CN112288886A - Tooth position arrangement method of accurate digital tooth model - Google Patents
Tooth position arrangement method of accurate digital tooth model Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T19/00—Manipulating 3D models or images for computer graphics
- G06T19/20—Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
- A61C7/002—Orthodontic computer assisted systems
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
- A61C7/002—Orthodontic computer assisted systems
- A61C2007/004—Automatic construction of a set of axes for a tooth or a plurality of teeth
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2219/00—Indexing scheme for manipulating 3D models or images for computer graphics
- G06T2219/20—Indexing scheme for editing of 3D models
- G06T2219/2004—Aligning objects, relative positioning of parts
Abstract
The invention discloses a tooth position arrangement method of an accurate digital tooth model. Carrying out digital dental three-dimensional model processing and CBCT data modeling to obtain a tooth model, a basic bone model of a maxilla and a basic bone model of a mandible; establishing a tooth movement local coordinate system and extracting tooth model characteristic points; determining an ideal dental arch line according to the characteristic points; processing the tooth model to obtain the three-dimensional position of an ideal dental arch line; and adjusting the position of the tooth root in a tooth movement local coordinate system according to the position relation between the tooth root of the tooth model and the basic bone model of the maxilla of the upper jaw and the lower jaw, and correcting the position of the tooth to obtain the final tooth position. The invention extracts the characteristics of the CBCT volume data and the three-dimensional dental jaw model, and simultaneously considers the accurate positions of the dental crown and the dental root, so that the tooth arrangement result is accurate.
Description
Technical Field
The invention belongs to a tooth model processing method in the field of oral cavity digital model processing, and particularly relates to a tooth position arrangement method of an accurate digital tooth model.
Technical Field
The computer simulation of tooth arrangement is one of key technologies for tooth correction, and the tooth digital models are arranged by using the computer technology, so that on one hand, the analysis of the orthodontic movement direction of each tooth in a three-dimensional space can be used as a reference for a doctor to formulate a treatment plan, and on the other hand, the visual display of the arrangement process of the digital three-dimensional tooth models can be carried out, and the correction result can be known in advance.
Cone Beam Computed Tomography (CBCT) is another imaging technique that is increasingly used in orthodontics. Compared with a panoramic picture, CBCT scanning can accurately display the true angle and three-dimensional inclination of the tooth root and the structure of the tooth in a ratio of 1: 1. The CBCT can clearly develop the soft and hard tissue structure of the jaw part of the tooth, meets the three-dimensional measurement requirement of the tooth, and gradually becomes an important data acquisition means for personalized correction. CBCT combines the intraoral scanning technique of digitization, can extract alveolar bone, root of a tooth and crown information completely, provide the basis for accurate digital tooth arrangement.
The prior art lacks a way and process to accurately digitize the tooth position placement of the tooth model.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a precise and safe tooth position arrangement method of a digital tooth model.
The technical scheme of the invention is as follows:
step 1) carrying out digital dental three-dimensional model processing and CBCT data modeling to obtain a tooth model MT, a basic bone model UJaw of a maxilla and a basic bone model Ljaw of a mandible;
step 2) establishing a tooth movement local coordinate system and extracting tooth model MT characteristic points;
step 3) determining an ideal dental arch line according to the characteristic points;
step 4) processing the tooth model MT to obtain the three-dimensional position of an ideal dental arch line; and then according to the position relation between the tooth root of the tooth model MT and the basic bone model of the maxilla of the upper jaw and the lower jaw, the position of the tooth root is adjusted in a tooth movement local coordinate system, the position of the tooth is corrected, and the final accurate tooth position is obtained.
The step 1) is as follows:
1.1) carrying out tooth segmentation on the digital jaw three-dimensional model with known input, and carrying out tooth abutment surface restoration to obtain a complete crown model set MT0 of each tooth; the digital dental three-dimensional model is a digital model in a computer.
