CN106803018B - A kind of personalization orthodontic wire Parameter Expression method - Google Patents
A kind of personalization orthodontic wire Parameter Expression method Download PDFInfo
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- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
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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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- A61C7/12—Brackets; Arch wires; Combinations thereof; Accessories therefor
- A61C7/28—Securing arch wire to bracket
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Abstract
A kind of personalization orthodontic wire Parameter Expression method, it is related to orthodontic wire and bends technical field, and the present invention establishes the parametrization mathematical model of orthodontic wire based on discrete and combined mode with reference to the process for bending orthodontic wire by hand.Technical essential are as follows: the foundation of patient's tooth position coordinate, the expression of offset, the expression of easement curve section, the conversion of every section of arch wire local coordinate system and global coordinate system, bracket straightway position adjustment and specific function song expression.The parametrization mathematical model of personalized orthodontic wire First ray song and the special arch function song of the second sequence is established, provides necessary modeling guarantee to realize that robot bends personalized orthodontic wire.
Description
Technical field
The present invention relates to a kind of personalized orthodontic wire Parameter Expression methods, belong to orthodontic wire and bend technical field.
Background technique
The expression of arch wire shape is the important foundation for designing orthodontic wire and bending algorithm, and realizes orthodontic wire digitlization
Bend and automate the prerequisite bent.Due to the limitation of bracket groove shape, arch wire and bracket contact-segment are generally-straight
Section, because of two-phase neighbour dental morphology and the personalized difference of position, causes to connect the shape of the arch wire easement curve between different brackets
State is not quite similar.According to patient's maxillary teeth data information, according to orthodontic treatment mechanism by bracket straightway and easement curve section
It is linked in sequence, available orthodontic wire curve bowed shape.Orthodontist passes through the spatial position for changing bracket straightway,
And then change the bowed shape of orthodontic wire curve, orthodontic force is applied by the restoring force that arch wire generates after deformation occurs, just
The traction on assigned direction is carried out to tooth under abnormal power effect, to achieve the purpose that correction.Tooth has edge in correcting process
Tooth flank of tooth lateral translation, perpendicular to the translation of dental surface, the mobile displacement of the rotation of dental surface, and tooth and tooth rotation
The smaller equal features of movement of gyration, therefore carried out relative to current location perpendicular to the movement on surface and around support using bracket straight line
The mode of the rotation of two endpoints of slot straightway adjusts the position of bracket straightway.
At present in the quantitative research of dental arch shape, the dental arch mathematical model that research worker proposes has power function mould
Type, Beta equation model, catenary equation model and elliptic equation model, can approximate expression orthodontic wire shape.But according to
The orthodontic wire mathematical model of dental arch shape model foundation does not simultaneously solve the patient personalized difference of correction, cannot accurately express and appoint
It anticipates the location and shape of one section of arch wire, inflexible to the expression of easement curve, the insertion position of specific function song and shape are difficult
To carry out accurate Parameter Expression.
Summary of the invention
In view of the above-mentioned problems, the technical problem to be solved in the present invention is to provide a kind of personalized orthodontic wire Parameter Expressions
Dental arch curve is divided into bracket straightway and easement curve section, shape expression in position is quasi- discrete by way of combining by method
Really, parameter setting is reasonable, clear logic, is suitble to the accurate expression of personalization orthodontic wire.
