CN104143209B - Method for engraving three-dimensional model based on line pattern - Google Patents

Abstract

A method for engraving a three-dimensional model based on a line drawing pattern, comprising: the user inputs a two-dimensional line drawing pattern to be engraved, the method preprocesses the input pattern, and extracts the line centerline in the input line drawing image as an engraving contour line through an edge contraction operation; For different types of 3D models, parameterize the area to be engraved on the surface of the model; discretize the obtained 2D engraved contour lines, and use parametric mapping to map them to discrete engraved lines on the surface of the 3D model; calculate the The distance from the vertices to be carved to the 3D engraved lines, using the engraving function to determine the translation distance and direction of the vertices in the area to be engraved, and then translate the vertices to be engraved to obtain the 3D engraving effect of the model.

Description

Three-dimensional model engraving method based on line drawing pattern

technical field

The patented design of the present invention aims at the two-dimensional line drawing pattern input by the user, and provides a method that can conveniently and quickly generate the engraving effect of the pattern on the three-dimensional model.

Background technique

As a mainstream representation of the shape of 3D objects, 3D models have been widely used in digital entertainment industry, industrial design field, virtual reality and other fields. The representation properties of the 3D model include two aspects: the geometric properties of the 3D model (such as vertex position information and topological connection information between vertices) and the appearance properties of the 3D model (such as surface material properties, geometric texture and color texture information, etc.). In order to make the generated 3D model more realistic and increase the aesthetics and artistry of the 3D model, 3D feature textures are usually added to the 3D model. In the existing technology, it can be divided into bump mapping technology, bump mapping technology and relief Texture mapping techniques. In recent years, many feature-based texture synthesis algorithms have been proposed, including 3D sculpting technology. 3D sculpting refers to the process of moving its vertices along specific lines on the model surface to generate complex geometric textures on the surface. It is a complex model surface An important method of texture generation. Digital sculpting of 3D models, as a means of generating complex models, can conveniently and efficiently generate complex models with rich surface relief textures on the basis of the original model through specific sculpting methods, thus greatly enriching the modeling of 3D complex models content, this method will have broad application prospects. The existing 3D engraving technology mainly draws lines on the 3D model, and uses the engraving function to calculate the translation direction and distance of the vertices within the texture width, so as to obtain a realistic 3D engraving effect. This technology is mainly realized through user interaction. However, Designing complex 3D engraving effects requires a large amount of user interaction. At the same time, since the contour line is generated by fitting the key points specified by the user, the specific trend is not directly controlled by the user, and it is difficult for the user to design the desired shape on the model. complex engraving effects. Our method directly takes the 2D line drawing pattern to be engraved as input, which can conveniently realize the engraving effect on the surface of the 3D model. Since the engraving outline in this method is automatically obtained from the input image, the user's operation is quite simple, and at the same time, a relatively complex three-dimensional engraving effect is realized.

Contents of the invention

In order to overcome the disadvantages of large interactive workload, time-consuming and simple engraving effect in the surface texture synthesis of the existing 3D mesh model, the present invention provides a two-dimensional line-based A three-dimensional sculpting method for drawing patterns.

The technical solution adopted by the present invention to solve its technical problems is:

Based on the three-dimensional model engraving method of line drawing pattern, described method comprises following four steps:

1) The user inputs the two-dimensional line drawing pattern that needs to be engraved, and the method preprocesses the input pattern, and extracts the center line of the line in the input line drawing image as the engraving contour line through the edge contraction operation;

Convert the input two-dimensional line drawing pattern into a grayscale image, and calculate the gradient value of each pixel, and use the pixel whose gradient value is greater than 10% of the maximum gradient value as the pixel to be moved, and record the total number of pixels to be moved n _move ; For the pixel to be moved, it moves toward the center along its unitized gradient direction, and each pixel to be moved stops when it moves near the center; the method for judging that the pixel stops moving is as follows: first, collect the neighbors of the pixel p _i Field N _i ＝{p _j |||p _j -p _i ||≤1}, judge the gradient direction of pixel point p _j in the neighborhood Gradient direction with pixel point p _i Is it consistent when , it means that there is already a pixel point p _j opposite to the moving direction in the neighborhood at this time, that is, p _j is a point obtained by moving on the boundary opposite to p _i relative to the contour center line, and at this time p _i is already close to the contour center line ; Then judge whether p _i moves beyond p _j , when satisfying When pi crosses p _j , it _means that _pi has reached the center line of the contour, so it stops moving. As the number of pixels that stop moving increases, the number of pixels to be moved becomes less and less. When the number of pixels to be moved does not exceed λ·n _move , the entire shrinking process ends (the parameter λ can be 0.01). After the shrinkage is finished, in order to deal with the situation that a small number of isolated points may appear, the pixel points _pi in which the number of pixels contained in the neighborhood N _i is less than 2 are removed as isolated points, so as to obtain a two-dimensional engraved contour line.

