CN110025387B - Automatic generation method of digital dental ideal model - Google Patents
Automatic generation method of digital dental ideal model Download PDFInfo
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- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
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- A—HUMAN NECESSITIES
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- 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
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Abstract
The invention discloses an automatic generation method of a digital dental ideal model. The invention determines the ideal dental arch characteristic line of a patient by extracting the characteristics of the dental model, constructs a tooth movement control data structure at the same time, arranges the teeth to the position and the shape of the ideal dental arch by an automatic arrangement algorithm, and adjusts the angle of the teeth according to the perfect dentition angle standard after determining the position of the target teeth so as to meet the characteristic requirements of the ideal dental arch. The invention can automatically finish the alignment and adjustment of the digital dental ideal dentition, and improves the efficiency of the formulation of the personalized ideal position scheme of the patient.
Description
Technical Field
The invention belongs to the field of digital models, and particularly relates to an automatic generation method of a digital dental ideal model.
Technical Field
The generation of the ideal position of the digital dental jaw is based on an individual digital dental jaw model of a patient, an individual ideal position scheme of the patient is specified through analysis and diagnosis of a case, each tooth of the patient is rearranged, and the ideal position of the dental jaw is finally generated in the process of arrangement by considering the standard of the ideal jaw and the actual condition of the patient in orthodontics. Under the existing conditions, the ideal position of the jaw is finally determined by artificially modifying the position of each tooth, which is not accurate enough and wastes time and labor.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention discloses an automatic generation method of an ideal digital dental position.
The technical scheme of the invention is as follows:
step 1) collecting all target teeth to be moved and adjusted of the digital three-dimensional dental model, selecting a plurality of target teeth in the digital three-dimensional dental model to extract feature points to obtain three different control point sets, and respectively obtaining an ideal arch feature line CFa of a occlusal surface, an ideal arch feature line CFf of a buccal side surface of the dental crown and an ideal arch feature line CFg of a gravity center of the dental crown according to the three control point sets.
Step 2) extracting respective characteristic points of all target teeth in the digital dental three-dimensional model respectively and constructing a corresponding position data set M:
M＝{PFa，PFf，PFg}
PFa is a tooth maxillofacial feature point, the tooth maxillofacial feature point of incisor is located at the midpoint of incisor cutting end in the direction of near-far center, the tooth maxillofacial feature point of cuspid is located at the cuspid, and the tooth maxillofacial feature points of premolars and molars are located in the central socket of tooth maxillofacial feature point.
PFf is the characteristic point of the facial side of the tooth crown, the characteristic points of the facial side of the tooth crown of incisors, canine teeth and premolars are all positioned at the central point of the facial part of the tooth crown, the characteristic point of the facial side of the tooth crown of premolars is positioned at the midpoint of the upper and lower connecting lines of the facial sulcus; PFg is the center of gravity of the crown.
Step 3) according to the three ideal dental arch characteristic lines obtained in the step 1) and the position data set M obtained in the step 2), sequentially carrying out position movement adjustment on each target tooth, wherein the position adjustment on one target tooth specifically comprises the following steps:
firstly, extracting a point closest to a tooth maxillofacial feature point PFa of a target tooth in an ideal arch feature line CFa of the occlusal surface, extracting a point closest to a tooth crown facial feature point PFf of the target tooth in an ideal arch feature line CFf of a tooth crown facial side, extracting a point closest to a tooth crown gravity center point PFg of the target tooth in a tooth crown arrangement arch feature line CFg, and generating a movement control point set K according to the three extracted points; and then, matching the position data set M with the movement control point set K by adopting an ICP (inductively coupled plasma) algorithm to obtain a transformation matrix of the target tooth, and updating the position of the target tooth according to the transformation matrix, thereby finishing the position adjustment of the target tooth.
Step 4) adjusting the angle of the target tooth after the position adjustment according to the ideal arch characteristic line CFg of the center of gravity of the dental crown, which comprises the following steps:
4.1) taking the direction vertical to the occlusal plane as the Z-axis direction of the global coordinate plane OXY, establishing a local coordinate system (Xi, Yi, Z) of each target tooth, wherein the OXiYi plane of the local coordinate system is parallel to the occlusal plane, and the establishment of the local coordinate system is specifically as follows:
and calculating to obtain the position of the crown gravity center point of the target tooth, taking the point closest to the crown gravity center point on the crown arrangement arch characteristic line CFg as a reference point CFgi, taking the tangential direction of the reference point CFgi as the Yi axis of a local coordinate system, taking the direction vertical to the Yi axis as the Xi axis of the local coordinate system, and taking the Z axis of the local coordinate system parallel to the Z axis of the global coordinate plane OXY.