Above-mentioned purpose is mainly realized by following scheme:
A kind of personalized orthodontic wire Parameter Expression method of the invention, it is characterised in that: the specific reality of the method
Existing process are as follows:
Step 1: the foundation of patient's tooth position coordinate
By taking common 14 teeth of the upper jaw as an example, preform orthodontic wire dental arch curve is subjected to sliding-model control, is divided into
14 bracket straightways and 13 transition connection sections, if the spatial line segment that two datum mark coordinates on every tooth are formed is institute
Bracket straightway in tooth position, if connecting two neighboring bracket straightway is easement curve section, the FDI tooth adopted international standards
Position writing-method, indicates its corresponding bracket straightway with the tooth positional representation of every tooth, is indicated with the tooth position of two adjacent teeth
Method indicates in-between easement curve section, is 18 using the tooth position sequence that FDI record of tooth position method indicates to import patient data ...,
11,21,…,28；If i is expressed as patient according to i-th of tooth (i=0,1 ..., 13) of tooth position sequence, so tooth position 18 is corresponding
I=0, two coordinates are (x on tooth position 180,y0,z0) and (x1,y1,z1), the corresponding i=7 in tooth position 21, according to tooth position sequence
Two coordinates on i-th of tooth are (x2i, y2i, z2i) and (x2i+1, y2i+1, z2i+1)；
Offset, which refers to, is set in the extended distance in bracket straightway two sides, and bracket straightway mathematical model is based on orthodontic arch
Silk datum mark is established, and orthodontic wire uses expression way known to doctor in the offset that bracket two sides are added: in i-th of bracket
Straightway adds nearly midpoint offset aiWith remote midpoint offset bi, mathematical model is by formula (1) expression
In formula: nearly midpoint offset aiWith remote midpoint offset biNumerical values recited indicate bracket straightway two it is extended
Apart from size, (X2i, Y2i, Z2i) indicate the starting point and ending point of straightway after addition offset on i-th of tooth；
Step 3: the expression of easement curve section
The shape of easement curve section can be adjusted by the size of Set scale parameter, in the easement curve of orthodontic wire curve
The selection of section part has the 3 rank Bezeir curves at 4 control points, and expression formula can simplify are as follows:
In formula: P0、P1、P2、P3Indicate 34 control points of rank Bezeir curve, t ∈ [0,1]；
Two adjacent bracket straightways determine an easement curve section, control point P0、P3It is the starting point of easement curve section
And terminating point, while being also the endpoint of bracket straightway after addition offset.Two adjacent bracket straightways are thrown in X/Y plane
X, y value of movie queen's intersection point are brought into the space line of every section of line segment, find out them in the coordinate of Z-direction, the x, y, z acquired
Value just forms an intermediate point (x, y, z), which is connected with corresponding bracket straightway endpoint again, and the line segment connected is pressed
After certain proportion distribution, the coordinate points of distributing point are two control point P0、P1；
Intersection point of the straight line where acquiring adjacent brackets straightway under X/Y plane projection is (X0, Y0)；
Shown in the space line general equation such as formula (3) of two bracket straightways:
By intersecting point coordinate (X0, Y0) substitute into formula (3) two intermediate point coordinates are (X0, Y0, Z1) and (X0, Y0, Z2).So
Four control points of easement curve section are as follows:
Wherein: ei、fiFor scale parameter, pass through setting ei、fiNumerical value change Bezeir curve control point P1、P2；
Step 4: the conversion of every section of arch wire local coordinate system and global coordinate system
Firstly, dental arch curve global coordinate O-XYZ is established according to patient's upper jaw data information that orthodontist provides,
Then using global coordinate coordinate origin O as origin, establishing part mark is O1-UVW, reference axis successively with global coordinate coordinate
Overlapping of axles then determine dental arch curve target insertion point position, here by endpoint P at left and right sides of any linkage section2、P3Coordinate
It acquires, finally, local coordinate system O1-UVW is converted into target position through coordinate transform, to realize the second sequence specific function
The digital expression of bowl line.P1(x1, y1, z1)、P2(x2, y2, z2)、P3(x3, y3, z3)、P4(x4, y4, z4) it is given bracket
Point coordinate.
