CN104504693A - Neck-edge line extraction method based on simple crown prosthesis mesh model of false tooth - Google Patents

Abstract

The invention discloses a neck-edge line extraction method based on a simple crown prosthesis mesh model of a false tooth. The neck-edge line extraction method comprises the following steps: scanning a tooth model, and generating a corresponding triangular mesh model and a corresponding point cloud model; analyzing the whole tooth model by adopting an analytical method based on curvature change rate coefficients, and determining the curvature of curvature calculation points and the curvature change rate coefficients through a local quadratic function fitting surface method; carrying out feature point screening on irregular-shaped triangles and regular triangles of the triangular mesh model respectively, and then generating feature lines according to the screened feature points; obtaining a tooth axle wire, automatically setting the initial points of neck-edge lines through the tooth axle wire, and then screening out a target neck-edge line from the feature lines by adopting an automatic iteration method in a mean direction; carrying out fitting and smoothening on the target neck-edge line so as to complete the extraction of the neck-edge line. The neck-edge line extraction method has the advantages of high extraction precision, reliability, high degree of intellectualization and low noise, and can be widely applied to the field of dental prosthesis.

Description

A kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth

Technical field

The present invention relates to oral restoration field, especially a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth.

Background technology

The application of CAD/CAM technology in oral restoration achieves development at full speed, and compared to traditional repaired by hand mode, oral cavity CAD/CAM technology not only drastically increases remediation efficiency, and possesses more excellent repairing quality.Tooth biological characteristic line comprises the neck edge line of leaf-comb Tooth preparation and the hole edge line of inlay Tooth preparation model.The extraction of dental preparations biological characteristic line is the key link of digitalized oral cavity dummy shape-designing, the extraction quality of biological characteristic line directly affects the modeling accuracy of dummy, be related to the comfort level that patient wears dummy, also have material impact for gums healthy.

Along with developing rapidly of computing machine, emerge in large numbers large quantities of oral restoration CAD/CAM system equipment abroad, domesticly also occur multiple neck edge line drawing algorithm.The people such as Dai Ning propose to utilize the curvature of point as the feature of neck edge line in " research and implementation of dental preparations neck edge line extracted in self-adaptive algorithm " (Research and Implementation for Automatic Extraction ofPreparation Line on Triangulated Surfaces of Preparation Tooth) paper, utilize the method for adaptable search to complete extraction to neck edge line by structure local feature guide line.But this algorithm just utilizes curvature as the sole criterion of unique point, the extraction accuracy of neck edge line can be caused to reduce.And structure local guide line can by neighbouring non-neck edge line but meet the point of feature guide, individual teeth can be caused correctly cannot to complete neck edge line drawing, not reliably.The people such as Zhang Changdong then propose at " the tooth biological characteristic line drawing technology based on illumination scan " paper the selection standard utilizing extreme value coefficient as unique point, and the heuristic search in conjunction with minimum cost completes the extraction of neck edge line.But this algorithm uses interactively neck edge line drawing, needs user to carry out the setting of initial point, intelligence degree is low and lack effective noise removing method.

Summary of the invention

In order to solve the problems of the technologies described above, the object of the invention is: propose that a kind of extraction accuracy is high, reliable, intelligence degree is high and noise is little, simply be preced with the neck edge line drawing method of repairing grid model based on artificial tooth.

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

Simply be preced with a neck edge line drawing method of repairing grid model based on artificial tooth, comprise:

S1, tooth model to be scanned, and generate corresponding triangle grid model and point cloud model;

S2, adopt and based on curvature variation coefficient analysis method, overall tooth model is analyzed, and obtain curvature and the Curvature varying rate coefficient of curvature estimation point by the method for local secondary Function Fitting curved surface;

S3, respectively unique point screening is carried out to the singular triangular of triangle grid model and canonical triangle, and then according to the unique point generating feature line of screening;

S4, acquisition tooth axis, and pass through the initial point of tooth axis Lookup protocol neck edge line, then adopt mean direction automatic Iterative method from characteristic curve, filter out target neck edge line;

S5, matching and fairing are carried out to target neck edge line, thus complete the extraction of neck edge line.

