CN102708591A - Hole repairing method for digital tooth grid model - Google Patents

Abstract

The invention discloses a hole repairing method for a digital tooth grid model. The method comprises the following steps: automatically searching the boundary of the digital tooth grid model and displaying all the vertexes of the boundary; alternately selecting vertexes belonging to the hole boundary from all the vertexes as starting and stopping vertexes of the hole boundary, and constructing a closed hole boundary based on the starting and stopping vertexes; performing triangular grid filling on the closed area in the closed hole boundary by adopting a forward travelling wave propelling algorithm and generating the grid mesh surface of the closed area; and optimizing the grid mesh surface in the closed area and near the original tooth grid model boundary by adopting a least squares grid algorithm. According to the hole repairing method, the surface mesh of the tooth model hole area can be rapidly generated by directly selecting the starting and stopping vertexes on the hole boundary of the originally input digital tooth grid model, then the newly generated grid can be optimized, so that the grid on the part of the hole area can be naturally spliced with the tooth grid on the original model, and the newly generated curve is smooth and has high quality.

Description

A kind of hole repair method of digital tooth grid model

Technical field

The present invention relates to the repairing field how much, particularly a kind of hole repair method of digital tooth grid model.

Background technology

Hidden tooth abnormal correction is one and relates to multi-disciplinary cross-application, at first accomplishes the editor to digital number tooth grid model through computer-aided design (CAD), and the correlation technique through materialogy generates the medical science facing then, is used for mouth cavity orthodontic.Numeral tooth grid model is made up of geological information and annexation two parts, and geological information has provided each summit at three-dimensional position coordinates, and annexation connects into special polygon curved surface with these positional informations.

Dentognathic model after 3-D scanning is rebuild is an integral body, can't satisfy the demand of each tooth being reset and rescued conceptual design, so the first step of gridding edition is that every tooth is split from whole tooth jaw grid model.Because existing, tooth and gum block; Spatial digitizer can not obtain two adjacent interdental proximal surface data; After using the mesh segmentation algorithm to be partitioned into tooth model; Just produced a hole that is formed by connecting border vertices at proximal surface, therefore a key problem of the editor of digital tooth grid model design is how the proximal surface hole after cutting apart to be carried out auto-mending.

The target of repairing for how much is to rebuild the curve form in hole zone, and its universal method is generally utilizes a smooth curved surface that the hole zone is filled up.

The hole repair method of existing a kind of grid model (referring to Wang Qian. the research and the application of triangle grid model transition and hole repair algorithm. Nanjing: Nanjing Aero-Space University, 2007) main thought following: obtain interpolation obligatory point and normal direction obligatory point; Set up variation implicit surface equation and gridding; Grid cutting and stitching.This method is repaired hole based on variation implicit surface method, then repairing area is carried out the triangle gridding discretize.Adopt variation implicit surface method hole to be repaired not only generating mesh is second-rate, and efficient is lower.

Summary of the invention

The invention provides a kind of hole repair method of digital tooth grid model, can improve quality and efficient that grid generates, solved generating mesh model in the prior art boundary can be more stiff problem.

A kind of hole repair method of digital tooth grid model comprises step:

(1) input digit tooth grid model is searched for the border of digital tooth grid model automatically and is shown all summits on this border;

(2) choose start-stop summit, the summit that belongs to the hole border in the above-mentioned summit alternately, based on structure border, blind bore hole, described start-stop summit as the hole border;

(3) employing advances algorithm that the triangle gridding filling is carried out in the closed region in the border, described blind bore hole to prewave, and generating mesh is topological automatically, and the grid surface of generation closed region obtains the digital tooth grid model through hole repair;

(4) adopt the least square trellis algorithm to optimize the grid surface of above-mentioned closed region and original dental grid model boundary vicinity, the digital tooth grid model after being optimized through hole repair.