Local coordinate system O1-UVW changes to target position at global coordinate O-XYZ, need to pass through coordinate transform three times, rotation
Turn-translation-rotation.Coordinate system O1-UVW is first by around the axis rotation alpha angle own axes O1W to coordinate system O1'-U'V'W', i.e.,
Multiplication cross transformation matrix R1；Coordinate system O1'-U'V'W' is by translation transformation to coordinate system O1 "-U " V " W ", i.e. multiplication cross transformation matrix
R2；Coordinate system O1 "-U " V " W " is around own axes O1 " V " rotation β angular transformation to target position O1 " '-U " ' V " ' W " ', i.e. multiplication cross
Transformation matrix R3；Assuming that specific function arch dental arch curve local coordinate system drag equation matrix is C, it is converted into overall seat
Mark is that the matrix equation of lower target position is D, then:
D=R2×(C×R1)×R3 (5)
In formula:
Step 5: the mathematical expression of the position adjustment of bracket straightway
According to the distance of adjustment translation, angle and rotation mode are rotated, realizes bracket straightway in the first sequence of orthodontic wire
The position adjustment in bent plane is arranged, the coordinate of gained position bracket straightway adjusted is by formula (5) at global coordinate O-XYZ
Indicate, dragging slot straightway local coordinate system O1 "-U " in V " W ", the translation of bracket straightway and the mathematical model rotated around Q2
It is A ' for A, the translation of bracket straightway and the mathematical model rotated around Q1, as shown in formula (6),
In formula: Q indicates that the bracket straightway coordinate points equation under local coordinate system, h indicate that bracket straightway moves in parallel
Distance, ω indicate rotation angle, l indicate Q1Q2 mould it is long；
Step 6: the expression of specific function song
Specific function song Parameter Expression method is coordinate system where the patient teeth's data information provided with orthodontist
O-XYZ is global coordinate, with the local coordinate system O1-UVW that two endpoints of easement curve section are established, to a variety of special arch function
Energy curve establishes the coordinates matrix C parameterized under local coordinate system O1-UVW, obtains global coordinate by formula (5) coordinate transform
The coordinates matrix D of specific function song under O-XYZ；
At local coordinate system O1-UVW, with reference to the method that manpower bends orthodontic wire, specific function song is regarded as several
Straightway, arc section and helical row combination, expression formula is respectively G, H, K, then the expression formula of specific function song is F=
F { G1, G2, H1, K1 ... }, then expression formula is converted into coordinates matrix C, it is that the coordinate of characteristic point is stored in a matrix in order；
Be inserted into specific function song position i (i=0 ..., 12), indicate according to patient data tooth position sequence, position i and
I-th of easement curve section is corresponding, is inserted into the type j (j=0,1 ...) of specific function song, j=0 under default conditions, indicates to insert
That enter is the easement curve section based on Bezeir curve, i.e. D0=P (t) indicates the type for respectively representing a kind of specific function song,
Its coordinates matrix is Dj, enable j=1 represent open vertical loop, j=2 represents T-type song, therefore Dj(j=1,2 ...) indicate specific function
The mathematical model database of curve, insertion specific function song indicate i-th of transition song on the position of i-th of transition curve section
Line segment expression formula Pi(t) it is substituted for the coordinates matrix D of the specific function song of jth seed typej。
The invention has the benefit that
1, dental arch curve is divided by bracket straightway and easement curve section two parts using the segmentation method of discretization, met
The characteristics of manually bending, each section curve is convenient for accurate expression, to realize the accurate expression of integrated curved.
2, using three rank Bezeir curve representation easement curve sections, shape expression is accurate and adjusts convenient for parameter, by setting
Set ei、fiNumerical value change Bezeir curve control point P1、P2, and then the convex hull shape of Bezeir curve is adjusted, transition can be made bent
Line segment achievees the purpose that orthodontic wire curve personalization is expressed more close to the actual conditions of various teeth.
3, the position adjustment of bracket straightway is mainly flat in orthodontic wire First ray plane by bracket straightway
The rotation of mobile and around bracket straightway two endpoints of row realizes that position adjusts, and easy to adjust, logic is simple, and operand is small.
4, suitable parameterized model is established to the location and shape of specific function song, it is special to be inserted into designated position
Fixed specific function song provides necessary model basis.
5, a kind of personalized orthodontic wire Parameter Expression method proposed by the present invention is covered including bracket straightway, mistake
Cross whole orthodontic wire component parts including curved section, specific function song, and the adjustment of reddendo signula singulis portion shape
Cheng Jinhang expression, can accurately express the shape feature of orthodontic wire, and easy to adjust, for being digitized into for orthodontic wire
Shape and automation forming provide necessary support.
Detailed description of the invention
Detailed description will be given by the following detailed implementation and drawings by the present invention for ease of explanation,.