2) For different types of 3D models, parameterize the area to be carved on the surface of the model;

For three-dimensional models such as cylindrical surfaces and spherical surfaces, the entire model can be used as a carving area, and the entire model can be parameterized with a simple parameterization method. For the semi-cylindrical model, let its height be parallel to the Z axis, take any point on the XOY plane as the reference point O, and the angle formed by the projection point of any point M on the XOY plane on the cylindrical surface and the reference point is θ, the cylinder If the body height is h, the parameter coordinates of point M are (s,t)=(θ/π,||z _M -z _O ||/h), where z _M and z _O are the z coordinates of point M and point O respectively . For the hemispherical model, the parameter coordinates of any point P(x, y, z) are (s, t) = (arccos(z/r), arctan(y/x)), where r is the radius of the sphere.

For a general 3D model, it is first necessary to select a local area on the surface of the model as the area to be sculpted, and then use the local parameterization method for parameterization. The area to be engraved can be drawn by the user in the center of the area to be engraved, and the system will automatically generate the engraved area according to the hand-drawn line. The specific process is as follows: a) first refine the hand-painted line; The intersection point between the hand-drawn line and the model surface, record the plane where each intersection point is located, and determine the patch set F _line that the hand _- drawn line _passes through _; Uniform resampling is performed on the passing triangles, and the uniformly resampled point set As the baseline point set of the engraving area; b) The user selects the area within the distance from the hand-drawn line as the area to be engraved; the product of the average side length of the 3D mesh model and the distance threshold given by the user is used as the distance reference The maximum geodesic distance d _max of the line point set; using the idea of graph theory, the k-neighborhood F _k area of the patch set F _line that the hand-drawn line passes through on the 3D mesh model is used as the candidate area and the weighted graph is established, respectively Take the vertices and edges of the grid model as the vertices and edges of the graph, and take the weight as the corresponding edge length; then set the baseline point set Add it to the weighted graph, connect each point with the three vertices of the triangular surface where it is located to form an edge, and use the length of the connected edge as the weight; at the same time, connect the points in the baseline point set to form an edge , and the weight value is 0; thus, after the weighted graph of the k-neighborhood F _k area is established, the shortest path d _i from each vertex v _i to the baseline is calculated by using the shortest path fast calculation SPFA algorithm; if F _k A facet F _i in the region satisfies that the shortest path from its three vertices to the baseline is less than d _max , then F _i is the facet to be carved, and all facet sets F _S that meet the conditions in the F _k region are The final engraved area, at this time After the engraving area is generated, the local area is parameterized. The parameter coordinates of any grid vertex v in the engraving area can be calculated from the position of the vertex relative to the baseline, so the parameter coordinates of the vertex v are where d is the geodesic distance from point v to the datum line, for parameter values on the freehand line, for arrive , L _l is the total length of the hand-drawn line; but at this time, the parameter coordinates on both sides of the reference line in the engraving area are the same, so it is necessary to further determine the direction of the vertex v relative to the reference line: for normal direction, yes Tangents on the base line, is v to The vector, the parameter coordinates of the vertex v are corrected as At this time, the value range of the vertex v in the s direction is [-1, 1], in order to convert it to [0, 1], it is necessary to translate all vertices in the engraved area to the right by d _max units relative to the reference line, so that In general, the final parameter coordinates of any vertex v in the local engraving area on the surface of a 3D model can be taken as

3) discretizing the obtained two-dimensional engraved contour lines, and using parametric mapping to map it to discrete engraved lines on the surface of the three-dimensional model;