4.2) calculating the near-far middle inclination angle of the target tooth, wherein the formula is as follows:
where θ 2 represents the mesial-distal tilt angle, and proj (YiOZ) (Zi) represents a projection vector of the tooth principal axis Zi of the i-th target tooth on the local coordinate plane YiOZ.
4.3) calculating the torque angle of the target tooth, wherein the formula is as follows:
where θ 3 represents a torque angle, and proj (XiOZ) and (Zi) represents a projection vector of a tooth principal axis Zi of the i-th target tooth on the local coordinate plane XiOZ.
And 4.4) carrying out the inclination, torsion and cheek-tongue side torque adjustment on the angle of the target tooth according to the inclination angle and the torque angle.
And 5) repeating the steps 3) -4) until the position and angle adjustment of all the target teeth is completed, so as to obtain the digital dental ideal model. In specific implementation, the digital dental ideal model is further input into a 3D printer, and the digital dental ideal model is printed out by the 3D printer.
The step 4.4) is specifically as follows:
4.4.1) adjusting the mesial-distal inclination angle of the target tooth according to the mesial-distal inclination angle of the standard tooth occlusion.
4.4.2) on the premise of adjusting the near-far and middle-distance inclination angle of the target tooth, adjusting the torsion angle of the target tooth around the self main shaft, specifically:
using the line connecting the near middle point TPm and the far middle point TPd of the target tooth as the first vector
The tangent vector at the reference point CFgi is taken as the second vector
Calculating a first vector
And second vector
Projecting an included angle formed under the global coordinate plane OXY, and adjusting the rotation angle of the target tooth around the main axis of the target tooth according to the included angle to enable the first vector
And second vector
And (4) parallel to complete the adjustment of the torsion angle of the target tooth around the self main shaft.
4.4.3) adjusting the torque angle of the target tooth according to the labial (buccal) lingual inclination angle of the standard tooth occlusion.
The calculation method of the crown gravity center point PFg in the step 2) is as follows:
wherein, PFgi represents the crown gravity center point of the ith target tooth, j represents the ordinal number of the triangular patch of the single target tooth model, n represents the total number of the triangular patches, m (fj) represents the gravity center point of the jth triangular patch, and area (fj) the area of the jth triangular patch.
The target teeth selected by the three control point sets in the step 1) are the same, but the positions of feature points of each extracted target tooth are different, and the target teeth comprise left and right incisors, left and right cuspids and left and right first molars.
The characteristic points selected by the control point set of the ideal arch characteristic line CFa of the occlusal surface are respectively as follows: the incisor ends (incisor occlusal ends) of the incisors are positioned at the midpoint of the mesial direction, the cuspid of the cuspid, and the center of the maxillofacial central socket of the first molar.
The characteristic points selected from the control point set of the ideal arch characteristic line CFg of the center of gravity of the dental crown are respectively as follows: the center of gravity of the crown portion of each target tooth.
The characteristic points selected from the control point set of the ideal arch characteristic line CFf on the side surface of the facial side of the crown are respectively as follows: the control points on incisors and canine teeth are positioned at the center of the crown surface of the tooth, and the control point of molar teeth is positioned at the midpoint of the upper and lower connecting lines of the buccal sulcus; and carrying out interpolation fitting on each control point set by adopting a Hermit interpolation method to obtain a corresponding ideal dental arch characteristic line.
According to the method, a tooth position data set for movement control is constructed simultaneously according to ideal dental arch characteristic lines, and teeth are arranged to the position and the shape of an ideal dental arch through an automatic arrangement method; after the position of the target tooth is determined, the angle of the tooth is adjusted according to the dentition angle standard, and the dental model under the ideal arrangement condition is automatically generated and output, so that the characteristic requirement of an ideal dental jaw is met.
The invention has the following beneficial effects:
the digital tooth arrangement device can automatically complete the alignment and adjustment of the digital tooth jaw ideal tooth row, improves the tooth arrangement efficiency, improves the tooth arrangement accuracy through accurate angle calculation, and simultaneously provides reference for a personalized ideal position scheme of the tooth arrangement.