Fig. 1 is the forming arch wire schematic diagram that the method for the present invention obtains；
Fig. 2 is that arch wire curve of the present invention adjusts process expression schematic diagram；
Fig. 3 is the special arch local coordinate system of the present invention and global coordinate relative positional relationship schematic diagram；
Fig. 4 is the Parameter Expression schematic diagram of specific function song of the present invention；
Fig. 5 is the orthodontic wire curve synoptic diagram that the present invention inserts open vertical loop, Ω song and T-type song.
Specific embodiment
In order to make the objectives, technical solutions and advantages of the present invention clearer, below by shown in the accompanying drawings specific
Embodiment describes the present invention.However, it should be understood that these descriptions are merely illustrative, and it is not intended to limit model of the invention
It encloses.In addition, in the following description, descriptions of well-known structures and technologies are omitted, it is of the invention to avoid unnecessarily obscuring
Concept.
As shown in figure 1, figure 2, figure 3, figure 4 and figure 5, present embodiment uses following technical scheme: it is a kind of it is personalized just
Abnormal arch wire Parameter Expression method, it is characterised in that: the specific implementation process of the method are as follows:
Step 1: the foundation of patient's tooth position coordinate
By taking common 14 teeth of the upper jaw as an example, preform orthodontic wire dental arch curve is subjected to sliding-model control, is divided into
14 bracket straightways and 13 transition connection sections, if the spatial line segment that two datum mark coordinates on every tooth are formed is institute
Bracket straightway in tooth position, if connecting two neighboring bracket straightway is easement curve section, the FDI tooth adopted international standards
Position writing-method, indicates its corresponding bracket straightway with the tooth positional representation of every tooth, is indicated with the tooth position of two adjacent teeth
Method indicates in-between easement curve section, is 18 using the tooth position sequence that FDI record of tooth position method indicates to import patient data ...,
11,21,…,28；If i is expressed as patient according to i-th of tooth (i=0,1 ..., 13) of tooth position sequence, so tooth position 18 is corresponding
I=0, two coordinates are (x on tooth position 180,y0,z0) and (x1,y1,z1), the corresponding i=7 in tooth position 21, according to tooth position sequence
Two coordinates on i-th of tooth are (x2i, y2i, z2i) and (x2i+1, y2i+1, z2i+1)；
Step 2: the expression of offset
Offset, which refers to, is set in the extended distance in bracket straightway two sides, and bracket straightway mathematical model is based on orthodontic arch
Silk datum mark is established, and orthodontic wire uses expression way known to doctor in the offset that bracket two sides are added: in i-th of bracket
Straightway adds nearly midpoint offset aiWith remote midpoint offset bi, mathematical model is by formula (1) expression
In formula: nearly midpoint offset aiWith remote midpoint offset biNumerical values recited indicate bracket straightway two it is extended
Apart from size, (X2i, Y2i, Z2i) indicate the starting point and ending point of straightway after addition offset on i-th of tooth；
Step 3: the expression of easement curve section
The shape of easement curve section can be adjusted by the size of Set scale parameter, in the easement curve of orthodontic wire curve
The selection of section part has the 3 rank Bezeir curves at 4 control points, and expression formula can simplify are as follows:
In formula: P0、P1、P2、P3Indicate 34 control points of rank Bezeir curve, t ∈ [0,1]；
Two adjacent bracket straightways determine an easement curve section, control point P0、P3It is the starting point of easement curve section
And terminating point, while being also the endpoint of bracket straightway after addition offset.Two adjacent bracket straightways are thrown in X/Y plane
X, y value of movie queen's intersection point are brought into the space line of every section of line segment, find out them in the coordinate of Z-direction, the x, y, z acquired
Value just forms an intermediate point (x, y, z), which is connected with corresponding bracket straightway endpoint again, and the line segment connected is pressed
After certain proportion distribution, the coordinate points of distributing point are two control point P1、P2；
Intersection point of the straight line where acquiring adjacent brackets straightway under X/Y plane projection is (X0, Y0)；
Shown in the space line general equation such as formula (3) of two bracket straightways:
By intersecting point coordinate (X0, Y0) substitute into formula (3) two intermediate point coordinates are (X0, Y0, Z1) and (X0, Y0, Z2).So
Four control points of easement curve section are as follows:
Wherein: ei、fiFor scale parameter, pass through setting ei、fiNumerical value change Bezeir curve control point P1、P2；
Step 4: the conversion of every section of arch wire local coordinate system and global coordinate system
Firstly, dental arch curve global coordinate O-XYZ is established according to patient's upper jaw data information that orthodontist provides,
Then using global coordinate coordinate origin O as origin, establishing part mark is O1-UVW, reference axis successively with global coordinate coordinate
Overlapping of axles then determine dental arch curve target insertion point position, here by endpoint P at left and right sides of any linkage section2、P3Coordinate
It acquires, finally, local coordinate system O1-UVW is converted into target position through coordinate transform, to realize the second sequence specific function
The digital expression of bowl line.P1(x1, y1, z1)、P2(x2, y2, z2)、P3(x3, y3, z3)、P4(x4, y4, z4) it is given bracket
Point coordinate.