Further, described step S2, it comprises:

S21, using any point in triangle grid model as current point, calculate the normal direction of current point, the computing formula of the normal direction of described current point is:

$N_i=\frac{\underset{A\∈\mathrm{mesh}}{\mathrm{\Σ}}{A}_i\·n_i}{\left|\right|\underset{A\∈\mathrm{mesh}}{\mathrm{\Σ}}{A}_i\·n_i\left|\right|},$

Wherein, N _ithe per unit system of i-th neighborhood triangular plate of representative point is vowed, A _irepresent the area of i-th triangular plate, n _irepresent that the method for i-th triangular plate is vowed, mesh represents whole triangle gridding structure;

S22, be initial point with current point, method vows n _pfor z-axis, set up a local coordinate system;

Coordinate (the u of all neighborhood summits in the local coordinate system set up of S23, calculating current point _j, v _j, h _j);

S24, according to conversion after apex coordinate adopt least square fitting method obtain quadric surface;

S25, calculate quadric first fundamental quantity and second fundamental quantity, and then the curvature of estimation current point in quadric surface;

The Curvature varying rate coefficient of S26, calculating current point, the computing formula of described Curvature varying rate coefficient is:

Wherein, for cotangent weight operator, P is summit, and T is the triangular network at place, summit, and ver is summit on limit, Δ k _i(T) be the rate of change of place, summit triangle gridding;

S27, using another point in triangle grid model neighborhood as current point, calculate the normal direction of current point, then return step S22, until calculate in triangle grid model Curvature varying rate coefficient a little.

Further, described step S3, it comprises:

S31, the point screened in canonical triangle on characteristic curve, described in the point that filters out meet the following conditions:

$\left\{\begin{array}{c}<\mathrm{\&Delta;}{E}_{\max },\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\max }^{\&RightArrow;}\left(p_i\right)><0\\ \left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\max }\left(p_i\right)\right|>\left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\min }\left(p_i\right)\right|\end{array}\right.,$

Wherein, Δ E _maxfor maximum principal curvatures variable gradient, represent and triangle gridding maximum principal curvatures cut arrow sum, with represent the minimum principal curvatures sum on three summits on triangle gridding and maximum principal curvatures sum respectively;

S32, in singular triangular, screen point on characteristic curve by traversal and labelling method.

Further, described step S32, it comprises:

S321, a selected singular triangular, then travel through the triangle on side, if adjacent side triangle is canonical triangle, then mark the end points be simultaneously present on the leg-of-mutton characteristic curve of canonical and singular triangular, traveling through three limits and marking proximal surface is the leg-of-mutton limit of canonical, at least marks a limit;

The number that S322, basis are labeled limit performs corresponding operation: if the number being labeled limit is 2, then connect point corresponding to 2 limits, and with connecting formed figure replacement singular triangular; If the number being labeled limit is 3, then add a point at the center of singular triangular, and this point is connected to other three end points of singular triangular; If the number being labeled limit is 1, then do not do any operation.

Further, described step S4, it comprises:

S41, acquisition tooth axis;

S42, initial point by tooth axis Lookup protocol neck edge line;

S43, employing mean direction automatic Iterative method filter out target neck edge line from characteristic curve.

Further, described step S41, it comprises:

The average coordinates of the frontier point on S411, calculating tooth model base, and the central point using the average coordinates calculated as tooth boundary surface;

S412, point according to whole tooth model, calculate the central point of whole tooth model;

S415, the straight line that formed using the central point of the central point and tooth boundary surface that connect tooth boundary surface are as tooth axis.

Further, described step S42, it comprises:

S421, the feature intrinsic according to tooth, axis sets a threshold range, is then removed by the noise spot of top and bottom, tooth axis according to this threshold range;

S422, adopt sciagraphy the projecting characteristic points on tooth model on tooth axis, and record the quantity of respective coordinates subpoint in tooth axis;

S423, using the maximum point of respective coordinates subpoint quantity in tooth axis as the initial point of neck edge line.

Further, described step S43, it comprises:

The threshold value that S431, basis are preset is screened characteristic curve, obtains the feature point set after screening, and remembers that neck edge line initial point is V ₀, initial radium is R ₀, direction, axis is neck edge line initial point direction is and neck edge line initial point principal direction is with V ₀for the center of circle, with R ₀for radius have the mean direction in a direction;

S432, neck edge line initial point is joined in neck edge line point set J as first unique point;

S433, get R _stepfor iteration radius, to gather last some V in J _sfor the center of circle, R _stepfor radius, calculate radius R _stepinterior the mean direction having a direction then radius R is allowed _stepwith for independent increment, from rise to recalculate thus obtain a set, wherein, for model average side length, α and β is regulated variable, λ _stepfrom increasing step number;

S434, from V _sstart to find next Average Iteration point V along neighborhood point _i, obtain V _sto V _idirection then judge with whether angle is less than 60 degree and R _stepobtain maximal value, if so, then by V _istored in set J, and return step S433, otherwise enter step S435;

S435, empty set J, principal direction is changed into then step S432 is returned,

Final acquisition target neck edge line.

