Three-dimensional model copyright marking method and device based on Boolean operation

Abstract

The present invention discloses a three-dimensional model copyright marking method and device based on Boolean operation, the method comprising: (1) forming a copyright character set S, a generation parameter set A and a registration parameter set B; (2) obtaining the closed boundary lines of each character in the character set S through Bezier interpolation, and storing the closed boundary lines of the copyright character set S in the boundary line set BL; (3) constructing a copyright mark three-dimensional model based on the boundary line set BL and the generation parameters in A; (4) performing affine transformation processing on the copyright mark three-dimensional model according to the spatial information of the target three-dimensional model to be embedded with a watermark and the spatial information of the copyright mark model, as well as the registration parameters in B; (5) embedding the copyright mark three-dimensional model into the target three-dimensional model based on the three-dimensional Boolean operation method, so as to realize the copyright information embedding including intaglio, salient and grid embedding. The present invention has high efficiency and high security.

Description

Technical Field

[0001] The present invention relates to the fields of information security and graphics, and in particular to a three-dimensional model copyright marking method and device based on Boolean operation. Background Art

[0002] With the continuous expansion of the application field of 3D models and the convenience of their storage, transmission and copying, the problems faced by 3D models such as illegal copying, modification, dissemination and theft are becoming more and more serious, which has brought huge economic losses to the producers of 3D geological models. Therefore, in view of the characteristics of various 3D models, how to protect the intellectual property rights of 3D models has become a scientific and application problem that needs to be solved urgently. Nowadays, digital watermark technology has been widely used in various types of digital files, including text files, image files, video files and audio files. The digital watermark embedding technology of these files has become increasingly mature and perfect with the rapid development of science and technology. It can well protect the copyright interests of digital files and has been widely used in actual production and life.

[0003] The research on digital watermarks of 3D models mainly shows the following characteristics: (1) The watermark of 3D models is mainly the embedding of invisible watermarks; however, in many cases, especially in 3D printing and 3DGIS scene display applications, it is necessary to clearly express the copyright information of the 3D model, that is, a visible watermark is required; (2) The existing visible watermark algorithms for 3D models still have defects such as being too complex, difficult to reuse, and limited in application methods, and are inefficient, which is far from user needs. In addition, relatively smooth areas are mainly selected as embedding locations, which objectively reduces the difficulty of erasure attacks, and security needs to be improved. With the continuous development of technologies such as 3DGIS, VR\AR\MR, and 3D printing, and the increasing richness of 3D geological models, the research and application needs for visible watermarks of 3D models are becoming increasingly urgent. Summary of the invention

[0004] Purpose of the invention: In view of the problems existing in the prior art, the present invention provides a three-dimensional model copyright marking method and device based on Boolean operations with high efficiency and high security.

[0005] Technical solution: The three-dimensional model copyright marking method based on Boolean operation described in the present invention includes:

[0006] (1) Reading copyright mark information and generation parameters and alignment parameters of the copyright mark model set by the user to form a copyright character set S, a generation parameter set A, and a alignment parameter set B;

[0007] (2) Obtain the closed boundary lines of each character in the character set S through Bezier interpolation, and store them in the boundary line set BL of the copyright character set S;

[0008] (3) constructing a three-dimensional model of the copyright mark based on the boundary line set BL and the generation parameters in the generation parameter set A;

[0009] (4) performing affine transformation processing on the copyright mark three-dimensional model according to the spatial information of the target three-dimensional model to be embedded with the watermark and the spatial information of the copyright mark model, as well as the relevant registration parameters in the registration parameter set B, and registering the copyright mark three-dimensional model to a suitable embedding position;

[0010] (5) Based on the three-dimensional Boolean operation method, the copyright mark three-dimensional model is embedded into the target three-dimensional model to achieve copyright information embedding including intaglio, relief and grid embedding.