Local coordinate system O1-UVW changes to target position at global coordinate O-XYZ, need to pass through coordinate transform three times, rotation
Turn-translation-rotation.Coordinate system O1-UVW is first by around the axis rotation alpha angle own axes O1W to coordinate system O1'-U'V'W', i.e.,
Multiplication cross transformation matrix R1；Coordinate system O1'-U'V'W' is by translation transformation to coordinate system O1 "-U " V " W ", i.e. multiplication cross transformation matrix
R2；Coordinate system O1 "-U " V " W " is around own axes O1 " V " rotation β angular transformation to target position O1 " '-U " ' V " ' W " ', i.e. multiplication cross
Transformation matrix R3；Assuming that specific function arch dental arch curve local coordinate system drag equation matrix is C, it is converted into overall seat
Mark is that the matrix equation of lower target position is D, then:
D=R2×(C×R1)×R3 (5)
In formula:
Step 5: the mathematical expression of the position adjustment of bracket straightway
According to the distance of adjustment translation, angle and rotation mode are rotated, realizes bracket straightway in the first sequence of orthodontic wire
The position adjustment in bent plane is arranged, the coordinate of gained position bracket straightway adjusted is by formula (5) at global coordinate O-XYZ
Indicate, dragging slot straightway local coordinate system O1 "-U " in V " W ", the translation of bracket straightway and the mathematical model rotated around Q2
It is A ' for A, the translation of bracket straightway and the mathematical model rotated around Q1, as shown in formula (6),
In formula: Q indicates that the bracket straightway coordinate points equation under local coordinate system, h indicate that bracket straightway moves in parallel
Distance, ω indicate rotation angle, l indicate Q1Q2 mould it is long；
Step 6: the expression of specific function song
Specific function song Parameter Expression method is coordinate system where the patient teeth's data information provided with orthodontist
O-XYZ is global coordinate, with the local coordinate system O1-UVW that two endpoints of easement curve section are established, to a variety of special arch function
Energy curve establishes the coordinates matrix C parameterized under local coordinate system O1-UVW, obtains global coordinate by formula (5) coordinate transform
The coordinates matrix D of specific function song under O-XYZ；
At local coordinate system O1-UVW, with reference to the method that manpower bends orthodontic wire, specific function song is regarded as several
Straightway, arc section and helical row combination, expression formula is respectively G, H, K, then the expression formula of specific function song is F=
F { G1, G2, H1, K1 ... }, then expression formula is converted into coordinates matrix C, it is that the coordinate of characteristic point is stored in a matrix in order；
Be inserted into specific function song position i (i=0 ..., 12), indicate according to patient data tooth position sequence, position i and
I-th of easement curve section is corresponding, is inserted into the type j (j=0,1 ...) of specific function song, j=0 under default conditions, indicates to insert
That enter is the easement curve section based on Bezeir curve, i.e. D0=P (t) indicates the type for respectively representing a kind of specific function song,
Its coordinates matrix is Dj, enable j=1 represent open vertical loop, j=2 represents T-type song, therefore Dj(j=1,2 ...) indicate specific function
The mathematical model database of curve, insertion specific function song indicate i-th of transition song on the position of i-th of transition curve section
Line segment expression formula Pi(t) it is substituted for the coordinates matrix D of the specific function song of jth seed typej。
The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
Claims (1)
1. a kind of personalization orthodontic wire Parameter Expression method, it is characterised in that: the specific implementation process of the method are as follows:
Step 1: the foundation of patient's tooth position coordinate
By taking common 14 teeth of the upper jaw as an example, preform orthodontic wire dental arch curve is subjected to sliding-model control, is divided into 14
Bracket straightway and 13 transition connection sections, if the spatial line segment that two datum mark coordinates on every tooth are formed is place tooth