After parameterizing the engraved area, the two-dimensional engraved contours should be mapped to the discrete engraved lines on the model surface. The process is as follows: Let the engraved area on the surface of the three-dimensional model be F _S , and the corresponding patch set on the plane parameter domain after parameterization is The method scales the parameter field to the same size as the two-dimensional image, maps the pixels of the engraved contour line to the parameter field, and judges each pixel point p after mapping according to the pixel coordinates and the coordinates of the three vertices of each parameter field patch falls on a patch on the surface of the model, let the pixel p be located at , then p can be given by the three points Expressed as follows: Where λ ₁ +λ ₂ +λ ₃ =1; suppose by The vertices of the corresponding 3D model engraving area patch F _i are respectively v ₀ , v ₁ , v ₂ , then the point v that maps the pixel point p to the 3D model patch F _i can be determined as v=λ ₁ v ₀ + λ ₂ v ₁ +λ ₃ v ₂ ; Before mapping the two-dimensional engraved contour lines to the model surface, it is usually necessary to downsample the two-dimensional contour lines, and for each parameter domain patch containing pixels Average the coordinates of all the included pixels to obtain the down-sampled 2D engraving contour pixel point p, and then use the parameterized mapping to obtain the 3D model surface point v from the pixel point p, and add all v to the original 3D model , so that the discrete sculpted lines on the surface of the 3D model are obtained from the 2D sculpted line mapping.

4) Calculate the distance from the vertices to be carved on the surface of the 3D model to the 3D engraving lines, use the engraving function to determine the translation distance and direction of the vertices in the area to be engraved, and translate the vertices to be engraved to obtain the three-dimensional engraving effect; calculate the vertices in the engraving area to the three-dimensional discrete When engraving the line distance, the user first specifies the engraving width, and the vertices whose distance is smaller than the engraving width are determined by the engraving function H(d) to determine the translation distance, and then translate along the normal direction of the vertices to finally achieve the three-dimensional engraving effect; the engraving function H(d) is taken as:

The technical idea of the present invention is: based on the two-dimensional line drawing pattern input by the user, extract the center line of the line as the engraved contour line through the edge contraction operation, discretize the two-dimensional engraved contour line and use parametric mapping to discrete engraving on the three-dimensional model Lines, using the engraving function defined as the distance from the vertex of the three-dimensional model to the engraving line set, this patent proposes a three-dimensional engraving method based on line drawing patterns.

The beneficial effects of the invention are mainly manifested in: simple operation, convenient engraving, and strong controllability of engraving effect.

Description of drawings

Fig. 1 is an example of a two-dimensional line drawing pattern input by a user in the present invention.

Fig. 2 is the two-dimensional engraving outline obtained after preprocessing with Fig. 1 as input.

Fig. 3 is an example diagram of mapping the two-dimensional engraved outlines to the discrete engraved lines on the surface of the three-dimensional model according to the present invention.

Fig. 4 is an example diagram of complex engraving effects realized on different model surfaces by using two-dimensional line drawing patterns according to the present invention.

detailed description

The technical method of the present invention and various sculpting effects of three-dimensional models generated will be further described and explained in detail below in conjunction with the accompanying drawings.

With reference to accompanying drawing 1---accompanying drawing 4, the three-dimensional model engraving method based on line drawing pattern, described method comprises the following four steps:

1) The user inputs the two-dimensional line drawing pattern that needs to be engraved, and the method preprocesses the input pattern, and extracts the center line of the line in the input line drawing image as the engraving contour line through the edge contraction operation;

Convert the input two-dimensional line drawing pattern (as shown in Figure 1) into a grayscale image, and calculate the gradient value of each pixel point, and use the pixel point whose gradient value is greater than 10% of the maximum gradient value as the pixel point to be moved, and record the pixel point to be moved. The total number of moving pixels n _move ; for the pixels to be moved, move toward the center along the direction of the unitized gradient, and each pixel to be moved stops when it moves near the center; the method for judging that the pixels stop moving is as follows: first collect Neighborhood N _i of pixel point p _i ={p _j |||p _j -p _i ||≤1}, determine the gradient direction of pixel point p _j in this neighborhood Gradient direction with pixel point p _i Is it consistent when , it means that there is already a pixel point p _j opposite to the moving direction in the neighborhood at this time, that is, p _j is a point obtained by moving on the boundary opposite to p _i relative to the contour center line, and at this time p _i is already close to the contour center line ; Then judge whether p _i moves beyond p _j , when satisfying When pi crosses p _j , it _means that _pi has reached the center line of the contour, so it stops moving. As the number of pixels that stop moving increases, the number of pixels to be moved becomes less and less. When the number of pixels to be moved does not exceed λ·n _move , the entire shrinking process ends (the parameter λ can be 0.01). After the shrinkage is over, in order to deal with the situation that a small number of isolated points may appear, the pixel points p _i that contain less than 2 pixel points in the neighborhood N _i are removed as isolated points, so as to obtain the two-dimensional engraved contour line as shown in Figure 2 .

