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

Abstract

The invention discloses a method for engraving a three-dimensional model based on a line pattern. The method for engraving the three-dimensional model based on the line pattern comprises the steps that the two-dimensional line pattern needing to be engraved by a user is input, the input pattern is pre-processed according to a method, and the line center of the input line pattern is extracted by conducting edge shrinkage to serve as an engraving contour line; for different types of three-dimensional models, parameterization is conducted on areas to be engraved on the surface of the model; the obtained two-dimensional engraving contour line is discretized and is mapped into discrete engraving lines on the surface of the three-dimensional model through parameterized mapping; the distances between the peak to be engraved on the three-dimensional model and the three-dimensional engraving lines are calculated, the horizontally-moving distance and the direction of the peak of the area to be engraved are determined according to an engraving function, and the peak to be engraved is moved horizontally, so that the three-dimensional engraving effect of the model is achieved.

Description

Threedimensional model engraving process based on line drawing pattern

Technical field

Two-dimensional line picture case of the Patent design of the present invention for user input, there is provided one kind can conveniently and efficiently three The method that dimension module generates the pattern engraving effect.

Background technology

Used as a kind of main flow representation of three-dimensional body profile, threedimensional model is led in digital entertainment industry, industrial design The fields such as domain, virtual reality are widely used.The characterization attributes of threedimensional model include two aspects：The geometry category of threedimensional model Property (such as the Topology connection information between vertex position information and summit) and threedimensional model appearance attribute (as Facing material category Property, geometric error modeling and color and vein information etc.).In order that the threedimensional model for generating has more sense of reality, while increasing three-dimensional mould The aesthetic property and artistry of type, it will usually three-dimensional feature texture is added to threedimensional model, in existing technology, can be divided into recessed Convex Mappings technology, bump mapping technology and relief grain mapping techniques.In recent years, the algorithm of the textures synthesis of many feature baseds It is suggested, including three dimensional sculpture technology, three dimensional sculpture refers to along the specific lines of model surface and its summit is moved To generate the process of surface complex geometry texture, it is a kind of important method that complex model superficial makings is generated.Threedimensional model Digital engraving as a kind of modelling meanses for generating complex model, can be on the basis of original model by specific engraving side Method easily and efficiently generates the complex model with abundant surface relief texture, so as to be greatly enriched 3 D complex model Modeling contents, this method will be with a wide range of applications.Existing three dimensional sculpture technology is mainly by threedimensional model Free hand line, using the translation direction and distance on summit of the engraving function calculating in texture width, obtains realistic Three dimensional sculpture effect, the technology is mainly realized by user mutual, however, the user of the complicated three dimensional sculpture effect requirements of design Interworking amount is larger, simultaneously because the generation of contour line is the curve fitted by user's designated key point, therefore specifically walks Gesture is not directly controlled by user, and user is difficult the complicated engraving effect that needs are designed on model.Our method is directly treating The two-dimensional line picture case of engraving can conveniently realize the engraving effect on threedimensional model surface as input.Due in the method Engraving contour line is obtained automatically from input picture, hence in so that the operation of user is quite easy, while also achieve comparing Complicated three dimensional sculpture effect.

The content of the invention

In order to the interworking amount in overcoming existing three-dimensional grid model superficial makings to synthesize is big, relatively time-consuming and engraving Effect is simply not enough, the invention provides a kind of simple to operate, engraving is convenient, engraving effect controllability is strong based on two-dimensional line The three dimensional sculpture method of picture case.