Drawings
FIG. 1 is an overall process flow diagram of the present invention;
FIG. 2 is a flow chart of a tooth alignment sequence of the present invention;
FIG. 3 is a flowchart of an angle adjustment method according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples.
As shown in FIG. 1, the automatic generation method of the ideal model of the dental jaw of the present invention comprises the following steps:
step 1) extracting the characteristics of the digitalized dental three-dimensional model, determining an ideal dental arch characteristic line of the model, firstly determining an ideal dental arch characteristic line SL of the lower jaw of the patient, and then determining an ideal dental arch characteristic line SU of the upper jaw of the patient. The method comprises the steps of obtaining an ideal dental arch characteristic line, firstly extracting shape characteristics of a patient's dental jaw, wherein the characteristics can be obtained by fitting characteristic points on each tooth or a plurality of teeth in the dental jaw, or can be obtained by extracting characteristics of gingival tissues of a digital dental jaw three-dimensional model, and the characteristic points form a control point set for generating the ideal dental arch characteristic line.
The lower jaw ideal arch characteristic line SL and the upper jaw ideal arch characteristic line SU include three characteristic lines, respectively, an occlusal ideal arch characteristic line CFa, a crown buccal side ideal arch characteristic line CFf, and a crown center of gravity ideal arch characteristic line CFg.
The ideal arch characteristic line CFa of the occlusal surface represents the ideal arch of the patient's occlusal surface. The CFa control point set consists of six points, namely, left and right incisor control points, left and right cuspid control points, and left and right first molar control points, and for an incisor, the control point positions thereof are located at the midpoints in the mesial-distal direction of the incisor cutting end. For cuspid teeth, the control point position is located at the cuspid tooth cusp position. For molars, the control point is located in the central socket of the maxillofacial surface of the tooth.
The ideal arch characteristic line CFg for the crown center of gravity represents the ideal arch for the patient's crown arrangement. CFg is composed of 6 points, namely left and right incisor control points, left and right cuspid control points, and left and right first molar control points. CFg is located at the center of gravity of the clinical crown part of the tooth, the method of calculating the center of gravity of the clinical crown part of the tooth is:
PFgi represents a crown center of gravity point of the ith tooth, j represents an ordinal number of a triangular patch of a single tooth model, n represents a total number of the triangular patches, m (fj) represents a center of gravity point of the jth triangular patch, and area (fj) represents an area of the jth triangular patch. The center of gravity of the tooth calculated by the method can accurately express the position of the center of the tooth, and the error of tooth center calculation caused by uneven subdivision degree of the surface patch is avoided.
The ideal arch characteristic line CFf of the facial side of the crown represents the ideal arch of the facial side of the crown of the patient. CFf is composed of 6 points, namely left and right incisor control points, left and right cuspid control points, and left and right first molar control points. For incisors and cuspids, the control point is located at the center of the clinical coronal plane. For molars, the control point is located at the midpoint of the upper and lower lines of the buccal sulcus; the buccal sulcus of a molar is a concave trough of the crown surface located between the mesial and distal sides of the molar cheek.
The generation of the ideal dental arch characteristic line is obtained by performing interpolation fitting on a given control point set, and in a specific embodiment, a Hermit interpolation method is adopted to obtain the ideal dental arch characteristic line of the patient through a given series of control point sets. And carrying out interpolation fitting on each control point set by adopting a Hermit interpolation method to obtain a corresponding ideal dental arch characteristic line.
And 2) respectively extracting respective feature points of all teeth in the digital dental three-dimensional model and constructing a corresponding position data set M, wherein the position data set M records the feature points of different positions of the teeth, and the feature points of different positions are used for matching ideal curves corresponding to different dental features.
M＝{PFa，PFf，PFg}
PFa is a tooth maxillofacial feature point, which is located at the midpoint of the incisor in the direction of the mesial-distal direction of the incisor. For cuspid teeth, the position of the characteristic point is located at the cuspid position of the cuspid teeth. For premolars and molars, the feature point is located in the central socket of the maxillofacial area of the tooth.
PFf is the characteristic point of the facial side of the crown, which is located at the center point of the clinical crown surface for incisors, canines and premolars. For molars, the characteristic point is located at the midpoint of the upper and lower lines of the buccal sulci;
PFg is the crown center of gravity point, which for all types of teeth refers to the center of gravity of the crown portion of the tooth.
