CN104143209A - 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

Three-dimensional model engraving process based on line drawing pattern

Technical field

Patent design of the present invention, for the two-dimensional line picture case of user's input, provides a kind of method that can generate quickly and easily this pattern engraving effect at three-dimensional model.

Background technology

A kind of main flow as three-dimensional body profile represents mode, and three-dimensional model has obtained being widely used in fields such as digital entertainment industry, industrial design field, virtual realities.The characterization attributes of three-dimensional model comprises two aspects: the geometric attribute (as the topological link information between vertex position information and summit) of three-dimensional model and the appearance attribute of three-dimensional model (as Facing material attribute, geometry texture and color and vein information etc.).In order to make the three-dimensional model generating have more the sense of reality; increase aesthetic property and the artistry of three-dimensional model simultaneously, conventionally can add three-dimensional feature texture to three-dimensional model, in existing technology; can be divided into bump mapping technology, bump mapping technology and relief grain mapping techniques.In recent years, many synthetic algorithms of texture based on feature are suggested, comprising three-dimensional engraving technology, three-dimensional engraving refers to the process that along the specific lines of model surface, its summit is moved to generate surperficial complex geometry texture, and it is a kind of important method that complex model superficial makings generates.The digital engraving of three-dimensional model is as a kind of modelling means that generates complex model, can on original model basis, generate easily and efficiently and there is the complex model that enriches surface relief texture by specific engraving process, thereby the modeling content of greatly having enriched 3 D complex model, this method will be with a wide range of applications.Existing three-dimensional engraving technology is mainly by hand-drawing line bar on three-dimensional model, utilize engraving function to calculate translation direction and the distance on the summit in texture width, obtain realistic three-dimensional engraving effect, this technology mainly realizes by user interactions, but, the user-interactive tasks amount that designs complicated three-dimensional engraving effect requirement is larger, simultaneously because the generation of outline line is the curve simulating by user's designated key point, therefore concrete tendency is not directly controlled by user, user is difficult to the complicated engraving effect that design needs on model.Our method directly, using two-dimensional line picture case to be carved as input, can conveniently realize the engraving effect on three-dimensional model surface.Because the engraving outline line in the method is automatic acquisition from input picture, therefore make user's operation quite easy, also realize the three-dimensional engraving effect of more complicated simultaneously.

Summary of the invention

For overcome the interworking amount of existing three-dimensional grid model superficial makings in synthetic greatly, more 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 three-dimensional engraving process based on two-dimensional line picture case.

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

Three-dimensional model engraving process based on line drawing pattern, described method comprises following four steps:

1) user inputs the two-dimensional line picture case that needs engraving, and method is carried out pre-service to input pattern, and the lines center line in drawing by edge shrinkage operation extraction input line is as engraving outline line;

Transfer the two-dimensional line picture case of input to gray-scale map, and calculate the Grad of each pixel, the pixel that Grad is greater than to maximum of gradients 10% is as treating mobile pixel, and mobile pixel sum n treated in record _move; For pixel to be moved, to move to center along its unit gradient direction, near each stopping in the time that mobile pixel moves to center moved; Judge that pixel stops mobile method as follows: first collect pixel p _ineighborhood N _i={ p _j|| | p _j-p _i||≤1}, judges pixel p in this neighborhood _jgradient direction with pixel p _igradient direction whether consistent, when time, illustrate now and had the pixel p contrary with moving direction within the scope of neighborhood _j, i.e. p _jbe by with p _ithe point that the contrary Boundary Moving of profile center line obtains relatively, now p _inear profile center line; Judge again p _iwhether move and cross p _j, when meeting time, p _icross p _j, p is described _iarrive profile centerline, therefore stop mobile.Along with stopping increasing of mobile pixel number, treat that mobile pixel is fewer and feweri, when treating that mobile pixel number is no more than λ n _movetime, whole contraction process finishes (wherein parameter lambda desirable 0.01).After contraction finishes, may there is a small amount of isolated point situation in order to process, wherein neighborhood N _iin the pixel number that comprises be less than the pixel p of 2 _ias isolated point remove, thereby obtain two dimension engraving outline line.

