, one gray, and seven primary colors is a quadrangular prism color model with 5 layers, 6 rows, and 48 columns, which is visually different from the cylindrical color model. The color model of the quadrangular prism of 5 layers, 6 rows, and 48 columns expressed by equation (100) can be converted into a cylindrical color model by coordinate transformation of the grid points. The method comprises the following specific steps:
setting the height of a cylinder of a cylindrical color model as 1 and the radius of the circle as 1, dividing the height of the cylinder 1 into 4 equal parts based on the characteristics of the quadrangular color model expressed by the formula (114), dividing the circumference with the radius of 1 into 48 equal parts to obtain 48 grid points, and passing through the sections of the 48 grid points and the axis of the cylinder; then 5 equal divisions are carried out on the radius of the circular column to obtain 6 grid points, the center of the circular column is taken as the center to cross 6 grid points on the radius of the circular column to be made into concentric cylinders, and thereby the concentric cylinders can be obtainedGrid points, as shown in fig. 5.
The polar coordinates of each grid point in the cylindrical gridding color model are:
(2) color value of grid point of cylindrical color mixing model
The color values corresponding to each grid point are:
(3) lattice point color mixing ratio of cylindrical color mixing model
The color mixing ratio corresponding to each grid point is:
firstly, based on gray dye liquor and each color dye liquor under the concentration of each level of dye liquor, respectively constructing a multi-primary dye liquor color mixing mode of hue gradient change, chroma gradient change and concentration gradient change by combining discretization of the quality of each dye liquor, and respectively obtaining the quality, color mixing ratio and color value of a multi-primary coupled color mixing sample under each mode; then, respectively constructing a multi-primary color dye liquor coupling color mixing sub-model under each mode; then respectively constructing a full-color phase color mixing model of the multi-primary color dye solution in each mode; finally, respectively constructing circular geometric models of the full color gamut color space under each mode; therefore, hue control, lightness control and chroma control can be realized in application, digital spinning can be efficiently realized, and the spinning color precision is improved.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.
Claims (11)
1. The full-color-domain color model for multi-dimensional gridding dye liquor mixing and the chromatogram construction thereof are characterized by comprising the following steps:
step A. Preset division based on dye liquor concentration from low to highThe concentration of each grade of dye liquor is presetThe quality of the color dye respectively corresponding to the concentration of each grade of dye liquor isThe quality of the gray dye corresponding to the concentration of each grade dye liquor isThe gray dye solutions are sorted according to the size of the hue angle respectively according to the dye solution concentration of each grade and the color dye solutions under the dye solution concentration of each grade; wherein,,,is shown asThe color dye corresponds toThe quality of the color dye liquor of the grade dye liquor concentration;indicates that the grey dye corresponds toQuality of the colour dye liquor of the grade dye liquor concentration, andandthe phase of the two phases is equal to each other, then entering the step B;
step B, respectively measuring the quality of each color dye liquorAccording to preset discrete quantityDiscretization is carried out as follows (1):
wherein,(ii) a And the quality of the grey dye liquorAccording to preset discrete quantityDiscretization is carried out as follows (2):
c, constructing a multi-primary dye liquor color mixing mode with color gradient change based on the multi-primary dye liquor to obtain the quality, the color mixing ratio and the color value of the multi-primary binary coupling color mixing sample;
constructing a multi-primary dye liquor color mixing mode with gradient changes of hue and chroma based on the multi-primary dye liquor, and obtaining the quality, the color mixing ratio and the color value of the multi-primary ternary dual coupling color mixing sample;
constructing a multi-primary dye liquor color mixing mode with changing hue, chroma and concentration gradient based on the multi-primary dye liquor, obtaining the quality, color mixing ratio and color value of the multi-primary ternary dual coupling color mixing sample with different levels of dye liquor concentration, and then entering the step D;
d, constructing a multi-primary dye liquor binary coupling color mixing sub-model based on the quality, the color mixing ratio and the color value of the multi-primary binary coupling color mixing sample;
constructing a multi-primary-color dye-liquor ternary double coupling color mixing sub-model based on the quality, the color mixing ratio and the color value of the multi-primary-color ternary double coupling color mixing sample;
constructing a multi-primary color dye liquor ternary double coupling color mixing sub-model based on different levels of dye liquor concentrations based on the quality, color mixing ratio and color value of the multi-primary color ternary double coupling color mixing sample with different levels of dye liquor concentrations; then entering step E;
e, constructing a one-dimensional full-color phase color mixing model of the multi-primary-color dye liquor according to the multi-primary-color dye liquor binary coupling color mixing sub-model;
constructing a two-dimensional full-color-domain color mixing model of the multi-primary-color dye liquor according to the multi-primary-color dye liquor ternary dual coupling color mixing sub-model;
constructing a three-dimensional full-color-domain color mixing model based on the multi-primary-color dye liquor with different levels of dye liquor concentrations according to the multi-primary-color dye liquor ternary dual coupling color mixing sub-model based on different levels of dye liquor concentrations, and then entering the step F;
f, constructing a circular geometric model of a one-dimensional panchromatic domain color space according to a one-dimensional panchromatic phase color mixing model of the multi-primary color dye solution;
constructing a circular geometric model of a two-dimensional panchromatic domain color space according to a two-dimensional panchromatic domain color mixing model of the multi-primary color dye solution;
and constructing a cylindrical geometric model of a three-dimensional panchromatic domain color space according to a three-dimensional panchromatic domain color mixing model based on the multi-primary-color dye liquor with different levels of dye liquor concentration.
