CN107822722B - Finite point searching and expanding method for orthodontic arch wire bending motion planning - Google Patents
Finite point searching and expanding method for orthodontic arch wire bending motion planning 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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- 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 a limited point searching and expanding method for orthodontic arch wire bending motion planning, which relates to the technical field of orthodontic arch wire bending, and is used for obtaining the limited point searching and expanding method for the orthodontic arch wire bending motion planning according to an individual orthodontic arch wire curve of a patient, based on an orthodontic arch wire curve forming control point information set and a robot motion information set of forming control points and combining the motion characteristics of a robot bending orthodontic arch wire. The technical points are as follows: inputting an orthodontic arch wire curve forming control point information set M and a robot motion information set N of a forming control point into an orthodontic arch wire bending system according to the individualized orthodontic arch wire curve of a patient; dividing an individual orthodontic arch wire curve; calculating the number of control points in the divided areas, and arranging the areas in a descending order; calculating a reverse bending information set; and detecting whether the bending point is interfered or not.
Description
Technical Field
The invention relates to a limited point searching and expanding method for orthodontic arch wire bending motion planning, and belongs to the technical field of orthodontic arch wire bending.
Background
With the improvement of living standard, beauty and health are more and more emphasized, beautiful appearance and healthy body can bring confidence to people, but the occlusal jaw which is always called as a door face sometimes hinders the realization of the desire, the health of the occlusal jaw not only directly influences the beauty of the face, but also relates to normal oral function, malocclusion deformity is a major oral disease which harms human health and has higher morbidity, and in clinical oral treatment, a patient wears more orthodontic appliances.
In the process of bending the personalized orthodontic arch wire by the existing orthodontic arch wire bending robot (CN103892929A), interference may occur between the personalized orthodontic arch wire and the robot bending paw, namely the personalized orthodontic arch wire collides with the robot bending paw, after the interference occurs, the bending precision of the personalized orthodontic arch wire is greatly influenced, and further the correction effect is influenced, so that the bent personalized orthodontic arch wire cannot be applied to clinical treatment; research shows that in the process of forward bending the individual orthodontic arch wire, the forward bending is to bend the unbent orthodontic arch wire into a complex formed arch wire, interference is often caused by unreasonable bending sequence of forming control points, the reasonable bending sequence of the forming control points can effectively avoid the occurrence of interference, and the reasonable bending sequence of the forming control points is a necessary premise for realizing digital bending of the orthodontic arch wire.
Disclosure of Invention
Aiming at the problems, the invention provides a limited point searching and expanding method for orthodontic arch wire bending motion planning, which solves the problem that a forward bending forming control point bending sequence planning method is lacked in the technical field of orthodontic arch wire bending at present, and further realizes digital bending of an orthodontic arch wire.
The scheme adopted by the invention to solve the problems is as follows:
a limited point searching and generating method for orthodontic arch wire bending motion planning is characterized in that: the method comprises the following concrete implementation processes:
step one, data import:
according to the individualized orthodontic arch wire curve with i shaping control points, g special function curves and g +1 sequence curve segments, a doctor inputs an individualized orthodontic arch wire curve shaping control point information set M ═ M1,m2,m3,…,mi},mi＝(ui,vi,wi) 'for each individual orthodontic archwire curve shaping control point's coordinates, each orthodontic archwire curve shaping control point miAll correspond to a forming control point robot motion information unit niSo the robot motion information set of the input shaping control point is N ═ N1,n2,n3,…,ni}，niIndicating robot bending forming control point miCoordinate of forming control point and bending angle, ni＝(ui,vi,wi,αi)′，ui、vi、wiFor the forming control point miαiActing on forming control points m for robotsiThe bending angle is set up, and an orthodontic arch wire curve forming control point information set M and a robot motion information set N of a forming control point are input into the orthodontic arch wire bending system;
step two, dividing the personalized orthodontic arch wire curve:
the personalized orthodontic arch wire curve consists of special function curves and sequence curve segments connected with the special function curves, and the personalized orthodontic arch wire curve with g special function curves and g +1 sequence curve segments can be divided into g special function curve regions and g +1 sequence curve regions to obtain a special function curve region information set Q ═ Q1,q2,q3,…,qg},qgAn area information unit indicating the g-th special function tune; sequence curve region information set X ═ X1,x2,x3,…,xg+1},xg+1A region information unit indicating the g +1 th sequence; generating an orthodontic arch wire curve area information set Z ═ x according to the arrangement mode of special function curves and sequence curve segments on the personalized orthodontic arch wire curve1,q1,x2,q2,x3,…,xg,qg,xg+1}；
Step three, calculating the number of control points in the areas, and arranging the areas in a descending order:
calculate each region (x)1,q1,x2,q2,x3,…,xg,qg,xg+1) The number B of the upper control points is obtained, and an information set B of the number of the control points is obtained1＝{bx1,bq1,bx2,bq2,...,bxg+1}，bx1Number of control points indicating 1 st sequence curve region information unit, bq1Number of control points b indicating 1 st special function music region information unitx2Number of control points representing 2 nd sequence plot area information unit, bq2Number of control points b indicating 2 nd special function music region information unitxg+1Control of information unit representing g +1 th sequence curve regionThe number of points is compared with the number b of control points in each area to obtain bq1＞bx1＞…＞bq2If the number b of the control points in the two regions is equal, the control points are arranged in descending order by taking the sequence number of the special function curved region as an index, and the bending order of the special function curved region is prior to the sequence curved region to obtain a descending region information set A1＝{q1,x1,…q2}；
Step four, sequencing the bending sequence of the bending points in the region:
region information set A in descending order1＝{q1,x1,…,q2Reading the robot motion information of the control point forming control points in each area, q1＝{n2,n3}、x1＝{n4,n5}…q2＝{ni-2,ni-1,niAccording to the robot motion information unit ni＝(ui,vi,wi,αi) ' middle αiIs used as an index, the forming control points of each area are arranged in descending order if α3>α2、α4>α5、…、αi>αi-2>αi-1The coordinate descending order matrix of the individual orthodontic arch wire curve forming control point is M1＝{m3,m2,m4,...,mi-1The robot motion descending order information set is N1＝{n3,n2,n4,...,ni-1}；
Step five, calculating a reverse bending information set:
the idea of reverse bending is applied, namely the formed individual orthodontic arch wire is bent back to the unprocessed orthodontic arch wire, and the coordinate descending matrix M of the curve forming control point of the individual orthodontic arch wire1＝{m3,m2,m4,...,mi-1And robot motion descending order information set N1＝{n3,n2,n4,...,ni-1Converting the curve into an individualized orthodontic arch wire curve forming control point coordinate reverse matrix M1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1′}；
Step six, detecting whether the bending point is interfered:
forming a control point coordinate reverse matrix M of the individualized orthodontic arch wire curve1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1' is input into the ROS system, m, in order of the coordinates of the shaped control points in the matrix3′,m2′,m4′,...,mi-1' simulate reverse system individualized just abnormal arch wire of bending in proper order, in the simulation process, robot model and individualized just abnormal arch wire model simultaneous movement, utilize ROS collision detection algorithm to detect the robot and when individualized just abnormal arch wire curve shaping control point carries out reverse system to individualized just abnormal arch wire, whether can take place to interfere with individualized just abnormal arch wire:
if interference occurs:
the forming control points at the interference position are bent and moved backwards, and a coordinate reverse matrix M of the forming control points of the individualized orthodontic arch wire curve is formed1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1' reordering to obtain a new coordinate matrix M of the individual orthodontic arch wire curve forming control point2＝{m3′,m2′,...,m4′,mi-1' } and robot motion information set N2＝{n3′,n2′,...,n4′,ni-1' }, the step six is operated again, and a new coordinate matrix M of the control point for forming the curve of the personalized orthodontic arch wire is used2＝{m3′,m2′,...,m4′,mi-1' } and robot motion information set N2＝{n3′,n2′,...,n4′,ni-1' } input into the ROS system;
if no interference occurs:
skipping to the step seven;
step seven, obtaining a final bending point bending sequence:
bending sequence M of forming control points2＝{m3′,m2′,...,m4′,mi-1′}、N2＝{n3′,n2′,...,n4′,ni-1' } reverse order arrangement, obtaining and outputting the final bending point bending order M3＝{mi-1′,m4′,...,m2′,m3′}、N3＝{ni-1′,n4′,...,n2′,n3' }, the procedure ends.
The invention has the beneficial effects that:
1. when the control point bending sequence planning is carried out, the individualized orthodontic arch wire curve forming control point information set of a patient and the robot motion information set of the forming control point are introduced into the ROS system, the process of bending the individualized orthodontic arch wire by the robot is simulated, meanwhile, the interference is detected by using a collision detection algorithm, and the orthodontic arch wire and the robot move simultaneously in the simulation process.