2), for dissimilar three-dimensional model, parametrization is carried out respectively in model surface region to be carved;

For the three-dimensional model such as the face of cylinder, sphere, can be using whole model as carving area, with simple parametric method by whole model parameterization.For semi-cylindrical model, establish its height parallel with Z axis, appoint and get a bit as reference point O in XOY plane, the angle that on the face of cylinder, the subpoint of arbitrfary point M in XOY plane opened with reference point is θ, and cylinder height is h, and putting M parameter coordinate is (s, t)=(θ/π, || z _m-z _o||/h), wherein z _mand z _orespectively a Μ and the z coordinate of putting O.For hemisphere face 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 general three-dimensional model, first need Selection Model surface local region as region to be carved, then adopt local parameter method to carry out parametrization.Line of regional center Freehandhand-drawing that wherein region to be carved can be carved at needs by user, system generates carving area automatically according to this hand-drawing line, and detailed process is as follows: a) first hand-drawing line bar is carried out to Refinement operation; In thinning process, can obtain successively the intersection point of these Freehandhand-drawing lines and model surface, record the plane at each intersection point place, determine the dough sheet collection F of Freehandhand-drawing lines process _line; After refinement finishes, to the intersection point collection v obtaining ₁, v ₂..., v _ltri patch along process carries out uniform resampling, by the point set after uniform resampling as the datum line point set of carving area; The region of b) being carved as needs by much scope inner regions of its Freehandhand-drawing lines of user's chosen distance; Using the product of the average length of side of three-dimensional grid model and the given distance threshold of user as the maximum geodesic line apart from datum line point set apart from d _max; Utilize graph theory thought, by the dough sheet collection F of hand-drawing line bar process on three-dimensional grid model _linek-neighborhood F _kregion is as candidate region and set up weighted graph, gets respectively the summit of grid model and limit summit and the limit as figure, and weights are taken as the corresponding length of side; Again by datum line point set join in weighted graph, three summits of each point and its place tri patch are connected to form respectively to limit, and the length on the limit obtaining using connection is as weights; Datum line is put to concentrated point simultaneously and be connected to form successively limit, weighting value is 0; Like this, k-neighborhood F _kafter the weighted graph in region has been set up, adopt shortest path to calculate fast SPFA algorithm and calculate each vertex v _ito the shortest path d of datum line _i; If F _kcertain dough sheet F in region _imeet its three summits and be all less than d to the shortest path of datum line _max, F so _ibe dough sheet to be carved, F _kall dough sheet set F that satisfy condition in region _sbe exactly the carving area finally obtaining, now after region to be carved generates, then localized region carries out parametrization, and the parameter coordinate of the arbitrary mess vertex v in carving area can be obtained with respect to the position calculation of datum line by this summit, therefore the parameter coordinate of vertex v is wherein d is the geodesic line distance of a v to datum line, for parameter value on hand-drawing line, for arrive length, L _lfor hand-drawing line total length; But now in carving area, the parameter coordinate of datum line both sides is identical, therefore need further to judge the direction of vertex v with respect to datum line: $\mathrm{sign}\left(v\right)=\mathrm{sign}(v{\stackrel{\‾}{v}}_i\·(T_{{\stackrel{\‾}{v}}_i}\×N_{{\stackrel{\‾}{v}}_i})),$ for normal direction, be tangent line on datum line, that v arrives vector, the parameter coordinate modification of vertex v is now vertex v is [1,1] in the codomain scope of s direction, in order to be translated into [0,1], and need to be by all summit relative datum alignment right translation d in carving area _maxindividual unit, thus in general three-dimensional model surface local carving area, the final argument coordinate of any vertex v can be taken as $(s,t)=((\mathrm{sign}\left(v\right)\·d+d_{\max })/(2\·d_{\max }),t\left({\stackrel{\‾}{v}}_i\right)).$