[0011] Furthermore, step (1) specifically includes:

[0012] (1-1) Read the copyright mark information and record it in the form of a string, denoted as cmark;

[0013] (1-2) Traverse each character of cmark from left to right and store them in the copyright character set S = {s i |i=1,2,...,SN}, where s i represents the ith independent character from left to right in the copyright mark information, and SN represents the length of the string of the copyright mark information;

[0014] (1-3) Reading the generation parameters of the copyright mark model set by the user, including the Bezier interpolation change interval t0, the copyright mark thickness d and the copyright mark top surface elevation h, and storing them in the generation parameter set A;

[0015] (1-4) Read the registration parameters of the copyright mark model set by the user, including the scaling adjustment coefficient scale and the z-axis translation adjustment coefficient distZ, and store them in the registration parameter set B.

[0016] Furthermore, step (2) specifically includes:

[0017] (2-1) Select any character s from the copyright character set S i ;

[0018] (2-2) Based on the FreeType algorithm library, obtain s i All Bezier boundary arcs and store them in character s i The arc set AL i ={al i,j |j=1,2,...,ANi}, where a i,j Represents character s i The jth Bezier arc segment in s i The number of Bezier arc segments in ;

[0019] (2-3) Select AL i Any Bezier arc segment al i,j , and obtain the Bezier control point set of the arc segment, recorded as BCP i,j ;

[0020] (2-4) According to the following formula, based on the Bezier interpolation change interval t0 in the generation parameter set A, for the arc segment al i,j Perform quadratic Bezier interpolation to obtain the interpolated arc point set BCP i,j ′, and form the interpolated arc segment al i,j ′;

[0021] P(t)=(1-t) 2 P0+2t(1-t)P1+t 2 P2,t∈[0,1]

[0022] Where P(t) represents the arc point set BCP i,j ′, P0, P1, P2 are BCP i,j The starting point, control point and end point of the quadratic Bezier curve in , t gradually changes from 0 to 1, and t0 increases each time;

[0023] (2-5) Repeat steps (2-3)-(2-4) until the arc set AL i After the traversal is completed, all the interpolated arc segments al i,j ′ is stored in the arc set AL i ′;

[0024] (2-6) AL i Merge the arc segments in the same closed boundary line in ′, and store the closed boundary line obtained after merging into the character s i The closed boundary line set BL i ;

[0025] (2-7) Loop through steps (2-1) to (2-6) until all characters in the copyright character set S are traversed, and store the boundary line sets of all characters into the boundary line set BL of set S = {BL i |i=1,2,...,SN}.

[0026] Furthermore, step (3) specifically includes:

[0027] (3-1) Traverse all points of all boundary lines in BL, translate the horizontal coordinates of each point according to the following formula to achieve the orderly arrangement of the boundary lines of each character, and then obtain the boundary line set BL′ after the orderly arrangement:

[0028]

[0029] In the formula, x i Indicates the horizontal coordinate of the origin of the boundary line of the i-th character, width m Represents character s m The width of the copyright mark, SN represents the length of the copyright mark string, pitch represents the width of the interval between characters, x i ′ Represents the horizontal coordinate of the origin of the i-th character after translation;

[0030] (3-2) According to the direction of the boundary line, the boundary line set BL′ is divided into two categories, namely, the outer boundary set OBL whose point sequence is in the clockwise direction, and the inner boundary set IBL whose point sequence is in the counterclockwise direction;

[0031] (3-3) Based on the Triangle interface and the copyright mark top surface elevation h in the generation parameter set A, with the outer boundary set OBL and the inner boundary set IBL as constraints, the top surface triangulated point set PT of the copyright mark three-dimensional model is constructed;

[0032] (3-4) According to the copyright mark thickness d in the generation parameter set A, the distance d is directly deduced downward based on the top surface triangular point set PT to obtain the bottom surface triangular point set PB of the copyright mark three-dimensional model;

[0033] (3-5) Based on the top triangular point set PT and the bottom triangular point set PB, as well as the boundary line set BL′, the top, side and bottom facets are stitched together to obtain a three-dimensional model of the copyright mark.

