Method for constructing meshed model and discrete chromatography of eight-element primary color HSB full color gamut color space

Abstract

A method for constructing a meshed model and a discrete chromatography of eight primary color HSB color space is provided. By a meshed digital model and a discrete algorithm of color space, the color value and the color distribution in any point, line, surface and space area in the HSB color space can be quickly obtained based on color values of eight primary colors and coordinate values of mesh points in the HSB color space, thereby (i) realizing the full color gamut discrete chromatography of the HSB color space, (ii) realizing the visualization of the full color gamut of the color space, and (iii) improving the work efficiency of color matching.

Claims

1. A method for constructing a meshed model a discrete chromatography of eight primary color HSB color space for realizing digital acquisition of colors in the eight-element primary color HSB color space based on mesh coordinates, comprising the following steps: step A: constructing a 12-surface cone, selecting eight primary colors respectively corresponding to each vertex of the 12-surface cone, defining an upper end the 12-surface cone as a 1.sup.st vertex and defining a lower end of the 12-surface cone as a 2.sup.nd vertex, and for a middle periphery, defining vertices successively as a 3.sup.rd vertex, a 4.sup.th vertex, a 5.sup.th vertex, a 6.sup.th vertex, a 7.sup.th vertex, and an 8.sup.th vertex; then for the 12-surface cone, obtaining a 1.sup.st ridgeline, a .sup.nd ridgeline, a 3.sup.rd ridgeline, a 4.sup.th ridgeline, a 5.sup.th ridgeline, a 6.sup.th ridgeline, a 7.sup.th ridgeline, an 8.sup.th ridgeline, a 9.sup.th ridgeline, a 10.sup.th ridgeline, an 11.sup.th ridgeline, a 12.sup.th ridgeline, a 13.sup.th ridgeline, a 14.sup.th ridgeline, a 15.sup.th ridgeline, a 16.sup.th ridgeline, a 17.sup.th ridgeline, an 18.sup.th ridgeline, a 19.sup.th ridgeline; obtaining a 1.sup.st triangle, a 2.sup.nd triangle, a 3.sup.rd triangle, a 4.sup.th triangle, a 5.sup.th triangle, a 6.sup.th triangle, a 7.sup.th triangle, an 8.sup.th triangle, a 9.sup.th triangle, a 10.sup.th triangle, an 11.sup.th triangle, a 12.sup.th triangle, a 13.sup.th triangle, a 14.sup.th triangle, a 15.sup.th triangle, a 16.sup.th triangle, a 17.sup.th triangle, an 18.sup.th triangle, a 19.sup.th triangle, a 20.sup.th triangle; obtaining a 1.sup.st tetrahedron, a 2.sup.nd tetrahedron, a 3.sup.rd tetrahedron, a 4.sup.th tetrahedron, a 5.sup.th tetrahedron, a 6.sup.th tetrahedron; obtaining a 1.sup.st hexahedron, a 2.sup.nd hexahedron; then proceeding to step B; step B: for each ridgeline respectively, performing a digital isometric division between two endpoints on each ridgeline to obtain (n−1) mesh points and coordinate values of the (n−1) mesh points, obtaining an interpolation function with the coordinate values of the (n−1) mesh points as independent variables in combination with tristimulus values of primary color respectively corresponding to the two endpoints on each ridgeline, and obtaining tristimulus values of color of each mesh point of the (n−1) mesh points based on the coordinate values of the (n−1) mesh points; wherein, tristimulus values of color corresponding to each mesh point on each ridgeline are as follows: $r_i=\frac{n-i+1}{n}*R_{\alpha }+\frac{i-1}{n}*R_{\beta }$ $g_i=\frac{n-i+1}{n}*G_{\alpha }+\frac{i-1}{n}*G_{\beta }$ $b_i=\frac{n-i+1}{n}*B_{\alpha }+\frac{i-1}{n}*B_{\beta }$ wherein, n is a first preset number of divisions, i∈{1, 2, . . . , n, n+1}, r.sub.i, g.sub.i, b.sub.i denote the tristimulus values of color corresponding to each mesh point on each ridgeline, R.sub.α, G.sub.α, B.sub.α denote tristimulus values of primary color α corresponding to a first endpoint on each ridgeline, and R.sub.β, G.sub.β, B.sub.β denote tristimulus values of primary color β corresponding to a second endpoint on each ridgeline; for each triangle respectively, performing a mesh digital equal-part division in each triangle to obtain n*(n+1)/2 mesh points and coordinate values of the n*(n+1)/2 mesh points, obtaining an interpolation function with the coordinate values of the n*(n+1)/2 mesh points as independent variables in combination with tristimulus values of primary color each triangle, and obtaining tristimulus values of color of each mesh point of the n*(n+1)/2 mesh points based on the coordinate values of the n*(n+1)/2 mesh points; wherein, tristimulus values of color corresponding to each mesh point in each triangle are as follows: $r_{\Delta i,j}=\frac{n-i-j+2}{n}\star R_{\alpha }+\frac{i-1}{n}\star R_{\beta }+\frac{j-1}{n}\star R_{\gamma }$ $g_{\Delta i,j}=\frac{n-i-j+2}{n}\star G_{\alpha }+\frac{i-1}{n}\star G_{\beta }+\frac{j-1}{n}\star G_{\gamma }$ $b_{\Delta i,j}=\frac{n-i-j+2}{n}\star B_{\alpha }+\frac{i-1}{n}\star B_{\beta }+\frac{j-1}{n}\star B_{\gamma }$ wherein, n*(n+1)/2 is a second preset number of divisions, i=1, 2, . . . n−1, n, n+1, j=1, 2, . . . n−1, n, n+1, i+j≤(n+2), r.sub.Δi,j, g.sub.Δi,j, b.sub.Δi,j denote the tristimulus values of color corresponding to each mesh point in each triangle, R.sub.α, G.sub.α, B.sub.α denote tristimulus values of primary color α corresponding to a first vertex of each triangle, R.sub.β, G.sub.β, B.sub.β denote tristimulus values of primary color β corresponding to a second vertex of each triangle, and R.sub.γ, G.sub.γ, B.sub.