Further, described step S5, it comprises:

S511, employing NURBS SPL carry out matching to target neck edge line;

S512, employing Laplacian method algorithm, carry out transformation calculations to each summit i of the target neck edge line of matching, the formula of described transformation calculations is:

${\mathrm{\&Delta;}}_{\mathrm{Ei}}\left(p\right)=\underset{q\&Element;\mathrm{ver}\left(p\right)}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}(E_i\left(q\right)-E_i\left(p\right)),$

Wherein, w _pqfor Laplce's weight coefficient, E _iq () is the Curvature varying rate coefficient of q point, E _ip () is the Curvature varying rate coefficient of p point, Δ _eip () is the curvature gradients of p point, ver (p) is neck edge line point set.

Further, described step S5, it comprises:

S521, employing NURBS SPL carry out matching to target neck edge line;

S522, employing Bi Pulasi Smoothing Algorithm, carry out fairing to the target neck edge line of matching.

The invention has the beneficial effects as follows: comprehensively choose curvature and Curvature varying coefficient as the standard of unique point, improve the extraction accuracy of neck edge line; According to the self structure feature of tooth, adopt tooth axis to complete neck edge line drawing in conjunction with the mode of mean direction automatic Iterative method, solve the problem that local guide line correctly cannot choose neck edge line, robustness is good, very reliably; By the initial point of tooth axis Lookup protocol neck edge line, carry out the setting of initial point without the need to user, intelligence degree is high; Set up the step of target neck edge line being carried out to fairing and matching, can effective stress release treatment, homogenize triangular plate.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described.

Fig. 1 is a kind of overall flow figure being simply preced with the neck edge line drawing method of repairing grid model based on artificial tooth of the present invention;

Fig. 2 is the process flow diagram of step S2 of the present invention;

Fig. 3 is the process flow diagram of step S3 of the present invention;

Fig. 4 is the process flow diagram of step S32 of the present invention;

Fig. 5 is the process flow diagram of step S4 of the present invention;

Fig. 6 is the process flow diagram of step S41 of the present invention;

Fig. 7 is the process flow diagram of step S42 of the present invention;

Fig. 8 is the process flow diagram of step S43 of the present invention;

Fig. 9 is a kind of implementing procedure figure of step S5 of the present invention;

Figure 10 is the another kind of implementing procedure figure of step S5 of the present invention;

Figure 11 is the overall flow figure of the embodiment of the present invention one;

Figure 12 is the geometrized structure graph of triangle gridding of the present invention;

Figure 13 and Figure 14 be axis of the present invention choose schematic diagram;

Figure 15 is that the present invention is the projective distribution figure that the projecting characteristic points on tooth model to axis obtains;

Figure 16 is the neck edge line design sketch that the present invention finally extracts.

Embodiment

With reference to Fig. 1, a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth, comprising:

S1, tooth model to be scanned, and generate corresponding triangle grid model and point cloud model;

S2, adopt and based on curvature variation coefficient analysis method, overall tooth model is analyzed, and obtain curvature and the Curvature varying rate coefficient of curvature estimation point by the method for local secondary Function Fitting curved surface;

S3, respectively unique point screening is carried out to the singular triangular of triangle grid model and canonical triangle, and then according to the unique point generating feature line of screening;

S4, acquisition tooth axis, and pass through the initial point of tooth axis Lookup protocol neck edge line, then adopt mean direction automatic Iterative method from characteristic curve, filter out target neck edge line;

S5, fairing and matching are carried out to target neck edge line, thus complete the extraction of neck edge line.

The present invention adopts scanner to scan tooth model, and generates corresponding triangle grid model and point cloud model.In triangle grid model, triangle is divided into canonical triangle and singular triangular.All operations of the present invention calculates and all carries out (as calculated, fairing, matching, projection etc.) based on triangle grid model.Wherein, if the tangent line rector on Atria point each other inner product be just, then claim this triangle to be canonical triangle, otherwise, then claim this triangle to be singular triangular.

With reference to Fig. 2, be further used as preferred embodiment, described step S2, it comprises:

S21, using any point in triangle grid model as current point, calculate the normal direction of current point, the computing formula of the normal direction of described current point is:

$N_i=\frac{\underset{A\&Element;\mathrm{mesh}}{\mathrm{\&Sigma;}}{A}_i\&CenterDot;n_i}{\left|\right|\underset{A\&Element;\mathrm{mesh}}{\mathrm{\&Sigma;}}{A}_i\&CenterDot;n_i\left|\right|},$

Wherein, N _ithe per unit system of i-th neighborhood triangular plate of representative point is vowed, A _irepresent the area of i-th triangular plate, n _irepresent that the method for i-th triangular plate is vowed, mesh represents whole triangle gridding structure;