[0034] Furthermore, step (4) specifically includes:

[0035] (4-1) Calculate the center point coordinates (cx0, cy0) and bounding box width w0 of the target 3D model, as well as the center point coordinates (cx1, cy1) and bounding box width w1 of the copyright mark 3D model;

[0036] (4-2) Calculate the affine transformation matrix T according to the following formula;

[0037]

[0038] Where scale represents the scaling adjustment coefficient of the copyright model in the registration parameter set B, distZ represents the z-axis translation adjustment coefficient of the copyright model in the registration parameter set B,

[0039] (4-3) Use the affine transformation matrix T to perform affine transformation on all vertices in the copyright mark 3D model to ensure that the copyright mark 3D model is located at the appropriate position of the target model:

[0040]

[0041] Where (x, y, z) is the coordinates of the original copyright mark 3D model point set, (x ′ ,y ′ 、z ′ ) are the coordinates of the copyright mark 3D model point set after affine transformation.

[0042] Furthermore, step (5) specifically includes:

[0043] (5-1) Based on the 3D Boolean operation interface of the CGAL library, the difference between the target 3D model and the copyright mark 3D model is calculated to obtain the copyright embedding effect model of the negative engraving, the union of the target 3D model and the copyright mark 3D model is calculated to obtain the copyright embedding effect model of the positive engraving, and the intersection of the target 3D model and the copyright mark 3D model is first calculated and then the union is calculated to obtain the embedding effect model of the hidden watermark;

[0044] (5-2) Assign material information to the Boolean operation effect model and bind the corresponding attribute file.

[0045] The three-dimensional model copyright marking device based on Boolean operation described in the present invention includes a processor and a computer program stored in a memory and executable on the processor, and the processor implements the above method when executing the program.

[0046] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention can support the efficient generation and reuse of three-dimensional copyright marks, and can carry out efficient development based on the existing class library, with high efficiency and relatively stable algorithm; the support of three embedding modes can meet the diverse needs of copyright marks, and supports multiple embedding, with a wider range of applications; the embedding position follows the target model, with higher security. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is the three-dimensional geological model map of Zijin Mountain used in this embodiment;

[0048] Figure 2 It is a flow chart of a three-dimensional model copyright marking method based on Boolean operation provided by the present invention;

[0049] Figure 3 This is an example of contour extraction based on TTF; (a) Bezier feature points of the letter "g", (b) arc point set of the letter "g" after quadratic Bezier interpolation, (c) boundary point set of the letter "g";

[0050] Figure 4 Schematic diagram of the combination and arrangement of multiple character outlines of "NNU" in this embodiment;

[0051] Figure 5 is a three-dimensional model of the copyright mark of "NNU" in this embodiment;

[0052] Figure 6 This is the result of the copyright mark information with the content "NNU" being embossed and embedded on the top surface of the Purple Mountain model in this embodiment; (a) is a rendering view, and (b) is an edge view;

[0053] Figure 7 The copyright mark "NNU" is engraved and embedded on the bottom surface of the Purple Mountain model; (a) is a rendering view, and (b) is an edge view;

[0054] Figure 8 The copyright mark information "NNU" is embedded in the bottom surface of the Purple Mountain model. (a) Rendering view, (b) Edge view;

[0055] Fig. 9 It is the result of the intaglio embedding of the complex Chinese copyright mark information, which reads "fine sandstone";

[0056] Fig.10 It is the result of the engraving and embedding of the copyright mark information of the graphic symbol of a compass. DETAILED DESCRIPTION

[0057] The technical solution of the present invention is further described in detail below. In this embodiment, a three-dimensional solid model of Nanjing Purple Mountain is selected as experimental data. Figure 1 As shown, the projection coordinate system used by the experimental data is WGS 84 / Pseudo-Mercator (3857), and the coordinate unit is meter. The copyright information is selected as "NNU". The following is further explained by combining the accompanying drawings and describing a specific embodiment.