2. The full-color-domain color model for multi-dimensional gridding dye liquor mixing and the chromatographic construction thereof according to claim 1 are characterized in that: in the step C, a multi-primary dye liquor color mixing mode with gradient change of hue is constructed based on the multi-primary dye liquor, and the quality, the color mixing ratio and the color value of the multi-primary binary coupling color mixing sample are obtained according to the following processing;
aiming at the concentration of the dye liquor in each grade, two kinds of color dye liquor are sequentially selected from the sequencing of the multi-base color dye liquor represented by the formula (1) for combined color mixing as follows:
wherein,is shown asConcentration of the dye liquor of gradeThe discrete mass of the seed color dye,is shown asUnder the concentration of the graded dye liquorA discrete mass of seed color dye;
performing binary coupling color mixing according to the formula (3) to obtainA mixed color sample corresponding to the binary coupled mixed color, each mixed color sampleThe following were used:
denotes the firstThe quality of a color mixing sample corresponding to binary coupling color mixing under the concentration of the level dye liquor;
according to formula (4), andcolor mixing ratio of color mixing sample corresponding to binary coupling color mixing under level dye liquor concentrationObtainingThe color mixing ratio of each color dye solution in each color mixing sample is as follows:
is shown asThe quality of the mixed color sample corresponding to the binary coupling mixed color under the concentration of the level dye solution isThe color mixture ratio of the colored dye liquor,is shown asThe quality of the mixed color sample corresponding to the binary coupling mixed color under the concentration of the level dye solution isThe color mixing ratio of the colored dye liquor;
according to the colour value of binary colour dyeing liquor、Obtained with respect to formula (4)The color values of the mixed color samples are respectively as follows:
3. The full-color-domain color model and the color spectrum construction thereof for multi-dimensional gridding dye liquor mixing according to claim 1 are characterized in that: in the step C, a multi-primary dye liquor color mixing mode with gradient changes of hue and chroma is constructed based on the multi-primary dye liquor, and the quality, the color mixing ratio and the color value of the multi-primary ternary dual coupling color mixing sample are obtained through the following processing;
respectively aiming at the concentration of each level of dye liquor, sequentially selecting two color dye liquors from the sequence of the multi-base color dye liquor represented by the formula (1), and combining and selecting the gray dye liquors with the same concentration of the dye liquor from the gray dye liquors represented by the formula (2) to perform combined color mixing as follows:
wherein,is shown asConcentration of the dye liquor of gradeThe discrete mass of the seed color dye,is shown asUnder the concentration of the graded dye liquorThe discrete mass of the seed color dye,is shown asDiscrete mass of grey dye at the level dye liquor concentration;
performing ternary double coupling color mixing according to the formula (8) to obtainThe quality of each mixed color sample is determined by the quality of the mixed color sample corresponding to the ternary double coupling mixed colorThe following were used:
denotes the firstThe quality of a color mixing sample corresponding to ternary double coupling color mixing under the concentration of the level dye solution;
according to formula (9), andcolor mixing ratio of color mixing sample corresponding to ternary double coupling color mixing under level dye liquor concentrationObtainingThe color mixing ratio of each dye solution in each color mixing sample is as follows:
denotes the firstThe quality of the mixed color sample corresponding to ternary double coupling mixed color under the concentration of the level dye solution isThe color mixing ratio of the gray dye liquor,is shown asThe quality of the mixed color sample corresponding to ternary double coupling mixed color under the concentration of the level dye solution isThe color mixture ratio of the colored dye solution;is shown asThe quality of the mixed color sample corresponding to ternary double coupling mixed color under the concentration of the level dye solution isThe color mixture ratio of the colored dye solution;
according to the colour values of two colour dyeing liquors、And color value of the grey dye liquorObtained with respect to formula (9)The color values of the mixed color samples are respectively as follows:
4. The full-color-domain color model for multi-dimensional gridding dye liquor mixing and the chromatographic construction thereof according to claim 1 are characterized in that: in the step C, a multi-primary dye solution color mixing mode with changing hue, chroma and concentration gradient is constructed based on the multi-primary dye solution, the quality, the color mixing ratio and the color value of the multi-primary ternary dual coupling color mixing sample with different levels of dye solution concentration are obtained according to the following processing,