2. The invention divides the complex individual orthodontic arch wire curve into the special function curve area and the sequence curve area, which accords with the classification mode of each curve segment in the orthodontic arch wire curve, and uses the number of the forming control points on each segment of the curve as the index to carry out the descending sequencing of the bending sequence of each curve, thereby improving the efficiency of the arch wire orthodontic bending motion planning.
3. Firstly, taking the number of forming control points on each section of curve as an index to obtain a forming control point bending sequence by a first method; inputting the bending sequence into an ROS system to simulate bending movement, detecting interference between the personalized orthodontic arch wire and the robot by using a collision detection algorithm in the ROS system, obtaining a new forming control point bending sequence by adopting a mode of moving the bending sequence of the forming control points which are interfered backwards as a second method, and detecting the new bending sequence by using the ROS system; therefore, in the process of obtaining the final bending sequence, the invention uses two methods for planning the bending sequence in sequence, and improves the reliability of the planning of the bending sequence.
4. The invention uses the idea of reverse bending, namely the complex formed arch wire is bent to form the unbent orthodontic arch wire, because in the process of reverse bending, the complex formed individual orthodontic arch wire occupies more space when being bent than the unprocessed orthodontic arch wire, and is easier to interfere with the robot, and in the process of reverse bending, the complexity of the individual orthodontic arch wire is gradually changed from high to low, so the space occupied when being bent is gradually changed from large to small, and the possibility of interference between the orthodontic arch wire and the robot when being bent is gradually changed from high to low; when the common forward bending idea is applied to bending the orthodontic arch wire, the forward bending is to bend the orthodontic arch wire which is not bent into a complex shaping arch wire, and the possibility that the orthodontic arch wire interferes with a robot during the forward bending is gradually changed from low to high, so that under the same bending sequence, the bending sequence meeting the reverse bending idea is more difficult to finish the bending of the personalized orthodontic arch wire under the condition that the interference does not occur, therefore, the bending sequence meeting the reverse bending is certainly suitable for the forward bending, the interference does not occur, and the correctness of the bending sequence planned by the invention is ensured.
5. When the invention is used for interference detection, a new bending point bending sequence is generated by adopting a method of moving back the bending sequence of the bending points at the interference position, and then the new bending point bending sequence is arranged in reverse order to generate a final bending point bending sequence, namely, in the final bending point bending sequence, the points which are easy to interfere are bent preferentially, and the invention conforms to the characteristic of bending an orthodontic arch wire by a robot.
6. According to the invention, the bending angles in the robot motion information are used as indexes, the forming control points of each area are arranged in a descending order to obtain the bending sequence of the forming control points in the area, the bending angles are used as the indexes to accord with the principle of bending the orthodontic arch wire by the robot, and the reliability of the planning method is improved.
Drawings
For ease of illustration, the invention is described in detail by the following detailed description and the accompanying drawings.
Fig. 1 is a flow chart of a limited point recovery generation method for orthodontic archwire bending motion planning;
fig. 2 is a schematic diagram of distribution of individual orthodontic archwire shaping control points;
fig. 3 is a schematic diagram of an individual orthodontic arch wire curve divided by a special function curve region and a sequence curve region.
Detailed Description
For the purposes of promoting a clear understanding of the objects, aspects and advantages of the invention, reference will now be made to the following description of the preferred embodiments illustrated in the accompanying drawings, with the understanding that the description is illustrative only and is not intended to limit the scope of the invention, and that the following description will omit descriptions of well-known structures and techniques in order to avoid unnecessarily obscuring the concepts of the invention.