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

Based on the threedimensional model engraving process of line drawing pattern, described method includes following four step：

1) user input needs the two-dimensional line picture case of engraving, method to carry out pretreatment to being input into pattern, receive by edge Lines centrage in contracting operation extraction input line picture is used as engraving contour line；

The two-dimensional line picture case of input is switched to into gray-scale maps, and calculates the Grad of each pixel, Grad is more than The pixel of maximum of gradients 10% records pixel sum n to be moved as pixel to be moved_move；For to be moved Pixel, moves along its unitization gradient direction to center, and each pixel to be moved stops moving when moving to immediate vicinity It is dynamic；Judge that pixel stops mobile method as follows：Pixel p is collected first_iNeighborhood N_i={ p_j|||p_j-p_i| |≤1 }, sentence Pixel p in the disconnected neighborhood_jGradient directionWith pixel p_iGradient directionIt is whether consistent, whenWhen, say There is the pixel p contrary with moving direction in bright now contiguous range_j, i.e. p_jBe by with p_iCounter-profile centrage is contrary The point that obtains of Boundary Moving, now p_iNear profile centrage；P is judged again_iWhether p is moved across_j, work as satisfactionWhen, p_iCross p_j, illustrate p_iProfile centerline is had arrived at, therefore stops movement.With stopping movement Pixel number increases, and pixel to be moved is fewer and feweri, when pixel number to be moved is less than λ n_moveWhen, it is whole to receive Compression process terminates (wherein parameter lambda desirable 0.01).After contraction terminates, a small amount of isolated point situation is likely to occur in order to process, by it Middle neighborhood N_iIn the pixel p of the pixel number that includes less than 2_iAs isolated point remove, so as to obtain two dimension engraving profile Line.

2) for different types of threedimensional model, parametrization is carried out respectively to model surface region to be carved；

For threedimensional models such as the face of cylinder, spheres, can be using whole model as carving area, with simple parametrization side Method is by whole model parameterization.For semi-cylindrical model, if it is high parallel with Z axis, appoints in XOY plane and take a little as benchmark Point O, the angle that subpoints of the arbitrfary point M on XOY plane and datum mark are opened on the face of cylinder is θ, a height of h of cylinder, then Point M parameters coordinate be (s, t)=(θ/π, | | z_M-z_O| |/h), wherein z_MAnd z_OIt is respectively the z coordinate of point Μ and point O.For half Sphere Measurement Model, the parameter coordinate of arbitrfary point P (x, y, z) is (s, t)=(arccos (z/r), arctan (y/x)), and wherein r is ball Radius surface.

For general threedimensional model, it is necessary first to which then Selection Model surface regional area is adopted as region to be carved Parametrization is carried out with localized parameterization method.Region wherein to be carved can pass through user in the regional center Freehandhand-drawing for needing engraving One line, system automatically generates carving area according to the hand-drawing line, and detailed process is as follows：A) first refinement behaviour is carried out to free hand line Make；In thinning process, the intersection point of the free hand line and model surface can be successively obtained, record the plane that each intersection point is located, Determine the dough sheet collection F that free hand line is passed through_line；After refinement terminates, to the intersection point collection v for obtaining₁,v₂,…,v_lAlong three for passing through Edged surface piece carries out uniform resampling, by the point set after uniform resamplingAs the datum line point set of carving area；b) By much scope inner regions of user's chosen distance its free hand line as the region for needing engraving；By the flat of three-dimensional grid model The product of the distance threshold that the equal length of side gives with user is as the maximum geodesic curve apart from datum line point set apart from d_max；Using figure By thought, the dough sheet collection F that free hand line on three-dimensional grid model is passed through_lineK- neighborhood F_kRegion is as candidate region and builds Vertical weighted graph, take respectively grid model summit and while the summit as figure and while, weights are taken as the corresponding length of side；Again by datum line Point setIn being added to weighted graph, each point and three summits of its place tri patch are respectively connected with forming side, And to connect the length on the side for obtaining as weights；Simultaneously the point that datum line point is concentrated is sequentially connected to form side, weighting value is 0；So, k- neighborhoods F_kAfter the completion of the weighted graph in region is set up, SPFA algorithms are quickly calculated using shortest path and calculates each Vertex v_iTo the shortest path d of datum line_i；If F_kCertain dough sheet F in region_iIts three summits are met to the most short of datum line Path is respectively less than d_max, then F_iDough sheet as to be carved, F_kAll dough sheet set F for meeting condition in region_SIt is exactly final The carving area for obtaining, nowAfter Area generation to be carved, then localized region carries out parametrization, in carving area Arbitrary mess vertex v parameter coordinate can be by the summit relative to datum line position calculation obtain, therefore the parameter of vertex v Coordinate isWherein d is geodesic curve distances of the point v to datum line,ForOn hand-drawing line Parameter value,ForArriveLength, L_lFor hand-drawing line total length；But now in carving area datum line both sides parameter Coordinate is identical, therefore needs to determine whether direction of the vertex v relative to datum line： ForNormal direction,It isTangent line on datum line,It is that v is arrivedVector, the parameter coordinate modification of vertex v isNow codomain scope of the vertex v in s directions is [- 1,1], in order to be translated into [0,1], Need all summit relative datum lines in carving area to right translation d_maxIndividual unit, so as to general threedimensional model surface office The final argument coordinate of any vertex v can be taken as in portion's carving area

