CN113538690A - HSV gridding model construction and chromatogram visualization method - Google Patents

HSV gridding model construction and chromatogram visualization method Download PDF

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CN113538690A
CN113538690A CN202110666688.7A CN202110666688A CN113538690A CN 113538690 A CN113538690 A CN 113538690A CN 202110666688 A CN202110666688 A CN 202110666688A CN 113538690 A CN113538690 A CN 113538690A
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薛元
李娟娟
孙显强
崔鹏
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Abstract

The invention relates to construction of an HSV gridding model, which is based on an HSV color space of a regular hexagonal prism and is decomposed into six regular triangular prism color general models, a gridding model capable of carrying out double coupling association on three dimensions such as hue angle, chroma, lightness and the like is constructed by gridding three bottom edges and edge heights of the regular triangular prism color general models, and the construction of an eight-primary-color HSV gridding model is realized by integrating and expanding the gridding model. The digital expression of grid point color values of the HSV color model by using grid point coordinates is realized on the basis of the eight-primary-color HSV gridding model, the construction of a grid point array model and a matrix of an equal lightness plane, an equal hue plane and an equal chroma plane of the eight-primary-color HSV color space is efficiently realized by the eight-primary-color HSV gridding model, and the digital expression and the visualization of grid point chromatograms of the equal lightness plane, the equal hue plane and the equal chroma plane of the eight-primary-color HSV are realized.

Description

HSV gridding model construction and chromatogram visualization method
Technical Field
The invention relates to an HSV gridding model construction and a chromatogram visualization method, and belongs to the technical field of spinning chromatograms.
Background
The HSV in the HSV color model is Hue, chroma, and lightness (Hue, Saturation). The HSV color model is a model that uses the hue circle as the circumference, chroma as the radius, and lightness as the high cylinder. The HSV color model is a cylinder of spatial colors, and is schematically shown in figure 1. The HSV color space is a cylinder, the brightness value of the upper top surface is 1, the brightness value of the lower bottom surface is 0, when the brightness value is changed from 1 to 0, the brightness value of each hue on the top surface is gradually reduced from 1 to 0, and the brightness value is completely changed into black, and on the central axis of the cylinder, the brightness value is gradually changed from white to black in the process from the center of the circle of the upper top surface to the center of the circle of the lower bottom surface; in the cylindrical HSV color space, the center of a cylinder is taken as the center, the central angle H swept by the radius of the cylinder is taken as a hue angle, wherein the hue angles of red, yellow, green, cyan, blue and magenta are 0 degree, 60 degree, 120 degree, 180 degree, 240 degree, 270 degree and 360 degree in sequence. When the hue angle is changed from 0-360 degrees, the hue is sequentially changed by red, orange, yellow, green, cyan, blue and purple; in the cylindrical HSV color space, the distance S from a certain point to the axis of the cylinder is chroma, and the equal-chroma surface is a cylindrical surface with the radius of S, so that when the chroma value is changed from 0 to 1, the change process of the chroma of each color phase is reflected. The coordinate values of the eight vertexes of the RGB color model in the HSV color model are shown in Table 1
TABLE 1
Figure BDA0003117705800000011
Visualization of HSV space panchromatic gamut colors is very important for color design using color variation rules. However, the existing HSV color space theory has the following problems:
1. although the hue angle, chroma and lightness and the value range of the HSV color model are defined based on a polar coordinate system, the quantitative analysis of the color distribution rule of the HSV color model from three dimensions of hue angle, chroma, lightness and the like is lacked;
2. although the HSV color model is deduced based on the RGB color model, a gridding HSV color model which can be used for a digital algorithm is not constructed, and variables of three dimensions such as hue angle, chroma and lightness of the HSV color model are related through grid point array coordinates;
3. although an equal brightness plane, an equal hue plane and an equal chroma plane are defined based on the HSV color model, a method for solving the grid point array chromatogram on the equal brightness plane, the equal hue plane and the equal chroma plane of the HSI color model is not provided.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an HSV meshing model construction method, an HSV color space based on a regular hexagonal prism is decomposed into six regular triangular prism color general models, a meshing model capable of carrying out double coupling association on three dimensions such as hue angle, chroma and lightness is constructed by meshing three bottom edges and edge heights of the regular triangular prism color general models, and the construction of an eight-primary-color HSV meshing model is realized by integrating and expanding the meshing model.