γ denote tristimulus values of primary color γ corresponding to a third vertex of each triangle; for each tetrahedron respectively, performing a mesh digital equal-part division in each tetrahedron to obtain $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)/2\right]$ mesh points and coordinate values of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)/2\right]$ mesh points, obtaining an interpolation function with the coordinate values of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)/2\right]$ mesh points as independent variables in combination with tristimulus values of primary color respectively corresponding to four vertices on each tetrahedron, and obtaining tristimulus values of color corresponding to each mesh point of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)/2\right]$ mesh points based on the coordinate values of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)/2\right]$ mesh points; wherein, tristimulus values of color corresponding to each mesh point in each tetrahedron are as follows: $r_{♯i,j,k}=\frac{n-i-j+2}{n}\star R_{\alpha }+\frac{j-1}{n}\star R_{\beta }+\frac{i-k}{n}\star R_{\gamma }+\frac{k-1}{n}\star R_{\delta }$ $g_{♯i,j,k}=\frac{n-i-j+2}{n}\star G_{\alpha }+\frac{j-1}{n}\star G_{\beta }+\frac{i-k}{n}\star G_{\gamma }+\frac{k-1}{n}\star G_{\delta }$ $b_{♯i,j,k}=\frac{n-i-j+2}{n}\star B_{\alpha }+\frac{j-1}{n}\star B_{\beta }+\frac{i-k}{n}\star B_{\gamma }+\frac{k-1}{n}\star B_{\delta }$ wherein, $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)/2\right]$ is a third preset number of divisions, i∈{1, 2, . . . , n, n+1}, j∈{1, 2, . . . , n, n+1}, k∈{1, 2, . . . , n, n+1}, i+j≤(n+2), i+k≤(n+2), k+j≤(n+2), r.sub.#i,j,k, g.sub.#i,j,k, b.sub.#i,j,k denote the tristimulus values of color corresponding to each mesh point in each tetrahedron, R.sub.α, G.sub.α, B.sub.α denote tristimulus values of primary color α corresponding to a first vertex on each tetrahedron, R.sub.β, G.sub.β, B.sub.β denote tristimulus values of primary color β corresponding to a second vertex on each tetrahedron, R.sub.γ, G.sub.γ, B.sub.γ denote tristimulus values of primary color γ corresponding to a third vertex on each tetrahedron, and R.sub.δ, G.sub.δ, B.sub.δ denote tristimulus values of primary color δ corresponding to a fourth vertex on each tetrahedron; for each hexahedron respectively, performing a mesh digital equal-part division in each hexahedron to obtain $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)\right]$ mesh points and coordinate values of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)\right]$ mesh points, obtaining an interpolation function with the coordinate values of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)\right]$ mesh points as independent variables in combination with tristimulus values of primary color respectively corresponding to five vertices on each hexahedron, and obtaining tristimulus values of color corresponding to each mesh point of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)\right]$ mesh points based on the coordinate values of the $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)\right]$ mesh points in each hexahedron are as follows: $r_{i,j,k,l}=\frac{n-i-j+2}{n}\star R_{\alpha }+\frac{j-1}{n}\star R_{\beta }+\frac{i-k}{n}\star R_{\gamma }+\frac{k-1}{n}\star R_{\delta }+\frac{l-1}{n}\star R_{\mathrm{.Math.}}$ $g_{i,j,k,l}=\frac{n-i-j+2}{n}\star G_{\alpha }+\frac{j-1}{n}\star G_{\beta }+\frac{i-k}{n}\star G_{\gamma }+\frac{k-1}{n}\star G_{\delta }+\frac{l-1}{n}\star G_{\mathrm{.Math.}}$ $b_{i,j,k,l}=\frac{n-i-j+2}{n}\star B_{\alpha }+\frac{j-1}{n}\star B_{\beta }+\frac{i-k}{n}\star B_{\gamma }+\frac{k-1}{n}\star B_{\delta }+\frac{l-1}{n}\star B_{\mathrm{.Math.}}$ wherein, $\underset{i=1}{\overset{n+1}{.Math.}}\left[i\star \left(i+1\right)\right]$ is a fourth preset number of divisions, i∈{1, 2, . . . , n, n+1}, j∈{1, 2, . . . , n, n+1}, k∈{1, 2, . . . , n, n+1}, l∈{1, 2, . . . , n, n+1}, i+j≤(n+2), i+k≤(n+2), i+l≤(n+2), j+k≤(n+2), j+1≤(n+2), k+1≤(n+2), i, j, k, l denote coordinates of hexahedron division mesh points, r.sub.i,j,k,l, g.sub.i,j,k,l, b.sub.i,j,k,l denote the tristimulus values of color corresponding to each mesh point in each hexahedron, R.sub.α, G.sub.α, B.sub.α denote tristimulus values of primary color α corresponding to a first endpoint on each hexahedron, R.sub.β, G.sub.β, B.sub.β denote tristimulus values of primary color β corresponding to a second endpoint on each hexahedron, R.sub.γ, G.sub.γ, B.sub.γ denote tristimulus values of primary color γ corresponding to a third endpoint on each hexahedron, R.sub.δ, G.sub.δ, B.sub.δ denote tristimulus values of primary color δ corresponding to a fourth endpoint on each hexahedron, and R.sub.ε, G.sub.ε, B.sub.ε denote tristimulus values of primary color ε corresponding to a fifth endpoint on each hexahedron; then proceeding to step C; step C: according to tristimulus values and mesh point coordinate values of the eight primary colors respectively corresponding to each vertex on the 12-surface cone, in each ridgeline, each triangle, each tetrahedron, and each hexahedron on the 12-surface cone, obtaining a discrete distribution function of the tristimulus values with the mesh point coordinate values as independent variables, so as to realize the construction of the meshed model and the discrete chromatography of eight-element primary color HSB color space; and performing tone control, saturation control, and brightness control based on the mesh coordinates of the meshed model to provide colorants of multi-element primary color for full chromatography of colors and color mixtures.