The bracket straightway of position, if connecting two neighboring bracket straightway is easement curve section, the FDI tooth position adopted international standards is remembered
Record method indicates its corresponding bracket straightway with the tooth positional representation of every tooth, with the tooth positional representation table of two adjacent teeth
Show in-between easement curve section, is 18 using the tooth position sequence that FDI record of tooth position method indicates to import patient data ..., 11,
21,…,28；If i is expressed as patient according to i-th of tooth (i=0,1 ..., 13) of tooth position sequence, so the corresponding i in tooth position 18
=0, two coordinates are (x on tooth position 180,y0,z0) and (x1,y1,z1), the corresponding i=7 in tooth position 21, according to tooth position sequence i-th
Two coordinates on a tooth are (x2i, y2i, z2i) and (x2i+1, y2i+1, z2i+1)；
Step 2: the expression of offset
Offset, which refers to, is set in the extended distance in bracket straightway two sides, and bracket straightway mathematical model is based on orthodontic wire base
It establishes on schedule, orthodontic wire uses expression way known to doctor in the offset that bracket two sides are added: in i-th of bracket straight line
The nearly midpoint offset a of Duan TianjiaiWith remote midpoint offset bi, mathematical model is by formula (1) expression
In formula: nearly midpoint offset aiWith remote midpoint offset biNumerical values recited indicate two extended distances of bracket straightway
Size, (X2i, Y2i, Z2i) indicate the starting point and ending point of straightway after addition offset on i-th of tooth；
Step 3: the expression of easement curve section
The shape of easement curve section can be adjusted by the size of Set scale parameter, in the easement curve section portion of orthodontic wire curve
Component selections have the 3 rank Bezeir curves at 4 control points, and expression formula can simplify are as follows:
In formula: P0、P1、P2、P3Indicate 34 control points of rank Bezeir curve, t ∈ [0,1]；
Two adjacent bracket straightways determine an easement curve section, control point P0、P3It is starting point and the end of easement curve section
Stop, while being also the endpoint of bracket straightway after addition offset；Two adjacent bracket straightways are after X/Y plane projection
X, y value of intersection point are brought into the space line of every section of line segment, find out them in the coordinate of Z-direction, and the x, y, z value acquired is just
An intermediate point (x, y, z) is formed, which is connected with corresponding bracket straightway endpoint again, and the line segment connected is according to one
After certainty ratio distribution, the coordinate points of distributing point are two control point P1、P2；
Intersection point of the straight line where acquiring adjacent brackets straightway under X/Y plane projection is (X0, Y0)；
Shown in the space line general equation such as formula (3) of two bracket straightways:
By intersecting point coordinate (X0, Y0) substitute into formula (3) two intermediate point coordinates are (X0, Y0, Z1) and (X0, Y0, Z2)；So transition
Four control points of curved section are as follows:
Wherein: ei、fiFor scale parameter, pass through setting ei、fiNumerical value change Bezeir curve control point P1、P2；
Step 4: the conversion of every section of arch wire local coordinate system and global coordinate system
Firstly, establishing dental arch curve global coordinate O-XYZ, then according to patient's upper jaw data information that orthodontist provides
Using global coordinate coordinate origin O as origin, establishing part mark is O1-UVW, reference axis successively with global coordinate reference axis weight
It closes, then determines dental arch curve target insertion point position, here by endpoint P at left and right sides of any linkage section2、P3Coordinate acquires,
Finally, local coordinate system O1-UVW is converted into target position through coordinate transform, to realize the second sequence specific function arch
The digital expression of curve； P1(x1, y1, z1)、P2(x2, y2, z2)、P3(x3, y3, z3)、P4(x4, y4, z4) it is given bracket point
Coordinate；