The invention adopts the following technical scheme for solving the technical problems: the invention designs an HSV gridding model construction, based on an HSV color space of a regular hexagonal prism with white W at the center of the top surface and black K at the bottom surface, aiming at that six primary colors of red R, yellow Y, green G, cyan C, blue B and magenta M respectively fall at the positions of the edges of the top surface of the HSV color space corresponding to six side edges according to the following steps by combining a hue angle H corresponding to the circumference of the regular hexagonal prism in a value range of 0-360 degrees, a chroma S corresponding to a distance from any point in the regular hexagonal prism to the center of the cylinder in a value range of 0-1 and a lightness V corresponding to the height of the regular hexagonal prism in a value range of 0-1;
step A, according to the fact that the positions of red R, yellow Y, green G, cyan C, blue B and magenta M corresponding to the bottom surface edge of the HSV color space along each side edge are respectively KR、KY、KG、KC、KB、KMDecomposing the HSV hexagonal prism color model into six regular triangular prism color channelsUsing models, respectively: WYR-KKYKR、WGY-KKGKY、WCG-KKCKG、WBC-KKBKC、WMB-KKMKB、WRM-KKRKMBecause the bottom surface of the regular hexagonal prism is black, the general color model of the six regular triangular prisms can be called as: a red-yellow-white-black color sub-model, a yellow-green-white-black color sub-model, a green-cyan-white-black color sub-model, a cyan-blue-white-black color sub-model, a blue-magenta-white-black color sub-model, a magenta-red-white-black color sub-model; the universal model WX for the six regular triangular prism color universal models1X2-KKX1KX2Is represented by, wherein X1＝{R、Y、G、C、B、M}，X1＝{R、Y、G、C、B、M}，X2≠X1Then entering step B;
and B, aiming at the regular triangular prism color general model, executing 10 equal parts on the side corresponding to the hue angle and the two sides corresponding to the chroma radius in the regular triangular prism color general model, and executing 100 equal parts on the height corresponding to the lightness in the regular triangular prism color general model, so that the regular triangular prism color general model is subjected to gridding division to obtain the coordinate of each grid point
Figure BDA0003117705800000021
Then entering step C; wherein, i is 1,2, …,10,11, j is 1,2, …,10,11, i + j is less than or equal to 12, t is 1,2, …,100, 101; i represents the interior slave X of the regular triangular prism color general model1To X2Side corresponding to hue angle
Figure BDA0003117705800000022
The hue sequence numbers of the grid points divided upwards; j represents grid point chroma serial numbers outwards from the center of the column along the radius on two edges corresponding to the chroma radius in the regular triangular prism color general model, and t represents grid point lightness serial numbers divided from white to black in the regular triangular prism color general model;
step C, needle positive general model
Figure BDA0003117705800000023
The corresponding four primary colors are
Figure BDA0003117705800000024
W(RW,GW,BW)、K(RK,GK,BK) On the equal lightness surface with lightness t, the hue number, chroma number and color value of the grid point are set
Figure BDA0003117705800000025
W(RW,GW,BW) Performing a first re-coupling, and then combining the color values with a lightness value number and a primary color value K (R)K,GK,BK) Performing second double coupling, and constructing a regular triangular prism color general model through the double coupling, thereby obtaining color values d of all grid points in the gridding general modeli,j,tThe following were used:
Figure BDA0003117705800000031
wherein, X1、X2W, K is the four primary colors color value of the regular triangular prism color general model, which is respectively:
Figure BDA0003117705800000032
Figure BDA0003117705800000033
W(RW,GW,BW)、K(RK,GK,BK)；di,j,tfor grid points within the gridded general model, its RGB color value is di,，j,t(Ri,，j,t,Gi,j,t,Bi,j,t) (ii) a Then entering step D;
d, respectively constructing a color conversion matrix Z of the regular triangular prism color general modeli,j,t、Z′i,j,tAnd Z ″)i,j,tThen enter step E as follows;
Figure BDA0003117705800000034
Figure BDA0003117705800000035
Figure BDA0003117705800000036
step E, respectively aiming at the general color model of each regular triangular prism and according to Zi,j,t、Z′i,j,t、Z″i,j,t、pi,j,t、di,j,tUpdating color value d of each grid point in regular triangular prism color general modeli,j,t＝Z″i,j,t×(Zi,j,t×αi,j,t+Z′i,j,t) And then obtaining the color value of each grid point in the HSV color space.