The step (3) of the hole repair method of digital tooth grid model of the present invention has adopted and has advanced algorithm to prewave (this algorithm specifically can be referring to George P. Louis; E.Seveno.The advancing front mesh generation method revisited [J] .International Journal of Numerical Methods Engineering; 1994; 37 (7): 3605-3619) hole is repaired, generating mesh is high-quality to possess very high formation efficiency simultaneously keeping.Because the grid model through above-mentioned algorithm generates can be more stiff at boundary; The present invention has also adopted the least square trellis algorithm (this algorithm specifically can be referring to Sorkine O. in step (4); Cohen-Or D.Least-squares meshes [C] .Shape Modeling Applications; 2004:191-199) near the original boundaries and newly-generated net region is optimized, obtains comparatively smooth digital tooth grid model through hole repair.The hole repair method of the present invention's numeral tooth grid model is through directly choosing the borderline start-stop of the digital tooth grid model hole summit of original input; Generate the surface mesh in dental cast hole zone fast; Optimize newly-generated grid then; This part grid and the tooth grid of master mould of hole zone spliced naturally, and newly-generated curved surface is smooth and quality is high.

Particularly, in the step (1), the border of described automatic search numeral tooth grid model comprises step:

(1.1) seek the borderline kind son vertex of tooth grid model: the decision criteria of searching is following:

Through all summits in the digital tooth grid model of inspection input; Search adjacent leg-of-mutton number and adjacent side number around the summit, the summit that first the adjacent triangle number that finds and adjacent side number are not waited is as the kind son vertex on tooth grid model border;

(1.2) use above-mentioned decision criteria the breadth First traversal to be made on digital tooth grid model summit from above-mentioned kind of son vertex; To meet the summit of the summit of above-mentioned decision criteria as tooth grid model border; Form the loop of a closure up to the summit on said tooth grid model border, this closed loop is the border of searching for the digital tooth grid model that obtains.

In the above-mentioned steps, the process of digital tooth grid model summit being made the breadth First traversal is: as initial starting point, at first son vertex is planted in visit with kind of son vertex; From above-mentioned kind of son vertex, each abutment points of not visited of visit kind of son vertex; With the abutment points that satisfies above-mentioned decision criteria (this abutment points is promptly as the summit on tooth grid model border) as new starting point; Visit the abutment points of not visited separately from above-mentioned new starting point; Promptly proceed range and preferably travel through, form the loop of a closure up to kind of son vertex and the abutment points (planting the summit that son vertex and abutment points are tooth grid model border) that satisfies above-mentioned decision criteria.Wherein, the adjacent vertex (plant son vertex with) that satisfies decision criteria is: around all adjacent leg-of-mutton numbers on this summit with unequal around all adjacent side numbers on this summit.System (if no special instructions; System among this paper refers to use method of the present invention is carried out repair operation to the hole of digital tooth grid model system) first summit that meets above-mentioned decision criteria that will find is as kind of a son vertex; With kind of son vertex is that initial starting point is made the breadth First traversal to digital tooth grid model summit; Automatically search obtains the border of digital tooth grid model, and hunting zone that can reduction system is improved the efficient on systematic search border greatly.

Particularly, described step (2) further comprises step:

(2.1) alternatively select to belong in two former net boundary summits the start-stop summit of the summit on hole border with mouse as the hole border;

(2.2) line between the discrete above-mentioned start-stop summit, the line after dispersing and the summit on original mesh model part border constitute border, a blind bore hole.

Line between the above-mentioned discrete start-stop summit is that the grid distance mean value with the original mesh border is that length is carried out the discrete of line.

Particularly, in the step (3), described employing advances algorithm that triangle gridding is carried out in the closed region in the border, described blind bore hole to prewave and fills, and generating mesh topology and generate the grid surface of closed region automatically, comprises step:

(3.1) calculate first adjacent edge on each summit, cap holes border and the angle between second adjacent edge; Wherein, described first adjacent edge is the line between target summit and clockwise first descendant vertex, and described second adjacent edge is the line between the target summit and counterclockwise second descendant vertex;

(3.2) select the minimum summit of above-mentioned angle as the target summit, generate new summit and/or triangle in the plane between said target summit first adjacent edge and second adjacent edge;

The distance relation on the summit that (3.3) the detection cap holes is new and other each each summits of cap holes;

(3.4) the lowest distance value min_dis of setpoint distance relation;

When the distance that has new summit and a certain summit less than lowest distance value min_dis, then new summit and this summit are merged;

(3.5) upgrade the angle value on all summits;

(3.6) repeating step (3.1)～(3.5), number is zero up to the summit on hole border.