2. The method of claim 1, wherein, the tristimulus values of the eight primary colors respectively corresponding to each vertex on the 12-surface cone are as follows: the 3.sup.rd vertex (255, 0, 0), the 4.sup.th vertex (255, 255, 0), the 5.sup.th vertex (0, 255, 0), the 6.sup.th vertex (0, 255, 255), the 7.sup.th vertex (0, 0, 255), the 8.sup.th vertex (255, 0, 255), the 1.sup.st vertex (255, 255, 255), the 2.sup.nd vertex (0, 0, 0); based on n=10, acquisition of discrete colors of eight primary color HSB color space is realized.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic flow chart of a method for constructing a meshed model and a discrete chromatography of eight primary color HSB color space according to the present invention.

(2) FIG. 2 is a schematic diagram of a 12-surface cone according to the present invention.

(3) FIG. 3 is a schematic diagram of an embodiment of a 12-surface cone according to the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(4) The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings of the description.

(5) The present invention provides a method for constructing a meshed model and a discrete chromatography of eight primary color HSB color space, for realizing digital acquisition of colors in eight primary color HSB full color gamut color space based on mesh coordinates. In the actual application, eight primary colors of red, yellow, green, blue, cyan, magenta, black, and white are selected for implementation and application. As shown in FIG. 1, the method specifically includes the following steps.

(6) Step A: as shown in FIG. 2, a 12-surface cone is constructed. Eight primary colors are selected to respectively correspond to each vertex of the 12-surface cone. An upper end and a lower end of the 12-surface cone are defined as vertex O.sub.1 and vertex O.sub.2, respectively. For the middle periphery, vertices are successively defined as vertex A, vertex B, vertex C, vertex D, vertex E, and vertex F. As shown in FIG. 3, eight primary colors of red, yellow, green, blue, cyan, magenta, black, and white respectively correspond to each vertex. Wherein, RGB (Red, Green and Blue) values and HSB values of the eight primary colors are shown in Table 1, that is, A(255, 0, 0), B(255, 255, 0), C(0, 255, 0), D(0, 255, 255), E(0, 0, 255), F(255, 0, 255), O.sub.1 (255, 255, 255), O.sub.1 (0, 0, 0).

(7) TABLE-US-00001 TABLE 1 primary color red yellow green cyan blue magenta white black R 255, 255,  0,  0,  0, 255, 255, 0, G  0, 255, 255, 255,  0,  0, 255, 0, B  0   0   0  255  255  255  255  0  H  0,  60, 120, 180, 240, 300,  0, 0, S 100%, 100%, 100%, 100%, 100%, 100%,  0, 0, B   0.5   0.5   0.5   0.5   0.5   0.5  1  0  vertex A B C D E F O.sub.1 O.sub.2

(8) Then, for the 12-surface cone, the following ridgelines are obtained: AB, BC, CD, DE, EF, FA, O.sub.1A, O.sub.1B, O.sub.1C, O.sub.1D, O.sub.1E, O.sub.1F, AO.sub.2, BO.sub.2, CO.sub.2, DO.sub.2, EO.sub.2, FO.sub.2, O.sub.1O.sub.2;

(9) the following triangles are obtained: ACE, FDB, ABO.sub.1, BCO.sub.1, CDO.sub.1, DEO.sub.1, EFO.sub.1, FAO.sub.1, ABO.sub.2, BCO.sub.2, CDO.sub.2, DEO.sub.2, EFO.sub.2, FAO.sub.2, O.sub.1O.sub.2A, O.sub.1O.sub.2B, O.sub.1O.sub.2C, O.sub.1O.sub.2D, O.sub.1O.sub.2E, O.sub.1O.sub.2F;

(10) the following tetrahedrons are obtained: O.sub.1O.sub.2AB, O.sub.1O.sub.2BC, O.sub.1O.sub.2CD, O.sub.1O.sub.2DE, O.sub.1O.sub.2EF, O.sub.1O.sub.2FA; and

(11) the following hexahedrons are obtained: O.sub.1O.sub.2ACE, O.sub.1O.sub.2BDF.

(12) Then proceeding to Step B.