S22, be initial point with current point, method vows n _pfor z-axis, set up a local coordinate system;

Coordinate (the u of all neighborhood summits in the local coordinate system set up of S23, calculating current point _j, v _j, h _j);

S24, according to conversion after apex coordinate adopt least square fitting method obtain quadric surface;

S25, calculate quadric first fundamental quantity and second fundamental quantity, and then the curvature of estimation current point in quadric surface;

The Curvature varying rate coefficient of S26, calculating current point, the computing formula of described Curvature varying rate coefficient is:

Wherein, for cotangent weight operator, P is summit, and T is the triangular network at place, summit, and ver is summit on limit, Δ k _i(T) be the rate of change of place, summit triangle gridding;

S27, using another point in triangle grid model neighborhood as current point, calculate the normal direction of current point, then return step S22, until calculate in triangle grid model Curvature varying rate coefficient a little.

Wherein, each quadric surface all has the first fundamental quantity and these two characteristic quantities of second fundamental quantity, and each characteristic quantity can be represented by 3 characteristic parameters, calculates the first fundamental quantity and second fundamental quantity just can learn whole quadric feature.

With reference to Fig. 3, be further used as preferred embodiment, described step S3, it comprises:

S31, the point screened in canonical triangle on characteristic curve, described in the point that filters out meet the following conditions:

$\left\{\begin{array}{c}<\mathrm{\&Delta;}{E}_{\max },\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\max }^{\&RightArrow;}\left(p_i\right)><0\\ \left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\max }\left(p_i\right)\right|>\left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\min }\left(p_i\right)\right|\end{array}\right.,$

Wherein, Δ E _maxfor maximum principal curvatures variable gradient, represent and triangle gridding maximum principal curvatures cut arrow sum, with represent the minimum principal curvatures sum on three summits on triangle gridding and maximum principal curvatures sum respectively;

S32, in singular triangular, screen point on characteristic curve by traversal and labelling method.

With reference to Fig. 4, be further used as preferred embodiment, described step S32, it comprises:

S321, a selected singular triangular, then travel through the triangle on side, if adjacent side triangle is canonical triangle, then mark the end points be simultaneously present on the leg-of-mutton characteristic curve of canonical and singular triangular, traveling through three limits and marking proximal surface is the leg-of-mutton limit of canonical, at least marks a limit;

The number that S322, basis are labeled limit performs corresponding operation: if the number being labeled limit is 2, then connect point corresponding to 2 limits, and with connecting formed figure replacement singular triangular; If the number being labeled limit is 3, then add a point at the center of singular triangular, and this point is connected to other three end points of singular triangular; If the number being labeled limit is 1, then do not do any operation.

With reference to Fig. 5, be further used as preferred embodiment, described step S4, it comprises:

S41, acquisition tooth axis;

S42, initial point by tooth axis Lookup protocol neck edge line;

S43, employing mean direction automatic Iterative method filter out target neck edge line from characteristic curve.

With reference to Fig. 6, be further used as preferred embodiment, described step S41, it comprises:

The average coordinates of the frontier point on S411, calculating tooth model base, and the central point using the average coordinates calculated as tooth boundary surface;

S412, point according to whole tooth model, calculate the central point of whole tooth model;

S415, the straight line that formed using the central point of the central point and tooth boundary surface that connect tooth boundary surface are as tooth axis.

With reference to Fig. 7, be further used as preferred embodiment, described step S42, it comprises:

S421, the feature intrinsic according to tooth, axis sets a threshold range, is then removed by the noise spot of top and bottom, tooth axis according to this threshold range;

S422, adopt sciagraphy the projecting characteristic points on tooth model on tooth axis, and record the quantity of respective coordinates subpoint in tooth axis;

S423, using the maximum point of respective coordinates subpoint quantity in tooth axis as the initial point of neck edge line.

With reference to Fig. 8, be further used as preferred embodiment, described step S43, it comprises:

The threshold value that S431, basis are preset is screened characteristic curve, obtains the feature point set after screening, and remembers that neck edge line initial point is V ₀, initial radium is R ₀, direction, axis is neck edge line initial point direction is and neck edge line initial point principal direction is with V ₀for the center of circle, with R ₀for radius have the mean direction in a direction;

S432, neck edge line initial point is joined in neck edge line point set J as first unique point;

S433, get R _stepfor iteration radius, to gather last some V in J _sfor the center of circle, R _stepfor radius, calculate radius R _stepinterior the mean direction having a direction then radius R is allowed _stepwith for independent increment, from rise to recalculate thus obtain a set, wherein, for model average side length, α and β is regulated variable, λ _stepfrom increasing step number;

S434, from V _sstart to find next Average Iteration point V along neighborhood point _i, obtain V _sto V _idirection then judge with whether angle is less than 60 degree and R _stepobtain maximal value, if so, then by V _istored in set J, and return step S433, otherwise enter step S435;

S435, empty set J, principal direction is changed into then step S432 is returned,

Final acquisition target neck edge line.