As a preferred technical scheme of the invention: color value d of each grid point in universal model based on colors of regular triangular prismsi,j,tFurther comprising the steps of:
step F, according to the coordinates of each grid point in the regular triangular prism color general model
Figure BDA0003117705800000037
Combining the serial number l of each regular triangular prism color general model to be 1,2, 5 and 6, and constructing coordinates p of each grid point in the eight-primary-color HSV gridding modeli,j,t,lThen step G is entered as follows;
Figure BDA0003117705800000041
g, according to the color value d of each grid point in the regular triangular prism color general modeli,j,tAnd combining the serial numbers l of the regular triangular prism color general models to be 1,2, 5 and 6, constructing color values d of grid points in the eight-primary-color HSV gridding modeli,j,t,lThen step H is entered as follows;
Figure BDA0003117705800000042
according to Zi,j,t、Zi',j,tAnd Zi”,j,tRespectively constructing color conversion matrix Z of the eight-primary-color HSV gridding modeli,j,t,l、Z′i,j,t,lAnd Z ″)i,j,t,lThen entering step I as follows;
Figure BDA0003117705800000043
Figure BDA0003117705800000044
Figure BDA0003117705800000045
according to Zi,j,t,l、Z′″i,j,t,l、Z″i,j,t,l、pi,j,t,l、di,j,t,lUpdating color value d of each grid point in the HSV gridding model with eight primary colorsi,j,t,l＝Zi”,j,t,l×(Zi,j,t,l×αi,j,t,l+Zi',j,t,l)。
The technical problem to be solved by the invention is to provide a chromatogram visualization method constructed based on an HSV meshing model, which realizes the digital expression of grid point color values of the HSV color model by using grid point coordinates based on the HSV meshing model with eight primary colors, and efficiently realizes the construction of a grid point array model and a matrix of an equal lightness plane, an equal hue plane and an equal chroma plane of an HSV color space with eight primary colors through the HSV meshing model with eight primary colors, thereby realizing the digital expression and visualization of grid point chromatograms of the equal lightness plane, the equal hue plane and the equal chroma plane of the HSV color space with eight primary colors.
The invention adopts the following technical scheme for solving the technical problems: the invention designs HSV gridA chromatogram visualization method for constructing a gridding model is based on 101 equal brightness surfaces which are respectively vertical to an axis where brightness V is located and correspond to 100 equal parts of brightness V executed in an eight-primary-color HSV gridding model, and based on t being 1,2, …,100 and 101, a grid point array matrix A which is respectively corresponding to each equal brightness surface in the eight-primary-color HSV gridding model is obtainedi,j,t,lThe following were used:
Figure BDA0003117705800000051
wherein, when t is 1,
Figure BDA0003117705800000052
when t is 2, …,100,
Figure BDA0003117705800000053
when t is 101, the process is repeated,
Figure BDA0003117705800000061
as a preferred technical scheme of the invention: obtaining a mixed color chromatographic matrix DA corresponding to each equal brightness surface in the eight-primary-color HSV gridding model respectively based on 100 equal brightness surfaces corresponding to equal brightness V in the eight-primary-color HSV gridding model and based on t being 1,2, …,100 and 101i,j,t,lThe following were used:
Figure BDA0003117705800000062
as a preferred technical scheme of the invention: the top surface center and the bottom surface center of the eight-primary-color HSV gridding model are connected and respectively combined with six lateral edges of a regular hexagonal prism to form six equal-color surfaces, and then the corresponding equal-color surfaces of the eight-primary-color HSV gridding model are obtainedGrid point array matrix Bi,j,t,lThe following were used:
Figure BDA0003117705800000063
and further obtaining a color mixing chromatographic matrix DB corresponding to each isochromatic phase surface in the eight-primary-color HSV gridding modeli,j,t,lThe following were used:
Figure BDA0003117705800000071
as a preferred technical scheme of the invention: six side surfaces of the regular hexagonal prism corresponding to the eight-primary-color HSV meshing model form six equal-chroma surfaces, and based on the condition that m is 1,2, …,10 and 11, a grid point array matrix C corresponding to each equal-chroma surface in the eight-primary-color HSV meshing model is obtainedi,j,t,lThe following were used:
Figure BDA0003117705800000072
wherein, when m is 1,
Figure BDA0003117705800000073
when m is 2, …,10,
Figure BDA0003117705800000074
when m is equal to 11, the compound is,
Figure BDA0003117705800000075
as a preferred technical scheme of the invention: obtaining a mixed color chromatographic matrix DC corresponding to each isochromatic surface in the eight-primary-color HSV gridding modeli,j,t,lThe following were used:
Figure BDA0003117705800000081
compared with the prior art, the HSV meshing model construction and chromatogram visualization method has the following technical effects by adopting the technical scheme:
the method comprises the steps of constructing an HSV gridding model designed by the invention, decomposing an HSV color space based on a regular hexagonal prism into six regular triangular prism color general models, constructing a gridding model capable of carrying out double coupling association on three dimensions such as hue angle, chroma, lightness and the like by gridding three bottom edges and edge heights of the regular triangular prism color general models, and realizing construction of the eight-primary-color HSV gridding model by integrating and expanding the gridding model. The digital expression of grid point color values of the HSV color model by using grid point coordinates is realized on the basis of the eight-primary-color HSV gridding model, the construction of a grid point array model and a matrix of an equal lightness plane, an equal hue plane and an equal chroma plane of the eight-primary-color HSV color space is efficiently realized by the eight-primary-color HSV gridding model, and the digital expression and the visualization of grid point chromatograms of the equal lightness plane, the equal hue plane and the equal chroma plane of the eight-primary-color HSV are realized.