(13) Step B: for each ridgeline respectively, digital isometric division is performed between two endpoints on the ridgeline to obtain (n−1) mesh points and coordinate values thereof. An interpolation function with mesh point coordinates as independent variables is obtained in combination with tristimulus values of primary color corresponding, respectively, to the two endpoints on the ridgeline, and tristimulus values of color corresponding to each mesh point are obtained based on mesh point coordinate values as follows:

(14) $r_i=\frac{n-i+1}{n}*R_{\alpha }+\frac{i-1}{n}*R_{\beta }{g}_i=\frac{n-i+1}{n}*G_{\alpha }+\frac{i-1}{n}*G_{\beta }{b}_i=\frac{n-i+1}{n}*B_{\alpha }+\frac{i-1}{n}*B_{\beta }$

(15) wherein, n is a preset number of divisions, i∈{1, 2, . . . , n, n+1}, r.sub.i, g.sub.i, b.sub.i denote tristimulus values of color corresponding to each mesh point on a ridgeline, R.sub.α, G.sub.α, B.sub.α denote tristimulus values of primary color α corresponding to one endpoint on the ridgeline, and R.sub.β, G.sub.β, B.sub.β denote tristimulus values of primary color β corresponding to the other endpoint on the ridgeline.

(16) The tristimulus values of color of each mesh point on each ridgeline in eight primary color HSB color space are shown in Table 2.

