CN101406412A - Method for produce digital tooth implantation planning auxiliary assembly - Google Patents

Method for produce digital tooth implantation planning auxiliary assembly Download PDF

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Publication number
CN101406412A
CN101406412A CNA2007101809155A CN200710180915A CN101406412A CN 101406412 A CN101406412 A CN 101406412A CN A2007101809155 A CNA2007101809155 A CN A2007101809155A CN 200710180915 A CN200710180915 A CN 200710180915A CN 101406412 A CN101406412 A CN 101406412A
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China
Prior art keywords
tooth
model
digital
agomphosis
anchored object
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CNA2007101809155A
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Chinese (zh)
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CN101406412B (en
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姚宏宗
郭川竹
陈俊仁
萧富介
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BAOYU BIOTECHNOLOGY CORP
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BAOYU BIOTECHNOLOGY CORP
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Abstract

The invention discloses a generating method for a digital tooth implantation planning aided component. The generating method is mainly as follows: the shape inside an disease oral cavity is copied and made into an oral cavity model, then the oral cavity model is scanned three-dimensionally to acquire a digital model of the oral cavity model, a digital model of the disease oral cavity, and a digital model of a hypodontia teeth model, and the digital model of the oral cavity model, the digital model of the disease oral cavity, and the digital model of the hypodontia teeth model are defined as a positioning object, a reference object and an adjoint positioning object respectively; then the positioning object and the adjoint positioning object are combined and a characteristic point is taken out, and the positioning object and the reference object are positioned by the characteristic point; and positioning data after the positioning of the adjoint positioning object and the adjoint positioning object are output together, and the output is the digital tooth implantation planning aided component.

Description

The production method of digital tooth implantation planning auxiliary assembly
Technical field
The present invention is relevant with tooth implantation technology, is meant a kind of production method of digital tooth implantation planning auxiliary assembly especially.
Background technology
Press, in the known tooth implantation technology, focus on the assessment of sclerotin environment mostly, and ignored tooth stinging good and bad situation.It is generally acknowledged and consider that planting body is the most important in tooth jawbone head position, if plant body after implantation, when its axial dipole field amplitude is excessive, utilizes angled platform tooth to correct again and gets final product afterwards.
Above-mentioned way is not best practice, its reason is, the quality of sclerotin is no doubt important, if but plant axially the departing from of body to stinging datum level, and then the upper jaw and the lower jaw tooth is to stinging or when stinging object, and what plant that body affords will not be an axial force, but add a bending moment, excessive bending moment will be destroyed the closed state that this plants body and alveolar bone easily, and can reduce the service life of planting body, or cause and plant body bone integration failure after a period of time that operation is finished.
Moreover if plant body after implantation, its axial crooked amplitude has surpassed this platform tooth institute can be corrigent during scope, and then loading onto behind the artificial tooth occlusal surface can whole departing from, and the function of dental articulation will completely lose.
In view of this, plant body position, angle and axially when planting tooth, promptly must before planting tooth, promptly carry out best planning.And assist the planning of planting tooth by computer assisted digital tooth mould, promptly be a kind of possible selection.
Summary of the invention
The object of the present invention is to provide a kind of production method of digital tooth implantation planning auxiliary assembly, it can pass through area of computer aided, produces the accessory part of digital tooth mould, and then makes the planning of planting tooth and install more accurate smooth.