With reference to Fig. 9, be further used as preferred embodiment, described step S5, it comprises:

S511, employing NURBS SPL carry out matching to target neck edge line;

S512, employing Laplacian method algorithm, carry out transformation calculations to each summit i of the target neck edge line of matching, the formula of described transformation calculations is:

${\mathrm{\&Delta;}}_{\mathrm{Ei}}\left(p\right)=\underset{q\&Element;\mathrm{ver}\left(p\right)}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}(E_i\left(q\right)-E_i\left(p\right)),$

Wherein, w _pqfor Laplce's weight coefficient, E _iq () is the Curvature varying rate coefficient of q point, E _ip () is the Curvature varying rate coefficient of p point, Δ _eip () is the curvature gradients of p point, ver (p) is neck edge line point set.

With reference to Figure 10, be further used as preferred embodiment, described step S5, it comprises:

S521, employing NURBS SPL carry out matching to target neck edge line;

S522, employing Bi Pulasi Smoothing Algorithm, carry out fairing to the target neck edge line of matching.

Below in conjunction with Figure of description and specific embodiment, the present invention is described in further detail.

With reference to Figure 11, the present invention is a kind of to be simply preced with the neck edge line drawing method of repairing grid model based on artificial tooth and to comprise the following steps:

Step one, importing model

The present invention utilizes scanner to scan tooth model, and generates corresponding triangle grid model and point cloud model.In triangle grid model, triangle is divided into canonical triangle and singular triangular.All operations of the present invention calculates and all carries out (as calculated, fairing, matching, projection etc.) based on triangle grid model.Wherein, if the tangent line rector on Atria point each other inner product be just, then claim this triangle to be canonical triangle, otherwise, then claim this triangle to be singular triangular.

Step 2, unique point calculate

The present invention adopts and analyzes overall tooth model based on curvature variation coefficient analysis, and utilize the method for local secondary Function Fitting curved surface to obtain the curvature of curvature estimation point, concrete computation process is:

(1) curvature of calculation level

The curvature calculating process of point of the present invention comprises:

A. the normal direction of calculation level, computing formula is:

$N_i=\frac{\underset{A\&Element;\mathrm{mesh}}{\mathrm{\&Sigma;}}{A}_i\&CenterDot;n_i}{\left|\right|\underset{A\&Element;\mathrm{mesh}}{\mathrm{\&Sigma;}}{A}_i\&CenterDot;n_i\left|\right|},$

Wherein, N _ithe per unit system of i-th neighborhood triangular plate of representative point is vowed, A _irepresent the area of i-th triangular plate, n _irepresent that the method for i-th triangular plate is vowed, mesh represents whole triangle gridding structure;

B. with this point for initial point, method vow n _pfor z-axis, set up a local coordinate system;

C. coordinate (the u of all neighborhood summits in the local coordinate system set up of this point is calculated _j, v _j, h _j)

D. general quadric surface is become by the data after conversion by least square fitting;

E. calculated first, second fundamental quantity of curved surface by surface equation, and then estimate the curvature of this point.

F. point each on model is carried out to the operation of step a-e.

(2) Curvature varying rate coefficient is estimated

Curvature varying rate coefficient theoretical expression is: Δ k _icurvature variation, it is the unit tangent vector on the line of curvature.

As shown in figure 12, e is the limit on triangle gridding, and θ l is the angle of the dihedral angle of e, be along e vector of unit length ( direction can select arbitrarily).Had by Figure 12:

Mean curvature

Graphic operation on limit $s\left(e\right)=M(\stackrel{\&RightArrow;}{e}\&times;{\stackrel{\&RightArrow;}{N}}_e){(\stackrel{\&RightArrow;}{e}\&times;{\stackrel{\&RightArrow;}{N}}_e)}^t$

Based on the adjacent side of summit gained

The practical expression that can obtain Curvature varying rate coefficient according to above-mentioned expression formula is:

Wherein, for cotangent weight operator, be used for the effect of each summit of weighting in expression formula.The Curvature varying rate coefficient of each point can be obtained by this formula.

Step 3, characteristic curve are chosen

The present invention carries out different operations to singular triangular from canonical triangle respectively, finally obtains the point on characteristic curve.