2) For different types of 3D models, parameterize the area to be carved on the surface of the model;

For three-dimensional models such as cylindrical surfaces and spherical surfaces, the entire model can be used as a carving area, and the entire model can be parameterized with a simple parameterization method. For the semi-cylindrical model, let its height be parallel to the Z axis, take any point on the XOY plane as the reference point O, and the angle formed by the projection point of any point M on the XOY plane on the cylindrical surface and the reference point is θ, the cylinder If the body height is h, the parameter coordinates of point M are (s,t)=(θ/π,||z _M -z _O ||/h), where z _M and z _O are the z coordinates of point M and point O respectively . For the hemispherical model, the parameter coordinates of any point P(x, y, z) are (s, t) = (arccos(z/r), arctan(y/x)), where r is the radius of the sphere.

For a general 3D model, it is first necessary to select a local area on the surface of the model as the area to be sculpted, and then use the local parameterization method for parameterization. The area to be engraved can be drawn by the user in the center of the area to be engraved, and the system will automatically generate the engraved area according to the hand-drawn line. The specific process is as follows: a) first refine the hand-painted line; The intersection point between the hand-drawn line and the model surface, record the plane where each intersection point is located, and determine the patch set F _line that the hand _- drawn line _passes through _; Uniform resampling is performed on the passing triangles, and the uniformly resampled point set As the baseline point set of the engraving area; b) The user selects the area within the distance from the hand-drawn line as the area to be engraved; the product of the average side length of the 3D mesh model and the distance threshold given by the user is used as the distance reference The maximum geodesic distance d _max of the line point set; using the idea of graph theory, the k-neighborhood F _k area (preferably k=120) of the patch set F _line on the 3D mesh model that the hand-painted line passes through is used as a candidate area and Establish a weighted graph, take the vertices and edges of the grid model as the vertices and edges of the graph respectively, and take the weight as the corresponding edge length; then set the baseline point set Add it to the weighted graph, connect each point with the three vertices of the triangular surface where it is located to form an edge, and use the length of the connected edge as the weight; at the same time, connect the points in the baseline point set to form an edge , and the weight value is 0; thus, after the weighted graph of the k-neighborhood F _k area is established, the shortest path d _i from each vertex v _i to the baseline is calculated by using the shortest path fast calculation SPFA algorithm; if F _k A facet F _i in the region satisfies that the shortest path from its three vertices to the baseline is less than d _max , then F _i is the facet to be carved, and all facet sets F _S that meet the conditions in the F _k region are The final engraved area, at this time After the engraving area is generated, the local area is parameterized. The parameter coordinates of any grid vertex v in the engraving area can be calculated from the position of the vertex relative to the baseline, so the parameter coordinates of the vertex v are where d is the geodesic distance from point v to the datum line, for parameter values on the freehand line, for arrive , L _l is the total length of the hand-drawn line; but at this time, the parameter coordinates on both sides of the reference line in the engraving area are the same, so it is necessary to further determine the direction of the vertex v relative to the reference line: for normal direction, yes Tangents on the base line, is v to The vector, the parameter coordinates of the vertex v are corrected as At this time, the value range of the vertex v in the s direction is [-1, 1], in order to convert it to [0, 1], it is necessary to translate all vertices in the engraved area to the right by d _max units relative to the reference line, so that In general, the final parameter coordinates of any vertex v in the local engraving area on the surface of a 3D model can be taken as

3) discretizing the obtained two-dimensional engraved contour lines, and using parametric mapping to map it to discrete engraved lines on the surface of the three-dimensional model;

After parameterizing the engraving area, the two-dimensional engraving contours should be mapped to discrete engraving lines on the model surface, the process is as follows: Let the engraving area on the surface of the three-dimensional model be F _S , and the corresponding patch set on the plane parameter domain after parameterization is Method After scaling the parameter field to the same size as the two-dimensional image, map the pixel points of the engraving contour line to the parameter field, and judge each pixel point p after mapping according to the pixel coordinates and the coordinates of the three vertices of each parameter field patch falls on a patch on the surface of the model, let the pixel p be located at , then p can be given by the three points Expressed as follows: Where λ ₁ +λ ₂ +λ ₃ =1; suppose by The vertices of the corresponding 3D model engraving area patch F _i are respectively v ₀ , v ₁ , v ₂ , then the point v that maps the pixel point p to the 3D model patch F _i can be determined as v=λ ₁ v ₀ + λ ₂ v ₁ +λ ₃ v ₂ ; Before mapping the two-dimensional engraved contour lines to the model surface, it is usually necessary to down-sample the two-dimensional contour lines, and for each parameter domain patch containing pixels Average the coordinates of all the included pixels to obtain the down-sampled 2D engraved contour pixel point p, and then use the parameterized mapping to obtain the 3D model surface point v from the pixel point p, and add all v to the original 3D model , so that the discrete engraved lines on the three-dimensional model as shown in Figure 3 are obtained from the two-dimensional engraved contour line mapping.