In the above-mentioned optimal technical scheme, step (3.4) is set up the summit merging of distance relation with new summit with it after, the former border of cap holes is split into two new closed boundaries, and former hole is split into two new holes; At this moment, the borderline summit of this cap holes (promptly setting up the summit of distance relation with above-mentioned new summit) promptly eliminated; Based on above-mentioned; Step (3.6) is described, and number is zero up to the summit on hole border; The borderline summit that promptly refers to cap holes is eliminated in the process of repeating step (3.1)～(3.5), accomplishes cap holes zone generating mesh topology and generate a series of processes of the grid surface of closed region automatically thus.This optimal technical scheme is to advance the concrete application examples in the hole repair method of algorithm at digital tooth grid model of the present invention to prewave, also possesses very high formation efficiency in the generating mesh in high quality in the cap holes zone.

More particularly, in the step of above-mentioned preferred version (3.2), generate new summit and/or triangle in the described plane between target summit first adjacent edge and second adjacent edge, comprise the steps:

If (3.2.1) the angle value on target summit is less than 75 °, directly connect first descendant vertex and second descendant vertex, constitute a new triangle;

If (3.2.2) the angle value on target summit is more than or equal to 75 ° and less than 135 °; Then on target summit and plane, descendant vertex place thereof, generate a new summit; Described new summit is divided equally on the money the angle on said target summit; Said new summit is linked to each other with target summit, first descendant vertex, second descendant vertex respectively, constitute two new triangles;

If (3.2.3) the angle value on target summit is more than or equal to 135 °; Then on target summit and plane, descendant vertex place thereof, generate two new summits; Described two new summits are respectively on two 1/3rd bisectors of said target summit angle; Said two new summits are linked to each other with target summit, first descendant vertex, second descendant vertex respectively, constitute three new triangles.

Further, in the step of above-mentioned preferred version (3.4), said lowest distance value min_dis satisfies following calculating formula:

min_dis＝min{[||v _new-v _i||，|v _new-v _i-1||，||v _new-v _i+1||}

In the formula, v _NewFor above-mentioned new summit at three-dimensional position coordinates, v _iFor the target summit at three-dimensional position coordinates, v _I-1For first descendant vertex on target summit at three-dimensional position coordinates, v _I+1For second descendant vertex on target summit at three-dimensional position coordinates.

Particularly, in the step (4), said employing least square trellis algorithm is optimized the grid surface of above-mentioned closed region and original dental grid model boundary vicinity, further comprises step:

(4.1) summit, fairing zone comprises each summit of grid surface of each summit of newly-generated grid surface and original dental grid model boundary vicinity, sets up the fairing model on summit, above-mentioned fairing zone;

(4.2) summit on the former tooth grid model curved surface of outside expansion two circles in introducing original dental grid model border rebuilds above-mentioned fairing model as the control vertex in above-mentioned fairing zone;

(4.3) use fairing model after least-squares algorithm is found the solution reconstruction, obtain and satisfy the new summit that rebuilds back fairing model; The new summit that obtains constitutes the grid surface after optimizing.

In above-mentioned preferred version: the fairing zone is the curved surface set at place, summit, said fairing zone;

The control vertex of above-mentioned introducing satisfies condition in (being the outwards summit on the former tooth grid model curved surface of expansion two circles, original dental grid model border); The implication of said outside expansion two circles is: on the former tooth grid model curved surface with former tooth grid model border on the summit be 2 apart (distance that wherein, the summit is adjacent between the summit on the former tooth grid model border is 1); Above-mentioned control vertex be with corresponding former tooth grid model border on the summit apart be 2 summit, and above-mentioned control vertex belongs to the summit on the tooth grid model curved surface.

Because through advance the grid model that algorithm generates can more stiff (other hole repair methods all have this problem) to prewave at boundary; In former step (4), the present invention has adopted the least square trellis algorithm that near the original boundaries and newly-generated net region is optimized.This optimal technical scheme is the concrete application of least square trellis algorithm in hole repair method of the present invention, can access the comparatively smooth digital tooth grid model through hole repair.