And 3) sequentially carrying out position movement adjustment on each tooth according to the ideal dental arch characteristic line and the movement control data set of the teeth, wherein the position adjustment on one target tooth specifically comprises the following steps:
firstly, extracting a point closest to a tooth maxillofacial feature point PFa of a target tooth in an ideal arch feature line CFa of a occlusal surface, extracting a point closest to a tooth crown facial feature point PFf of the target tooth in an ideal arch feature line CFf of a tooth crown facial side, extracting a point closest to a tooth crown gravity center point PFg of the target tooth in an arch feature line CFg of a tooth crown arrangement, and generating a movement control point set K according to the three extracted points, wherein the number of the feature points in the position data set M is equal to the number of the feature points in the movement control point set K; and then, matching the position data set M with the movement control point set K by adopting an ICP (inductively coupled plasma) algorithm to obtain a transformation matrix of the target tooth, and updating the position of the tooth according to the transformation matrix so as to finish the position adjustment of the target tooth.
Step 4) performing angle adjustment on the position-adjusted target tooth according to the crown arrangement arch characteristic line CFg, as shown in fig. 3:
4.1) taking the direction vertical to the occlusal plane as the Z-axis direction of the global coordinate plane OXY, establishing a local coordinate system (Xi, Yi, Z) of each tooth, wherein the global coordinate plane OXY and the OXiYi plane of the local coordinate system are both parallel to the occlusal plane, and the establishment of the local coordinate system is specifically as follows:
calculating the position of the center of gravity point of the dental crown of the target tooth, taking the point closest to the center of gravity point of the dental crown on the dental crown arrangement arch characteristic line CFg as a reference point CFgi, taking the tangential direction of the reference point CFgi as the Yi axis of a local coordinate system, taking the direction vertical to the Yi axis as the Xi axis of the local coordinate system, and taking the Z axis of the local coordinate system parallel to the Z axis of the global coordinate plane OXY;
4.2) calculating the near-far middle inclination angle of the target tooth, wherein the near-far middle inclination angle is an included angle between a tooth main axis Zi and the Z axis of the global coordinate plane OXY, and the tooth main axis Zi refers to the long axis of the target tooth. The tooth principal axis Zi before angle adjustment may be a Z axis not parallel to the global coordinate plane OXY. The calculation formula is as follows:
wherein θ 2 represents the mesial-distal tilt angle, proj (YioZ) (Zi) represents a projection vector of the tooth principal axis Zi of the ith tooth on the local coordinate plane YioZ;
4.3) calculating a torque angle of the target tooth, wherein the torque angle is a rotation angle of the tooth around the crown towards the lip (buccal) side or the tongue (palatal) side. The formula is as follows:
wherein θ 3 represents a torque angle, and proj (XiOZ) and (Zi) represents a projection vector of a tooth principal axis Zi of the ith tooth on the local coordinate plane XiOZ;
4.3) adjusting the angle of the teeth by tilting, twisting and torque on the buccal and lingual sides according to the tilting angle and the torque angle;
the step 4.3) is specifically as follows:
4.3.1) adjusting the inclination angle of the near-far center of the target tooth according to the inclination angle of the near-far center of the standard tooth occlusion;
4.3.2) on the premise of adjusting the inclination angle of the near-far center of the tooth, adjusting the torsion angle of the target tooth around the main shaft of the target tooth, specifically:
using the line connecting the near middle point TPm and the far middle point TPd of the target tooth as the first vector
The tangent vector at the reference point CFgi is taken as the second vector
Calculating a first vector
And second vector
An included angle formed by projection under the overall coordinate plane OXY is adjusted according to the included angle to enable the rotation angle of the tooth around the main axis of the tooth to enable the first vector to be measured
And second vector
And the adjustment of the torsion angle of the teeth around the self main shaft is completed.
The tooth near-middle point and the tooth far-middle point are the near-middle surface central point and the far-middle surface central point of the partial anatomical structure of the dental crown of the dental body, and for a relatively regular dentition, the near-middle point of the tooth is mutually contacted with the far-middle point of the adjacent tooth.
4.3.3) adjusting the torque angle of the target tooth according to the labial (buccal) lingual inclination angle of the standard tooth occlusion.