3) by the two dimension engraving outline line discretize obtaining, and utilize parametric maps to be mapped as the discrete engraving lines on three-dimensional model surface;

After carving area parametrization, two dimension be carved to outline line and be mapped as the discrete engraving lines of model surface, this process is as follows: establishing three-dimensional model surface engraving region is F _s, dough sheet collection corresponding on parametrization back plane parameter field is method parameter field zoom in the same size with two dimensional image after, the pixel of engraving outline line is mapped on parameter field, after judging each pixel p mapping according to three apex coordinates of pixel coordinate and each parameter field dough sheet, drop on certain dough sheet of model surface, establish pixel p and be positioned at in, p can be by three points be expressed as follows: $p={\mathrm{\λ}}_1{\stackrel{\‾}{p}}_0+{\mathrm{\λ}}_2{\stackrel{\‾}{p}}_1+{\mathrm{\λ}}_3{\stackrel{\‾}{p}}_2,$ Wherein λ ₁+ λ ₂+ λ ₃=1; If by corresponding three-dimensional model carving area dough sheet F _isummit be respectively v ₀, v ₁, v ₂, pixel p is mapped to three-dimensional model dough sheet F _ion some v can be defined as v=λ ₁v ₀+ λ ₂v ₁+ λ ₃v ₂; Conventionally need to carry out down-sampled processing to 2-d contour before being mapped to model surface two dimension being carved to lines of outline, to each parameter field dough sheet that comprises pixel comprised all pixel coordinates are averaging, obtain the two dimension engraving wire-frame image vegetarian refreshments p after down-sampled, again pixel p is obtained to three-dimensional model surface point v by parametric maps, and all v are joined in original three-dimensional model, so just obtained the discrete engraving lines on three-dimensional model surface from the mapping of two dimension engraving lines.

4) calculate the summit to be carved on three-dimensional model surface to the distance of three-dimensional engraving lines, utilize engraving function to determine translation distance and the direction on summit, region to be carved, translation is carried out in summit to be carved and obtain three-dimensional engraving effect; When the distance of lines is carved to 3 d-dem in summit in calculating carving area, first specify engraving width by user, distance is less than to the summit of carve width and determines translation distance by carving function H (d), then carry out translation along vertex normal, finally realize three-dimensional engraving effect; Engraving function H (d) is wherein taken as:

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

Technical conceive of the present invention is: based on the two-dimensional line picture case of user's input, extract lines center line as engraving outline line by edge shrinkage operation, two dimension is carved to outline line discretize and be the discrete engraving lines on three-dimensional model by parametric maps, utilization is defined as the engraving function of three-dimensional model summit to engraving lines collection distance, and this patent has proposed a kind of three-dimensional engraving process based on line drawing pattern.

Beneficial effect of the present invention is mainly manifested in: simple to operate, engraving facilitates, engraving effect controllability is strong.

Brief description of the drawings

Fig. 1 is the two-dimensional line picture case example of user's input of the present invention.

Fig. 2 is the two dimension engraving outline line obtaining after using Fig. 1 as the pre-service of input.

Fig. 3 exemplary plot that to be the present invention carve outline line and be mapped as three-dimensional model discretization of half-space surface engraving lines by two dimension.

Fig. 4 is the complicated engraving effect exemplary plot that the present invention utilizes two-dimensional line picture case to realize at different model surfaces.

Embodiment

Below in conjunction with accompanying drawing, the various three-dimensional model engraving effects of technical method of the present invention and generation are further described and are described in detail.