Drawings
FIG. 1 is a schematic diagram of an HSV color model;
FIG. 2 is a schematic of an eight-primary-color regular hexagonal prism HSV color model;
FIG. 3 is an exploded view of a general regular triangular prism color model corresponding to an eight-primary-color regular hexagonal prism HSV color model;
FIG. 4 is a schematic of an equal lightness plane within the eight primary color HSV color model;
FIG. 5 is an illustration of an isochromatic plane within an eight primary HSV color model;
FIG. 6 is an illustration of an isochromatic plane in an eight primary HSV color model.
Detailed Description
The following description will explain embodiments of the present invention in further detail with reference to the accompanying drawings.
HSV color modelThe top surface of the cylindrical model is centered at W, the top surface is divided by taking the red color as a reference and taking the 60-degree hue angle as a gradient, and 6 points such as R, Y, G, C, B, M can be obtained, as shown in FIG. 2. R, Y, G, C, B, M, W and other 7 points of the top surface intersect the bottom surface of the cylinder at KR、KY、KG、KC、KB、KMK, thereby obtaining six bus bars and a cylindrical axis which are respectively connected with R, Y, G, C, B, M on the top surface and K on the bottom surfaceR、KY、KG、KC、KB、KMThereby, an eight-primary HSV hexagonal prism model as shown in fig. 1 is obtained. According to the definition of HSV color model, six bus lines R-KR、Y-KY、G-KG、C-KC、B-KB、M-KMRespectively reflects the change process of the lightness values of six primary colors of R, Y, G, C, B, M and the like from 1 to 0, and is arranged on the bottom surface KR、KY、KG、KC、KB、KMIs equal to black and is (0,0, 0).
The primary colors used by the HSV hexagonal prism model are R, Y, G, C, B, M, W, K, respectively, which can be decomposed into six triangular prism color models as shown in fig. 3, which are: WYR-KKYKR、WGY-KKGKY、WCG-KKCKG、WBC-KKBKC、WMB-KKMKB、WRM-KKRKM. Because the bottom surface of the hexagonal prism is black, the six triangular prism color models can be called as follows: a red-yellow-white-black color sub-model, a yellow-green-white-black color sub-model, a green-cyan-white-black color sub-model, a cyan-blue-white-black color sub-model, a blue-magenta-white-black color sub-model, a magenta-red-white-black color sub-model.
In the eight-primary-color regular hexagonal prism HSV color model, as shown in fig. 4, the colors with different hues and different chroma have the same lightness value on the plane perpendicular to the WK axis, so that the plane is called an equal lightness plane, i.e. an R 'Y' G 'C' B 'M' regular hexagonal plane shown in fig. 4, and the plane can move up and down in the HSV space along the WK axis to obtain different equal lightness planes.
In the eight-primary-color regular hexagonal prism HSV color model, a plane formed by the WK axis and one of the six primary colors has the same hue for colors of different lightness and chroma, and is called an isochromatic plane. WKK as shown in FIG. 5R’The regular quadrilateral of R may be referred to as an isochromatic surface.
In the eight-primary-color regular hexagonal prism HSV color model, six side surfaces of a hexagonal prism formed around the WK axis in the HSV color space have the same chroma for colors of different lightness and different hue on the plane, and are called as equal chroma planes. The hexagonal prism shown in FIG. 6, R "Y" G "C" B "M" -KR’KY’KG’KC’KB’KM’These planes may be referred to as isochromatic planes.
Based on the analysis of the eight-primary-color regular hexagonal prism HSV color model, the eight-primary-color regular hexagonal prism HSV color model is divided into six regular triangular prism color general models of alpha-beta-W-K, beta-gamma-W-K, gamma-delta-W-K, delta-epsilon-W-K, epsilon-omega-W-K and alpha-omega-W-K. The method is used for designing an HSV gridding model to be constructed, based on an HSV color space of a regular hexagonal prism with white W at the center of the top surface and black K at the bottom surface, aiming at the fact that six primary colors of red R, yellow Y, green G, cyan C, blue B and magenta M respectively fall at the positions of the edges of the top surface of the HSV color space corresponding to six side edges, the construction of an HSV gridding model with eight primary colors is realized according to the following steps A to I by combining a hue angle H corresponding to the circumferential numeric area of the regular hexagonal prism of 0-360 degrees, a chroma S corresponding to the numeric area from any point in the regular hexagonal prism to the center of the cylinder and a lightness V corresponding to the numeric area of 0-1 of the regular hexagonal prism.