3) by the two dimension engraving contour line discretization for obtaining, and threedimensional model surface is mapped as using parametric maps Discrete engraving lines；

After to carving area parametrization, two dimension engraving contour line is mapped as into the discrete engraving lines of model surface, the mistake Journey is as follows：If threedimensional model surface engraving region is F_S, corresponding dough sheet collection is on plane parameter domain after parametrizationMethod handle Parameter field zoom to it is in the same size with two dimensional image after, by engraving contour line pixel be mapped on parameter field, according to pixel Three apex coordinates of coordinate and each parameter field dough sheet judge to fall in certain dough sheet of model surface after each pixel p mappings On, if pixel p is located atInterior, then p can be byThree pointsIt is expressed as follows：Wherein λ₁ +λ₂+λ₃=1；If byCorresponding threedimensional model carving area dough sheet F_iSummit be respectively v₀,v₁,v₂, then pixel p is reflected It is mapped to threedimensional model dough sheet F_iOn point v can be identified as v=λ₁v₀+λ₂v₁+λ₃v₂；Two dimension engraving lines of outline is being mapped to into mould Generally need to carry out down-sampled process to 2-d contour before type surface, to each parameter field dough sheet comprising pixel The all pixels point coordinates for being included is averaging, obtain it is down-sampled after two dimension engraving wire-frame image vegetarian refreshments p, then by pixel p Threedimensional model surface point v is obtained by parametric maps, and all v are added in original three-dimensional model, so just from two dimension Engraving lines mapping has obtained the discrete engraving lines on threedimensional model surface.

4) distance on the summit to be carved on threedimensional model surface to three dimensional sculpture lines is calculated, is determined using engraving function and is treated The translation distance on carving area summit and direction, carry out translation and obtain three dimensional sculpture effect to summit to be carved；Calculate carved region Summit in domain to 3 d-dem carve lines apart from when, first engraving width is specified by user, will be apart from wide less than engraving The summit of degree determines translation distance by engraving function H (d), is translated then along vertex normal, finally realizes three dimensional sculpture Effect；Engraving function H (d) therein is taken as：

The present invention technology design be：Based on the two-dimensional line picture case of user input, line is extracted by edge shrinkage operation Bar centrage as engraving contour line, by two dimension engraving contour line discretization and by parametric maps be threedimensional model on from Engraving lines are dissipated, using engraving function of the threedimensional model summit to engraving lines collection distance is defined as, this patent proposes one kind Three dimensional sculpture method based on line drawing pattern.

Beneficial effects of the present invention are mainly manifested in：Simple to operate, engraving is convenient, engraving effect controllability is strong.

Description of the drawings

Fig. 1 is that the two-dimensional line of the user input of the present invention draws pattern instance.

Fig. 2 be using Fig. 1 as input pretreatment after obtain two dimension engraving contour line.

Fig. 3 is that two dimension engraving contour line is mapped as the exemplary plot that threedimensional model discretization of half-space surface carves lines by the present invention.