4) Calculate the distance from the vertices to be carved on the surface of the 3D model to the 3D engraving lines, use the engraving function to determine the translation distance and direction of the vertices in the area to be engraved, and translate the vertices to be engraved to obtain the three-dimensional engraving effect; calculate the vertices in the engraving area to the three-dimensional discrete When engraving the line distance, the user first specifies the engraving width, and the vertices whose distance is smaller than the engraving width determine the translation distance according to the engraving function H(d), and then translate along the normal direction of the vertices to finally realize the three-dimensional engraving effect, as shown in Figure 4 As shown, as an example, the engraving function H(d) is taken as:

Claims (1)

1. Based on the three-dimensional model engraving method of line drawing pattern, described method comprises following four steps: 1) The user inputs the two-dimensional line drawing pattern that needs to be engraved, and the method preprocesses the input pattern, and extracts the center line of the line in the input line drawing image as the engraving contour line through the edge contraction operation; Convert the input two-dimensional line drawing pattern into a grayscale image, and calculate the gradient value of each pixel, and use the pixel whose gradient value is greater than 10% of the maximum gradient value as the pixel to be moved, and record the total number of pixels to be moved n _move ; For the pixel to be moved, it moves toward the center along its unitized gradient direction, and each pixel to be moved stops when it moves near the center; the method for judging that the pixel stops moving is as follows: First, collect the neighborhood of the pixel p _i N _i ＝{p _j |||p _j -p _i ||≤1}, judge whether the gradient direction ▽ _j of the pixel point p _j in the neighborhood is consistent with the gradient direction ▽ _i of the pixel point p _i , when ▽ _i · When ▽ _j ≤ 0, it means that there is already a pixel point p _j opposite to the moving direction in the neighborhood at this time, that is, p _j is a point obtained by moving on the boundary opposite to p _i relative to the center line of the contour. At this time, p _i has Close to the center line of the contour; then judge whether p _i moves past p _j , when (p _j -p _i )▽ _i <0, p _i crosses p _j , indicating that p _i has reached the center line of the contour, so stop moving ;As the number of pixels that stop moving increases, the number of pixels to be moved becomes less and less. When the number of pixels to be moved does not exceed λ·n _move , the parameter λ is set to 0.01, and the entire shrinking process ends; After the contraction is over, in order to deal with the isolated point situation, the pixel point p _i which contains less than 2 pixel points in the neighborhood N _i is removed as an isolated point, so as to obtain a two-dimensional engraved contour line; 2) For different types of 3D models, parameterize the engraved areas on the model surface; For 3D models of cylindrical and spherical surfaces, the entire model is used as the engraving area, and the entire model is parameterized with a simple parameterization method; for the semi-cylindrical model, its height is set parallel to the Z axis, and any point on the XOY plane is taken as a reference Point O, the angle formed by the projection point of any point M on the cylindrical surface on the XOY plane and the reference point is θ, and the height of the cylinder is h, then the parameter coordinates of point M are (s,t)=(θ/π,| |z _M -z _O ||/h), where z _M and z _O are the z coordinates of point M and point O respectively; for the hemispherical model, the parameter coordinates of any point P(x, y, z) are (s ,t)=(arccos(z/r),arctan(y/x)), where r is the spherical radius; For other types of 3D models, it is first necessary to select a local area on the surface of the model as the engraving area, and then use the local parameterization method for parameterization; the engraving area is drawn by the user in the center of the area to be engraved, and the system automatically generates it based on the hand-drawn line The specific process of engraving the area is as follows: a) Thinning the hand-painted lines first; during the thinning process, sequentially obtain the intersection points of the hand-drawn lines and the model surface, record the plane where each intersection point is located, and determine the set of patches that the hand-painted lines pass through F _line ; after refinement, uniformly resample the obtained intersection point set c ₁ ,c ₂ ,…,c _l along the passed triangle patch, and uniformly resample the point set As the baseline point set of the engraving area; b) select the area whose distance from the hand-drawn line is D as the area to be engraved, where the parameter D is selected by the user; the average side length of the three-dimensional mesh model and the distance threshold given by the user The product of is taken as the maximum geodesic distance d _max from the baseline point set; using the idea of graph theory, the k-neighborhood F _k area of the patch set F _line that the hand-drawn line passes through on the 3D grid model is taken as the candidate area and established Weighted graph, the vertices and edges of the grid model are taken as the vertices and edges of the graph respectively, and the weight is taken as the corresponding edge length; then the baseline point set Add to