And 5) repeating the steps 3) -4) until the position and angle adjustment of all teeth is finished, so as to obtain the digital dental ideal model. The standard position angle of different standard tooth templates is different, and the commonly used standard can use the Andrews standard or the MBT standard, etc. Thus, the generation of ideal positions of the upper and lower dental arches is completed, and the aim of orthodontic correction can be achieved by adjusting the whole model according to the ideal model in the later stage, such as occlusion and the like.
As shown in fig. 2, a corresponding movement control point set Ki is generated according to the position data set Mi of each tooth, all the movement control point sets are arranged in a certain order to obtain an arrangement order set P, where P is { K1, K2, K3 … Ki }, and a target tooth arrangement queue Q of the digitized tooth jaw three-dimensional model is constructed according to the arrangement order set P, where Q is { M1, M2, M3 … Mi }, so that Mi in the target tooth arrangement queue Q corresponds to Ki one to one. The method specifically comprises the following steps:
a. selecting a first position data set M1 in the target tooth arrangement queue Q according to a starting arrangement point set of the arrangement sequence set P, namely a first movement control point set K1, wherein teeth corresponding to the first position data set M1 are used as first teeth to be placed on the ideal dental arch, and Q is Q-M1;
b. matching the first position data set M1 with the movement control point set K1, adjusting the position and angle of the first target tooth to be as close to an ideal arc shape as possible, and recording the position of the aligned target tooth;
c. and c, selecting the next tooth in the target tooth arrangement queue Q to be arranged according to the step b, and enabling Q to be Q-Mi.
d. Repeating step c until Q is an empty set, i.e. Q { }.
e. The dental abutment relationship is checked against the dental abutment points in the movement control data structure. The examination is to ensure that the teeth have better contact between adjacent surfaces, and the distance between the near and far middle points of the adjacent teeth is controlled within 0.2mm by calculating the distance between the near and far middle points of the teeth. If the adjacent distance exceeds this threshold, the teeth need to be translated along the arch line to correct the abutment.
For an ideal arch, the ranked order set P may begin at the arch midpoint or may begin at the leftmost and rightmost sides of the arch. The initial arrangement positions of the arrangement order sets P are different, and thus the order of teeth arranged by being placed in an ideal dental arch is also different. For example, for teeth that enter the ideal arch with the central arch area as the starting point, the central incisor is generally the first tooth to enter the ideal arch, and the target tooth alignment Q is constructed in front-to-back order.
The method can automatically finish the alignment and adjustment of the ideal tooth row of the digital tooth jaw, and improve the efficiency specified by the personalized ideal position scheme of the patient.
Claims (4)
1. A method for automatically generating a digital dental ideal model is characterized by comprising the following steps:
step 1) collecting all target teeth of the obtained digital dental three-dimensional model, selecting a plurality of target teeth in the digital dental three-dimensional model to extract characteristic points to obtain three different control point sets, and respectively obtaining an ideal arch characteristic line CFa of an occlusal surface, an ideal arch characteristic line CFf of a buccal side surface of a dental crown and an ideal arch characteristic line CFg of a gravity center of the dental crown according to the three control point sets;
step 2) extracting respective characteristic points of all target teeth in the digital dental three-dimensional model respectively and constructing a corresponding position data set M:
M＝{PFa，PFf，PFg}
wherein PFa is a tooth maxillofacial feature point, PFf is a tooth crown facial feature point, and PFg is a tooth crown gravity center point;
step 3) according to the three ideal dental arch characteristic lines obtained in the step 1) and the position data set M obtained in the step 2), sequentially carrying out position movement adjustment on each target tooth, wherein the position adjustment on one target tooth specifically comprises the following steps:
firstly, extracting a point closest to a tooth maxillofacial feature point PFa of a target tooth in an ideal arch feature line CFa of the occlusal surface, extracting a point closest to a tooth crown facial feature point PFf of the target tooth in an ideal arch feature line CFf of a tooth crown facial side, extracting a point closest to a tooth crown gravity center point PFg of the target tooth in a tooth crown arrangement arch feature line CFg, and generating a movement control point set K according to the three extracted points; then, matching the position data set M with the movement control point set K by adopting an ICP (inductively coupled plasma) algorithm to obtain a transformation matrix of the target tooth, and updating the position of the target tooth according to the transformation matrix so as to complete the position adjustment of the target tooth;