Fig. 4 is the complicated engraving effect exemplary plot that the present invention is realized using two-dimensional line picture case in different model surfaces.

Specific embodiment

Technical method and the various threedimensional model engraving effects of generation below in conjunction with the accompanying drawings to the present invention is further retouched State and describe in detail.

Referring to the drawings 1--- accompanying drawings 4, based on the threedimensional model engraving process of line drawing pattern, described method includes following four Individual step：

1) user input needs the two-dimensional line picture case of engraving, method to carry out pretreatment to being input into pattern, receive by edge Lines centrage in contracting operation extraction input line picture is used as engraving contour line；

Two-dimensional line picture case (such as accompanying drawing 1) of input is switched to into gray-scale maps, and calculates the Grad of each pixel, by ladder Angle value is more than the pixel of maximum of gradients 10% as pixel to be moved, records pixel sum n to be moved_move；For Pixel to be moved, moves along its unitization gradient direction to center, and each pixel to be moved moves to immediate vicinity When stop movement；Judge that pixel stops mobile method as follows：Pixel p is collected first_iNeighborhood N_i={ p_j|||p_j-p_i|| ≤ 1 }, pixel p in the neighborhood is judged_jGradient directionWith pixel p_iGradient directionIt is whether consistent, whenWhen, illustrate there be the pixel p contrary with moving direction in now contiguous range_j, i.e. p_jBe by with p_iRelative wheel The point that the contrary Boundary Moving of wide centrage is obtained, now p_iNear profile centrage；P is judged again_iWhether it is moved across p_j, work as satisfactionWhen, p_iCross p_j, illustrate p_iProfile centerline is had arrived at, therefore stops movement.With stopping The pixel number for only moving increases, and pixel to be moved is fewer and feweri, when pixel number to be moved is less than λ n_move When, whole contraction process terminates (wherein parameter lambda desirable 0.01).After contraction terminates, in order to process a small amount of isolated point is likely to occur Situation, will wherein neighborhood N_iIn the pixel p of the pixel number that includes less than 2_iAs isolated point remove, so as to obtain as attached The two dimension engraving contour line of Fig. 2.

2) for different types of threedimensional model, parametrization is carried out respectively to model surface region to be carved；

For threedimensional models such as the face of cylinder, spheres, can be using whole model as carving area, with simple parametrization side Method is by whole model parameterization.For semi-cylindrical model, if it is high parallel with Z axis, appoints in XOY plane and take a little as benchmark Point O, the angle that subpoints of the arbitrfary point M on XOY plane and datum mark are opened on the face of cylinder is θ, a height of h of cylinder, then Point M parameters coordinate be (s, t)=(θ/π, | | z_M-z_O| |/h), wherein z_MAnd z_OIt is respectively the z coordinate of point Μ and point O.For half Sphere Measurement Model, the parameter coordinate of arbitrfary point P (x, y, z) is (s, t)=(arccos (z/r), arctan (y/x)), and wherein r is ball Radius surface.