the weighted graph, connect each baseline point with the three vertices of the triangular surface where it is located to form an edge, and use the length of the connected edge as the weight; at the same time, connect the points in the baseline point set in turn To form an edge, the weight value is 0; thus, after the weighted graph of the k-neighborhood F _k region is established, the shortest path d _i from each vertex v _i to the baseline is calculated by using the shortest path fast calculation SPFA algorithm; if A facet F _i in the F _k region satisfies that the shortest path from its three vertices to the baseline is less than d _max , then F _i is the face to be engraved, and all facets in the F _k region that meet the condition set F _S is the final engraving area, at this time After the engraving area is generated, the local area is parameterized. The parameter coordinates of any vertex v of the model in the engraving area are calculated from the position of the vertex relative to the baseline, so the parameter coordinates of the vertex v are where d is the geodesic distance from the vertex v to the baseline, for parameter values on the freehand line, for arrive , L _l is the total length of the hand-drawn line; but at this time, the parameter coordinates on both sides of the reference line in the engraving area are the same, so it is necessary to further determine the direction of the vertex v relative to the reference line: for normal direction, yes The tangent direction on the datum line, is v to The vector, the parameter coordinates of the vertex v are corrected as At this time, the value range of the vertex v in the s direction is [-1,1]. In order to convert it to [0,1], it is necessary to translate all vertices in the engraving area to the right by d _max units relative to the baseline, so that The final parameter coordinates of any vertex v in the local carving area on the surface of other types of 3D models are taken as 3) discretizing the obtained two-dimensional engraved contour lines, and using parametric mapping to map it to discrete engraved lines on the surface of the three-dimensional model; After parameterizing the engraved area, the two-dimensional engraved contours should be mapped to the discrete engraved lines on the model surface. The process is as follows: Let the engraved area on the surface of the three-dimensional model be F _S , and the corresponding patch set on the plane parameter domain after parameterization is After scaling the plane parameter domain to the same size as the two-dimensional image, map the pixels of the engraved contour line to the plane parameter domain, and judge each pixel point p according to the pixel coordinates and the coordinates of the three vertices of each plane parameter domain patch After mapping, it lands on a patch on the model surface, and the pixel point p is located in the plane parameter domain patch , then p is determined by three pixels of Expressed as follows: Where λ ₁ +λ ₂ +λ ₃ =1; suppose by The vertices of the corresponding 3D model engraving area patch F _i are respectively v ₀ , v ₁ , v ₂ , then the pixel point p is mapped to the vertex v on the 3D model patch F _i and determined as v=λ ₁ v ₀ +λ ₂ v ₁ +λ ₃ v ₂ ; Before mapping the two-dimensional engraved contour lines to the model surface, it is necessary to down-sample the two-dimensional contour lines, and for each parameter domain patch containing pixels Average the coordinates of all the included pixels to obtain the down-sampled two-dimensional engraved contour pixel p, and then use the parameterized mapping to obtain the vertex v on the surface of the three-dimensional model, and add all vertices v to the original In the three-dimensional model, the discrete engraving lines on the surface of the three-dimensional model are obtained from the mapping of the two-dimensional engraving lines; 4) Calculate the distance from the vertex to be engraved on the surface of the 3D model to the 3D engraving line, use the engraving function to determine the translation distance and direction of the vertex in the engraving area, and translate the vertices to be engraved to obtain the three-dimensional engraving effect; calculate the vertices in the engraving area to the three-dimensional discrete engraving For the line distance, firstly, the user specifies the engraving width, and the vertices whose distance is smaller than the engraving width are determined by the engraving function H(d) to determine the translation distance, and then translate along the normal direction of the vertices, and finally realize the three-dimensional engraving effect; the engraving function H (d) is taken as: $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}\sqrt{\frac{{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 25</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 32</span>}\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; 45</span>}}& <span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; <</span>\frac{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; )</span>\\ \frac{\mathrm{<span\; class="notranslate">\; 4</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 50</span>}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 5</span>}\mathrm{<span\; class="notranslate">\; W</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; 45</span>}}& <span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; 5</span>}}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; W</span>}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; .</span>$