In set M a little, the ridge point of following rule judgment characteristic curve can be adopted:

$E_{\max }=0:<\mathrm{\&Delta;}{E}_{\max },{\stackrel{\&RightArrow;}{k}}_{\max }><0,\left|k_{\max }\right|>\left|k_{\min }\right|---\left(1\right)$

$E_{\min }=0:<\mathrm{\&Delta;}{E}_{\min },{\stackrel{\&RightArrow;}{k}}_{\min }>>0,\left|k_{\max }\right|<\left|k_{\min }\right|---\left(2\right)$

If direction of curve is contrary with given direction of normal, then need E _maxand E _minvalue exchange.

That is, meeting the null point of Curvature varying rate coefficient is exactly the unique point screened required for us.

According to this rule, unique point screening process of the present invention comprises:

A () screens unique point in canonical triangle

Select the k on triangular facet _max(p _i) and E _max(p _i), we can estimate its rate of change Δ E _max.

According to equation (1) requirement, it meets on triangular facet:

$<\mathrm{\&Delta;}{E}_{\max },\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}\stackrel{\&RightArrow;}{k_{\max }}\left(p_i\right)><0---\left(3\right)$

$\left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\max }\left(p_i\right)\right|>\left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\min }\left(p_i\right)\right|---\left(4\right)$

Triangular facet is selected the point meeting equation (3) and (4), and acquired results is exactly the point on characteristic curve.

B () selects the point on characteristic curve in singular triangular

Because singular triangular is not suitable for simple Curvature varying coefficient calculation method, the present invention is by carrying out the calculating of curvature variation factor to the leg-of-mutton process of adjacent canonical, detailed process is:

A selected singular triangular, the triangle on traversal side, if adjacent side triangle is canonical triangle, then marks the end points be simultaneously present on the leg-of-mutton characteristic curve of canonical and singular triangular.Traveling through three limits and marking proximal surface is the leg-of-mutton limit of canonical, at least marks a limit.There are following three kinds of situations in the result of mark:

Mark two limits: connect corresponding point, replace singular triangular;

Mark three limits: add a point at singular triangular center, and connect him to other three points.

Mark a limit: do not do any operation.

Step 4, neck edge line drawing

The present invention utilizes principal direction analytic approach iteration to screen the target neck edge line in characteristic curve, and detailed process is:

(1) automatically the choosing of initial point

Automatically the process of choosing of initial point is:

First, frontier point according to the base of tooth model calculates average coordinates, and using the central point of this average coordinates as tooth boundary surface, again according to the point of whole tooth model, calculate the central point of whole tooth model, finally connect these two central points as tooth axis, as shown in the arrow in Figure 13 or Figure 14.Wherein, direction, axis is bottom surface (i.e. tooth boundary surface) central point direction model central point.

Then, the design feature (neck edge line there will not be in tooth top and least significant end) intrinsic according to tooth, removes, the unique point of upper end, axis and lower end to remove the noise data on tooth top and bottom.

Then, utilize sciagraphy, the projecting characteristic points on tooth model on axis, and record the quantity of respective coordinates subpoint in axis, as shown in figure 15.Neck edge line is a closed ring curve on tooth, and when utilizing sciagraphy, neck edge line region there will be a peak value.Peak value place and the most intensive place of representation feature point, point is herein the initial point of neck edge line.

(2) dense characteristic point range on model annular characteristic curve is found

The present invention adopts mean direction automatic Iterative method to find dense characteristic point range on model annular characteristic curve, to increase the robust performance of algorithm, is convenient to extract effective feature point range.In order to reduce the situation of iteration failure, the present invention has mainly carried out 2 iteration, namely carries out difference iteration from the principal direction of initial point and the negative direction of initial point principal direction, to prevent first time iteration failure.Detailed process is:

1), first set threshold value, obtain the feature point set after screening, setting initial point is V ₀, setting initial radium R ₀, direction, axis is setting initial point direction is designated as initial point principal direction should meet with V ₀for the center of circle, with R ₀for radius, to direction be a little averaged direction.

2), initial point is iterated to neck edge line point set J.

3) last some V in set J, is got _s, iteration radius is R _step, R _stepfrom arrive increase, independent increment is got wherein, with V _sfor the center of circle, with R _stepfor radius, to calculate in radius direction a little, be averaged direction, be set to allow R _stepfrom arrive increase, increasing step-length is repeatedly calculate obtain a set.Then, from V _sstart to find next some V along neighborhood point _i, obtain V _sto V _idirection if with angle is less than 60 degree, and R _stepcan reach and obtain maximal value, then by this point stored in set J in, repeat step 3); Otherwise, then step 4 is entered).