1.2) CBCT data processing, namely obtaining a tooth root image through CBCT, performing three-dimensional reconstruction, obtaining a complete tooth root model set MT1 of each tooth, and performing fusion restoration on corresponding teeth in the sets MT0 and MT1 to obtain a tooth model set MT containing a complete tooth crown and a tooth root;
1.3) processing of the dental jaw bone by CBCT data, acquiring cortical bone partial images of the upper and lower dental jaw bones through CBCT, and performing three-dimensional reconstruction to acquire a basic bone model UJaw of the upper dental jaw bone and a basic bone model Ljaw of the lower dental jaw bone.
In step 2), the tooth movement local coordinate system includes 4 three-dimensional vectors Xi, Yi, Zi, Oi, and specifically:
for each tooth model Mti in the tooth model set MT, the buccal/lingual direction of the tooth is taken as the Xi axis direction, the mesial/distal direction of the tooth is taken as the Yi axis direction, the long axis direction of the tooth body of the tooth is taken as the Zi axis direction, and the geometric center of the tooth model Mti is taken as the origin Oi of the tooth movement local coordinate system.
The tooth model MT feature extraction in the step 2) specifically comprises the step of extracting feature points for each tooth, wherein the feature points are specifically extracted by taking the central point of the tooth crown buccal side part of the tooth as the feature points.
The step 3) of determining the ideal dental arch line specifically comprises the following steps:
3.1) determining the plane and coordinates of the jaw:
determining a mesial adjacent point of the middle incisor on the upper jaw at two sides and a mesial cheek cusp of the first molar at two sides, and forming a dental jaw plane through the three points;
3.2) constructing a horizontal-vertical coordinate system OXY on a dental jaw plane;
3.2.1) projecting the geometric central point of the whole dental jaw including the upper jaw and the lower jaw onto a dental jaw plane as an origin O of a horizontal vertical coordinate system;
3.2.2) projecting a straight line containing a connecting line Lm between two first premolars of the whole dentognathic jaw of the upper and lower jaws onto a dentognathic plane as an X axis;
3.2.3) projecting a straight line which is perpendicular to the connecting line Lm and passes through the middle point between the incisors on the two sides of the upper jaw onto the dental plane as a Y axis;
3.3) firstly obtaining the distance d1 between characteristic points Fai of second premolars on the left side and the right side of the lower jaw, and drawing a circle by taking the distance d1 as a diameter and taking an origin O of a horizontal, vertical and vertical coordinate system as a center of the circle; drawing a straight line on each of the left and right sides of the jaw as a posterior segment initial arch such that an average value of distances from the straight line to characteristic points Fai of all anterior molars and all molars on the left and right sides of the upper and lower jaws is the shortest; the two rear-section initial dental arches are intersected with the circle at two intersection points respectively, the intersection point with the larger Y-axis coordinate in the two intersection points is used as an end point, two end points corresponding to the two rear-section initial dental arches are respectively CPl and CPr, the circle is divided into two circular arc parts by the two end points CPl and CPr, and the part with the shorter circular arc is used as the front-section initial dental arch;
an initial ideal arch line C0 is constructed at the jaw plane, the expression being as follows:
wherein k and b respectively represent the slope and intercept of a straight line of the initial dental arch of the posterior segment; d1 represents the distance between the characteristic points Fai of the second premolars on the left and right sides of the lower jaw, and x and y represent the horizontal and vertical coordinates on the horizontal and vertical coordinate system OXY respectively; CPl and CPr are two endpoints respectively; the x-axis component of cpl.x, representing the coordinates of endpoint CPl, the abscissa of endpoint CPl;
3.4) fine adjustment of the arch wire shape to obtain the final ideal arch wire shape;
the Hermite curve fitting is firstly carried out on the initial ideal dental arch line C0, and then the curve-fitted initial ideal dental arch line C0 is adjusted through the position of a control point.