For achieving the above object, the production method of digital tooth implantation planning auxiliary assembly provided by the invention is mainly undertaken by the area of computer aided and the equipment that scans, and this method includes the following step:
A) obtain oral cavity model: turn over the intraoral shape of system sufferer, and make an oral cavity model;
B) obtain anchored object and follow the numerical data of anchored object: this oral cavity model is carried out the 3D solid scan by scanning equipment, the mathematical model of obtaining is defined as anchored object, in addition, load the digital agomphosis tooth model of a corresponding thread form in this anchored object agomphosis place, and be defined as and follow anchored object;
C) obtain the numerical data of references object: CT Scan is carried out in the sufferer oral cavity, and the mathematical model of obtaining is defined as references object;
D) set characteristic point: the plural similitude of setting this anchored object and this references object is as characteristic point;
E) location: carry out this anchored object by these characteristic points and combine the location with the overlapping of this references object, this follows anchored object promptly to be positioned on this references object thereupon; And
F) output: the locator data after following anchored object location to finish this follows anchored object itself to export together with this, and that is exported is a digital tooth implantation planning auxiliary assembly.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step e), mainly this anchored object is positioned on the references object, with the overlapping of finishing both in conjunction with the location.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step f), this locator data comprises this coordinate of following anchored object and stressed axial at least.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step b), the head place of stinging of this numeral agomphosis tooth model takes out 3 points respectively, be defined as a biteplane, and be datum mark with the nest of stinging of this numeral agomphosis tooth model, define a straight line perpendicular to this biteplane, this straight line promptly be this numeral agomphosis tooth model when interlock stressed axially.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step d), this characteristic point be particular tooth sting head, sting the adjacent contact point of nest, tooth one of them.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step b), this follows anchored object by selecting out a digital agomphosis tooth model that is fit among the standard tooth data base.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step b), this follows the selected of anchored object is to produce the agomphosis tooth model according to sufferer agomphosis kenel, and the agomphosis tooth model is scanned the digital agomphosis tooth model that is produced.
The present invention also provides a kind of production method of digital tooth implantation planning auxiliary assembly, is mainly undertaken by the area of computer aided and the equipment that scans, and this method includes the following step:
A) obtain oral cavity model: turn over the intraoral shape of system sufferer, and make an oral cavity model;
B) make interim facing: produce interim facing according to the oral cavity model kenel, and on interim facing, make plural individually defined thing as characteristic point;
C) obtain anchored object and follow the numerical data of anchored object: this interim facing is carried out the 3D solid scan by scanning equipment, the mathematical model of obtaining is defined as anchored object, and this anchored object has a plurality of characteristic points, in addition, load the digital agomphosis tooth model of a corresponding thread form in this anchored object agomphosis place, and be defined as and follow anchored object;
D) obtain the numerical data of references object: allow sufferer put on this interim facing, CT Scan is carried out in the sufferer oral cavity, the mathematical model of obtaining is defined as references object, and this references object has a plurality of characteristic points;
E) location: carry out this anchored object by these characteristic points and combine the location with the overlapping of this references object, this follows anchored object promptly to be positioned on this references object thereupon; And
F) output: the locator data after following anchored object location to finish this follows anchored object itself to export together with this, and that is exported is a digital tooth implantation planning auxiliary assembly.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step e), mainly this anchored object is positioned on the references object, with the overlapping of finishing both in conjunction with the location.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step f), this locator data comprises this coordinate of following anchored object and stressed axial at least.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step c), the head place of stinging of this numeral agomphosis tooth model takes out 3 points respectively, be defined as a biteplane, and be datum mark with the nest of stinging of this numeral agomphosis tooth model, define a straight line perpendicular to this biteplane, this straight line promptly be this numeral agomphosis tooth model when interlock stressed axially.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step c), this follows anchored object is by selecting out a digital agomphosis tooth model that is fit among the standard tooth data base.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step c), this follows the selected of anchored object is to produce the agomphosis tooth model according to sufferer agomphosis kenel, and the agomphosis tooth model is scanned the digital agomphosis tooth model that is produced.
The production method of described digital tooth implantation planning auxiliary assembly, wherein: in step c), this interim facing can be sheathed on earlier before the 3D solid scans and carry out the 3D solid on this oral cavity model again and scan.
By above-mentioned steps, can produce digital tooth implantation planning auxiliary assembly, and then make the planning of planting tooth and install more accurate smooth.
Description of drawings
Fig. 1 is the flow chart of steps of the present invention's first preferred embodiment.
Fig. 2 is the sketch map of the present invention's first preferred embodiment, shows the form of oral cavity model.
Fig. 3 is the sketch map of the present invention's first preferred embodiment, shows the form of anchored object.
Fig. 4 is the sketch map of the present invention's first preferred embodiment, shows anchored object and follows the bonded form of anchored object.
Fig. 5 is the sketch map of the present invention's first preferred embodiment, shows the stressed axial of dental articulation.
Fig. 6 is the sketch map of the present invention's first preferred embodiment, shows the form of references object.