(17) TABLE-US-00002 TABLE 2 No. ridgeline ridgeline endpoint RGB value ridgeline mesh point RGB value 1 AB a(R.sub.a, G.sub.a, B.sub.a) b(R.sub.b, G.sub.b, B.sub.b) 0$r_{\stackrel{\_}{\mathrm{ab}}i}=\frac{n-i+1}{n}*R_a+\frac{i-1}{n}*R_b$$g_{\stackrel{\_}{\mathrm{ab}}i}=\frac{n-i+1}{n}*G_a+\frac{i-1}{n}*G_b$$r_{\stackrel{\_}{\mathrm{ab}}i}=\frac{n-i+1}{n}*B_a+\frac{i-1}{n}*B_b$ 2 BC b(R.sub.b, G.sub.b, B.sub.b) c(R.sub.c, G.sub.c, B.sub.c) $r_{\stackrel{\_}{\mathrm{bc}}i}=\frac{n-i+1}{n}*R_a+\frac{i-1}{n}*R_b$$g_{\stackrel{\_}{\mathrm{bc}}i}=\frac{n-i+1}{n}*G_a+\frac{i-1}{n}*G_b$$r_{\stackrel{\_}{\mathrm{bc}}i}=\frac{n-i+1}{n}*B_a+\frac{i-1}{n}*B_b$ 3 CD c(R.sub.c, G.sub.c, B.sub.c) d(R.sub.d, G.sub.d, B.sub.d) $r_{\stackrel{\_}{cd}i}=\frac{n-i+1}{n}*R_c+\frac{i-1}{n}*R_d$$g_{\stackrel{\_}{cd}i}=\frac{n-i+1}{n}*G_c+\frac{i-1}{n}*G_d$$r_{\stackrel{\_}{cd}i}=\frac{n-i+1}{n}*B_c+\frac{i-1}{n}*B_d$ 4 DE d(R.sub.d, G.sub.d, B.sub.d) e(R.sub.e, G.sub.e, B.sub.e) $r_{\stackrel{\_}{\mathrm{de}}i}=\frac{n-i+1}{n}*R_d+\frac{i-1}{n}*R_d$$g_{\stackrel{\_}{\mathrm{de}}i}=\frac{n-i+1}{n}*G_d+\frac{i-1}{n}*G_e$$r_{\stackrel{\_}{\mathrm{de}}i}=\frac{n-i+1}{n}*B_d+\frac{i-1}{n}*B_e$ 5 EF e(R.sub.e, G.sub.e, B.sub.e) f(R.sub.f, G.sub.f, B.sub.f) $r_{\stackrel{\_}{\mathrm{ef}}i}=\frac{n-i+1}{n}*R_e+\frac{i-1}{n}*R_f$$g_{\stackrel{\_}{\mathrm{ef}}i}=\frac{n-i+1}{n}*G_e+\frac{i-1}{n}*G_f$$r_{\stackrel{\_}{\mathrm{ef}}i}=\frac{n-i+1}{n}*B_e+\frac{i-1}{n}*B_f$ 6 FA f(R.sub.f, G.sub.f, B.sub.f) a(R.sub.a, G.sub.a, B.sub.a) $r_{\stackrel{\_}{\mathrm{fa}}i}=\frac{n-i+1}{n}*R_f+\frac{i-1}{n}*R_a$$g_{\stackrel{\_}{\mathrm{fa}}i}=\frac{n-i+1}{n}*G_f+\frac{i-1}{n}*G_a$$r_{\stackrel{\_}{\mathrm{fa}}i}=\frac{n-i+1}{n}*B_f+\frac{i-1}{n}*B_a$ 7 O.sub.1A o1(R.sub.o1, G.sub.o1, B.sub.o1) a(R.sub.a, G.sub.a, B.sub.a) $\begin{array}{c}{r}_{\stackrel{\_}{o1\mathrm{ai}}}=\frac{n-i+1}{n}*R_{o1}+\frac{i-1}{n}*R_a\\ g_{\stackrel{\_}{o1\mathrm{ai}}}=\frac{n-i+1}{n}*G_{o1}+\frac{i-1}{n}*G_a\\ r_{\stackrel{\_}{o1\mathrm{ai}}}=\frac{n-i+1}{n}*B_{o1}+\frac{i-1}{n}*B_a\end{array}$ 8 O.sub.1B o1(R.sub.o1, G.sub.o1, B.sub.o1) b(R.sub.b, G.sub.b, B.sub.b) $\begin{array}{c}{r}_{\stackrel{\_}{o1\mathrm{bi}}}=\frac{n-i+1}{n}*R_{o1}+\frac{i-1}{n}*R_b\\ g_{\stackrel{\_}{o1\mathrm{bi}}}=\frac{n-i+1}{n}*G_{o1}+\frac{i-1}{n}*G_b\\ r_{\stackrel{\_}{o1\mathrm{bi}}}=\frac{n-i+1}{n}*B_{o1}+\frac{i-1}{n}*B_b\end{array}$ 9 O.sub.1C o1(R.sub.o1, G.sub.o1, B.sub.o1) c(R.sub.c, G.sub.c, B.sub.c) $\begin{array}{c}{r}_{\stackrel{\_}{o1\mathrm{ci}}}=\frac{n-i+1}{n}*R_{o1}+\frac{i-1}{n}*R_c\\ g_{\stackrel{\_}{o1\mathrm{ci}}}=\frac{n-i+1}{n}*G_{o1}+\frac{i-1}{n}*G_c\\ 10r_{\stackrel{\_}{o1\mathrm{ci}}}=\frac{n-i+1}{n}*B_{o1}+\frac{i-1}{n}*B_c\end{array}$ 10 O.sub.1D o1(R.sub.o1, G.sub.o1, B.sub.o1) d(R.sub.d, G.sub.d, B.sub.d) $\begin{array}{c}{r}_{\stackrel{\_}{o1\mathrm{di}}}=\frac{n-i+1}{n}*R_{o1}+\frac{i-1}{n}*R_d\\ g_{\stackrel{\_}{o1\mathrm{di}}}=\frac{n-i+1}{n}*G_{o1}+\frac{i-1}{n}*G_d\\ r_{\stackrel{\_}{o1\mathrm{di}}}=\frac{n-i+1}{n}*B_{o1}+\frac{i-1}{n}*B_d\end{array}$ 11 O.sub.1E o1(R.sub.o1, G.sub.o1, B.sub.o1) e(R.sub.e, G.sub.e, B.sub.e) 0$\begin{array}{c}{r}_{\stackrel{\_}{o1\mathrm{ei}}}=\frac{n-i+1}{n}*R_{o1}+\frac{i-1}{n}*R_e\\ g_{\stackrel{\_}{o1\mathrm{ei}}}=\frac{n-i+1}{n}*G_{o1}+\frac{i-1}{n}*G_e\\ r_{\stackrel{\_}{o1\mathrm{ei}}}=\frac{n-i+1}{n}*B_{o1}+\frac{i-1}{n}*B_e\end{array}$ 12 O.sub.1F o1(R.sub.o1, G.sub.o1, B.sub.o1) f(R.sub.f, G.sub.f, B.sub.f) $\begin{array}{c}{r}_{\stackrel{\_}{o1\mathrm{fi}}}=\frac{n-i+1}{n}*R_{o1}+\frac{i-1}{n}*R_f\\ g_{\stackrel{\_}{o1\mathrm{fi}}}=\frac{n-i+1}{n}*G_{o1}+\frac{i-1}{n}*G_f\\ r_{\stackrel{\_}{o1\mathrm{fi}}}=\frac{n-i+1}{n}*B_{o1}+\frac{i-1}{n}*B_f\end{array}$ 13 O.sub.2A o2(R.sub.o2, G.sub.o2, B.sub.o2) a(R.sub.a, G.sub.a, B.sub.a) $\begin{array}{c}{r}_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*R_{o2}+\frac{i-1}{n}*R_a\\ g_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*G_{o2}+\frac{i-1}{n}*G_a\\ r_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*B_{o2}+\frac{i-1}{n}*B_a\end{array}$ 14 O.sub.2B o2(R.sub.o2, G.sub.o2, B.sub.o2) b(R.sub.b, G.sub.b, B.sub.b) $\begin{array}{c}{r}_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*R_{o2}+\frac{i-1}{n}*R_b\\ g_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*G_{o2}+\frac{i-1}{n}*G_b\\ r_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*B_{o2}+\frac{i-1}{n}*B_b\end{array}$ 15 O.sub.2C o2(R.sub.o2, G.sub.o2, B.sub.o2) c(R.sub.c, G.sub.c, B.sub.c) $\begin{array}{c}{r}_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*R_{o2}+\frac{i-1}{n}*R_c\\ g_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*G_{o2}+\frac{i-1}{n}*G_c\\ r_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*B_{o2}+\frac{i-1}{n}*B_c\end{array}$ 16 O.sub.2D o2(R.sub.o2, G.sub.o2, B.sub.o2) d(R.sub.d, G.sub.d, B.sub.d) $\begin{array}{c}{r}_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*R_{o2}+\frac{i-1}{n}*R_d\\ g_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*G_{o2}+\frac{i-1}{n}*G_d\\ r_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*B_{o2}+\frac{i-1}{n}*B_d\end{array}$ 17 O.sub.2E o2(R.sub.o2, G.sub.o2, B.sub.o2) e(R.sub.e, G.sub.e, B.sub.e) $\begin{array}{c}{r}_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*R_{o2}+\frac{i-1}{n}*R_e\\ g_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*G_{o2}+\frac{i-1}{n}*G_e\\ r_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*B_{o2}+\frac{i-1}{n}*B_e\end{array}$ 18 O.sub.2F o2(R.sub.o2, G.sub.o2, B.sub.o2) f(R.sub.f, G.sub.f, B.sub.f) $r_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*R_{o2}+\frac{i-1}{n}*R_f$$g_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*G_{o2}+\frac{i-1}{n}*G_f$$r_{\stackrel{\_}{o2\mathrm{ai}}}=\frac{n-i+1}{n}*B_{o2}+\frac{i-1}{n}*B_f$ 19 O.sub.1O.sub.2 o1(R.sub.o1, G.sub.o1, B.sub.o1) o2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\stackrel{\_}{o1i}}=\frac{n-i+1}{n}*R_{o1}+\frac{i-1}{n}*R_{o2}$$g_{\stackrel{\_}{o1i}}=\frac{n-i+1}{n}*G_{o1}+\frac{i-1}{n}*G_{o2}$$r_{\stackrel{\_}{o1i}}=\frac{n-i+1}{n}*B_{o1}+\frac{i-1}{n}*B_{o2}$