[0058] This embodiment discloses a three-dimensional model copyright marking method based on Boolean operations, such as Figure 2 As shown, including:

[0059] (1) Read the copyright mark information and the generation parameters and alignment parameters of the copyright mark model set by the user to form a copyright character set S, a generation parameter set A and a alignment parameter set B.

[0060] This step specifically includes:

[0061] (1-1) Read the copyright mark information and record it in the form of a character string, denoted as cmark; in this embodiment, cmark = "NNU";

[0062] (1-2) Traverse each character of cmark from left to right and store them in the copyright character set S = {s i |i=1,2,...,SN}, where s irepresents the ith independent character from left to right in the copyright mark information, and SN represents the length of the character string of the copyright mark information; in this embodiment, SN=3;

[0063] (1-3) Reading the generation parameters of the copyright mark model set by the user, including the Bezier interpolation change interval t0, the copyright mark thickness d and the copyright mark top surface elevation h, and storing them in the generation parameter set A;

[0064] (1-4) Read the registration parameters of the copyright mark model set by the user, including the scaling adjustment coefficient scale and the z-axis translation adjustment coefficient distZ, and store them in the registration parameter set B.

[0065] (2) Obtain the closed boundary lines of each character in the character set S through Bezier interpolation, and store them in the boundary line set BL of the copyright character set S.

[0066] Step (2) specifically includes:

[0067] (2-1) Select any character s from the copyright character set S i ;

[0068] (2-2) Based on the FreeType algorithm library, obtain s i All Bezier boundary arcs and store them in character s i The arc set AL i ={al i,j |j=1,2,...,ANi}, where a i,j Represents character s i The jth Bezier arc segment in s i The number of Bezier arc segments in ;

[0069] (2-3) Select AL i Any Bezier arc segment al i,j , and obtain the Bezier control point set of the arc segment, recorded as BCP i,j ;like Figure 3 As shown in (a);

[0070] (2-4) According to the following formula, based on the Bezier interpolation change interval t0 in the generation parameter set A, for the arc segment al i,j Perform quadratic Bezier interpolation to obtain the interpolated arc point set BCP i,j ′, and form the interpolated arc segment al i,j ′;

[0071] P(t)=(1-t) 2 P0+2t(1-t)P1+t 2 P2,t∈[0,1]

[0072] Where P(t) represents the arc point set BCP i,j ′, P0, P1, P2 are BCP i,j The starting point, control point and end point of the quadratic Bezier curve in , t gradually changes from 0 to 1, and t0 increases each time. In this embodiment, t0 is 0.1;

[0073] (2-5) Repeat steps (2-3)-(2-4) until the arc set AL i After the traversal is completed, all the interpolated arc segments al i,i ′ is stored in the arc set AL i ';like Figure 3 As shown in (b);

[0074] (2-6) AL i Merge the arc segments in the same closed boundary line in ′, and store the closed boundary line obtained after merging into the character s i The closed boundary line set BL i ;

[0075] (2-7) Loop through steps (2-1) to (2-6) until all characters in the copyright character set S are traversed, and store the boundary line sets of all characters into the boundary line set BL of set S = {BL i |i=1,2,...,SN}.

[0076] (3) Based on the boundary line set BL and the generation parameters in the generation parameter set A, a three-dimensional model of the copyright mark is constructed.