Fig. 7 is the sketch map of the present invention's first preferred embodiment, the state when showing the location.
Fig. 8 is the sketch map of the present invention's first preferred embodiment, shows the state after finish the location.
Fig. 9 is the flow chart of steps of the present invention's second preferred embodiment.
Figure 10 is the sketch map of the present invention's second preferred embodiment, shows the form in sufferer oral cavity.
Figure 11 is the sketch map of the present invention's second preferred embodiment, shows the form of interim facing.
Figure 12 is the sketch map of the present invention's second preferred embodiment, and the demonstration sufferer is put on the state of interim facing.
Primary clustering symbol description in the accompanying drawing:
11 oral cavity model
12 anchored objects
121 characteristic points
13 digital agomphosis tooth models
14 follow anchored object
16 references object
161 characteristic points
21 oral cavity model
22 anchored objects
221 characteristic points
23 digital agomphosis tooth models
24 follow anchored object
26 references object
261 characteristic points
29 interim facings
291 characteristic points
The H biteplane
The X straight line
The specific embodiment
In order to describe technical characterstic of the present invention place in detail, lift following two preferred embodiments and conjunction with figs. explanation as after, wherein:
As shown in Figure 1, the production method of a kind of digital tooth implantation planning auxiliary assembly that the present invention's first preferred embodiment is provided includes the following step:
A) obtain oral cavity model: as shown in Figure 2, turn over the intraoral shape of system sufferer, and make an oral cavity model 11.
B) obtain anchored object and follow the numerical data of anchored object: as Fig. 3 to shown in Figure 4, this oral cavity model 11 is carried out the 3D solid scan by scanning the equipment (not shown), the mathematical model of obtaining is defined as anchored object 12, in addition, the agomphosis place is by a digital agomphosis tooth model 13 that loads corresponding thread form in the standard tooth data base (not shown) on this anchored object 12, and is defined as and follows anchored object 14.Again, this scans the digital agomphosis tooth model 13 that is produced to this agomphosis tooth model after following anchored object 14 also to produce agomphosis tooth model (not shown) according to sufferer agomphosis kenel again.The head place of stinging to this numeral agomphosis tooth model 13 takes out 3 points, be defined as a biteplane H, and be datum mark with the nest of stinging of this numeral agomphosis tooth model 13, definition one straight line X perpendicular to this biteplane H, its state as shown in Figure 5, this straight line X promptly be this numeral agomphosis tooth model 13 when interlock stressed axially.Wherein, because standard tooth data base belongs to known technology, and general each tooth Autocad that sees, therefore there is not necessity of graphic representation.
C) obtain the numerical data of references object: CT Scan is carried out in the sufferer oral cavity, and the mathematical model of obtaining is defined as references object 16, as shown in Figure 6.
D) set characteristic point: the plural similitude of setting this anchored object 12 and this references object 16 is as characteristic point 121,161.These characteristic points 121,161 in the present embodiment for the stinging head, sting nest of particular tooth, contact point that tooth is adjacent one of them, characteristic point 121,161 is shown in Fig. 3 and Fig. 6 respectively.
E) location: shown in Figure 7, by these characteristic points 121,161 carry out this anchored object 12 combines the location with the overlapping of this references object 16, that is, make the characteristic point 121 of this anchored object 12 be overlapped in the characteristic point 161 of this references object 16, and then this anchored object 12 is positioned on this references object 16.This follows anchored object 14 promptly to be positioned on this references object 16 thereupon, the locator data after can obtaining this and follow anchored object 14 location with this, as shown in Figure 8.When carrying out, carry out this kind overlapping in conjunction with localized action by computer.
F) output: follow the locator data (not shown) after finish anchored object 14 location to follow anchored object 14 output itself together with this this, that is exported is a digital tooth implantation planning auxiliary assembly.Wherein, this locator data comprised at least this coordinate of following anchored object 14 and stressed axially.