As shown in fig. 1, 2 and 3, the following technical solutions are adopted in the present embodiment: a limited point searching and developing method for orthodontic arch wire bending motion planning,
the method is characterized in that: the method comprises the following concrete implementation processes:
step one, data import:
according to the individualized orthodontic arch wire curve with i shaping control points, g special function curves and g +1 sequence curve segments, a doctor inputs an individualized orthodontic arch wire curve shaping control point information set M ═ M1,m2,m3,…,mi},mi＝(ui,vi,wi) 'for each individual orthodontic archwire curve shaping control point's coordinates, each orthodontic archwire curve shaping control point miAll correspond to a forming control point robot motion information unit niSo the robot motion information set of the input shaping control point is N ═ N1,n2,n3,…,ni}，niIndicating robot bending forming control point miCoordinate of forming control point and bending angle, ni＝(ui,vi,wi,αi)′，ui、vi、wiFor the forming control point miαiActing on forming control points m for robotsiThe bending angle is set up, and an orthodontic arch wire curve forming control point information set M and a robot motion information set N of a forming control point are input into the orthodontic arch wire bending system;
step two, dividing the personalized orthodontic arch wire curve:
the personalized orthodontic arch wire curve consists of special function curves and sequence curve segments connected with the special function curves, and the personalized orthodontic arch wire curve with g special function curves and g +1 sequence curve segments can be divided into g special function curve regions and g +1 sequence curve regions to obtain a special function curve region information set Q ═ Q1,q2,q3,…,qg},qgAn area information unit indicating the g-th special function tune; sequence curve region information set X ═ X1,x2,x3,…,xg+1},xg+1A region information unit indicating the g +1 th sequence; generating an orthodontic arch wire curve area information set Z ═ x according to the arrangement mode of special function curves and sequence curve segments on the personalized orthodontic arch wire curve1,q1,x2,q2,x3,…,xg,qg,xg+1}；
Step three, calculating the number of control points in the areas, and arranging the areas in a descending order:
calculate each region (x)1,q1,x2,q2,x3,…,xg,qg,xg+1) The number B of the upper control points is obtained, and an information set B of the number of the control points is obtained1＝{bx1,bq1,bx2,bq2,...,bxg+1}，bx1Number of control points indicating 1 st sequence curve region information unit, bq1Number of control points b indicating 1 st special function music region information unitx2Number of control points representing 2 nd sequence plot area information unit, bq2Number of control points b indicating 2 nd special function music region information unitxg+1The number of control points of the g +1 th sequence curve region information unit is shown, the number b of the control points in each region is compared to obtain bq1＞bx1＞…＞bq2If the number b of the control points in the two regions is equal, the control points are arranged in descending order by taking the sequence number of the special function curved region as an index, and the bending order of the special function curved region is prior to the sequence curved region to obtain a descending region information set A1＝{q1,x1,…q2}；
Step four, sequencing the bending sequence of the bending points in the region:
region information set A in descending order1＝{q1,x1,…,q2Reading the robot motion information of the control point forming control points in each area, q1＝{n2,n3}、x1＝{n4,n5}…q2＝{ni-2,ni-1,niAccording to the robot motion information unit ni＝(ui,vi,wi,αi) ' middle αiIs used as an index, the forming control points of each area are arranged in descending order if α3>α2、α4>α5…、αi>αi-2>αi-1The coordinate descending order matrix of the individual orthodontic arch wire curve forming control point is M1＝{m3,m2,m4,...,mi-1The robot motion descending order information set is N1＝{n3,n2,n4,...,ni-1}；
Step five, calculating a reverse bending information set:
the idea of reverse bending is applied, namely the formed individual orthodontic arch wire is bent back to the unprocessed orthodontic arch wire, and the coordinate descending matrix M of the curve forming control point of the individual orthodontic arch wire1＝{m3,m2,m4,...,mi-1Androbot motion descending order information set N1＝{n3,n2,n4,...,ni-1Converting the curve into an individualized orthodontic arch wire curve forming control point coordinate reverse matrix M1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1′}；
Step six, detecting whether the bending point is interfered:
forming a control point coordinate reverse matrix M of the individualized orthodontic arch wire curve1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1' is input into the ROS system, m, in order of the coordinates of the shaped control points in the matrix3′,m2′,m4′,...,mi-1' simulate reverse system individualized just abnormal arch wire of bending in proper order, in the simulation process, robot model and individualized just abnormal arch wire model simultaneous movement, utilize ROS collision detection algorithm to detect the robot and when individualized just abnormal arch wire curve shaping control point carries out reverse system to individualized just abnormal arch wire, whether can take place to interfere with individualized just abnormal arch wire:
if interference occurs:
the forming control points at the interference position are bent and moved backwards, and a coordinate reverse matrix M of the forming control points of the individualized orthodontic arch wire curve is formed1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1' reordering to obtain a new coordinate matrix M of the individual orthodontic arch wire curve forming control point2＝{m3′,m2′,...,m4′,mi-1' } and robot motion information set N2＝{n3′,n2′,...,n4′,ni-1' }, the step six is operated again, and the new individualized orthodontic arch wire curve shaping control point is usedCoordinate matrix M2＝{m3′,m2′,...,m4′,mi-1' } and robot motion information set N2＝{n3′,n2′,...,n4′,ni-1' } input into the ROS system;
if no interference occurs:
skipping to the step seven;
step seven, obtaining a final bending point bending sequence:
bending sequence M of forming control points2＝{m3′,m2′,...,m4′,mi-1′}、N2＝{n3′,n2′,...,n4′,ni-1' } reverse order arrangement, obtaining and outputting the final bending point bending order M3＝{mi-1′,m4′,...,m2′,m3′}、N3＝{ni-1′,n4′,...,n2′,n3' }, the procedure ends.