Step A, according to the fact that the positions of red R, yellow Y, green G, cyan C, blue B and magenta M corresponding to the bottom surface edge of the HSV color space along each side edge are respectively KR、KY、KG、KC、KB、KMDecomposing the HSV hexagonal prism color model into six regular triangular prism color general models which are respectively as follows: WYR-KKYKR、WGY-KKGKY、WCG-KKCKG、WBC-KKBKC、WMB-KKMKB、WRM-KKRKMBecause the bottom surface of the regular hexagonal prism is black, the general color model of the six regular triangular prisms can be called as: a red-yellow-white-black color sub-model, a yellow-green-white-black color sub-model, a green-cyan-white-black color sub-model, a cyan-blue-white-black color sub-model, a blue-magenta-white-black color sub-model, a magenta-red-white-black color sub-model; the universal model WX for the six regular triangular prism color universal models1X2-KKX1KX2Is represented by, wherein X1＝{R、Y、G、C、B、M}，X1＝{R、Y、G、C、B、M}，X2≠X1Then, step B is entered.
And B, aiming at the regular triangular prism color general model, executing 10 equal parts on the side corresponding to the hue angle and the two sides corresponding to the chroma radius in the regular triangular prism color general model, and executing 100 equal parts on the height corresponding to the lightness in the regular triangular prism color general model, so that the regular triangular prism color general model is subjected to gridding division to obtain the coordinate of each grid point
Figure BDA0003117705800000101
Then entering step C; wherein, i is 1,2, …,10,11, j is 1,2, …,10,11, i + j is less than or equal to 12, t is 1,2, …,100, 101; i represents the interior slave X of the regular triangular prism color general model1To X2Side corresponding to hue angle
Figure BDA0003117705800000102
The hue sequence numbers of the grid points divided upwards; j represents the mesh point chroma serial number from the center of the column to the outside along the radius on two edges corresponding to the chroma radius in the regular triangular prism color general model, and t represents the mesh point lightness serial number divided from white to black in the regular triangular prism color general model.
Step C, needle positive general model
Figure BDA0003117705800000103
The corresponding four primary colors are
Figure BDA0003117705800000104
W(RW,GW,BW)、K(RK,GK,BK) On the equal lightness surface with lightness t, the hue number, chroma number and color value of the grid point are set
Figure BDA0003117705800000105
W(RW,GW,BW) Performing a first re-coupling, and then combining the color values with a lightness value number and a primary color value K (R)K,GK,BK) Performing second double coupling, and constructing a regular triangular prism color general model through the double coupling, thereby obtaining color values d of all grid points in the gridding general modeli,j,tThe following were used:
Figure BDA0003117705800000106
wherein, X1、X2W, K is the four primary colors color value of the regular triangular prism color general model, which is respectively:
Figure BDA0003117705800000107
Figure BDA0003117705800000108
W(RW,GW,BW)、K(RK,GK,BK)；di,j,tfor grid points within the gridded general model, its RGB color value is di,j,t(Ri,j,t,Gi,j,t,Bi,j,t) (ii) a Then step D is entered.
D, respectively constructing a color conversion matrix Z of the regular triangular prism color general modeli,j,t、Z′i,j,tAnd Z ″)i,j,tThen enter step E as follows;
Figure BDA0003117705800000109
Figure BDA00031177058000001010
Figure BDA0003117705800000111
step E, respectively aiming at the general color model of each regular triangular prism and according to Zi,j,t、Z′i,j,t、Z″i,j,t、pi,j,t、di,j,tUpdating color value d of each grid point in regular triangular prism color general modeli,j,t＝Z″i,j,t×(Zi,j,t×αi,j,t+Zi',j,t) And then obtaining color values of grid points in the HSV color space, and then proceeding to step F.
Step F, according to the coordinates of each grid point in the regular triangular prism color general model
Figure BDA0003117705800000112
Combining the serial number l of each regular triangular prism color general model to be 1,2, 5 and 6, and constructing coordinates p of each grid point in the eight-primary-color HSV gridding modeli,j,t,lThen step G is entered as follows;
Figure BDA0003117705800000113
g, according to the color value d of each grid point in the regular triangular prism color general modeli,j,tAnd combining the serial numbers l of the regular triangular prism color general models to be 1,2, 5 and 6, constructing color values d of grid points in the eight-primary-color HSV gridding modeli,j,t,lThen step H is entered as follows;
Figure BDA0003117705800000114
according to Zi,j,t、Z′i,j,tAnd Z ″)i,j,tAre respectively constructedColor conversion matrix Z for building eight-primary-color HSV gridding modeli,j,t,l、Z″i,j,t,lAnd Z ″)i,j,t,lThen entering step I as follows;
Figure BDA0003117705800000115
Figure BDA0003117705800000116
Figure BDA0003117705800000117
according to Zi,j,t,l、Z′i,j,t,l、Z″i,j,t,l、pi,j,t,l、di,j,t,lUpdating color value d of each grid point in the HSV gridding model with eight primary colorsi,j,t,l＝Z″i,j,t,l×(Zi,j,t,l×αi,j,t,l+Z′i,j,t,l)。
Based on 100 equal parts of 101 equal brightness surfaces which are respectively corresponding to 100 equal brightness surfaces executed by a brightness V in the eight-primary-color HSV meshing model and are respectively vertical to an axis where the brightness V is positioned, and based on t being 1,2, …,100 and 101, a grid point array matrix A which is respectively corresponding to each equal brightness surface in the eight-primary-color HSV meshing model is obtainedi,j,t,lThe following were used:
Figure BDA0003117705800000121
wherein, when t is 1,
Figure BDA0003117705800000122
when t is 2, …,100,
Figure BDA0003117705800000131
when t is 101, the process is repeated,
Figure BDA0003117705800000132
for 101 equal brightness surfaces corresponding to 100 equal parts executed on brightness V in the eight-primary-color HSV gridding model, obtaining a mixed-color chromatographic matrix DA corresponding to each equal brightness surface in the eight-primary-color HSV gridding model based on t ═ 1,2, …,100,101i,j,t,lThe following were used:
Figure BDA0003117705800000133
the three-dimensional matrix can respectively represent six triangular prism models of alpha-beta-W-K, beta-gamma-W-K, gamma-delta-W-K, delta-epsilon-W-K, epsilon-omega-W-K and alpha-omega-W-K by the values of 1,2, 3, 4, 5 and 6 of l. A total of 6 × 101 to 606 equal brightness planes can be obtained. Here, the expansion of the chromatogram matrix is similar to that of the grid point array matrix, and is not necessarily expanded.