By above-mentioned steps, can before planting tooth, promptly promptly form a digital tooth implantation planning auxiliary assembly in advance, follow anchored object 14 (being the mathematical model of digital agomphosis tooth model 13) and this to follow the locator data of anchored object 14 (being coordinate and stressed related data such as axial) and this digital tooth implantation planning auxiliary assembly has comprised this.This digital tooth implantation planning auxiliary assembly can make things convenient for dentist to understand the sufferer tooth to the situation of stinging before planting tooth, plants the angle and the position of tooth, increases the correctness of planting tooth.Again, when the picture by computer shows this digital tooth implantation planning auxiliary assembly, can allow doctor and sufferer can learn postoperative result in advance before operation, Fig. 8 promptly shows this kind prediction result.
Fig. 9 is to shown in Figure 12 for another example, and the production method of a kind of digital tooth implantation planning auxiliary assembly that the present invention's second preferred embodiment is provided includes the following step:
A) obtain oral cavity model: turn over the intraoral shape of system sufferer, and make an oral cavity model 21.
B) make interim facing: produce an interim facing 29 according to this oral cavity model kenel, and on this interim facing 29, make plural individually defined thing as characteristic point 291.
C) obtain anchored object and follow the numerical data of anchored object: this oral cavity model 21 is carried out the 3D solid scan by scanning the equipment (not shown), the mathematical model of obtaining is defined as anchored object 22, and has a plurality of characteristic points 221 on this anchored object 22.Again, this oral cavity model 21 is being carried out before the 3D solid scans, also can earlier this interim facing 29 be sheathed on and carry out the 3D solid on this oral cavity model 21 again and scan, and can form characteristic point 221 on this anchored object 22 by the characteristic points 291 of this interim facing 29 itself.In addition, the agomphosis place and is defined as and follows anchored object 24 by a digital agomphosis tooth model 23 that loads corresponding thread form in the standard tooth data base (not shown) on this anchored object 22.Again, this scans the digital agomphosis tooth model 23 that is produced to this agomphosis tooth model after following anchored object 24 also to produce agomphosis tooth model (not shown) according to sufferer agomphosis kenel again.The head place of stinging to this numeral agomphosis tooth model 23 takes out 3 points, be defined as a biteplane H, and be datum mark with the nest of stinging of this numeral agomphosis tooth model 23, definition one straight line X, this straight line X perpendicular to this biteplane H promptly be this numeral agomphosis tooth model 23 when interlock stressed axially.Wherein, because standard tooth data base belongs to known technology, and general each tooth Autocad that sees, therefore there is not necessity of graphic representation.
D) obtain the numerical data of references object: allow sufferer put on this interim facing 29, CT Scan is carried out in the sufferer oral cavity, the mathematical model of obtaining is defined as references object 26, and this references object has a plurality of characteristic points 261.
E) location: by these characteristic points 221,261 carry out this anchored object 22 combines the location with the overlapping of this references object 26, that is, make the characteristic point 221 of this anchored object 22 be overlapped in the characteristic point 261 of this references object 26, and then this anchored object 22 is positioned on this references object 26.This follows anchored object 24 promptly to be positioned on this references object 26 thereupon, the locator data after can obtaining this by this and following anchored object 24 location.When carrying out, be to carry out this kind overlapping in conjunction with localized action by computer.
F) output: follow the locator data (not shown) after finish anchored object 24 location to follow anchored object 24 itself to export together with this this, the exporter of institute is a digital tooth implantation planning auxiliary assembly.Wherein, this locator data comprised at least this coordinate of following anchored object 24 and stressed axially.
This second embodiment is identical with first embodiment substantially, and different is in the setting that has increased by an interim facing 19, and the sufferer that can be used to complete mouthful agomphosis is carried out tooth implantation planning.
As from the foregoing, the attainable effect of the present invention is: by area of computer aided, can produce digital tooth implantation planning auxiliary assembly, and then make the planning of planting tooth and install more accurate smooth.