While there has been shown and described what are at present considered the fundamental principles and essential features of the invention and its advantages, it will be understood by those skilled in the art that the invention is not limited by the embodiments described above, which are given by way of illustration of the principles of the invention and which are within the spirit and scope of the invention as defined by the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (1)
1. A limited point searching and generating method for orthodontic arch wire bending motion planning is characterized in that: the method comprises the following concrete implementation processes:
step one, data import:
according to the individualized orthodontic arch wire curve with i shaping control points, g special function curves and g +1 sequence curve segments, a doctor inputs an individualized orthodontic arch wire curve shaping control point information set M ═ M1,m2,m3,…,mi},mi＝(ui,vi,wi) 'for each individual orthodontic archwire curve shaping control point's coordinates, each orthodontic archwire curve shaping control point miAll correspond to a forming control point robot motion information unit niSo the robot motion information set of the input shaping control point is N ═ N1,n2,n3,…,ni}，niIndicating robot bending forming control point miCoordinate of forming control point and bending angle, ni＝(ui,vi,wi,αi)′，ui、vi、wiFor the forming control point miαiActing on forming control points m for robotsiThe bending angle is set up, and an orthodontic arch wire curve forming control point information set M and a robot motion information set N of a forming control point are input into the orthodontic arch wire bending system;
step two, dividing the personalized orthodontic arch wire curve:
the personalized orthodontic arch wire curve consists of special function curves and sequence curve segments connected with the special function curves, and the personalized orthodontic arch wire curve with g special function curves and g +1 sequence curve segments can be divided into g special function curve regions and g +1 sequence curve regions to obtain a special function curve region information set Q ═ Q1,q2,q3,…,qg},qgAn area information unit indicating the g-th special function tune; sequence curve region information set X ═ X1,x2,x3,…,xg+1},xg+1A region information unit indicating the g +1 th sequence; generating an orthodontic arch wire curve area information set Z ═ x according to the arrangement mode of special function curves and sequence curve segments on the personalized orthodontic arch wire curve1,q1,x2,q2,x3,…,xg,qg,xg+1}；
Step three, calculating the number of control points in the areas, and arranging the areas in a descending order:
calculate each region (x)1,q1,x2,q2,x3,…,xg,qg,xg+1) The number B of the upper control points is obtained, and an information set B of the number of the control points is obtained1＝{bx1,bq1,bx2,bq2,...,bxg+1}，bx1Number of control points indicating 1 st sequence curve region information unit, bq1Number of control points b indicating 1 st special function music region information unitx2Number of control points representing 2 nd sequence plot area information unit, bq2Number of control points b indicating 2 nd special function music region information unitxg+1The number of control points of the g +1 th sequence curve region information unit is shown, the number b of the control points in each region is compared to obtain bq1＞bx1＞…＞bq2If the number b of the control points in the two regions is equal, the control points are arranged in descending order by taking the sequence number of the special function curved region as an index, and the bending order of the special function curved region is prior to the sequence curved region to obtain a descending region information set A1＝{q1,x1,…q2}；
Step four, sequencing the bending sequence of the bending points in the region:
region information set A in descending order1＝{q1,x1,…,q2Reading the robot motion information of the control point forming control points in each area, q1＝{n2,n3}、x1＝{n4,n5}…q2＝{ni-2,ni-1,niAccording to the robot motion information unit ni＝(ui,vi,wi,αi) ' middle αiIs used as an index, the forming control points of each area are arranged in descending order if α3>α2、α4>α5…、αi>αi-2>αi-1The coordinate descending order matrix of the individual orthodontic arch wire curve forming control point is M1＝{m3,m2,m4,...,mi-1The robot motion descending order information set is N1＝{n3,n2,n4,...,ni-1}；
Step five, calculating a reverse bending information set:
the idea of reverse bending is applied, namely the formed individual orthodontic arch wire is bent back to the unprocessed orthodontic arch wire, and the coordinate descending matrix M of the curve forming control point of the individual orthodontic arch wire1＝{m3,m2,m4,...,mi-1And robot motion descending order information set N1＝{n3,n2,n4,...,ni-1Converting the curve into an individualized orthodontic arch wire curve forming control point coordinate reverse matrix M1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1′}；
Step six, detecting whether the bending point is interfered:
forming a control point coordinate reverse matrix M of the individualized orthodontic arch wire curve1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1' is input into the ROS system, m, in order of the coordinates of the shaped control points in the matrix3′,m2′,m4′,...,mi-1' simulate reverse system individualized just abnormal arch wire of bending in proper order, in the simulation process, robot model and individualized just abnormal arch wire model simultaneous movement, utilize ROS collision detection algorithm to detect the robot and when individualized just abnormal arch wire curve shaping control point carries out reverse system to individualized just abnormal arch wire, whether can take place to interfere with individualized just abnormal arch wire:
if interference occurs:
the forming control points at the interference position are bent and moved backwards, and a coordinate reverse matrix M of the forming control points of the individualized orthodontic arch wire curve is formed1′＝{m3′,m2′,m4′,...,mi-1' } and robot motion reverse information set N1′＝{n3′,n2′,n4′,...,ni-1' } intoThe rows are rearranged and sequenced again to obtain a new coordinate matrix M of the control point for forming the curve of the individual orthodontic arch wire2＝{m3′,m2′,...,m4′,mi-1' } and robot motion information set N2＝{n3′,n2′,...,n4′,ni-1' }, the step six is operated again, and a new coordinate matrix M of the control point for forming the curve of the personalized orthodontic arch wire is used2＝{m3′,m2′,...,m4′,mi-1' } and robot motion information set N2＝{n3′,n2′,...,n4′,ni-1' } input into the ROS system;
if no interference occurs:
skipping to the step seven;
step seven, obtaining a final bending point bending sequence:
bending sequence M of forming control points2＝{m3′,m2′,...,m4′,mi-1′}、N2＝{n3′,n2′,...,n4′,ni-1' } reverse order arrangement, obtaining and outputting the final bending point bending order M3＝{mi-1′,m4′,...,m2′,m3′}、N3＝{ni-1′,n4′,...,n2′,n3' }, the procedure ends.
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| CN109009499A (en) * | 2018-06-16 | 2018-12-18 | 哈尔滨理工大学 | A kind of manpower bends orthodontic wire motion model method for building up |
| CN111588505B (en) * | 2020-06-01 | 2021-07-09 | 哈尔滨理工大学 | Plane variable-radius circular domain dividing method for orthodontic arch wire bending sequence planning |
| CN111588499B (en) * | 2020-06-01 | 2021-06-04 | 哈尔滨理工大学 | Plane equal-radius circular domain dividing radius determining method based on orthodontic arch wire bending point density |
| CN111588503B (en) * | 2020-06-01 | 2021-05-28 | 哈尔滨理工大学 | Orthodontic arch wire variable-radius circular domain dividing method based on bending point density |
| CN111588502B (en) * | 2020-06-01 | 2021-05-18 | 哈尔滨理工大学 | Orthodontic arch wire variable-radius circular domain dividing method based on bending point-angular distance ratio sum |
| CN111588500B (en) * | 2020-06-01 | 2021-06-04 | 哈尔滨理工大学 | Equal-angle division angle determination method for orthodontic arch wire bending sequence planning |
| CN111588497B (en) * | 2020-06-01 | 2021-06-04 | 哈尔滨理工大学 | Plane equal-radius circular domain dividing radius determination method based on orthodontics arch wire bending point-angle-distance ratio sum |
| CN114972184B (en) * | 2022-04-18 | 2023-07-21 | 哈尔滨理工大学 | Orthodontic archwire error evaluation method based on weight ratio method |
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| KR101658113B1 (en) * | 2014-12-29 | 2016-09-21 | 한라대학교산학협력단 | Method for calculating bending points and angles of orthodontic archwires using computer and program thereof |
| US10575929B2 (en) * | 2015-03-24 | 2020-03-03 | Acme Monaco Corporation | Multiforce orthodontic archwire |
| CN105726144A (en) * | 2016-02-01 | 2016-07-06 | 北京正齐口腔医疗技术有限公司 | Arch wire bending method and device |
| CN106803018B (en) * | 2017-01-16 | 2019-03-12 | 哈尔滨理工大学 | A kind of personalization orthodontic wire Parameter Expression method |
| CN106803276B (en) * | 2017-01-16 | 2020-02-11 | 哈尔滨理工大学 | Personalized orthodontic arch wire curve interactive adjustment method |
| CN107137152B (en) * | 2017-06-10 | 2020-11-13 | 哈尔滨理工大学 | First-sequence orthodontic arch wire bending parameter generation and bending method |
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