(18) For each triangle respectively, mesh digital equal-part division is performed in the triangle to obtain n*(n+1)/2 mesh points and coordinate values thereof. An interpolation function with mesh point coordinate values as independent variables is obtained in combination with tristimulus values of primary color respectively corresponding to three vertices on the triangle, and tristimulus values of color corresponding to each mesh point are obtained based on mesh point coordinate values as follows:

(19) $r_{\Delta i,j}=\frac{n-i-j+2}{n}*R_{\alpha }+\frac{i-1}{n}*R_{\beta }+\frac{j-1}{n}*R_{\gamma }{g}_{\Delta i,j}=\frac{n-i-j+2}{n}*G_{\alpha }+\frac{i-1}{n}*G_{\beta }+\frac{j-1}{n}*G_{\gamma }{b}_{\Delta i,j}=\frac{n-i-j+2}{n}*B_{\alpha }+\frac{i-1}{n}*B_{\beta }+\frac{j-1}{n}*B_{\gamma }$

(20) wherein, n*(n+1)/2 is a preset number of divisions, i=1, 2, . . . n−1, n, n+1, j=1, 2, . . . n−1, n, n+1, i+j≤(n+2), r.sub.Δi,j, g.sub.Δi,j, b.sub.Δi,j denote tristimulus values of color corresponding to each mesh point in a triangle, R.sub.α, G.sub.α, B.sub.α denote tristimulus values of primary color α corresponding to a first vertex of the triangle, R.sub.β, G.sub.β, B.sub.β denote tristimulus values of primary color β corresponding to a second vertex of the triangle, and R.sub.γ, G.sub.γ, B.sub.γ denote tristimulus values of primary color γ corresponding to a third vertex of the triangle.

(21) The tristimulus values of color of each mesh point on each triangle in eight primary color HSB color space are shown in Table 3.