Claims (14)

1, a kind of production method of digital tooth implantation planning auxiliary assembly is mainly undertaken by the area of computer aided and the equipment that scans, and this method includes the following step:
A) obtain oral cavity model: turn over the intraoral shape of system sufferer, and make an oral cavity model;
B) obtain anchored object and follow the numerical data of anchored object: this oral cavity model is carried out the 3D solid scan by scanning equipment, the mathematical model of obtaining is defined as anchored object, in addition, load the digital agomphosis tooth model of a corresponding thread form in this anchored object agomphosis place, and be defined as and follow anchored object;
C) obtain the numerical data of references object: CT Scan is carried out in the sufferer oral cavity, and the mathematical model of obtaining is defined as references object;
D) set characteristic point: the plural similitude of setting this anchored object and this references object is as characteristic point;
E) location: carry out this anchored object by these characteristic points and combine the location with the overlapping of this references object, this follows anchored object promptly to be positioned on this references object thereupon; And
F) output: the locator data after following anchored object location to finish this follows anchored object itself to export together with this, and that is exported is a digital tooth implantation planning auxiliary assembly.
2, the production method of digital tooth implantation planning auxiliary assembly according to claim 1, wherein: in step e), mainly this anchored object is positioned on the references object, with the overlapping of finishing both in conjunction with the location.
3, the production method of digital tooth implantation planning auxiliary assembly according to claim 1, wherein: in step f), this locator data comprises this coordinate of following anchored object and stressed axial at least.
4, the production method of digital tooth implantation planning auxiliary assembly according to claim 3, wherein: in step b), the head place of stinging of this numeral agomphosis tooth model takes out 3 points respectively, be defined as a biteplane, and be datum mark with the nest of stinging of this numeral agomphosis tooth model, define a straight line perpendicular to this biteplane, this straight line promptly be this numeral agomphosis tooth model when interlock stressed axially.
5, the production method of digital tooth implantation planning auxiliary assembly according to claim 1, wherein: in step d), this characteristic point be particular tooth sting head, sting the adjacent contact point of nest, tooth one of them.
6, the production method of digital tooth implantation planning auxiliary assembly according to claim 1, wherein: in step b), this follows anchored object by selecting out a digital agomphosis tooth model that is fit among the standard tooth data base.
7, the production method of digital tooth implantation planning auxiliary assembly according to claim 1, wherein: in step b), this follows the selected of anchored object is to produce the agomphosis tooth model according to sufferer agomphosis kenel, and the agomphosis tooth model is scanned the digital agomphosis tooth model that is produced.
8, a kind of production method of digital tooth implantation planning auxiliary assembly, main system is undertaken by the area of computer aided and the equipment that scans, and this method includes the following step:
A) obtain oral cavity model: turn over the intraoral shape of system sufferer, and make an oral cavity model;
B) make interim facing: produce interim facing according to the oral cavity model kenel, and on interim facing, make plural individually defined thing as characteristic point;
C) obtain anchored object and follow the numerical data of anchored object: this interim facing is carried out the 3D solid scan by scanning equipment, the mathematical model of obtaining is defined as anchored object, and this anchored object has a plurality of characteristic points, in addition, load the digital agomphosis tooth model of a corresponding thread form in this anchored object agomphosis place, and be defined as and follow anchored object;
D) obtain the numerical data of references object: allow sufferer put on this interim facing, CT Scan is carried out in the sufferer oral cavity, the mathematical model of obtaining is defined as references object, and this references object has a plurality of characteristic points;
E) location: carry out this anchored object by these characteristic points and combine the location with the overlapping of this references object, this follows anchored object promptly to be positioned on this references object thereupon; And
F) output: the locator data after following anchored object location to finish this follows anchored object itself to export together with this, and that is exported is a digital tooth implantation planning auxiliary assembly.
9, the production method of digital tooth implantation planning auxiliary assembly according to claim 8, wherein: in step e), mainly this anchored object is positioned on the references object, with the overlapping of finishing both in conjunction with the location.
10, the production method of digital tooth implantation planning auxiliary assembly according to claim 8, wherein: in step f), this locator data comprises this coordinate of following anchored object and stressed axial at least.
11, the production method of digital tooth implantation planning auxiliary assembly according to claim 10, wherein: in step c), the head place of stinging of this numeral agomphosis tooth model takes out 3 points respectively, be defined as a biteplane, and be datum mark with the nest of stinging of this numeral agomphosis tooth model, define a straight line perpendicular to this biteplane, this straight line promptly be this numeral agomphosis tooth model when interlock stressed axially.