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

1) user inputs the two-dimensional line picture case that needs engraving, and method is carried out pre-service to input pattern, and the lines center line in drawing by edge shrinkage operation extraction input line is as engraving outline line;

Transfer the two-dimensional line picture case (as accompanying drawing 1) of input to gray-scale map, and calculate the Grad of each pixel, the pixel that Grad is greater than to maximum of gradients 10% is as treating mobile pixel, and mobile pixel sum n treated in record _move; For pixel to be moved, to move to center along its unit gradient direction, near each stopping in the time that mobile pixel moves to center moved; Judge that pixel stops mobile method as follows: first collect pixel p _ineighborhood N _i={ p _j|| | p _j-p _i||≤1}, judges pixel p in this neighborhood _jgradient direction with pixel p _igradient direction whether consistent, when time, illustrate now and had the pixel p contrary with moving direction within the scope of neighborhood _j, i.e. p _jbe by with p _ithe point that the contrary Boundary Moving of profile center line obtains relatively, now p _inear profile center line; Judge again p _iwhether move and cross p _j, when meeting time, p _icross p _j, p is described _iarrive profile centerline, therefore stop mobile.Along with stopping increasing of mobile pixel number, treat that mobile pixel is fewer and feweri, when treating that mobile pixel number is no more than λ n _movetime, whole contraction process finishes (wherein parameter lambda desirable 0.01).After contraction finishes, may there is a small amount of isolated point situation in order to process, wherein neighborhood N _iin the pixel number that comprises be less than the pixel p of 2 _ias isolated point remove, thereby obtain the two dimension engraving outline line as accompanying drawing 2.

2), for dissimilar three-dimensional model, parametrization is carried out respectively in model surface region to be carved;

For the three-dimensional model such as the face of cylinder, sphere, can be using whole model as carving area, with simple parametric method by whole model parameterization.For semi-cylindrical model, establish its height parallel with Z axis, appoint and get a bit as reference point O in XOY plane, the angle that on the face of cylinder, the subpoint of arbitrfary point M in XOY plane opened with reference point is θ, and cylinder height is h, and putting M parameter coordinate is (s, t)=(θ/π, || z _m-z _o||/h), wherein z _mand z _orespectively a Μ and the z coordinate of putting O.For hemisphere face 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 general three-dimensional model, first need Selection Model surface local region as region to be carved, then adopt local parameter method to carry out parametrization.Line of regional center Freehandhand-drawing that wherein region to be carved can be carved at needs by user, system generates carving area automatically according to this hand-drawing line, and detailed process is as follows: a) first hand-drawing line bar is carried out to Refinement operation; In thinning process, can obtain successively the intersection point of these Freehandhand-drawing lines and model surface, record the plane at each intersection point place, determine the dough sheet collection F of Freehandhand-drawing lines process _line; After refinement finishes, to the intersection point collection v obtaining ₁, v ₂..., v _ltri patch along process carries out uniform resampling, by the point set after uniform resampling as the datum line point set of carving area; The region of b) being carved as needs by much scope inner regions of its Freehandhand-drawing lines of user's chosen distance; Using the product of the average length of side of three-dimensional grid model and the given distance threshold of user as the maximum geodesic line apart from datum line point set apart from d _max; Utilize graph theory thought, by the dough sheet collection F of hand-drawing line bar process on three-dimensional grid model _linek-neighborhood F _kregion (desirable k=120) is as candidate region and set up weighted graph, gets respectively the summit of grid model and limit summit and the limit as figure, and weights are taken as the corresponding length of side; Again by datum line point set join in weighted graph, three summits of each point and its place tri patch are connected to form respectively to limit, and the length on the limit obtaining using connection is as weights; Datum line is put to concentrated point simultaneously and be connected to form successively limit, weighting value is 0; Like this, k-neighborhood F _kafter the weighted graph in region has been set up, adopt shortest path to calculate fast SPFA algorithm and calculate each vertex v _ito the shortest path d of datum line _i; If F _kcertain dough sheet F in region _imeet its three summits and be all less than d to the shortest path of datum line _max, F so _ibe dough sheet to be carved, F _kall dough sheet set F that satisfy condition in region _sbe exactly the carving area finally obtaining, now after region to be carved generates, then localized region carries out parametrization, and the parameter coordinate of the arbitrary mess vertex v in carving area can be obtained with respect to the position calculation of datum line by this summit, therefore the parameter coordinate of vertex v is wherein d is the geodesic line distance of a v to datum line, for parameter value on hand-drawing line, for arrive length, L _lfor hand-drawing line total length; But now in carving area, the parameter coordinate of datum line both sides is identical, therefore need further to judge the direction of vertex v with respect to datum line: $\mathrm{sign}\left(v\right)=\mathrm{sign}(v{\stackrel{\&OverBar;}{v}}_i\&CenterDot;(T_{{\stackrel{\&OverBar;}{v}}_i}\&times;N_{{\stackrel{\&OverBar;}{v}}_i})),$ for normal direction, be tangent line on datum line, that v arrives vector, the parameter coordinate modification of vertex v is now vertex v is [1,1] in the codomain scope of s direction, in order to be translated into [0,1], and need to be by all summit relative datum alignment right translation d in carving area _maxindividual unit, thus in general three-dimensional model surface local carving area, the final argument coordinate of any vertex v can be taken as $(s,t)=((\mathrm{sign}\left(v\right)\&CenterDot;d+d_{\max })/(2\&CenterDot;d_{\max }),t\left({\stackrel{\&OverBar;}{v}}_i\right)).$