Below further introduce the optimal technical scheme that adopts the least square trellis algorithm that near the original boundaries and newly-generated net region (being above-mentioned fairing zone) is optimized.

As preferably, the fairing model on each summit, described fairing zone is:

$v_i-\frac{1}{d_i}\underset{j:(i,j)\&Element;E}{\mathrm{\&Sigma;}}{v}_j=0,v_i\&Element;\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA0000158575210000012.png,HDA0000158575210000021.png"\; state="\{\{state\}\}">V</figure-callout>}$ ①

Formula 1. in, v _iBe i summit at three-dimensional position coordinates, d _iBe the degree on i summit, v _jBe v _iAdjacent vertex, represent that j summit is at three-dimensional position coordinates; E is the set on fairing area grid curved surface limit, j: (i, j) implication of ∈ E belongs to the adjacent vertex of summit i in the fairing area grid curved surface for summit j; V={v ₁, v ₂..., v _iIt is the set on summit, fairing zone.

It is following to be write all the grid vertex fairing models in the fairing zone as matrix form equation:

LX＝0 ②

Formula 2. in, L is Laplce's matrix, $L_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& i=j\\ -\frac{1}{d_i},& (i,j)\&Element;E\\ 0,& \mathrm{Otherwise}\end{array}\right.,$ L _IjIt is the element of the capable j row of matrix L i.

More preferably, the fairing model of rebuilding behind the described adding control vertex is following:

AX＝b ③

3. formula satisfies: $A=\left(\begin{array}{c}L\\ F\end{array}\right),$ $L_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& i=j\\ -\frac{1}{d_i},& (i,j)\&Element;E\\ 0,& \mathrm{Otherwise}\end{array}\right.,$ $F_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& j=s_i\&Element;C\\ 0,& \mathrm{Otherwise}\end{array}\right.,$

$b_k=\left\{\begin{array}{cc}0,& k\&le;n\\ (x_{s_{k-n}},y_{s_{k-n}},z_{s_{k-n}}),& n<k\&le;n+m\end{array}\right.;$

Wherein L is Laplce's matrix, and F is the control vertex matrix, L _IjBe the element of the capable j row of i in the matrix L, F _IjBe the element of the capable j row of i in the matrix F, b _kBe matrix b interior element; M is the number of control vertex, and k is the number of fairing regional connectivity figure, satisfies m＞=k, and n is the number on each summit, fairing zone, and the coordinates table of control vertex is shown as formula v _s=(x _s, y _s, z _s), s ∈ C, wherein C={s ₁, s ₂..., s _mIt is the numbering of control vertex.

Further, described least-squares algorithm is found the solution the fairing model after the reconstruction, promptly finds the solution X and satisfies:

$\min {\left|\right|\mathrm{AX}-b\left|\right|}^2=\min ({\left|\right|\mathrm{LX}\left|\right|}^2+\underset{s\&Element;C}{\mathrm{\&Sigma;}}{|x_s-v_s^{\left(x\right)}|}^2)$ ④

4. can get unique solution by formula: X=(A ^TA) ^-1A ^TB.

The hole repair method of the present invention's numeral tooth grid model is through user's input digit tooth grid model; Choose 2 structure hole borders alternately, interactive operation is simple, convenient, and system generates the surface mesh in dental cast hole zone fast then; Newly-generated surface mesh quality is high; Optimize newly-generated grid at last, this part grid and tooth grid are spliced naturally, newly-generated curved surface is smooth.

Description of drawings

Fig. 1 is the schematic flow sheet of hole repair method of the present invention;

Fig. 2 is the synoptic diagram that concerns between the border vertices in the hole repair method of the present invention;

Fig. 3 in the hole repair method of the present invention several kinds advance the process of rule synoptic diagram to prewave;

Fig. 4 is the process synoptic diagram of wavefront point in the hole repair method of the present invention with frontier point merging recently;

Fig. 5 is the organigram of matrix A in the least square trellis algorithm in the hole repair method of the present invention.