In the step 4), the method specifically comprises the following steps:
4.1) in the tooth model set MT, determining the three-dimensional position of an ideal dental arch line of the upper jaw and the lower jaw according to the shape of the ideal dental arch line, wherein the three-dimensional position comprises the front-back position and the vertical position of the dental arch line;
firstly, determining the front and back positions of upper and lower anterior teeth, and then translating and rotating an ideal dental arch line on a dental jaw plane to enable the front part of the ideal dental arch line of the upper and lower jaws to be consistent with the front and back positions of the upper and lower anterior teeth;
then determining the vertical position of the dental arch line, taking the plane of the upper jaw as a horizontal plane, translating the ideal dental arch line in the upper jaw upwards, wherein the translation distance is the distance from the central point of the crown of the middle incisor in the upper jaw to the incisal margin of the middle incisor in the upper jaw; the ideal arch line in the lower jaw translates downward by the distance of the crown center point of the mandibular central incisor to the incisal margin of the mandibular central incisor minus 1 mm.
4.2) in the tooth moving local coordinate system, arranging two upper and lower middle incisors firstly, and arranging the lower jaw and then the upper jaw;
4.3) adjusting the inclination and the axial inclination of the teeth according to the position relation between the tooth root of the tooth model Mti and the basic bone model of the maxilla of the upper jaw and the lower jaw:
inclination adjustment: traversing each tooth, checking the position relation between the tooth root and the inner side and the outer side of the fundamental bone model of the jaw bone of the tooth, and adjusting the position of the tooth root of the tooth model Mti to enable the tooth root to be positioned in the middle of the inner side and the outer side of the jaw bone of the tooth;
and adjusting the inclination of the shaft, traversing all the teeth, and adjusting the root position of the tooth model Mti to enable the long shafts of the tooth bodies between the adjacent teeth to be parallel.
The tooth inclination is the included angle between the tooth long axis in the local coordinate buccolingual direction and the normal direction of the dental jaw plane.
The tooth axis inclination is the included angle between the tooth long axis and the tooth jaw plane in the direction of the near-far center of the local coordinate of the tooth long axis.
The invention carries out the generation method of the ideal arch line by carrying out the characteristic extraction on the CBCT volume data and the three-dimensional dental model, and processes the positions and the arrangement of the teeth and the tooth roots to be close to the real positions and shapes by arrangement, so that the tooth arrangement result is accurate and effective.
The invention simultaneously considers the accurate positions of the dental crowns and the dental roots, and improves the safety and the accuracy of the tooth arrangement result.
According to the invention, accurate tooth root information and tooth jaw bone information are obtained by combining the digital tooth jaw three-dimensional model and CBCT data, and meanwhile, an accurate ideal dental arch line shape is constructed for tooth arrangement and is processed to obtain accurate tooth and tooth root accurate positions.
The invention has the following beneficial effects:
the invention adds the tooth root into the process of tooth position arrangement, constructs an accurate ideal arch line shape for tooth arrangement, and considers the position relation between the tooth root and the tooth jaw bone in the process of tooth arrangement, so that the tooth arrangement result is more accurate and is closer to the condition of a real tooth.
Drawings
FIG. 1 is an overall process flow diagram of the present invention;
FIG. 2 is a flow chart of a method of determining an accurate dental arch according to the present invention;
FIG. 3 is a diagram of the effect of the initial ideal arch line C0 on the dental plane of the present invention;
FIG. 4 is a flow chart of the present invention for creating an ideal dental arch;
fig. 5 is a flow chart of a tooth placement method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples.
The embodiment of the invention is concretely as follows:
step 1) digital dental three-dimensional model processing and CBCT model modeling. Obtaining accurate dental crown model data by segmenting and processing the digital dental model; the CBCT data comprises tooth root information and alveolar bone information, and tooth root model data and alveolar bone model data are respectively obtained by extracting relevant characteristics in the CBCT; accurate dental crown model data obtained through digital dental jaw treatment and dental root model data obtained in CBCT are combined to obtain accurate and complete dental model data. The specific operation method comprises the following steps:
1.1, the digital tooth jaw three-dimensional model is subjected to tooth segmentation and tooth adjacent surface restoration, and a complete crown model set MT0 of each tooth is obtained.