3) by the two dimension engraving outline line discretize obtaining, and utilize parametric maps to be mapped as the discrete engraving lines on three-dimensional model surface;

After carving area parametrization, two dimension be carved to outline line and be mapped as the discrete engraving lines of model surface, this process is as follows: establishing three-dimensional model surface engraving region is F _s, dough sheet collection corresponding on parametrization back plane parameter field is method parameter field zoom in the same size with two dimensional image after, the pixel of engraving outline line is mapped on parameter field, after judging each pixel p mapping according to three apex coordinates of pixel coordinate and each parameter field dough sheet, drop on certain dough sheet of model surface, establish pixel p and be positioned at in, p can be by three points be expressed as follows: $p={\mathrm{\&lambda;}}_1{\stackrel{\&OverBar;}{p}}_0+{\mathrm{\&lambda;}}_2{\stackrel{\&OverBar;}{p}}_1+{\mathrm{\&lambda;}}_3{\stackrel{\&OverBar;}{p}}_2,$ Wherein λ ₁+ λ ₂+ λ ₃=1; If by corresponding three-dimensional model carving area dough sheet F _isummit be respectively v ₀, v ₁, v ₂, pixel p is mapped to three-dimensional model dough sheet F _ion some v can be defined as v=λ ₁v ₀+ λ ₂v ₁+ λ ₃v ₂; Conventionally need to carry out down-sampled processing to 2-d contour before being mapped to model surface two dimension being carved to lines of outline, to each parameter field dough sheet that comprises pixel comprised all pixel coordinates are averaging, obtain the two dimension engraving wire-frame image vegetarian refreshments p after down-sampled, again pixel p is obtained to three-dimensional model surface point v by parametric maps, and all v are joined in original three-dimensional model, so just obtain the discrete engraving lines three-dimensional model as shown in Figure 3 from the mapping of two dimension engraving lines of outline.

4) calculate the summit to be carved on three-dimensional model surface to the distance of three-dimensional engraving lines, utilize engraving function to determine translation distance and the direction on summit, region to be carved, translation is carried out in summit to be carved and obtain three-dimensional engraving effect; When the distance of lines is carved to 3 d-dem in summit in calculating carving area, first specify engraving width by user, distance is less than to the summit of carve width and determines translation distance by carving function H (d), then carry out translation along vertex normal, finally realize three-dimensional engraving effect, as shown in Figure 4, engraving function H (d) is wherein taken as an example:

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

Claims (1)

1. the three-dimensional model engraving process based on line drawing pattern, described method comprises following four steps:

1) user inputs the two-dimensional line picture case that needs engraving, and method is carried out pre-service to input pattern, and the lines center line in drawing by edge shrinkage operation extraction input line is as engraving outline line;

Transfer the two-dimensional line picture case of input to gray-scale map, and calculate the Grad of each pixel, the pixel that Grad is greater than to maximum of gradients 10% is as treating mobile pixel, and mobile pixel sum n treated in record _move; For pixel to be moved, to move to center along its unit gradient direction, near each stopping in the time that mobile pixel moves to center moved; Judge that pixel stops mobile method as follows: first collect pixel p _ineighborhood N _i={ p _j|| | p _j-p _i||≤1}, judges pixel p in this neighborhood _jgradient direction with pixel p _igradient direction whether consistent, when time, illustrate now and had the pixel p contrary with moving direction within the scope of neighborhood _j, i.e. p _jbe by with p _ithe point that the contrary Boundary Moving of profile center line obtains relatively, now p _inear profile center line; Judge again p _iwhether move and cross p _j, when meeting time, p _icross p _j, p is described _iarrive profile centerline, therefore stop mobile.Along with stopping increasing of mobile pixel number, treat that mobile pixel is fewer and feweri, when treating that mobile pixel number is no more than λ n _movetime, whole contraction process finishes (wherein parameter lambda desirable 0.01);

After contraction finishes, may there is a small amount of isolated point situation in order to process, wherein neighborhood N _iin the pixel number that comprises be less than the pixel p of 2 _ias isolated point remove, thereby obtain two dimension engraving outline line;

2), for dissimilar three-dimensional model, parametrization is carried out respectively in model surface region to be carved;

For the three-dimensional model of the face of cylinder, sphere, can be using whole model as carving area, with simple parametric method by whole model parameterization; For semi-cylindrical model, establish its height parallel with Z axis, appoint and get a bit as reference point O in XOY plane, the angle that on the face of cylinder, the subpoint of arbitrfary point M in XOY plane opened with reference point is θ, and cylinder height is h, and putting M parameter coordinate is (s, t)=(θ/π, || z _m-z _o||/h), wherein z _mand z _orespectively a Μ and the z coordinate of putting O; For hemisphere face 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 general three-dimensional model, first need Selection Model surface local region as region to be carved, then adopt local parameter method to carry out parametrization; Line of regional center Freehandhand-drawing that wherein region to be carved can be carved at needs by user, system generates carving area automatically according to this hand-drawing line, and detailed process is as follows: a) first hand-drawing line bar is carried out to Refinement operation; In thinning process, can obtain successively the intersection point of these Freehandhand-drawing lines and model surface, record the plane at each intersection point place, determine the dough sheet collection F of Freehandhand-drawing lines process _line; After refinement finishes, to the intersection point collection v obtaining ₁, v ₂..., v _ltri patch along process carries out uniform resampling, by the point set after uniform resampling as the datum line point set of carving area; The region of b) being carved as needs by much scope inner regions of its Freehandhand-drawing lines of user's chosen distance; Using the product of the average length of side of three-dimensional grid model and the given distance threshold of user as the maximum geodesic line apart from datum line point set apart from d _max; Utilize graph theory thought, by the dough sheet collection F of hand-drawing line bar process on three-dimensional grid model _linek-neighborhood F _kregion is as candidate region and set up weighted graph, gets respectively the summit of grid model and limit summit and the limit as figure, and weights are taken as the corresponding length of side; Again by datum line point set join in weighted graph, three summits of each point and its place tri patch are connected to form respectively to limit, and the length on the limit obtaining using connection is as weights; Datum line is put to concentrated point simultaneously and be connected to form successively limit, weighting value is 0; Like this, k-neighborhood F _kafter the weighted graph in region has been set up, adopt shortest path to calculate fast SPFA algorithm and calculate each vertex v _ito the shortest path d of datum line _i; If F _kcertain dough sheet F in region _imeet its three summits and be all less than d to the shortest path of datum line _max, F so _ibe dough sheet to be carved, F _kall dough sheet set F that satisfy condition in region _sbe exactly the carving area finally obtaining, now after region to be carved generates, then localized region carries out parametrization, and the parameter coordinate of the arbitrary mess vertex v in carving area can be obtained with respect to the position calculation of datum line by this summit, therefore the parameter coordinate of vertex v is wherein d is the geodesic line distance of a v to datum line, for parameter value on hand-drawing line, for arrive length, L _lfor hand-drawing line total length; But now in carving area, the parameter coordinate of datum line both sides is identical, therefore need further to judge the direction of vertex v with respect to datum line: $\mathrm{sign}\left(v\right)=\mathrm{sign}(v{\stackrel{\&OverBar;}{v}}_i\&CenterDot;(T_{{\stackrel{\&OverBar;}{v}}_i}\&times;N_{{\stackrel{\&OverBar;}{v}}_i})),$ for normal direction, be tangent line on datum line, that v arrives vector, the parameter coordinate modification of vertex v is now vertex v is [1,1] in the codomain scope of s direction, in order to be translated into [0,1], and need to be by all summit relative datum alignment right translation d in carving area _maxindividual unit, thus in general three-dimensional model surface local carving area, the final argument coordinate of any vertex v can be taken as $(s,t)=((\mathrm{sign}\left(v\right)\&CenterDot;d+d_{\max })/(2\&CenterDot;d_{\max }),t\left({\stackrel{\&OverBar;}{v}}_i\right));$