For general threedimensional model, it is necessary first to which then Selection Model surface regional area is adopted as region to be carved Parametrization is carried out with localized parameterization method.Region wherein to be carved can pass through user in the regional center Freehandhand-drawing for needing engraving One line, system automatically generates carving area according to the hand-drawing line, and detailed process is as follows：A) first refinement behaviour is carried out to free hand line Make；In thinning process, the intersection point of the free hand line and model surface can be successively obtained, record the plane that each intersection point is located, Determine the dough sheet collection F that free hand line is passed through_line；After refinement terminates, to the intersection point collection v for obtaining₁,v₂,…,v_lAlong three for passing through Edged surface piece carries out uniform resampling, by the point set after uniform resamplingAs the datum line point set of carving area；b) By much scope inner regions of user's chosen distance its free hand line as the region for needing engraving；By the flat of three-dimensional grid model The product of the distance threshold that the equal length of side gives with user is as the maximum geodesic curve apart from datum line point set apart from d_max；Using figure By thought, the dough sheet collection F that free hand line on three-dimensional grid model is passed through_lineK- neighborhood F_kRegion (desirable k=120) conduct Weighted graph is simultaneously set up in candidate region, take respectively grid model summit and while the summit as figure and while, weights are taken as corresponding edge It is long；Again by datum line point setIn being added to weighted graph, by each point and three summits minute of its place tri patch Side is not connected to form, and to connect the length on the side for obtaining as weights；Simultaneously shape is sequentially connected to the point that datum line point is concentrated Cheng Bian, weighting value is 0；So, k- neighborhoods F_kAfter the completion of the weighted graph in region is set up, SPFA is quickly calculated using shortest path and is calculated Method calculates each vertex v_iTo the shortest path d of datum line_i；If F_kCertain dough sheet F in region_iMeet its three summits to arrive The shortest path of datum line is respectively less than d_max, then F_iDough sheet as to be carved, F_kAll dough sheet collection for meeting condition in region Close F_SThe carving area for exactly finally giving, nowAfter Area generation to be carved, then localized region carries out parametrization, The parameter coordinate of the arbitrary mess vertex v in carving area can be by the summit relative to datum line position calculation obtain, therefore The parameter coordinate of vertex v isWherein d is geodesic curve distances of the point v to datum line,For Parameter value on hand-drawing line,ForArriveLength, L_lFor hand-drawing line total length；But now datum line both sides in carving area Parameter coordinate it is identical, therefore need to determine whether direction of the vertex v relative to datum line： ForNormal direction,It isTangent line on datum line,It is that v is arrivedVector, the parameter coordinate modification of vertex v isNow codomain scope of the vertex v in s directions is [- 1,1], in order to be translated into [0,1], Need all summit relative datum lines in carving area to right translation d_maxIndividual unit, so as to general threedimensional model surface office The final argument coordinate of any vertex v can be taken as in portion's carving area

3) by the two dimension engraving contour line discretization for obtaining, and threedimensional model surface is mapped as using parametric maps Discrete engraving lines；

After to carving area parametrization, two dimension engraving contour line is mapped as into the discrete engraving lines of model surface, the mistake Journey is as follows：If threedimensional model surface engraving region is F_S, corresponding dough sheet collection is on plane parameter domain after parametrizationMethod handle Parameter field zoom to it is in the same size with two dimensional image after, by engraving contour line pixel be mapped on parameter field, according to pixel Three apex coordinates of coordinate and each parameter field dough sheet judge to fall in certain dough sheet of model surface after each pixel p mappings On, if pixel p is located atInterior, then p can be byThree pointsIt is expressed as follows：Wherein λ₁ +λ₂+λ₃=1；If byCorresponding threedimensional model carving area dough sheet F_iSummit be respectively v₀,v₁,v₂, then pixel p is reflected It is mapped to threedimensional model dough sheet F_iOn point v can be identified as v=λ₁v₀+λ₂v₁+λ₃v₂；Two dimension engraving lines of outline is being mapped to into mould Generally need to carry out down-sampled process to 2-d contour before type surface, to each parameter field dough sheet comprising pixel The all pixels point coordinates for being included is averaging, obtain it is down-sampled after two dimension engraving wire-frame image vegetarian refreshments p, then by pixel p Threedimensional model surface point v is obtained by parametric maps, and all v are added in original three-dimensional model, so just from two dimension Engraving lines of outline mapping has obtained the discrete engraving lines on threedimensional model as shown in Figure 3.