12, the production method of digital tooth implantation planning auxiliary assembly according to claim 8, wherein: in step c), this follows anchored object is by selecting out a digital agomphosis tooth model that is fit among the standard tooth data base.
13, the production method of digital tooth implantation planning auxiliary assembly according to claim 8, wherein: in step c), this follows the selected of anchored object is to produce the agomphosis tooth model according to sufferer agomphosis kenel, and the agomphosis tooth model is scanned the digital agomphosis tooth model that is produced.
14, the production method of digital tooth implantation planning auxiliary assembly according to claim 8, wherein: in step c), this interim facing can be sheathed on earlier before the 3D solid scans and carry out the 3D solid on this oral cavity model again and scan.
CN2007101809155A 2007-10-09 2007-10-09 Method for producing digital tooth implantation planning auxiliary assembly Expired - Fee Related CN101406412B (en)

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CN102078225A (en) * 2009-11-26 2011-06-01 东莞宝钰精瓷工业有限公司 Method for producing digital model applied to dental implant and method for producing artificial teeth
CN101869510B (en) * 2009-04-21 2013-01-09 宝钰生技股份有限公司 Method for manufacturing dental implantation surgical guide plate
CN103284808A (en) * 2013-06-17 2013-09-11 上海正雅齿科科技有限公司 Method for preparing positioning guide plate of oral and dental implants
CN104027177A (en) * 2013-03-07 2014-09-10 方晶晶 Implant path planning method and system
CN114681091A (en) * 2022-04-18 2022-07-01 四川大学 Method and equipment for evaluating occlusion condition of dental prosthesis
CN115281866A (en) * 2022-08-15 2022-11-04 北京美立刻医疗器械有限公司 Tooth model acquisition auxiliary device, acquisition method, system, medium and equipment
WO2023213255A1 (en) * 2022-05-02 2023-11-09 先临三维科技股份有限公司 Scanning apparatus, connecting method and apparatus therefor, electronic device, and medium

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US5975893A (en) * 1997-06-20 1999-11-02 Align Technology, Inc. Method and system for incrementally moving teeth
CN1578646A (en) * 2001-10-31 2005-02-09 画像诊断株式会社 Medical simulation apparatus and method for controlling 3-dimensional image display in the medical simulation apparatus
JP3820390B2 (en) * 2002-08-26 2006-09-13 株式会社アイキャット Artificial root placement position calculation method, artificial root placement position calculation device, computer program, and recording medium
US7241142B2 (en) * 2004-03-19 2007-07-10 Align Technology, Inc. Root-based tooth moving sequencing
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Publication number Priority date Publication date Assignee Title
CN101869510B (en) * 2009-04-21 2013-01-09 宝钰生技股份有限公司 Method for manufacturing dental implantation surgical guide plate
CN102078225A (en) * 2009-11-26 2011-06-01 东莞宝钰精瓷工业有限公司 Method for producing digital model applied to dental implant and method for producing artificial teeth
CN102078225B (en) * 2009-11-26 2012-10-03 东莞宝钰精瓷工业有限公司 Method for producing digital model applied to dental implant and method for producing artificial teeth
CN104027177A (en) * 2013-03-07 2014-09-10 方晶晶 Implant path planning method and system
CN103284808A (en) * 2013-06-17 2013-09-11 上海正雅齿科科技有限公司 Method for preparing positioning guide plate of oral and dental implants
CN103284808B (en) * 2013-06-17 2015-12-23 上海正雅齿科科技有限公司 A kind of manufacture method of oral cavity implanting tooth positioning guide plate
CN114681091A (en) * 2022-04-18 2022-07-01 四川大学 Method and equipment for evaluating occlusion condition of dental prosthesis
WO2023213255A1 (en) * 2022-05-02 2023-11-09 先临三维科技股份有限公司 Scanning apparatus, connecting method and apparatus therefor, electronic device, and medium
CN115281866A (en) * 2022-08-15 2022-11-04 北京美立刻医疗器械有限公司 Tooth model acquisition auxiliary device, acquisition method, system, medium and equipment
CN115281866B (en) * 2022-08-15 2023-11-17 北京美立刻医疗器械有限公司 Tooth model acquisition auxiliary device, acquisition method, system, medium and equipment

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