1.2, processing CBCT data, acquiring a tooth root partial image through CBCT, performing three-dimensional reconstruction, acquiring a complete tooth root model set MT1 of each tooth, and performing fusion restoration on corresponding teeth in the sets MT0 and MT1 to obtain a tooth model set MT containing a complete tooth crown and a tooth root;
and 1.3, processing the jaw bone of the tooth by CBCT data, acquiring cortical bone partial images of the upper and lower jaw bones by CBCT, performing three-dimensional reconstruction, and acquiring a basic bone model UJaw of the upper jaw bone and a basic bone model Ljaw of the lower jaw bone.
Step 2) tooth model feature extraction, which comprises the steps of establishing a moving tooth movement local coordinate system for each tooth and extracting the features of the teeth, wherein the tooth movement local coordinate system defines the direction of the teeth during movement or rotation, and then each tooth is moved and transformed according to an axis in the tooth movement local coordinate system; tooth feature extraction is to extract feature points of the maxillofacial surface for subsequent alignment with an ideal dental arch line. The concrete mode is as follows:
2.1 establishing a tooth movement local coordinate system, defining tooth three-dimensional directions and centers, and defining 4 three-dimensional vectors Xi, Yi, Zi and Oi for a given tooth model Mti. Xi is defined as the buccal/lingual direction of the tooth, Yi is defined as the mesial/distal direction of the tooth, Zi is defined as the tooth's long axis direction, Oi is the origin of the tooth's moving local coordinate system, and the extraction method is to calculate the geometric center of the tooth model Mti and determine it as Oi.
2.2 given a tooth model Mti, first judge the crown portion and then take the center of the facial portion of the crown as the feature point Fai.
Step 3) determining an ideal dental arch line, wherein the method uses simulation and digitization interaction, the specific inventive content comprises the construction of an initial ideal dental arch line according to the characteristics of the dental jaw, the fine adjustment of the shape of the dental arch line and the position adjustment of the dental arch line, and the specific implementation mode is as follows:
3.1 determining a dental plane and coordinates, determining approximate middle adjacent points of upper jaw middle incisors on two sides and approximate middle cheek cusps of first molars on two sides, and forming the dental plane by the 3 points;
3.2 constructing a horizontal-vertical coordinate system OXY on the dental jaw plane for drawing dental arch lines. Projecting the central point of the whole dental jaw onto a dental jaw plane as an origin O of a vertical coordinate system, projecting a straight line formed by connecting lines Lm of two first premolars of the whole dental jaw onto the dental jaw plane as an X-axis of the coordinate system, projecting a straight line which is perpendicular to the Lm and formed by connecting lines between incisors on two sides of the upper dental jaw onto the dental jaw plane as a Y-axis of the coordinate system, and finally correcting the Y-axis by taking the X-axis of the coordinate system as a basis to ensure that the Y-axis is perpendicular to the X-axis.
3.3 construct the initial ideal arch line C0 on the jaw plane.
3.3) firstly obtaining the distance d1 between characteristic points Fai of second premolars on the left side and the right side of the lower jaw, and drawing a circle by taking the distance d1 as a diameter and taking an origin O of a horizontal, vertical and vertical coordinate system as a center of the circle; drawing a straight line on each of the left and right sides of the jaw as a posterior segment initial arch such that an average value of distances from the straight line to characteristic points Fai of all anterior molars and all molars on the left and right sides of the upper and lower jaws is the shortest; the two rear-section initial dental arches are intersected with the circle at two intersection points respectively, the intersection point with the larger Y-axis coordinate in the two intersection points is used as an end point, two end points corresponding to the two rear-section initial dental arches are respectively CPl and CPr, the circle is divided into two circular arc parts by the two end points CPl and CPr, and the part with the shorter circular arc is used as the front-section initial dental arch;
the two posterior segment initial dental arches are in a bilateral symmetry straight line structure, and the straight lines are expressed as follows:
y＝±kx+b
wherein, the slope of the rear section straight line on the left side is k, the slope of the rear section straight line on the right side is-k, and b represents the intercept of the initial dental arch of the rear section.