Embodiment

Below in conjunction with accompanying drawing hole repair method of the present invention is elaborated.

A kind of hole repair method of digital tooth grid model as shown in Figure 1 comprises step:

(1) input digit tooth grid model, the border of digital tooth grid model is searched for and automatically with all summits on this border of the bright demonstration of height by system.

The boundary search algorithm of numeral tooth grid model further comprises the steps:

(1.1) seek the borderline kind son vertex of tooth grid model: the decision criteria of searching is following:

Through all summits in the digital tooth grid model of inspection input; Search adjacent leg-of-mutton number and adjacent side number around the summit, the summit that first the adjacent triangle number that finds and adjacent side number are not waited is as the kind son vertex on tooth grid model border;

(1.2) use above-mentioned decision criteria the breadth First traversal to be made on digital tooth grid model summit from above-mentioned kind of son vertex; To meet the summit of the summit of above-mentioned decision criteria as tooth grid model border; Form the loop of a closure up to the summit on said tooth grid model border, this closed loop is the border of searching for the digital tooth grid model that obtains.

(2) the user summit of using mouse to choose alternately to belong to the hole border in the above-mentioned summit is as the start-stop summit on hole border, based on structure border, blind bore hole, described start-stop summit.

The construction algorithm on hole border further comprises the steps:

(2.1) alternatively select to belong in two former net boundary summits the start-stop summit of the summit on hole border with mouse as the hole border;

(2.2) the grid distance mean value with the original mesh border is the line between the above-mentioned start-stop of the discrete length summit, and the line after dispersing and the summit on original mesh model part border constitute border, a blind bore hole.

(3) employing advances algorithm that the triangle gridding filling is carried out in the closed region in the cap holes border to prewave, and generating mesh is topological automatically, and the grid surface of generation closed region obtains the digital tooth grid model through hole repair.

In conjunction with Fig. 2, Fig. 3 and Fig. 4, step (3) further comprises the steps:

(3.1) first adjacent edge on each summit on calculating cap holes border and the angle between second adjacent edge;

(3.2) select the minimum summit of above-mentioned angle as the target summit; And according to following new summit and/or the triangle of rule generation; Wherein, Described first adjacent edge is the line between target summit and clockwise first descendant vertex, and described second adjacent edge is the line between the target summit and counterclockwise second descendant vertex:

If (3.2.1) the angle value on target summit is less than 75 °, directly connect first descendant vertex and second descendant vertex, constitute a new triangle;

If (3.2.2) the angle value on target summit is more than or equal to 75 ° and less than 135 °; Then on target summit and plane, descendant vertex place thereof, generate a new summit; Described new summit is divided equally on the money the angle on said target summit; Said new summit is linked to each other with target summit, first descendant vertex, second descendant vertex respectively, constitute two new triangles;

If (3.2.3) the angle value on target summit is more than or equal to 135 °; Then on target summit and plane, descendant vertex place thereof, generate two new summits; Described two new summits are respectively on two 1/3rd bisectors of said target summit angle; Said two new summits are linked to each other with target summit, first descendant vertex, second descendant vertex respectively, constitute three new triangles;

The distance relation on the summit that (3.3) the detection cap holes is new and each summit of other each cap holes; If the distance that has new summit and an a certain summit is less than apart from min dis; Then new summit and this summit are merged; The former border of cap holes is split into two new closed boundaries, and former hole is split into two new holes;

Satisfy following calculating formula apart from min_dis:

min_dis＝min{||v _new-v _i||，||v _new-v _i-1||，||v _new-v _i+1||}

In the formula, v _NewFor above-mentioned new summit at three-dimensional position coordinates, v _iFor the target summit at three-dimensional position coordinates, v _I-1For first descendant vertex on target summit at three-dimensional position coordinates, v _I+1For second descendant vertex on target summit at three-dimensional position coordinates.

(3.4) upgrade the angle value on all summits;

(3.5) repeating step (3.1)～(3.4), number is zero up to the summit on hole border.

(4) adopt the least square trellis algorithm to optimize above-mentioned closed region and near the grid surface of original boundaries, the digital tooth grid model after being optimized through hole repair.