based on the color dye solutions under the dye solution concentrations of all levels, two color dye solutions are selected from the dye solution concentrations of different levels, and the gray dye solutions are selected from the gray dye solutions represented by the formula (2) to carry out combined color mixing as follows:
wherein,、、,is shown asDiscrete mass of grey dye at the level dye liquor concentration,is shown asUnder the concentration of the graded dye liquorThe discrete mass of the seed color dye,is shown asUnder the concentration of the graded dye liquorA discrete mass of seed color dye;
performing ternary double coupling color mixing according to formula (12) to obtainThe quality of each mixed color sample is determined by the quality of the mixed color sample corresponding to the ternary double coupling mixed colorThe following were used:
representing the quality of a color mixing sample corresponding to ternary double coupling color mixing under different levels of dye liquor concentration; according to the formula (13) and the color mixing ratio of the color mixing sample corresponding to the ternary double coupling color mixing under different levels of dye liquor concentrationTo obtainThe color mixing ratio of each dye liquor in each color mixing sampleThe following were used:
the quality of the mixed color sample corresponding to ternary double coupling mixed color under different levels of dye liquor concentration is shown asThe color mixing ratio of the gray dye liquor of (1),the quality of the mixed color sample corresponding to ternary double coupling mixed color under different levels of dye liquor concentration is shown asThe color mixing ratio of the colored dye liquor;the quality of the mixed color sample corresponding to ternary double coupling mixed color under different levels of dye liquor concentration is shown asThe color mixture ratio of the colored dye solution;
according to the colour values of two colour dyeing liquors、And color value of the grey dye liquorAs to formula (13)ObtainThe color values of the mixed color samples are respectively as follows:
5. The full-color-domain color model and the color spectrum construction thereof for multi-dimensional gridding dye liquor mixing according to claim 1 are characterized in that: in the step D, based on the quality, the color mixing ratio and the color value of the multi-primary-color binary coupling color mixing sample, constructing a multi-primary-color dye solution binary coupling color mixing sub-model as follows:
(1) the quality matrix of the multi-primary color dye liquor binary coupling color mixing sub-model is as follows:
is shown asThe quality of a color mixing sample corresponding to binary coupling color mixing under the concentration of the level dye liquor;
(2) the color mixing ratio matrix of the multi-primary color dye liquor binary coupling color mixing submodel is as follows:
is shown asThe color mixing ratio of the color mixing sample corresponding to the binary coupling color mixing under the concentration of the level dye liquor;
(3) the color matrix of the multi-primary color dye liquor binary coupling color mixing submodel is as follows:
is shown asColor values of color mixing samples corresponding to binary coupling color mixing under the concentration of the graded dye solution;
based on the quality, the color mixing ratio and the color value of the multi-primary-color ternary and dual coupling color mixing sample, the multi-primary-color dye-liquor ternary and dual coupling color mixing sub-model is constructed as follows:
(1) the quality matrix of the multi-primary-color dye liquor ternary double-coupling color mixing sub-model is as follows:
is shown asThe quality of a color mixing sample corresponding to ternary double coupling color mixing under the concentration of the level dye solution;
(2) the color mixing ratio matrix of the multi-primary-color dye liquor ternary double coupling color mixing submodel is as follows:
is shown asThe color mixing ratio of the color mixing sample corresponding to the ternary double coupling color mixing under the concentration of the level dye solution;
(3) the color matrix of the multi-primary color dye liquor ternary double coupling color mixing submodel is as follows:
is shown asColor values of color mixing samples corresponding to ternary double coupling color mixing under the concentration of the level dye solution;
based on the quality, the color mixing ratio and the color value of the multi-primary-color ternary double-coupling color mixing sample with different levels of dye liquor concentration, a multi-primary-color ternary double-coupling color mixing sub-model based on different levels of dye liquor concentration is constructed as follows:
(1) the quality matrix of the multi-primary color dye liquor ternary double-coupling color mixing sub-model based on different levels of dye liquor concentrations is as follows:
representing the quality of a color mixing sample corresponding to ternary double coupling color mixing under different levels of dye liquor concentration;
(2) the color mixing ratio matrix of the multi-primary color dye liquor ternary double-coupling color mixing submodel based on different levels of dye liquor concentration is as follows:
representing the color mixing ratio of the color mixing sample corresponding to the ternary double coupling color mixing under different levels of dye liquor concentration;
(3) the color matrix of the multi-primary color dye liquor ternary double-coupling color mixing submodel based on different levels of dye liquor concentration is as follows:
6. The full-color-domain color model for multi-dimensional gridding dye liquor mixing and the chromatographic construction thereof according to claim 5 are characterized in that: in the step E, according to the multi-primary color dye solution binary coupling color mixing sub-model, a one-dimensional full-color phase color mixing model of the multi-primary color dye solution is constructed as follows:
order toIs provided withThen, the expressions (16), (17) and (18) correspond to allThe quality, color mixing ratio, and color of the binary coupled color mixture sample are measured by 1 lineThe matrix of columns is represented as follows:
the compounds of the formulae (16), (17) and (18)And expanding to obtain a quality matrix of the one-dimensional full-hue gridding color mixing model as follows:
the color mixing ratio matrix of the one-dimensional full-hue gridding color mixing model is obtained as follows:
the color matrix of the one-dimensional full-hue gridding color mixing model is obtained as follows:
namely, a one-dimensional full-color phase color mixing model of the multi-primary color dye solution constructed based on the multi-primary color dye solution binary coupling color mixing is obtained.
7. The full-color-domain color model and the color spectrum construction thereof for multi-dimensional gridding dye liquor mixing according to claim 6 are characterized in that: in the step F, according to the one-dimensional full-color phase color mixing model of the multi-primary-color dye solution, the circular geometric model of the one-dimensional full-color domain color space is constructed as follows:
respectively aiming at the dye liquor concentration of each grade according toRespective mixed color samples of respective grid pointsThe hue angle is arranged in sequence and evenly distributed on the circumference with the radius of 1, and each color value is setPolar angle of grid point ofPolar radius ofThen each color valueThe polar coordinates of the grid points of (a) are:
according toThen, the color values of the grid points are obtained by equations (5) and (6)The following:
namely, based on the formulae (25) (26), obtainedThe annular geometric model of one-dimensional full color gamut color space constructed by combining multi-primary color dye liquor binary coupling color mixing is uniformly divided into hue circlesThe polar coordinates of each grid point and its color value can be obtained by equations (25) and (26).
8. The full-color-domain color model for multi-dimensional gridding dye liquor mixing and the chromatographic construction thereof according to claim 5 are characterized in that: in the step E, according to the multi-primary-color dye liquor ternary double-coupling color mixing sub-model, a two-dimensional full-color-domain color mixing model of the multi-primary-color dye liquor is constructed as follows:
based on the formulas (13), (14) and (15), it can be seen that the dye solutions of multiple primary colors are respectively used for the dye solution concentrations of each gradeThe group-element dual-coupling color mixing submodel comprisesA grid point, passingLine ofA matrix representation of the columns, andthe group-ternary dual-coupling color-mixing gridding submodel is spliced and combined in sequence from head to tail corresponding to each line to obtain gray dye solutionAnd a colored dye liquorForming a multi-primary color panchromatic domain gridding color mixing model;
when the temperature is higher than the set temperatureWhen the temperature of the water is higher than the set temperature,,and is made of;
When the temperature is higher than the set temperatureWhen the utility model is used, the water is discharged,,and is and;
when the temperature is higher than the set temperatureWhen the temperature of the water is higher than the set temperature,,and is and;
based on the aboveObtained by double coupling and color mixing of group-three dye solutionsColor mixture sample, and constructionLine ofA gridding matrix of columns, thereby constructing a full color gamut gridding color mixing model, and developing the formula (27) to obtain the full color gamut gridding color mixing modelLine ofThe column quality matrix is as follows, namely the quality matrix of the two-dimensional panchromatic gamut color mixing model of the multi-primary color dye solution;
and (4) obtaining a color mixing ratio matrix of a two-dimensional panchromatic gamut color mixing model of the multi-primary color dye solution corresponding to the formula (28):
and (5) obtaining a color matrix of a two-dimensional full-color-domain color mixing model of the multi-primary color dye solution, corresponding to the formula (29):
namely, a two-dimensional full-color-domain color mixing model of the multi-primary-color dye solution constructed based on the multi-primary-color dye solution ternary double-coupling color mixing sub-model is obtained.