The posterior initial arch is obtained in the following operating manner:
a) a set of target points Faproj is obtained,
calculating the projection on the dental plane for all characteristic points Fai of the premolars and molars on the right side of the dental jaw, and adding a target point set Faproj;
calculating the projection on the dental plane for all the characteristic points of the premolars and the molars on the left side of the dental jaw, and adding a target point set after taking the point which is symmetrical to the Y axis of the horizontal, vertical and vertical coordinate system OXY;
b) performing least square fitting on the target point set Faproj, and giving the target function of y-kx + b, k>0, obtaining the optimal solution
And obtaining the straight line of the initial dental arch of the posterior segment.
And after the straight line of the rear-section initial dental arch is finished, respectively calculating the intersection point set of the left and right straight lines of the rear-section initial dental arch and the circle corresponding to the front-section initial dental arch, recording the intersection point of the left rear-section initial dental arch and the straight line as { CPl1, CPl2}, and recording the intersection point of the right rear-section initial dental arch and the straight line as { CPr1, CPr2 }. The intersection point corresponding to the maximum y value of the left and right intersection points is taken, and finally the points CPl and CPr are obtained.
An initial ideal arch line C0 is constructed at the jaw plane, the expression being as follows:
fig. 3 illustrates the basic shape of the initial ideal arch wire C0.
3.4 Fine adjustment of the arch wire shape, including Hermite curve fitting of the arch wire, and adjustment of the arch wire by control point position.
First, an x-direction range | x | ≦ δ is given based on the initial ideal arch line C0. Where δ >0 is a given parameter, related to the maximum width of the entire arch, generally δ needs to be greater than 1/2 of the maximum width.
Then, sampling is carried out at equal intervals in the range of | x | < delta > and substituting into the expression of the initial ideal dental arch line C0 to calculate the y value, and finally a sampling point set CP is obtained; and performing Heimite curve fitting on points in the sampling point set CP to obtain an arch line shape C1 in a Hermite curve form, then adjusting the vertical projection and the lateral projection of the arch line by taking the arch line shape C1 as a basic arch, and respectively completing the construction of the upper arch CU and the lower arch CL by adding and moving control points.
3.4.1 Fine adjustment procedure for dental arch wire vertical projection:
step 1: switching the visual angle to the overlook of the jaw plane, adding a new control point CPi on the dental arch line, and generating the same control point CPi1 on the symmetrical side;
step 2: moving the control point CPi at one side, and symmetrically moving the control point CPi1 at the other side, wherein the moving direction of the control point CPi at one side is only capable of moving on the dental jaw plane;
step 3: updating the dental arch line again by using Hermite interpolation;
step 4: repeating steps 1 to 3 until fine adjustment of the dental arch is completed.
3.4.2 Fine adjustment procedure for the lateral projection of the dental arch wire is as follows:
step 1: switching the visual angle to the left side view or the right side view of the dental jaw plane, adding a new control point CPj on the dental arch line, and simultaneously generating the same control point CPj1 on the symmetrical side;
step 2: one side CPj is moved and the control point CPj1 on the other side is moved symmetrically, the control point CPj on one side is moved only in the direction perpendicular to the plane of the jaw;
step 3: updating the dental arch line again by using Hermite interpolation;
step 4: repeating steps 1 through 3 until fine adjustment of the dental arch is completed.
Step 4) carrying out tooth arrangement operation on the tooth model MT according to the ideal dental arch wire and the tooth model characteristics to obtain an ideal dental crown position and direction P0, wherein the specific implementation mode is as follows:
4.1 determining the three-dimensional position of the ideal dental arch of the upper jaw and the lower jaw. Including determining the anterior-posterior position of the arch wire and the vertical position of the arch wire.
Determining the front and back positions of the upper and lower anterior teeth, and then translating and rotating the dental arch line on the dental jaw plane to enable the front parts of the dental arch line of the upper and lower jaws to be consistent with the front and back positions of the ideal upper and lower anterior teeth.
Then determining the dental jaw plane as a horizontal plane, and determining the distance of the upward translation of the upper jaw dental arch line as the distance from the central point of the upper middle incisor crown to the incisal edge. The distance of the lower jaw arch line translating downwards is the distance between the central point of the lower incised crown and the incisal margin of the lower incised tooth minus 1 mm.