(22) TABLE-US-00003 TABLE 3 triangle endpoint triangle mesh point No. triangle RGB value RGB value 1 ΔABO.sub.1 A(R.sub.a, G.sub.a, B.sub.a) B(R.sub.b, G.sub.b, B.sub.b) O1(R.sub.o1, G.sub.o1, B.sub.o1) 0$r_{\Delta \stackrel{\_}{\mathrm{ABO}1}i,j}=\frac{n-i-j+2}{n}*R_a+\frac{i-1}{n}*R_b+\frac{j-1}{n}*R_{o1}$$g_{\Delta \stackrel{\_}{\mathrm{ABO}1}i,j}=\frac{n-i-j+2}{n}*G_a+\frac{i-1}{n}*G_b+\frac{j-1}{n}*G_{o1}$$b_{\Delta \stackrel{\_}{\mathrm{ABO}1}i,j}=\frac{n-i-j+2}{n}*B_a+\frac{i-1}{n}*B_b+\frac{j-1}{n}*B_{o1}$ 2 ΔBCO.sub.1 B(R.sub.b, G.sub.b, B.sub.b) C(R.sub.c, G.sub.c, B.sub.c) O1(R.sub.o1, G.sub.o1, B.sub.o1) $r_{\Delta \stackrel{\_}{\mathrm{BCO}1}i,j}=\frac{n-i-j+2}{n}*R_b+\frac{i-1}{n}*R_c+\frac{j-1}{n}*R_{o1}$$g_{\Delta \stackrel{\_}{\mathrm{BCO}1}i,j}=\frac{n-i-j+2}{n}*G_B+\frac{i-1}{n}*G_C+\frac{j-1}{n}*G_{o1}$$b_{\Delta \stackrel{\_}{\mathrm{BCO}1}i,j}=\frac{n-i-j+2}{n}*B_B+\frac{i-1}{n}*B_C+\frac{j-1}{n}*B_{o1}$ 3 ΔCDO.sub.1 C(R.sub.c, G.sub.c, B.sub.c) D(R.sub.d, G.sub.d, B.sub.d) O1(R.sub.o1, G.sub.o1, B.sub.o1) $r_{\Delta \stackrel{\_}{\mathrm{CDO}1}i,j}=\frac{n-i-j+2}{n}*R_c+\frac{i-1}{n}*R_d+\frac{j-1}{n}*R_{o1}$$g_{\Delta \stackrel{\_}{\mathrm{CDO}1}i,j}=\frac{n-i-j+2}{n}*G_c+\frac{i-1}{n}*G_d+\frac{j-1}{n}*G_{o1}$$b_{\Delta \stackrel{\_}{\mathrm{CDO}1}i,j}=\frac{n-i-j+2}{n}*B_c+\frac{i-1}{n}*B_d+\frac{j-1}{n}*B_{o1}$ 4 ΔDEO.sub.1 D(R.sub.d, G.sub.d, B.sub.d) E(R.sub.e, G.sub.e, B.sub.e) O1(R.sub.o1, G.sub.o1, B.sub.o1) $r_{\Delta \stackrel{\_}{\mathrm{DEO}1}i,j}=\frac{n-i-j+2}{n}*R_d+\frac{i-1}{n}*R_e+\frac{j-1}{n}*R_{o1}$$g_{\Delta \stackrel{\_}{\mathrm{DEO}1}i,j}=\frac{n-i-j+2}{n}*G_d+\frac{i-1}{n}*G_e+\frac{j-1}{n}*G_{o1}$$b_{\Delta \stackrel{\_}{\mathrm{DEO}1}i,j}=\frac{n-i-j+2}{n}*B_d+\frac{i-1}{n}*B_e+\frac{j-1}{n}*B_{o1}$ 5 ΔEFO.sub.1 E(R.sub.e, G.sub.e, B.sub.e) F(R.sub.f, G.sub.f, B.sub.f) O1(R.sub.o1, G.sub.o1, B.sub.o1) $r_{\Delta \stackrel{\_}{\mathrm{EFO}1}i,j}=\frac{n-i-j+2}{n}*R_e+\frac{i-1}{n}*R_f+\frac{j-1}{n}*R_{o1}$$g_{\Delta \stackrel{\_}{\mathrm{EFO}1}i,j}=\frac{n-i-j+2}{n}*G_e+\frac{i-1}{n}*G_f+\frac{j-1}{n}*G_{o1}$$b_{\Delta \stackrel{\_}{\mathrm{EFO}1}i,j}=\frac{n-i-j+2}{n}*B_e+\frac{i-1}{n}*B_f+\frac{j-1}{n}*B_{o1}$ 6 ΔFAO.sub.1 F(R.sub.f, G.sub.f, B.sub.f) A(R.sub.a, G.sub.a, B.sub.a) O1(R.sub.o1, G.sub.o1, B.sub.o1) $r_{\Delta \stackrel{\_}{\mathrm{FAO}1}i,j}=\frac{n-i-j+2}{n}*R_f+\frac{i-1}{n}*R_a+\frac{j-1}{n}*R_{o1}$$g_{\Delta \stackrel{\_}{\mathrm{FAO}1}i,j}=\frac{n-i-j+2}{n}*G_f+\frac{i-1}{n}*G_a+\frac{j-1}{n}*G_{o1}$$b_{\Delta \stackrel{\_}{\mathrm{FAO}1}i,j}=\frac{n-i-j+2}{n}*B_f+\frac{i-1}{n}*B_a+\frac{j-1}{n}*B_{o1}$ 7 ΔABO.sub.2 A(R.sub.a, G.sub.a, B.sub.a) B(R.sub.b, G.sub.b, B.sub.b) O2(R.sub.o2, G.sub.o1, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{ABO}2}i,j}=\frac{n-i-j+2}{n}*R_a+\frac{i-1}{n}*R_b+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{ABO}2}i,j}=\frac{n-i-j+2}{n}*G_a+\frac{i-1}{n}*G_b+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{ABO}2}i,j}=\frac{n-i-j+2}{n}*B_a+\frac{i-1}{n}*B_b+\frac{j-1}{n}*B_{o2}$ 8 ΔBCO.sub.2 B(R.sub.b, G.sub.b, B.sub.b) C(R.sub.c, G.sub.c, B.sub.c) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{BCO}2}i,j}=\frac{n-i-j+2}{n}*R_b+\frac{i-1}{n}*R_c+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{BCO}2}i,j}=\frac{n-i-j+2}{n}*G_b+\frac{i-1}{n}*G_c+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{BCO}2}i,j}=\frac{n-i-j+2}{n}*B_b+\frac{i-1}{n}*B_c+\frac{j-1}{n}*B_{o2}$ 9 ΔCDO.sub.2 C(R.sub.c, G.sub.c, B.sub.c) D(R.sub.d, G.sub.d, B.sub.d) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{CDO}2}i,j}=\frac{n-i-j+2}{n}*R_c+\frac{i-1}{n}*R_d+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{CDO}2}i,j}=\frac{n-i-j+2}{n}*G_c+\frac{i-1}{n}*G_d+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{CDO}2}i,j}=\frac{n-i-j+2}{n}*B_c+\frac{i-1}{n}*B_d+\frac{j-1}{n}*B_{o2}$ 