4) distance on the summit to be carved on threedimensional model surface to three dimensional sculpture lines is calculated, is determined using engraving function and is treated The translation distance on carving area summit and direction, carry out translation and obtain three dimensional sculpture effect to summit to be carved；Calculate carved region Summit in domain to 3 d-dem carve lines apart from when, first engraving width is specified by user, will be apart from wide less than engraving The summit of degree determines translation distance by engraving function H (d), is translated then along vertex normal, finally realizes three dimensional sculpture Effect, as shown in Figure 4, engraving function H (d) therein as an example is taken as：

Claims (1)

1. the threedimensional model engraving process based on line drawing pattern, described method includes following four step：

1) user input needs the two-dimensional line picture case of engraving, method to carry out pretreatment to being input into pattern, shrink by edge and grasp Make the lines centrage during extraction input line is drawn as engraving contour line；

The two-dimensional line picture case of input is switched to into gray-scale maps, and calculates the Grad of each pixel, Grad is more than into gradient The pixel of maximum 10% records pixel sum n to be moved as pixel to be moved_move；For pixel to be moved, Move to center along its unitization gradient direction, each pixel to be moved stops movement when moving to immediate vicinity；Judge It is as follows that pixel stops mobile method：Pixel p is collected first_iNeighborhood N_i={ p_j|||p_j-p_i| |≤1 }, judge the neighborhood Interior pixel p_jGradient direction ▽_jWith pixel p_iGradient direction ▽_iIt is whether consistent, work as ▽_i·▽_jWhen≤0, illustrate now There is the pixel p contrary with moving direction in contiguous range_j, i.e. p_jBe by with p_iThe contrary border of counter-profile centrage The point for obtaining is moved, now p_iNear profile centrage；P is judged again_iWhether p is moved across_j, as satisfaction (p_j-p_i)·▽_i During ＜ 0, p_iCross p_j, illustrate p_iProfile centerline is had arrived at, therefore stops movement；With the pixel number for stopping movement Increase, pixel to be moved is fewer and feweri, when pixel number to be moved is less than λ n_moveWhen, wherein parameter lambda takes 0.01, Whole contraction process terminates；

After contraction terminates, in order to process the isolated point situation of appearance, will wherein neighborhood N_iIn the pixel number that includes less than 2 Pixel p_iAs isolated point remove, so as to obtain two dimension engraving contour line；

2) for different types of threedimensional model, parametrization is carried out respectively to model surface carving area；

For the face of cylinder, the threedimensional model of sphere, using whole model as carving area, will be whole with simple parametric method Model parameterization；For semi-cylindrical model, if it is high parallel with Z axis, appoints in XOY plane and take a little as datum mark O, cylinder The angle that subpoints of the arbitrfary point M on XOY plane and datum mark opens on face is θ, a height of h of cylinder, then point M parameters seat Be designated as (s, t)=(θ/π, | | z_M-z_O| |/h), wherein z_MAnd z_OIt is respectively the z coordinate of point Μ and point O；For hemisphere surface model, The parameter coordinate of arbitrfary point P (x, y, z) is (s, t)=(arccos (z/r), arctan (y/x)), and wherein r is spherical radius；