4.2 arranging two middle incisors of the upper jaw and the lower jaw, enabling the adjacent points of the middle incisors on the two sides of the upper jaw and the lower jaw to be positioned at the central point of an ideal dental arch line, enabling Fai characteristic points of teeth to be on the ideal dental arch line, and adjusting the near-far direction of each tooth from the view angle of the maxillofacial surface to enable the near-far direction of each tooth to be consistent with the tangential direction of the ideal dental arch line.
4.3 lower jaw first and upper jaw second. The other teeth are arranged from front to back in sequence so that the Fai characteristic point of the other teeth is on the ideal dental arch line, and the mesial-distal direction of each tooth is adjusted from the view point of the maxillofacial surface so as to be consistent with the tangential direction of the ideal dental arch line.
4.4 according to the normal dental jaw angle data, the inclination and the shaft inclination of the teeth are adjusted, so that the inclination and the shaft inclination of the teeth accord with the normal data range.
a) And (3) adjusting the inclination, traversing all the teeth, checking the position relation between the tooth roots and the inner side and the outer side of the dental bone, and enabling the tooth roots to be positioned in the middle of the inner side and the outer side of the dental bone within the allowable range of the data in the table 1.
b) And (3) adjusting the inclination of the axis, and traversing all the teeth to enable the long axes of the tooth bodies between the adjacent teeth to be parallel within the allowable range of the data in the table 1.
Therefore, the invention combines the digital tooth jaw three-dimensional model and the CBCT data to obtain accurate tooth root information and tooth jaw bone information, processes to obtain accurate ideal dental arch line shape for tooth arrangement simulation, and obtains accurate tooth and tooth root accurate positions.
Claims (6)
1. A method for accurately arranging tooth positions of a digital tooth model, comprising the steps of:
step 1) carrying out digital dental three-dimensional model processing and CBCT data modeling to obtain a tooth model MT, a basic bone model UJaw of a maxilla and a basic bone model Ljaw of a mandible;
step 2) establishing a tooth movement local coordinate system and extracting tooth model MT characteristic points;
step 3) determining an ideal dental arch line according to the characteristic points;
step 4) processing the tooth model MT to obtain the three-dimensional position of an ideal dental arch line; and adjusting the position of the tooth root in a tooth movement local coordinate system according to the position relation between the tooth root of the tooth model MT and the basic bone model of the maxilla of the upper jaw and the lower jaw, correcting the position of the tooth and obtaining the final tooth position.
2. A method for accurately placing tooth positions on a digital tooth model according to claim 1, wherein: the step 1) is as follows:
1.1) carrying out tooth segmentation on the digital tooth jaw three-dimensional model, and carrying out tooth abutment surface restoration to obtain a complete dental crown model set MT0 of each tooth;
1.2) CBCT data processing, namely obtaining a tooth root image through CBCT, performing three-dimensional reconstruction, obtaining a complete tooth root model set MT1 of each tooth, and performing fusion restoration on corresponding teeth in the sets MT0 and MT1 to obtain a tooth model set MT containing a complete tooth crown and a tooth root;
1.3) processing of the dental jaw bone by CBCT data, acquiring cortical bone partial images of the upper and lower dental jaw bones through CBCT, and performing three-dimensional reconstruction to acquire a basic bone model UJaw of the upper dental jaw bone and a basic bone model Ljaw of the lower dental jaw bone.
3. A method for accurately placing tooth positions on a digital tooth model according to claim 1, wherein: in the step 2), the tooth movement local coordinate system specifically comprises:
for each tooth model Mti in the tooth model set MT, the buccal/lingual direction of the tooth is taken as the Xi axis direction, the mesial/distal direction of the tooth is taken as the Yi axis direction, the long axis direction of the tooth body of the tooth is taken as the Zi axis direction, and the geometric center of the tooth model Mti is taken as the origin Oi of the tooth movement local coordinate system.