10 ΔDEO.sub.2 D(R.sub.d, G.sub.d, B.sub.d) E(R.sub.e, G.sub.e, B.sub.e) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{DEO}2}i,j}=\frac{n-i-j+2}{n}*R_d+\frac{i-1}{n}*R_e+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{DEO}2}i,j}=\frac{n-i-j+2}{n}*G_d+\frac{i-1}{n}*G_e+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{DEO}2}i,j}=\frac{n-i-j+2}{n}*B_d+\frac{i-1}{n}*B_e+\frac{j-1}{n}*B_{o2}$ 11 ΔEFO.sub.2 E(R.sub.e, G.sub.e, B.sub.e) F(R.sub.f, G.sub.f, B.sub.f) O2(R.sub.o2, G.sub.o2, B.sub.o2) 0$r_{\Delta \stackrel{\_}{\mathrm{EFO}2}i,j}=\frac{n-i-j+2}{n}*R_e+\frac{i-1}{n}*R_f+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{EFO}2}i,j}=\frac{n-i-j+2}{n}*G_e+\frac{i-1}{n}*G_f+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{EFO}2}i,j}=\frac{n-i-j+2}{n}*B_e+\frac{i-1}{n}*B_f+\frac{j-1}{n}*B_{o2}$ 12 ΔFAO.sub.2 F(R.sub.f, G.sub.f, B.sub.f) A(R.sub.a, G.sub.a, B.sub.a) O2(R.sub.o2, G.sub.o1, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{FAO}2}i,j}=\frac{n-i-j+2}{n}*R_f+\frac{i-1}{n}*R_a+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{FAO}2}i,j}=\frac{n-i-j+2}{n}*G_f+\frac{i-1}{n}*G_a+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{FAO}2}i,j}=\frac{n-i-j+2}{n}*B_f+\frac{i-1}{n}*B_a+\frac{j-1}{n}*B_{o2}$ 13 ΔAO.sub.1O.sub.2 A(R.sub.a, G.sub.a, B.sub.a) O1(R.sub.o1, G.sub.o1, B.sub.o1) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{AO}1O2}i,j}=\frac{n-i-j+2}{n}*R_a+\frac{i-1}{n}*R_{o1}+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{AO}1O2}i,j}=\frac{n-i-j+2}{n}*G_a+\frac{i-1}{n}*G_{o1}+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{AO}1O2}i,j}=\frac{n-i-j+2}{n}*B_a+\frac{i-1}{n}*B_{o1}+\frac{j-1}{n}*B_{o2}$ 14 ΔBO.sub.1O.sub.2 B(R.sub.b, G.sub.b, B.sub.b) O1(R.sub.o1, G.sub.o1, B.sub.o1) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{BO}1O2}i,j}=\frac{n-i-j+2}{n}*R_b+\frac{i-1}{n}*R_{o1}+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{BO}1O2}i,j}=\frac{n-i-j+2}{n}*G_b+\frac{i-1}{n}*G_{o1}+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{BO}1O2}i,j}=\frac{n-i-j+2}{n}*B_b+\frac{i-1}{n}*B_{o1}+\frac{j-1}{n}*B_{o2}$ 15 ΔCO.sub.1O.sub.2 C(R.sub.c, G.sub.c, B.sub.c) O1(R.sub.o1, G.sub.o1, B.sub.o1) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{CO}1O2}i,j}=\frac{n-i-j+2}{n}*R_c+\frac{i-1}{n}*R_{o1}+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{CO}1O2}i,j}=\frac{n-i-j+2}{n}*G_c+\frac{i-1}{n}*G_{o1}+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{CO}1O2}i,j}=\frac{n-i-j+2}{n}*B_c+\frac{i-1}{n}*B_{o1}+\frac{j-1}{n}*B_{o2}$ 16 ΔDO.sub.1O.sub.2 D(R.sub.d, G.sub.d, B.sub.d) O1(R.sub.o1, G.sub.o1, B.sub.o1) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{DO}1O2}i,j}=\frac{n-i-j+2}{n}*R_d+\frac{i-1}{n}*R_{o1}+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{DO}1O2}i,j}=\frac{n-i-j+2}{n}*G_d+\frac{i-1}{n}*G_{o1}+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{DO}1O2}i,j}=\frac{n-i-j+2}{n}*B_d+\frac{i-1}{n}*B_{o1}+\frac{j-1}{n}*B_{o2}$ 17 ΔEO.sub.1O.sub.2 E(R.sub.e, G.sub.e, B.sub.e) O1(R.sub.o1, G.sub.o1, B.sub.o1) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{EO}1O2}i,j}=\frac{n-i-j+2}{n}*R_e+\frac{i-1}{n}*R_{o1}+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{EO}1O2}i,j}=\frac{n-i-j+2}{n}*G_e+\frac{i-1}{n}*G_{o1}+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{EO}1O2}i,j}=\frac{n-i-j+2}{n}*B_e+\frac{i-1}{n}*B_{o1}+\frac{j-1}{n}*B_{o2}$ 18 ΔFO.sub.1O.sub.2 F(R.sub.f, G.sub.f, B.sub.f) O1(R.sub.o1, G.sub.o1, B.sub.o1) O2(R.sub.o2, G.sub.o2, B.sub.o2) $r_{\Delta \stackrel{\_}{\mathrm{FO}1O2}i,j}=\frac{n-i-j+2}{n}*R_f+\frac{i-1}{n}*R_{o1}+\frac{j-1}{n}*R_{o2}$$g_{\Delta \stackrel{\_}{\mathrm{FO}1O2}i,j}=\frac{n-i-j+2}{n}*G_f+\frac{i-1}{n}*G_{o1}+\frac{j-1}{n}*G_{o2}$$b_{\Delta \stackrel{\_}{\mathrm{FO}1O2}i,j}=\frac{n-i-j+2}{n}*B_f+\frac{i-1}{n}*B_{o1}+\frac{j-1}{n}*B_{o2}$