step 4) adjusting the angle of the target tooth after the position adjustment according to the ideal arch characteristic line CFg of the center of gravity of the dental crown, which comprises the following steps:
4.1) taking the direction vertical to the occlusal plane as the Z-axis direction of the global coordinate plane OXY, establishing a local coordinate system (Xi, Yi, Z) of each target tooth, wherein the OXiYi plane of the local coordinate system is parallel to the occlusal plane, and the establishment of the local coordinate system is specifically as follows:
calculating the position of the center of gravity point of the dental crown of the target tooth, taking the point closest to the center of gravity point of the dental crown on the dental crown arrangement arch characteristic line CFg as a reference point CFgi, taking the tangential direction of the reference point CFgi as the Yi axis of a local coordinate system, taking the direction vertical to the Yi axis as the Xi axis of the local coordinate system, and taking the Z axis of the local coordinate system parallel to the Z axis of the global coordinate plane OXY;
4.2) calculating the near-far middle inclination angle of the target tooth, wherein the formula is as follows:
wherein θ 2 represents the mesial-distal tilt angle, proj (YiOZ) (Zi) represents a projection vector of the tooth principal axis Zi of the ith target tooth on the local coordinate plane YiOZ;
4.3) calculating the torque angle of the target tooth, wherein the formula is as follows:
wherein θ 3 represents a torque angle, and proj (XiOZ) and (Zi) represents a projection vector of a tooth principal axis Zi of the ith target tooth on the local coordinate plane XiOZ;
4.4) carrying out inclination, torsion and torque adjustment on the angle of the target tooth on the mesial-distal direction according to the inclination angle and the torque angle;
and 5) repeating the steps 3) -4) until the position and angle adjustment of all the target teeth is completed, so as to obtain the digital dental ideal model.
2. The method for automatically generating the digital ideal dental model according to claim 1, wherein: the step 4.4) is specifically as follows:
4.4.1) adjusting the inclination angle of the near-far center of the target tooth according to the inclination angle of the near-far center of the standard tooth occlusion;
4.4.2) on the premise of adjusting the near-far and middle-distance inclination angle of the target tooth, adjusting the torsion angle of the target tooth around the self main shaft, specifically:
using the line connecting the near middle point TPm and the far middle point TPd of the target tooth as the first vector
The tangent vector at the reference point CFgi is taken as the second vector
Calculating a first vector
And second vector
Projecting an included angle formed under the global coordinate plane OXY, and adjusting the rotation angle of the target tooth around the main axis of the target tooth according to the included angle to enable the first vector
And second vector
Parallel to complete the adjustment of the torsion angle of the target tooth around the self main shaft;
4.4.3) adjusting the torque angle of the target tooth according to the lip-lingual inclination angle of the standard tooth occlusion.
3. The method for automatically generating the digital ideal dental model according to claim 1, wherein:
the calculation method of the crown gravity center point PFg in the step 2) is as follows:
PFgi represents a crown gravity point of the ith target tooth, j represents the ordinal number of a triangular patch of a single target tooth model, n represents the total number of the triangular patches, m (fj) represents a gravity point of the jth triangular patch, and area (fj) represents the area of the jth triangular patch.
4. The method for automatically generating the digital ideal dental model according to claim 1, wherein: the target teeth selected by the three control point sets in the step 1) are the same, but the positions of feature points of each extracted target tooth are different, and the target teeth comprise left and right incisors, left and right cuspids and left and right first molars;
the characteristic points selected by the control point set of the ideal arch characteristic line CFa of the occlusal surface are respectively as follows: the central point of the incisor in the direction of the near-far middle, the cusp position of the cuspid and the central position of the maxillofacial central socket of the first molar;
the characteristic points selected from the control point set of the ideal arch characteristic line CFg of the center of gravity of the dental crown are respectively as follows: the position of the center of gravity of the crown portion of each target tooth;
the characteristic points selected from the control point set of the ideal arch characteristic line CFf on the side surface of the facial side of the crown are respectively as follows: the control points on incisors and canine teeth are positioned at the center of the crown surface of the tooth, and the control point of molar teeth is positioned at the midpoint of the upper and lower connecting lines of the buccal sulcus;
and carrying out interpolation fitting on each control point set by adopting a Hermit interpolation method to obtain a corresponding ideal dental arch characteristic line.
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