3) by the two dimension engraving outline line discretize obtaining, and utilize parametric maps to be mapped as the discrete engraving lines on three-dimensional model surface;

After carving area parametrization, two dimension be carved to outline line and be mapped as the discrete engraving lines of model surface, this process is as follows: establishing three-dimensional model surface engraving region is F _s, dough sheet collection corresponding on parametrization back plane parameter field is method parameter field zoom in the same size with two dimensional image after, the pixel of engraving outline line is mapped on parameter field, after judging each pixel p mapping according to three apex coordinates of pixel coordinate and each parameter field dough sheet, drop on certain dough sheet of model surface, establish pixel p and be positioned at in, p can be by three points be expressed as follows: $p={\mathrm{\&lambda;}}_1{\stackrel{\&OverBar;}{p}}_0+{\mathrm{\&lambda;}}_2{\stackrel{\&OverBar;}{p}}_1+{\mathrm{\&lambda;}}_3{\stackrel{\&OverBar;}{p}}_2,$ Wherein λ ₁+ λ ₂+ λ ₃=1; If by corresponding three-dimensional model carving area dough sheet F _isummit be respectively v ₀, v ₁, v ₂, pixel p is mapped to three-dimensional model dough sheet F _ion some v can be defined as v=λ ₁v ₀+ λ ₂v ₁+ λ ₃v ₂; Conventionally need to carry out down-sampled processing to 2-d contour before being mapped to model surface two dimension being carved to lines of outline, to each parameter field dough sheet that comprises pixel comprised all pixel coordinates are averaging, obtain the two dimension engraving wire-frame image vegetarian refreshments p after down-sampled, again pixel p is obtained to three-dimensional model surface point v by parametric maps, and all v are joined in original three-dimensional model, so just obtained the discrete engraving lines on three-dimensional model surface from the mapping of two dimension engraving lines;

4) calculate the summit to be carved on three-dimensional model surface to the distance of three-dimensional engraving lines, utilize engraving function to determine translation distance and the direction on summit, region to be carved, translation is carried out in summit to be carved and obtain three-dimensional engraving effect; When the distance of lines is carved to 3 d-dem in summit in calculating carving area, first specify engraving width by user, distance is less than to the summit of carve width and determines translation distance by carving function H (d), then carry out translation along vertex normal, finally realize three-dimensional engraving effect; Engraving function H (d) is wherein taken as:

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