In conjunction with Fig. 5, step (4) further comprises following steps:

(4.1) summit, fairing zone comprises each summit of grid surface of each summit of newly-generated grid surface and original dental grid model boundary vicinity, sets up the fairing model on above-mentioned summit:

$v_i-\frac{1}{d_i}\underset{j:(i,j)\&Element;E}{\mathrm{\&Sigma;}}{v}_j=0,v_i\&Element;\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="HDA0000158575210000012.png,HDA0000158575210000021.png"\; state="\{\{state\}\}">V</figure-callout>}$ ①

Formula 1. in, v _iBe i summit at three-dimensional position coordinates, d _iBe the degree on i summit, v _jBe v _iAdjacent vertex, represent that j summit is at three-dimensional position coordinates; E is the set on fairing area grid curved surface limit, j: (i, j) implication of ∈ E belongs to the adjacent vertex of summit i in the fairing area grid curved surface for summit j; V={v ₁, v ₂..., v _iIt is the set on summit, fairing zone.

It is following to be write all the grid vertex fairing models in the fairing zone as matrix form equation:

LX＝0 ②

Formula 2. in, L is Laplce's matrix, $L_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& i=j\\ -\frac{1}{d_i},& (i,j)\&Element;E\\ 0,& \mathrm{Otherwise}\end{array}\right.,$ L _IjIt is the element of the capable j row of matrix L i.

(4.2) summit on the former tooth grid model curved surface of outside expansion two circles in introducing original dental grid model border rebulids the fairing model as the control vertex in above-mentioned fairing zone:

AX＝b ③

3. formula satisfies: $A=\left(\begin{array}{c}L\\ F\end{array}\right),$ $L_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& i=j\\ -\frac{1}{d_i},& (i,j)\&Element;E\\ 0,& \mathrm{Otherwise}\end{array}\right.,$ $F_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& j=s_i\&Element;C\\ 0,& \mathrm{Otherwise}\end{array}\right.,$

$b_k=\left\{\begin{array}{cc}0,& k\&le;n\\ (x_{s_{k-n}},y_{s_{k-n}},z_{s_{k-n}}),& n<k\&le;n+m\end{array}\right.;$

Wherein L is Laplce's matrix, and F is the control vertex matrix, L _IjBe the element of the capable j row of i in the matrix L, F _IjBe the element of the capable j row of i in the matrix F, b _kBe matrix b interior element; M is the number of control vertex, and k is the number of fairing regional connectivity figure, is 1 here, satisfies m＞=k, and n is the number on each summit, fairing zone, and the coordinates table of control vertex is shown as formula v _s=(x _s, y _s, z _s), s ∈ C, wherein C={s ₁, s ₂..., s _mIt is the numbering of control vertex.

(4.3) use least-squares algorithm to find the solution above-mentioned fairing model, find the solution X and satisfy:

$\min {\left|\right|\mathrm{AX}-b\left|\right|}^2=\min ({\left|\right|\mathrm{LX}\left|\right|}^2+\underset{s\&Element;C}{\mathrm{\&Sigma;}}{|x_s-v_s^{\left(x\right)}|}^2)$ ④

The least-squares algorithm of formula shown in 4. has unique solution, i.e. X=(A ^TA) ^-1A ^TB, the said unanimity of parameter meaning (4.2).

Fig. 5 is the organigram of matrix A in the least square trellis algorithm in the hole repair method of the present invention.V among Fig. 5 (1) wherein ₁, V ₂, V ₆Be control vertex, V ₃, V ₄, V ₅, V ₇, V ₈Be the fairing summit, then utilize above-mentioned fairing model construction to go out matrix A shown in Fig. 5 (2).

Claims (10)

1. the hole repair method of a digital tooth grid model is characterized in that, comprises step:

(1) input digit tooth grid model is searched for the border of digital tooth grid model automatically and is shown all summits on this border;

(2) choose start-stop summit, the summit that belongs to the hole border in the above-mentioned summit alternately, based on structure border, blind bore hole, described start-stop summit as the hole border;

(3) employing advances algorithm that the triangle gridding filling is carried out in the closed region in the border, described blind bore hole to prewave, and generating mesh is topological automatically, and the grid surface of generation closed region obtains the digital tooth grid model through hole repair;

(4) adopt the least square trellis algorithm to optimize the grid surface of above-mentioned closed region and original dental grid model boundary vicinity, the digital tooth grid model after being optimized through hole repair.