[0077] This step specifically includes:

[0078] (3-1) Traverse all points of all boundary lines in BL, translate the horizontal coordinates of each point according to the following formula to achieve the orderly arrangement of the boundary lines of each character, and then obtain the boundary line set BL′ after the orderly arrangement:

[0079]

[0080] In the formula, x i Indicates the horizontal coordinate of the origin of the boundary line of the i-th character, width m Represents character s m The width of the copyright mark, SN represents the length of the copyright mark string, pitch represents the width of the interval between characters, x i ′ represents the horizontal coordinate of the origin of the i-th character after translation; in this embodiment, pitch = 0.5*width m ,like Figure 4 As shown;

[0081] (3-2) According to the direction of the boundary line, the boundary line set BL′ is divided into two categories, namely the outer boundary set OBL whose point sequence is in the clockwise direction, and the inner boundary set IBL whose point sequence is in the counterclockwise direction; Figure 3 As shown in (c);

[0082] (3-3) Based on the Triangle interface and the copyright mark top elevation h in the generation parameter set A, the top triangulated point set PT of the copyright mark three-dimensional model is constructed with the outer boundary set OBL and the inner boundary set IBL as constraints; in this embodiment, h=120m;

[0083] (3-4) According to the copyright mark thickness d in the generation parameter set A, the distance d is directly deduced downward on the basis of the top triangular point set PT to obtain the bottom triangular point set PB of the copyright mark three-dimensional model; in this embodiment, d=60m;

[0084] (3-5) Based on the top triangular point set PT and the bottom triangular point set PB, as well as the boundary line set BL′, the top, side and bottom facets are stitched together to obtain a three-dimensional model of the copyright mark, such as Figure 5 shown.

[0085] (4) Based on the spatial information of the target three-dimensional model to be embedded with the watermark and the spatial information of the copyright mark model, as well as the registration parameters in the registration parameter set B, the copyright mark three-dimensional model is affine transformed to align the copyright mark three-dimensional model to a suitable embedding position.

[0086] This step specifically includes:

[0087] (4-1) Calculate the center point coordinates (cx0, cy0) and bounding box width w0 of the target 3D model, and the center point coordinates (cx1, cy1) and bounding box width w1 of the copyright mark 3D model; in this embodiment, cx0 = 13230740.5, cy0 = 3773167.86, cx1 = 31.27, cy1 = -8.67, w0 = 5989m, w1 = 63.19m;

[0088] (4-2) Calculate the affine transformation matrix T according to the following formula;

[0089]

[0090] Wherein, scale represents the scaling adjustment coefficient of the copyright model in the registration parameter set B, and distZ represents the z-axis translation adjustment coefficient of the copyright model in the registration parameter set B; in this embodiment, scale=0.4, distZ=20;

[0091] (4-3) Use the affine transformation matrix T to perform affine transformation on all vertices in the copyright mark 3D model to ensure that the copyright mark 3D model is located at the appropriate position of the target model:

[0092]

[0093] Where (x, y, z) is the coordinates of the original copyright mark 3D model point set, (x ′ ,y ′ 、z ′ ) are the coordinates of the copyright mark 3D model point set after affine transformation.

[0094] (5) Based on the three-dimensional Boolean operation method, the copyright mark three-dimensional model is embedded into the target three-dimensional model to achieve copyright information embedding including intaglio, relief and grid embedding.

[0095] This step specifically includes:

[0096] (5-1) Based on the 3D Boolean operation interface of the CGAL library, the difference between the target 3D model and the copyright mark 3D model is calculated to obtain the copyright embedding effect model of the negative engraving, and the union of the target 3D model and the copyright mark 3D model is calculated to obtain the copyright embedding effect model of the positive engraving. The intersection of the target 3D model and the copyright mark 3D model is first calculated, and then the union is calculated to obtain the embedding effect model of the hidden watermark. In this embodiment, the union Boolean operation is used to obtain the result of the "NNU" copyright information being positively engraved on the Purple Mountain model, as shown in FIG. Figure 6 As shown;

[0097] (5-2) Assign material information to the Boolean operation effect model and bind the corresponding attribute file.

[0098] This embodiment only uses positive engraving as an example to embed the copyright information into the target model. The copyright information can also be negative engraved or embedded into the target model through surface mesh hiding according to different needs, such as Figure 7 , Figure 8 shown.