4) if search unsuccessfully, then empty set J, principal direction is changed into ${\stackrel{\&RightArrow;}{V}}_0=(-x_0,-y_0,{-z}_0),$ Then step 2 is entered)

Final acquisition target neck edge line.

Step 5, the line matching of neck edge and fairing

The present invention adopts NURBS SPL to carry out matching to target neck edge line.

After matching completes, the present invention recycles Laplace formula and carries out transformation calculations to the point on triangle gridding.

Wherein, Laplacian method theoretical equation is: Δ μ-μ _t=0.

Classical Laplace's equation is: ${\mathrm{\&Delta;}}_h\left(u\right)\left(p\right)=\underset{q\&Element;\mathrm{link}\left(p\right)}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}(u\left(q\right)-u\left(p\right)).$

Wherein, Δ _hfor Laplace operator.

The present invention applies classical Laplacian method algorithm, carries out transformation calculations, thus have each summit:

${\mathrm{\&Delta;}}_{\mathrm{Ei}}\left(p\right)=\underset{q\&Element;\mathrm{ver}\left(p\right)}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}(E_i\left(q\right)-E_i\left(p\right)).$

After the line matching of neck edge and fairing, the final neck edge line extracted is as shown in the black line of Figure 16.

Compared with prior art, the present invention can solve the problem that local guide line correctly cannot choose neck edge line, simultaneously the present invention proposes a kind of method of automatic extraction neck edge line, by carrying out Lookup protocol initial point in conjunction with the architectural feature of tooth self, and with the effect of matching and fairing.Adopt method of the present invention can obtain high-quality neck edge line more intelligently.

More than that better enforcement of the present invention is illustrated, but the invention is not limited to described embodiment, those of ordinary skill in the art also can make all equivalent variations or replacement under the prerequisite without prejudice to spirit of the present invention, and these equivalent distortion or replacement are all included in the application's claim limited range.

Claims (10)

1. be simply preced with a neck edge line drawing method of repairing grid model based on artificial tooth, it is characterized in that: comprising:

S1, tooth model to be scanned, and generate corresponding triangle grid model and point cloud model;

S2, adopt and based on curvature variation coefficient analysis method, overall tooth model is analyzed, and obtain curvature and the Curvature varying rate coefficient of curvature estimation point by the method for local secondary Function Fitting curved surface;

S3, respectively unique point screening is carried out to the singular triangular of triangle grid model and canonical triangle, and then according to the unique point generating feature line of screening;

S4, acquisition tooth axis, and pass through the initial point of tooth axis Lookup protocol neck edge line, then adopt mean direction automatic Iterative method from characteristic curve, filter out target neck edge line;

S5, matching and fairing are carried out to target neck edge line, thus complete the extraction of neck edge line.

2. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 1, it is characterized in that: described step S2, it comprises:

S21, using any point in triangle grid model as current point, calculate the normal direction of current point, the computing formula of the normal direction of described current point is:

$N_i=\frac{\underset{A\&Element;\mathrm{mesh}}{\mathrm{\&Sigma;}}{A}_i\&CenterDot;n_i}{\left|\right|\underset{A\&Element;\mathrm{mesh}}{\mathrm{\&Sigma;}}{A}_i\&CenterDot;n_i\left|\right|},$

Wherein, N _ithe per unit system of i-th neighborhood triangular plate of representative point is vowed, A _irepresent the area of i-th triangular plate, n _irepresent that the method for i-th triangular plate is vowed, mesh represents whole triangle gridding structure;

S22, be initial point with current point, method vows n _pfor z-axis, set up a local coordinate system;

Coordinate (the u of all neighborhood summits in the local coordinate system set up of S23, calculating current point _j, v _j, h _j);

S24, according to conversion after apex coordinate adopt least square fitting method obtain quadric surface;

S25, calculate quadric first fundamental quantity and second fundamental quantity, and then the curvature of estimation current point in quadric surface;

The Curvature varying rate coefficient of S26, calculating current point, the computing formula of described Curvature varying rate coefficient is:

Wherein, for cotangent weight operator, P is summit, and T is the triangular network at place, summit, and ver is summit on limit, Δ k _i(T) be the rate of change of place, summit triangle gridding;

S27, using another point in triangle grid model neighborhood as current point, calculate the normal direction of current point, then return step S22, until calculate in triangle grid model Curvature varying rate coefficient a little.

3. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 1, it is characterized in that: described step S3, it comprises:

S31, the point screened in canonical triangle on characteristic curve, described in the point that filters out meet the following conditions:

$\left\{\begin{array}{c}<\mathrm{\&Delta;}{E}_{\max },\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\max }^{\&RightArrow;}\left(p_i\right)><0\\ \left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\max }\left(p_i\right)\right|>\left|\underset{p_i\&Element;T}{\mathrm{\&Sigma;}}{k}_{\min }\left(p_i\right)\right|\end{array}\right.,$

Wherein, Δ E _maxfor maximum principal curvatures variable gradient, represent and triangle gridding maximum principal curvatures cut arrow sum, with represent the minimum principal curvatures sum on three summits on triangle gridding and maximum principal curvatures sum respectively;

S32, in singular triangular, screen point on characteristic curve by traversal and labelling method.

4. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 3, it is characterized in that: described step S32, it comprises:

S321, a selected singular triangular, then travel through the triangle on side, if adjacent side triangle is canonical triangle, then mark the end points be simultaneously present on the leg-of-mutton characteristic curve of canonical and singular triangular, traveling through three limits and marking proximal surface is the leg-of-mutton limit of canonical, at least marks a limit;

The number that S322, basis are labeled limit performs corresponding operation: if the number being labeled limit is 2, then connect point corresponding to 2 limits, and with connecting formed figure replacement singular triangular; If the number being labeled limit is 3, then add a point at the center of singular triangular, and this point is connected to other three end points of singular triangular; If the number being labeled limit is 1, then do not do any operation.

5. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 1, it is characterized in that: described step S4, it comprises:

S41, acquisition tooth axis;

S42, initial point by tooth axis Lookup protocol neck edge line;

S43, employing mean direction automatic Iterative method filter out target neck edge line from characteristic curve.

6. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 5, it is characterized in that: described step S41, it comprises:

The average coordinates of the frontier point on S411, calculating tooth model base, and the central point using the average coordinates calculated as tooth boundary surface;

S412, point according to whole tooth model, calculate the central point of whole tooth model;

S415, the straight line that formed using the central point of the central point and tooth boundary surface that connect tooth boundary surface are as tooth axis.

7. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 5, it is characterized in that: described step S42, it comprises:

S421, the feature intrinsic according to tooth, axis sets a threshold range, is then removed by the noise spot of top and bottom, tooth axis according to this threshold range;

S422, adopt sciagraphy the projecting characteristic points on tooth model on tooth axis, and record the quantity of respective coordinates subpoint in tooth axis;

S423, using the maximum point of respective coordinates subpoint quantity in tooth axis as the initial point of neck edge line.

8. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 5, it is characterized in that: described step S43, it comprises:

The threshold value that S431, basis are preset is screened characteristic curve, obtains the feature point set after screening, and remembers that neck edge line initial point is V ₀, initial radium is R ₀, direction, axis is neck edge line initial point direction is and neck edge line initial point principal direction is with V ₀for the center of circle, with R ₀for radius have the mean direction in a direction;

S432, neck edge line initial point is joined in neck edge line point set J as first unique point;

S433, get R _stepfor iteration radius, to gather last some V in J _sfor the center of circle, R _stepfor radius, calculate radius R _stepinterior the mean direction having a direction then radius R is allowed _stepwith for independent increment, from rise to recalculate thus obtain a set, wherein, for model average side length, α and β is regulated variable, λ _stepfrom increasing step number;

S434, from V _sstart to find next Average Iteration point V along neighborhood point _i, obtain V _sto V _idirection then judge with whether angle is less than 60 degree and R _stepobtain maximal value, if so, then by V _istored in set J, and return step S433, otherwise enter step S435;

S435, empty set J, principal direction is changed into then step S432 is returned, final acquisition target neck edge line.

9. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 1, it is characterized in that: described step S5, it comprises:

S511, employing NURBS SPL carry out matching to target neck edge line;

S512, employing Laplacian method algorithm, carry out transformation calculations to each summit i of the target neck edge line of matching, the formula of described transformation calculations is:

${\mathrm{\&Delta;}}_{\mathrm{Ei}}\left(p\right)=\underset{q\&Element;\mathrm{ver}\left(p\right)}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}(E_i\left(q\right)-E_i\left(p\right)),$

Wherein, w _pqfor Laplce's weight coefficient, E _iq () is the Curvature varying rate coefficient of q point, E _ip () is the Curvature varying rate coefficient of p point, Δ _eip () is the curvature gradients of p point, ver (p) is neck edge line point set.

10. a kind of neck edge line drawing method being simply preced with reparation grid model based on artificial tooth according to claim 1, it is characterized in that: described step S5, it comprises:

S521, employing NURBS SPL carry out matching to target neck edge line;

S522, employing Bi Pulasi Smoothing Algorithm, carry out fairing to the target neck edge line of matching.