2. the hole repair method of digital tooth grid model as claimed in claim 1 is characterized in that, in the step (1), the border of said automatic search numeral tooth grid model comprises step:

(1.1) seek the borderline kind son vertex of tooth grid model: the decision criteria of searching is following:

Through all summits in the digital tooth grid model of inspection input; Search adjacent leg-of-mutton number and adjacent side number around the summit, the summit that first the adjacent triangle number that finds and adjacent side number are not waited is as the kind son vertex on tooth grid model border;

(1.2) use above-mentioned decision criteria the breadth First traversal to be made on digital tooth grid model summit from above-mentioned kind of son vertex; To meet the summit of the summit of above-mentioned decision criteria as tooth grid model border; Form the loop of a closure up to the summit on said tooth grid model border, this closed loop is the border of searching for the digital tooth grid model that obtains.

3. the hole repair method of digital tooth grid model as claimed in claim 1 is characterized in that, described step (2) further comprises step:

(2.1) alternatively select to belong in two former net boundary summits the start-stop summit of the summit on hole border with mouse as the hole border;

(2.2) the grid distance mean value with the original mesh border is the line between the above-mentioned start-stop of the discrete length summit, and the line after dispersing and the summit on original mesh model part border constitute border, a blind bore hole.

4. the hole repair method of digital tooth grid model as claimed in claim 1; It is characterized in that; In the step (3); Described employing advances algorithm that triangle gridding is carried out in the closed region in the border, described blind bore hole to prewave and fills, and generating mesh topology and generate the grid surface of closed region automatically, comprises step:

(3.1) calculate first adjacent edge on each summit, cap holes border and the angle between second adjacent edge; Wherein, described first adjacent edge is the line between above-mentioned summit and clockwise first descendant vertex, and described second adjacent edge is the line between the above-mentioned summit and counterclockwise second descendant vertex;

(3.2) select the minimum summit of above-mentioned angle as the target summit, generate new summit and/or triangle in the plane between said target summit first adjacent edge and second adjacent edge;

The distance relation on the summit that (3.3) the detection cap holes is new and each summit of other each cap holes;

(3.4) the lowest distance value min dis of setpoint distance relation;

When the distance that has new summit and a certain summit less than lowest distance value min dis, then new summit and this summit are merged;

(3.5) upgrade the angle value on all summits;

(3.6) repeating step (3.1)～(3.5), number is zero up to the summit on hole border.

5. the hole repair method of digital tooth grid model as claimed in claim 4; It is characterized in that; In the step (3.2), generate new summit and/or triangle in the described plane between target summit first adjacent edge and second adjacent edge, comprise the steps:

If (3.2.1) the angle value on target summit is less than 75 °, directly connect first descendant vertex and second descendant vertex, constitute a new triangle;

If (3.2.2) the angle value on target summit is more than or equal to 75 ° and less than 135 °; Then on target summit and plane, descendant vertex place thereof, generate a new summit; Described new summit is divided equally on the money the angle on said target summit; Said new summit is linked to each other with target summit, first descendant vertex, second descendant vertex respectively, constitute two new triangles;

If (3.2.3) the angle value on target summit is more than or equal to 135 °; Then on target summit and plane, descendant vertex place thereof, generate two new summits; Described two new summits are respectively on two 1/3rd bisectors of said target summit angle; Said two new summits are linked to each other with target summit, first descendant vertex, second descendant vertex respectively, constitute three new triangles.

6. the hole repair method of digital tooth grid model as claimed in claim 4 is characterized in that, in the step (3.4), said lowest distance value min dis satisfies following calculating formula:

min_dis＝min{||v _new-v _i||，||v _new-v _i-1||，||v _new-v _i+1||}

In the formula, v _NewFor above-mentioned new summit at three-dimensional position coordinates, v _iFor the target summit at three-dimensional position coordinates, v _I-1For first descendant vertex on target summit at three-dimensional position coordinates, v _I+1For second descendant vertex on target summit at three-dimensional position coordinates.