[0099] This embodiment only shows the copyright information embedded in English letters, and digital fingerprints, complex Chinese characters ( Fig. 9 ) or cartographic symbols ( Fig.10 ) and other vector contents are embedded into the target model.

[0100] In this embodiment, only the Boolean operation processing interface provided by the CGAL open source code is used to process the Boolean operation between the copyright mark model and the target model. Other 3D software or libraries such as 3dsmax can also be used to perform 3D Boolean operations. In this embodiment, only the Delauney meshing of the top surface of the copyright mark model is performed based on the Triangle algorithm library. Other libraries or software such as ArcGIS can also be used to perform triangulation meshing.

[0101] This embodiment also provides a three-dimensional model copyright marking device based on Boolean operations, including a processor and a computer program stored in a memory and executable on the processor, and the processor implements the above method when executing the program.

[0102] The above disclosure is only a preferred embodiment of the present invention, which cannot be used to limit the scope of the present invention. Therefore, equivalent changes made according to the claims of the present invention are still within the scope of the present invention.

Claims

1. A three-dimensional model copyright marking method based on Boolean operations, characterized in that The method includes: (1) Reading copyright mark information and generation parameters and alignment parameters of the copyright mark model set by the user to form a copyright character set S, a generation parameter set A, and a alignment parameter set B; (2) Obtain the closed boundary lines of each character in the character set S through Bezier interpolation, and store them in the boundary line set BL of the copyright character set S; (3) constructing a three-dimensional model of the copyright mark based on the boundary line set BL and the generation parameters in the generation parameter set A; (4) performing affine transformation processing on the copyright mark three-dimensional model according to the spatial information of the target three-dimensional model to be embedded with the watermark and the spatial information of the copyright mark model, as well as the registration parameters in the registration parameter set B, and registering the copyright mark three-dimensional model to a suitable embedding position; (5) Based on the three-dimensional Boolean operation method, the copyright mark three-dimensional model is embedded into the target three-dimensional model to achieve copyright information embedding including intaglio, relief and grid embedding; Wherein, step (3) specifically includes: (3-1) Traverse all points of all boundary lines in BL, translate the horizontal coordinates of each point according to the following formula to achieve the orderly arrangement of the boundary lines of each character, and then obtain the boundary line set BL′ after the orderly arrangement: In the formula, x i Indicates the horizontal coordinate of the origin of the boundary line of the i-th character, width m Represents character s m The width of the copyright mark, SN represents the length of the copyright mark string, pitch represents the width of the interval between characters, x i ′ Represents the horizontal coordinate of the origin of the i-th character after translation; (3-2) According to the direction of the boundary line, the boundary line set BL′ is divided into two categories, namely, the outer boundary set OBL whose point sequence is in the clockwise direction, and the inner boundary set IBL whose point sequence is in the counterclockwise direction; (3-3) Based on the Triangle interface and the copyright mark top surface elevation h in the generation parameter set A, with the outer boundary set OBL and the inner boundary set IBL as constraints, the top surface triangulated point set PT of the copyright mark three-dimensional model is constructed; (3-4) According to the copyright mark thickness d in the generation parameter set A, the distance d is directly deduced downward based on the top surface triangular point set PT to obtain the bottom surface triangular point set PB of the copyright mark three-dimensional model; (3-5) Based on the top triangulated point set PT and the bottom triangulated point set PB, as well as the boundary line set BL′, stitch the top, side and bottom facets to obtain a three-dimensional model of the copyright mark; Wherein, step (4) specifically includes: (4-1) Calculate the center point coordinates (cx0, cy0) and bounding box width w0 of the target 3D model, as well as the center point coordinates (cx1, cy1) and bounding box width w1 of the copyright mark 3D model; (4-2) Calculate the affine transformation matrix T according to the following formula; Where scale represents the scaling adjustment coefficient of the copyright model in the registration parameter set B, distZ represents the z-axis translation adjustment coefficient of the copyright model in the registration parameter set B, (4-3) Use the affine transformation matrix T to perform affine transformation on all vertices in the copyright mark 3D model to ensure that the copyright mark 3D model is located at the appropriate position of the target model: Where (x, y, z) is the coordinates of the original copyright mark 3D model point set, (x ′ ,y ′ 、z ′ ) are the coordinates of the copyright mark 3D model point set after affine transformation.