4. A method for accurately placing tooth positions on a digital tooth model according to claim 1, wherein: the tooth model MT feature extraction in the step 2) specifically comprises the step of extracting feature points for each tooth, wherein the feature points are specifically extracted by taking the central point of the tooth crown buccal side part of the tooth as the feature points.
5. A method for accurately placing tooth positions on a digital tooth model according to claim 1, wherein: the step 3) of determining the ideal dental arch line specifically comprises the following steps:
3.1) determining the plane and coordinates of the jaw:
determining a mesial adjacent point of the middle incisor on the upper jaw at two sides and a mesial cheek cusp of the first molar at two sides, and forming a dental jaw plane through the three points;
3.2) constructing a horizontal-vertical coordinate system OXY on a dental jaw plane;
3.2.1) projecting the central point of the whole dental jaw containing the upper jaw and the lower jaw onto a dental jaw plane as an origin O of a horizontal vertical coordinate system;
3.2.2) projecting a straight line containing a connecting line Lm between two first premolars of the whole dentognathic jaw of the upper and lower jaws onto a dentognathic plane as an X axis;
3.2.3) projecting a straight line which is perpendicular to the connecting line Lm and passes through the middle point between the incisors on the two sides of the upper jaw onto the dental plane as a Y axis;
3.3) firstly obtaining the distance d1 between characteristic points Fai of second premolars on the left side and the right side of the lower jaw, and drawing a circle by taking the distance d1 as a diameter and taking an origin O of a horizontal, vertical and vertical coordinate system as a center of the circle; drawing a straight line on each of the left and right sides of the jaw as a posterior-segment initial arch such that an average value of distances from the straight line to characteristic points Fai of all anterior molars and all molars on both sides of the upper and lower jaws is the shortest; the two rear-section initial dental arches are intersected with the circle at two intersection points respectively, the intersection point with the larger Y-axis coordinate in the two intersection points is used as an end point, two end points corresponding to the two rear-section initial dental arches are respectively CPl and CPr, the circle is divided into two circular arc parts by the two end points CPl and CPr, and the part with the shorter circular arc is used as the front-section initial dental arch;
an initial ideal arch line C0 is constructed at the jaw plane, the expression being as follows:
wherein k and b respectively represent the slope and intercept of a straight line of the initial dental arch of the posterior segment; d1 represents the distance between the characteristic points Fai of the second premolars on the left and right sides of the lower jaw, and x and y represent the horizontal and vertical coordinates on the horizontal and vertical coordinate system OXY respectively; CPl and CPr are two endpoints respectively; the x-axis component of cpl.x, representing the coordinates of endpoint CPl, the abscissa of endpoint CPl;
3.4) fine adjustment of the arch wire shape to obtain the final ideal arch wire shape;
the Hermite curve fitting is firstly carried out on the initial ideal dental arch line C0, and then the curve-fitted initial ideal dental arch line C0 is adjusted through the position of a control point.
6. A method for accurately placing tooth positions on a digital tooth model according to claim 1, wherein: in the step 4), the method specifically comprises the following steps:
4.1) in the tooth model set MT, determining the three-dimensional position of an ideal dental arch line of the upper jaw and the lower jaw according to the shape of the ideal dental arch line, wherein the three-dimensional position comprises the front-back position and the vertical position of the dental arch line;
4.2) in the tooth moving local coordinate system, arranging two upper and lower middle incisors firstly, and arranging the lower jaw and then the upper jaw;
4.3) adjusting the inclination and the axial inclination of the teeth according to the position relation between the tooth root of the tooth model Mti and the basic bone model of the maxilla of the upper jaw and the lower jaw:
inclination adjustment: traversing each tooth, checking the position relation between the tooth root and the inner side and the outer side of the fundamental bone model of the jaw bone of the tooth, and adjusting the position of the tooth root of the tooth model Mti to enable the tooth root to be positioned in the middle of the inner side and the outer side of the jaw bone of the tooth;
and adjusting the inclination of the shaft, traversing all the teeth, and adjusting the root position of the tooth model Mti to enable the long shafts of the tooth bodies between the adjacent teeth to be parallel.
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