The top surface center and the bottom surface center of the eight-primary-color HSV gridding model are connected and respectively combined with six lateral edges of a regular hexagonal prism to form six equal-color surfaces, and a grid point array matrix B corresponding to each equal-color surface in the eight-primary-color HSV gridding model is obtainedi,j,t,lThe following were used:
Figure BDA0003117705800000141
and further obtaining a color mixing chromatographic matrix DB corresponding to each isochromatic phase surface in the eight-primary-color HSV gridding modeli,j,t,lThe following were used:
Figure BDA0003117705800000142
the values of l of the two-dimensional matrix can be 1,2, 3, 4, 5 and 6 respectively representing six triangular prism models of alpha-beta-W-K, beta-gamma-W-K, gamma-delta-W-K, delta-epsilon-W-K, epsilon-omega-W-K and alpha-omega-W-K. A total of 6 isochromatic planes may be obtained. Here, the expansion of the chromatogram matrix is similar to that of the grid point array matrix, and is not necessarily expanded.
Six side surfaces of the regular hexagonal prism corresponding to the eight-primary-color HSV meshing model form six equal-chroma surfaces, and based on the condition that m is 1,2, …,10 and 11, a grid point array matrix C corresponding to each equal-chroma surface in the eight-primary-color HSV meshing model is obtainedi,j,t,lThe following were used:
Figure BDA0003117705800000143
wherein, when m is 1,
Figure BDA0003117705800000144
when m is 2, …,10,
Figure BDA0003117705800000151
when m is equal to 11, the compound is,
Figure BDA0003117705800000152
further obtaining a mixed color chromatographic matrix DC corresponding to each isochromatic surface in the eight-primary-color HSV gridding modeli,j,t,lThe following were used:
Figure BDA0003117705800000153
the three-dimensional matrix needs to satisfy the condition that the coordinates of the rows are greater than zero, and if the coordinates of the rows are less than 0, alpha isi,j,t,l0, i.e. di,j,t,l0. The values 1,2, 3, 4, 5 and 6 of the two-dimensional matrix can respectively represent six triangular prism models of alpha-beta-W-K, beta-gamma-W-K, gamma-delta-W-K, delta-epsilon-W-K, epsilon-omega-W-K and alpha-omega-W-K, and 6 x 11 ═ 66 isochromatic planes can be obtained in total. Here, the expansion of the chromatogram matrix is similar to that of the grid point array matrix, and is not necessarily expanded.
The HSV meshing model designed by the technical scheme is constructed, based on the HSV color space of a regular hexagonal prism, the HSV color space is decomposed into six regular triangular prism color general models, the meshing model capable of carrying out double coupling association on three dimensions such as hue angle, chroma and lightness is constructed through meshing of three bottom edges and the edge height of the regular triangular prism color general models, and the construction of the eight-primary-color HSV meshing model is realized through integration and expansion of the meshing model. The digital expression of grid point color values of the HSV color model by using grid point coordinates is realized on the basis of the eight-primary-color HSV gridding model, the construction of a grid point array model and a matrix of an equal lightness plane, an equal hue plane and an equal chroma plane of the eight-primary-color HSV color space is efficiently realized by the eight-primary-color HSV gridding model, and the digital expression and the visualization of grid point chromatograms of the equal lightness plane, the equal hue plane and the equal chroma plane of the eight-primary-color HSV are realized.