For other kinds of threedimensional model, it is necessary first to which then Selection Model surface regional area adopts as carving area Localized parameterization method carries out parametrization；One line of regional center Freehandhand-drawing that wherein carving area is carved by user in needs, System automatically generates carving area according to the hand-drawing line, and detailed process is as follows：A) first Refinement operation is carried out to free hand line；Refinement During, the intersection point of the free hand line and model surface is obtained successively, the plane that each intersection point is located is recorded, determine free hand line Through dough sheet collection F_line；After refinement terminates, to the intersection point collection c for obtaining₁,c₂,…,c_lCarry out along the tri patch for passing through Even resampling, by the point set after uniform resamplingAs the datum line point set of carving area；B) its hands of chosen distance The region that line drawing bar is carved for the region of D as needs, wherein parameter D is selected by user；By the average side of three-dimensional grid model The product of the long distance threshold given with user is as the maximum geodesic curve apart from datum line point set apart from d_max；Thought using graph theory Think, the dough sheet collection F that free hand line on three-dimensional grid model is passed through_lineK- neighborhood F_kRegion is as candidate region and sets up band Weight graph, take respectively grid model summit and while the summit as figure and while, weights are taken as the corresponding length of side；Again by datum line point setIn being added to weighted graph, each datum line point is respectively connected with being formed with three summits of its place tri patch Side, and to connect the length on the side for obtaining as weights；Simultaneously the point that datum line point is concentrated is sequentially connected to form side, weighting value For 0；So, k- neighborhoods F_kAfter the completion of the weighted graph in region is set up, SPFA algorithms are quickly calculated using shortest path and is calculated often Individual vertex v_iTo the shortest path d of datum line_i；If F_kCertain dough sheet F in region_iMeet its three summits to datum line most Short path is respectively less than d_max, then F_iDough sheet as to be carved, F_kAll dough sheet set F for meeting condition in region_SIt is exactly most The carving area for obtaining eventually, nowAfter carving area is generated, then localized region carries out parametrization, in carving area Position calculation of the parameter coordinate of any vertex v of model by the summit relative to datum line is obtained, therefore the parameter coordinate of vertex v ForWherein d is geodesic curve distance of the vertex v to datum line,ForGinseng on hand-drawing line Numerical value,ForArriveLength, L_lFor hand-drawing line total length；But now in carving area datum line both sides parameter coordinate It is identical, therefore need to determine whether direction of the vertex v relative to datum line： ForMethod To,It isTangential direction on datum line,It is that v is arrivedVector, the parameter coordinate modification of vertex v isNow codomain scope of the vertex v in s directions is [- 1,1], in order to be translated into [0,1], Need all summit relative datum lines in carving area to right translation d_maxIndividual unit, so as to other kinds of threedimensional model The final argument coordinate of any vertex v is taken as in the carving area of surface local

3) by obtain two dimension engraving contour line discretization, and using parametric maps be mapped as threedimensional model surface from Dissipate engraving lines；

After to carving area parametrization, two dimension engraving contour line is mapped as into the discrete engraving lines of model surface, the process is such as Under：If threedimensional model surface engraving region is F_S, corresponding dough sheet collection is on plane parameter domain after parametrizationPlane parameter Domain zoom to it is in the same size with two dimensional image after, by engraving contour line pixel be mapped on plane parameter domain, according to pixel Three apex coordinates of coordinate and each plane parameter domain dough sheet judge each pixel p mapping after fall model surface certain On dough sheet, if pixel p is located at plane parameter domain dough sheetIt is interior, then p byThree pixelsIt is expressed as follows：Wherein λ₁+λ₂+λ₃=1；If byCorresponding threedimensional model carving area dough sheet F_iSummit be respectively v₀,v₁,v₂, then pixel p is mapped to into threedimensional model dough sheet F_iOn vertex v be defined as v=λ₁v₀+λ₂v₁+λ₃v₂；By two Dimension engraving lines of outline is mapped to before model surface and needs to carry out down-sampled process to 2-d contour, and to each pixel is included The parameter field dough sheet of pointThe all pixels point coordinates for being included is averaging, obtain it is down-sampled after two dimension engraving wire-frame image Vegetarian refreshments p, then pixel p is obtained the vertex v on threedimensional model surface by parametric maps, and all vertex vs are added to In original three-dimensional model, so just from two dimension engraving lines mapping the discrete engraving lines on threedimensional model surface have been obtained；

4) distance on the summit to be carved on threedimensional model surface to three dimensional sculpture lines is calculated, using engraving function carved region is determined The translation distance on domain summit and direction, carry out translation and obtain three dimensional sculpture effect to summit to be carved；Calculate in carving area Summit to 3 d-dem carve lines apart from when, first by user specify engraving width, by distance less than engraving width top Press engraving function H (d) and determine translation distance, translated then along vertex normal, finally realize three dimensional sculpture effect；Its In engraving function H (d) be taken as：

$H\left(d\right)=\left\{\begin{array}{cc}\sqrt{\frac{W^2}{25}-d^2}+\frac{32W}{45}& (0\&le;d<\frac{W}{5})\\ \frac{4W^2}{50d-5W}-\frac{4W}{45}& (\frac{W}{5}\&le;d\&le;W)\end{array}\right..$