9. The full-color-domain color model and the color spectrum construction thereof for multi-dimensional gridding dye liquor mixing according to claim 8 are characterized in that: in the step F, according to a two-dimensional panchromatic range color mixing model of the multi-primary color dye solution, a circular geometric model of a two-dimensional panchromatic range color space is constructed according to the following operation;
according to the formulas (32), (34) and (36), the two-dimensional full-color-domain color mixing model based on the multi-primary-color dye liquor is a modelLine ofA rectangular color model of the column expressed by equation (36) by coordinate transformation of the grid pointsLine for mobile communication terminalThe rectangular color model of the column is converted into a circular color model as follows:
with circular colour modelsRadius of 1, based on the characteristics of the rectangular color model expressed by equation (36), along the circumference of radius 1Is divided equally to obtainA grid point is drawnConnecting lines of the grid points and the circle center; then the radius of the circle is processedIs divided equally to obtainA grid point on the circle radius centered at the center of the circleMaking concentric circles at each grid point, thereby obtainingThe polar coordinates of each grid point in the circular gridding color model are as follows:
the color value of each grid point in the circular gridding color model is as follows:
the color mixing ratio of each grid point in the circular gridding color model is as follows:
10. the full-color-domain color model for multi-dimensional gridding dye liquor mixing and the chromatographic construction thereof according to claim 5 are characterized in that: in the step E, according to the multi-primary color dye liquor ternary double-coupling color mixing sub-model based on different levels of dye liquor concentration, a three-dimensional full-color-domain color mixing model based on the multi-primary color dye liquor with different levels of dye liquor concentration is constructed as follows:
a first of the multi-primary dyebaths at different dye liquor concentrations based on formula (40)Layer oneThe group-ternary double coupling color mixing is constructedSub-models, each sub-model comprisingIndividual grid points, should work the firstLayer oneOf group (a)Line ofMatrix representation of the columns, will allOf a layerThe group-ternary dual-coupling color-mixing gridding submodel is spliced and combined in sequence from head to tail corresponding to each line to obtain gray dye solutionAnd color dye liquorForming a multi-primary color panchromatic domain gridding color mixing model;
When the temperature is higher than the set temperatureWhen the temperature of the water is higher than the set temperature,,and is made of;
based on formula (44), under different levels of dye liquor concentrationLayer(s)Obtained by double coupling and color mixing of group-three dye solutionsColor mixing sample constructionAnLine for mobile communication terminalA gridding matrix of columns, thereby constructing a full color gamut gridding color mixing model, and developing the formula (44) to obtain the full color gamut gridding color mixing modelAnLine for mobile communication terminalColumn quality matrix:
corresponding to the formula (44), under different levels of dye liquor concentration, obtaining a color mixing ratio matrix of the three-dimensional full-color-gamut gridding color mixing model as follows:
or:
corresponding to the formula (46), under different levels of dye liquor concentration, the color matrix of the two-dimensional full color gamut gridding color mixing model is obtained as follows:
or:
namely, a three-dimensional full-color-domain color mixing model based on multi-primary-color dye liquor with different levels of dye liquor concentration is constructed.
11. The full-color-domain color model and the color spectrum construction thereof for multi-dimensional gridding dye liquor mixing according to claim 10 are characterized in that: in the step F, according to a three-dimensional panchromatic range color mixing model based on multi-primary-color dye liquor with different levels of dye liquor concentration, a cylindrical geometric model of a three-dimensional panchromatic range color space is constructed according to the following operations:
according to the formulas (45), (47) and (49), the three-dimensional full-color-domain color mixing model based on the multi-primary-color dye liquor with different levels of dye liquor concentration is a modelLayer(s)Line ofA quadrangular prism color model of the columns expressed by equation (49) by coordinate conversion of grid pointsLayer(s)Line ofThe rectangular color model of the column is converted into a cylindrical color model as follows:
setting the cylinder height of the cylindrical color model as 1 and the radius of the circle as 1, and based on the characteristics of the quadrangular color model expressed by the formula (49), making the cylinder height of 1 asEqually dividing the circumference with the radius of 1 intoIs divided equally to obtainA grid pointA tangent plane of each grid point and the center of the cylinder; then the radius of the cylinder is adjustedIs divided equally to obtainA grid point on the radius of the circle with the center of the cylinder as the centerMaking concentric cylinders at each grid point, thereby obtainingThe polar coordinates of each grid point in the cylindrical gridding color model are as follows:
the color values of each grid point in the cylindrical gridding color model are as follows:
the color mixing ratio of each grid point in the cylindrical gridding color model is as follows:
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