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 (7)

  1. The construction of the HSV gridding model is characterized in that: based on an HSV color space of a regular hexagonal prism with white W at the center of the top surface and black K at the bottom surface, aiming at the fact that six primary colors of red R, yellow Y, green G, cyan C, blue B and magenta M respectively fall at the positions of the edges of the top surface of the HSV color space corresponding to six side edges, the construction of an eight-primary-color HSV gridding model is realized according to the following steps by combining a hue angle H corresponding to the circumference of the regular hexagonal prism in a value range of 0-360 degrees, a chroma S corresponding to the distance from any point in the regular hexagonal prism to the center of a column in a value range of 0-1 and a lightness V corresponding to the height of the regular hexagonal prism in a value range of 0-1;
    step A, according to the fact that the positions of red R, yellow Y, green G, cyan C, blue B and magenta M corresponding to the bottom surface edge of the HSV color space along each side edge are respectively KR、KY、KG、KC、KB、KMDecomposing the HSV hexagonal prism color model into six regular triangular prism color general models which are respectively as follows: WYR-KKYKR、WGY-KKGKY、WCG-KKCKG、WBC-KKBKC、WMB-KKMKB、WRM-KKRKMBecause the bottom surface of the regular hexagonal prism is black, the general color model of the six regular triangular prisms can be called as: a red-yellow-white-black color sub-model, a yellow-green-white-black color sub-model, a green-cyan-white-black color sub-model, a cyan-blue-white-black color sub-model, a blue-magenta-white-black color sub-model, a magenta-red-white-black color sub-model; the six regular triangular prism color universal models are used as universal models
    Figure FDA0003117705790000011
    Is represented by, wherein X1＝{R、Y、G、C、B、M}，X2＝{R、Y、G、C、B、M}，X2≠X1Then entering step B;
    and B, aiming at the regular triangular prism color general model, executing 10 equal parts on the side corresponding to the hue angle and the two sides corresponding to the chroma radius in the regular triangular prism color general model, and executing 100 equal parts on the height corresponding to the lightness in the regular triangular prism color general model, so that the regular triangular prism color general model is subjected to gridding division to obtain the coordinate of each grid point
    Figure FDA0003117705790000012
    Then entering step C; wherein, i is 1,2, …,10,11, j is 1,2, …,10,11, i + j is less than or equal to 12, t is 1,2, …,100, 101; i represents the interior slave X of the regular triangular prism color general model1To X2Side corresponding to hue angle
    Figure FDA0003117705790000013
    The hue sequence numbers of the grid points divided upwards; j represents grid point chroma serial numbers outwards from the center of the column along the radius on two edges corresponding to the chroma radius in the regular triangular prism color general model, and t represents grid point lightness serial numbers divided from white to black in the regular triangular prism color general model;
    step C, aiming at the general model
    Figure FDA0003117705790000014
    The corresponding four primary colors are
    Figure FDA0003117705790000015
    W(RW,GW,BW)、K(RK,GK,BK) On the equal lightness surface with lightness t, the hue number, chroma number and color value of the grid point are set
    Figure FDA0003117705790000016
    W(RW,GW,BW) Performing a first re-coupling, and then combining the color values with a lightness value number and a primary color value K (R)K,GK,BK) Performing second double coupling, and constructing a regular triangular prism color general model through the double coupling, thereby obtaining color values d of all grid points in the gridding general modeli,j,tThe following were used:
    Figure FDA0003117705790000021
    wherein, X1、X2W, K is the four primary colors color value of the regular triangular prism color general model, which is respectively:
    Figure FDA0003117705790000022
    W(RW,GW,BW)、K(RK,GK,BK)；di,j,tfor grid points within the gridded general model, its RGB color value is di,j,t(Ri,j,t,Gi,j,t,Bi,j,t) (ii) a Then entering step D;
    d, respectively constructing a color conversion matrix Z of the regular triangular prism color general modeli,j,t、Z′i,j,tAnd Z ″)i,j,tThen enter step E as follows;
    Figure FDA0003117705790000023
    Figure FDA0003117705790000024
    Figure FDA0003117705790000025
    step E, aiming at the common model of the colors of the regular triangular prism, according to Zi,j,t、Z′i,j,t、Z″i,j,t、pi,j,t、di,j,tUpdating color value d of each grid point in regular triangular prism color general modeli,j,t＝Z″i,j,t×(Zi,j,t×αi,j,t+Zi',j,t) And then obtaining the color value of each grid point in the HSV color space.