7. the hole repair method of digital tooth grid model as claimed in claim 1; It is characterized in that; In the step (4), said employing least square trellis algorithm is optimized the grid surface of above-mentioned closed region and original dental grid model boundary vicinity, further comprises step:

(4.1) summit, fairing zone comprises each summit of grid surface of each summit of newly-generated grid surface and original dental grid model boundary vicinity, sets up the fairing model on summit, above-mentioned fairing zone;

(4.2) summit on the former tooth grid model curved surface of outside expansion two circles in introducing original dental grid model border rebuilds above-mentioned fairing model as the control vertex in above-mentioned fairing zone;

(4.3) use fairing model after least-squares algorithm is found the solution reconstruction, obtain and satisfy the new summit that rebuilds back fairing model; The new summit that obtains constitutes the grid surface after optimizing.

8. the hole repair method of digital tooth grid model as claimed in claim 7 is characterized in that, the fairing model on each summit, described fairing zone is:

$v_i-\frac{1}{d_i}\underset{j:(i,j)\&Element;E}{\mathrm{\&Sigma;}}{v}_j=0,v_i\&Element;V$ ①

Formula 1. in, v _iBe i summit at three-dimensional position coordinates, d _iBe the degree on i summit, v _jBe v _iAdjacent vertex, represent that j summit is at three-dimensional position coordinates; E is the set on fairing area grid curved surface limit, j: (i, j) implication of ∈ E belongs to the adjacent vertex of summit i in the fairing area grid curved surface for summit j; V={v ₁, v ₂..., v _iIt is the set on summit, fairing zone;

It is following to be write all the grid vertex fairing models in the fairing zone as matrix form equation:

LX＝0 ②

Formula 2. in, L is Laplce's matrix, $L_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& i=j\\ -\frac{1}{d_i},& (i,j)\&Element;E\\ 0,& \mathrm{Otherwise}\end{array}\right.,$ L _IjIt is the element of the capable j row of matrix L i.

9. the hole repair method of digital tooth grid model as claimed in claim 8 is characterized in that, the fairing model of rebuilding behind the described adding control vertex is following:

AX＝b ③

3. formula satisfies: $A=\left(\begin{array}{c}L\\ F\end{array}\right),$ $L_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& i=j\\ -\frac{1}{d_i},& (i,j)\&Element;E\\ 0,& \mathrm{Otherwise}\end{array}\right.,$ $F_{\mathrm{Ij}}=\left\{\begin{array}{cc}1,& j=s_i\&Element;C\\ 0,& \mathrm{Otherwise}\end{array}\right.,$

$b_k=\left\{\begin{array}{cc}0,& k\&le;n\\ (x_{s_{k-n}},y_{s_{k-n}},z_{s_{k-n}}),& n<k\&le;n+m\end{array}\right.;$

Wherein L is Laplce's matrix, and F is the control vertex matrix, L _IjBe the element of the capable j row of i in the matrix L, F _IjBe the element of the capable j row of i in the matrix F, b _kBe matrix b interior element; M is the number of control vertex, and k is the number of fairing regional connectivity figure, satisfies m＞=k, and n is the number on each summit, fairing zone, and the coordinates table of control vertex is shown as formula v _s=(x _s, y _s, z _s), s ∈ C, wherein C={s ₁, s ₂..., s _mIt is the numbering of control vertex.

10. the hole repair method of digital tooth grid model as claimed in claim 9 is characterized in that, described least-squares algorithm is found the solution the fairing model after the reconstruction, promptly finds the solution X and satisfies:

$\min {\left|\right|\mathrm{AX}-b\left|\right|}^2=\min ({\left|\right|\mathrm{LX}\left|\right|}^2+\underset{s\&Element;C}{\mathrm{\&Sigma;}}{|x_s-v_s^{\left(x\right)}|}^2)$ ④

4. can get unique solution by formula: X=(A ^TA) ^-1A ^TB.

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