2. The three-dimensional model copyright marking method based on Boolean operation according to claim 1 is characterized in that: Step (1) specifically includes: (1-1) Read the copyright mark information and record it in the form of a string, denoted as cmark; (1-2) Traverse each character of cmark from left to right and store them in the copyright character set S = {s i |i=1,2,...,SN}, where s i represents the ith independent character from left to right in the copyright mark information, and SN represents the length of the string of the copyright mark information; (1-3) Reading the generation parameters of the copyright mark model set by the user, including the Bezier interpolation change interval t0, the copyright mark thickness d and the copyright mark top surface elevation h, and storing them in the generation parameter set A; (1-4) Read the registration parameters of the copyright mark model set by the user, including the scaling adjustment coefficient scale and the z-axis translation adjustment coefficient distZ, and store them in the registration parameter set B.

3. The three-dimensional model copyright marking method based on Boolean operation according to claim 1 is characterized in that: Step (2) specifically includes: (2-1) Select any character s from the copyright character set S i ; (2-2) Based on the FreeType algorithm library, obtain s i All Bezier boundary arcs and store them in character s i The arc set AL i ={al i,j |j=1,2,...,ANi}, where a i,j Represents character s i The jth Bezier arc segment in s i The number of Bezier arc segments in ; (2-3) Select AL i Any Bezier arc segment al i,j , and obtain the Bezier control point set of the arc segment, recorded as BCP i,j ; (2-4) According to the following formula, based on the Bezier interpolation change interval t0 in the generation parameter set A, for the arc segment al i,j Perform quadratic Bezier interpolation to obtain the interpolated arc point set BCP i,j ′, and form the interpolated arc segment al i,j ′; P(t)=(1-t) 2 P0+2t(1-t)P1+t 2 P2,t∈[0,1] Where P(t) represents the arc point set BCP i,j ′, P0, P1, P2 are BCP i,j The starting point, control point and end point of the quadratic Bezier curve in , t gradually changes from 0 to 1, and t0 increases each time; (2-5) Repeat steps (2-3)-(2-4) until the arc set AL i After the traversal is completed, all the interpolated arc segments al i,j ′ is stored in the arc set AL i ′; (2-6) AL i Merge the arc segments in the same closed boundary line in ′, and store the closed boundary line obtained after merging into the character s i The closed boundary line set BL i ; (2-7) Loop through steps (2-1) to (2-6) until all characters in the copyright character set S are traversed, and store the boundary line sets of all characters into the boundary line set BL of set S = {BL i |i=1,2,...,SN}.

4. The three-dimensional model copyright marking method based on Boolean operation according to claim 1 is characterized in that: Step (5) specifically includes: (5-1) Based on the 3D Boolean operation interface of the CGAL library, the difference between the target 3D model and the copyright mark 3D model is calculated to obtain the copyright embedding effect model of the negative engraving, the union of the target 3D model and the copyright mark 3D model is calculated to obtain the copyright embedding effect model of the positive engraving, and the intersection of the target 3D model and the copyright mark 3D model is first calculated and then the union is calculated to obtain the embedding effect model of the hidden watermark; (5-2) Assign material information to the Boolean operation effect model and bind the corresponding attribute file.

5. A three-dimensional model copyright marking device based on Boolean operation, comprising a processor and a computer program stored in a memory and executable on the processor, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 4 is implemented.

Images