  2. 2. The HSV gridding model construction of claim 1, wherein: color value d of each grid point in universal model based on colors of regular triangular prismsi,j,tFurther comprising the steps of:
    step F, according to the coordinates of each grid point in the regular triangular prism color general model
    Figure FDA0003117705790000026
    Combining the serial number l of each regular triangular prism color general model to be 1,2, 5 and 6, and constructing coordinates p of each grid point in the eight-primary-color HSV gridding modeli,j,t,lThen step G is entered as follows;
    Figure FDA0003117705790000027
    g, according to the color value d of each grid point in the regular triangular prism color general modeli,j,tAnd combining the serial numbers l of the regular triangular prism color general models to be 1,2, 5 and 6, constructing color values d of grid points in the eight-primary-color HSV gridding modeli,j,t,lThen step H is entered as follows;
    Figure FDA0003117705790000031
    according to Zi,j,t、Z′i,j,tAnd Z ″)i,j,tRespectively constructing color conversion matrix Z of the eight-primary-color HSV gridding modeli,j,t,l、Z′i,j,t,lAnd Z ″)i,j,t,lThen entering step I as follows;
    Figure FDA0003117705790000032
    Figure FDA0003117705790000033
    Figure FDA0003117705790000034
    according to Zi,j,t,l、Z′i,j,t,l、Z″i,j,t,l、pi,j,t,l、di,j,t,lUpdating color value d of each grid point in the HSV gridding model with eight primary colorsi,j,t,l＝Z″i,j,t,l×(Zi,j,t,l×αi,j,t,l+Z′i,j,t,l)。
  3. 3. Color built based on the HSV gridding model of claim 2A method of spectral visualization, characterized by: obtaining grid point array matrixes A corresponding to all equal brightness surfaces in the eight-primary-color HSV meshing model respectively based on 101 equal brightness surfaces which are respectively and equally corresponding to 100 equal brightness surfaces executed by the brightness V in the eight-primary-color HSV meshing model and are vertical to an axis where the brightness V is located, and based on t being 1,2, …,100 and 101i,j,t,lThe following were used:
    Figure FDA0003117705790000035
    wherein, when t is 1,
    Figure FDA0003117705790000041
    when t is 2, …,100,
    Figure FDA0003117705790000042
    when t is 101, the process is repeated,
    Figure FDA0003117705790000043
  4. 4. the method for visualizing the color spectrum constructed by the HSV meshing model of claim 3, wherein: obtaining a mixed color chromatographic matrix DA corresponding to each equal brightness surface in the eight-primary-color HSV gridding model respectively based on 100 equal brightness surfaces corresponding to equal brightness V in the eight-primary-color HSV gridding model and based on t being 1,2, …,100 and 101i,j,t,lThe following were used:
    Figure FDA0003117705790000051
  5. 5. according to claim 2The chromatogram visualization method for the HSV gridding model construction is characterized by comprising the following steps: the top surface center and the bottom surface center of the eight-primary-color HSV gridding model are connected and respectively combined with six lateral edges of a regular hexagonal prism to form six equal-color surfaces, and a grid point array matrix B corresponding to each equal-color surface in the eight-primary-color HSV gridding model is obtainedi,j,t,lThe following were used:
    Figure FDA0003117705790000052
    and further obtaining a color mixing chromatographic matrix DB corresponding to each isochromatic phase surface in the eight-primary-color HSV gridding modeli,j,t,lThe following were used:
    Figure FDA0003117705790000053
  6. 6. the method for visualizing the color spectrum constructed by the HSV meshing model of claim 2, wherein: six side surfaces of the regular hexagonal prism corresponding to the eight-primary-color HSV meshing model form six equal-chroma surfaces, and based on the condition that m is 1,2, …,10 and 11, a grid point array matrix C corresponding to each equal-chroma surface in the eight-primary-color HSV meshing model is obtainedi,j,t,lThe following were used:
    Figure FDA0003117705790000054
    wherein, when m is 1,
    Figure FDA0003117705790000061
    when m is 2, …,10,
    Figure FDA0003117705790000062
    when m is equal to 11, the compound is,
    Figure FDA0003117705790000063
  7. 7. the method for visualizing the color spectrum constructed by the HSV meshing model according to claim 6, wherein: obtaining a mixed color chromatographic matrix DC corresponding to each isochromatic surface in the eight-primary-color HSV gridding modeli,j,t,lThe following were used:
    Figure FDA0003117705790000064
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Publication number Priority date Publication date Assignee Title
CN110490981A (en) * 2019-08-14 2019-11-22 愉悦家纺有限公司 A kind of eight yuan of primary colours HSB full gamut color space gridding methods and its discrete chromatography construction method
CN112347683A (en) * 2020-11-30 2021-02-09 江南大学 Color fiber six-dimensional color mixing space grid model and grid point array color matrix construction method and application thereof

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110490981A (en) * 2019-08-14 2019-11-22 愉悦家纺有限公司 A kind of eight yuan of primary colours HSB full gamut color space gridding methods and its discrete chromatography construction method
CN112347683A (en) * 2020-11-30 2021-02-09 江南大学 Color fiber six-dimensional color mixing space grid model and grid point array color matrix construction method and application thereof

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