Local coordinate system O1-UVW changes to target position at global coordinate O-XYZ, need to pass through coordinate transform three times, rotation-
Translation-rotation；Coordinate system O1-UVW is first by around the axis rotation alpha angle own axes O1W to coordinate system O1'-U'V'W', i.e. multiplication cross
Transformation matrix R1；Coordinate system O1'-U'V'W' is by translation transformation to coordinate system O1 "-U " V " W ", i.e. multiplication cross transformation matrix R2；It sits
Mark system O1 "-U " V " W " is around own axes O1 " V " rotation β angular transformation to target position O1 " '-U " ' V " ' W " ', i.e. multiplication cross convert square
Battle array R3；Assuming that specific function arch dental arch curve local coordinate system drag equation matrix is C, it is converted under global coordinate
The matrix equation of target position is D, then:
D=R2×(C×R1)×R3 (5)
In formula:
Step 5: the mathematical expression of the position adjustment of bracket straightway
According to the distance of adjustment translation, angle and rotation mode are rotated, realizes that bracket straightway is bent in orthodontic wire First ray
Position adjustment in plane, the coordinate of gained position bracket straightway adjusted is by formula (5) table at global coordinate O-XYZ
Show, dragging slot straightway local coordinate system O1 "-U " in V " W ", the translation of bracket straightway and the mathematical model rotated around Q2 are
A, the translation of bracket straightway and the mathematical model rotated around Q1 are A ', as shown in formula (6),
In formula: Q indicate under local coordinate system bracket straightway coordinate points equation, h indicate bracket straightway move in parallel away from
From ω indicates the angle of rotation, and l indicates that the mould of Q1Q2 is long；
Step 6: the expression of specific function song
Specific function song Parameter Expression method is coordinate system O-XYZ where the patient teeth's data information provided with orthodontist
It is bent to a variety of special arch functions with the local coordinate system O1-UVW that two endpoints of easement curve section are established for global coordinate
Line establishes the coordinates matrix C parameterized under local coordinate system O1-UVW, obtains global coordinate O- by formula (5) coordinate transform
The coordinates matrix D of specific function song under XYZ；
At local coordinate system O1-UVW, with reference to the method that manpower bends orthodontic wire, specific function song is regarded as several straight
Line segment, arc section and helical row combination, expression formula are respectively G, H, K, then the expression formula of specific function song is F=F
{ G1, G2, H1, K1 ... }, then expression formula is converted into coordinates matrix C, it is that the coordinate of characteristic point is stored in a matrix in order；
Be inserted into the position i (i=0 ..., 12) of specific function song, indicate according to patient data tooth position sequentially, position i and i-th
Easement curve section is corresponding, is inserted into the type j (j=0,1 ...) of specific function song, j=0 under default conditions, and indicate insertion is
Easement curve section based on Bezeir curve, i.e. D0=P (t) indicates the type for respectively representing a kind of specific function song, coordinate
Matrix is Dj, enable j=1 represent open vertical loop, j=2 represents T-type song, therefore Dj(j=1,2 ...) indicate specific function curve
Mathematical model database, insertion specific function song indicate i-th of easement curve segment table on the position of i-th of transition curve section
Up to formula Pi(t) it is substituted for the coordinates matrix D of the specific function song of jth seed typej。
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| CN111588494B (en) * | 2020-06-01 | 2021-07-09 | 哈尔滨理工大学 | Orthodontic arch wire variable-angle dividing method based on bending point density |
| CN114431989B (en) * | 2022-01-07 | 2023-05-16 | 可丽尔医疗科技（常州）有限公司 | Method for establishing coordinate system based on target dental arch curve, automatic tooth arrangement method and tooth movement evaluation method |
| CN114943058B (en) * | 2022-04-18 | 2023-07-25 | 哈尔滨理工大学 | Orthodontic archwire error fluctuation degree evaluation method based on position error judgment |
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