CN113920253B - Tooth model fast cutting method based on three-dimensional oral cavity model - Google Patents

Tooth model fast cutting method based on three-dimensional oral cavity model Download PDF

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CN113920253B
CN113920253B CN202111388896.1A CN202111388896A CN113920253B CN 113920253 B CN113920253 B CN 113920253B CN 202111388896 A CN202111388896 A CN 202111388896A CN 113920253 B CN113920253 B CN 113920253B
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张泽初
方美娥
陈学谦
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Guangzhou University
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Abstract

The invention discloses a tooth model fast cutting method based on a three-dimensional oral cavity model, which comprises the following steps of collecting the three-dimensional oral cavity model based on a segment automatic division technology, preprocessing the tooth edge of the three-dimensional oral cavity model, and obtaining an edge cutting curve of the tooth model; simplifying the edge cutting curve into a skeleton containing a plurality of control points, establishing a cubic Bezier curve by taking the skeleton as a control polygon, and obtaining a cutting curve for cutting the tooth model by adjusting the control points to control the curve shape of the cubic Bezier curve; converting the cutting curve into a tubular model, and segmenting the tubular model into tooth models through a pool operation; the invention solves the problems of more manual adjustment steps and low speed due to the error of automatic identification, and greatly improves the tooth cutting speed when the orthodontic software processes the oral scanning model.

Description

Tooth model fast cutting method based on three-dimensional oral cavity model
Technical Field
The invention relates to the field of 3D (three-dimensional) software for orthodontic treatment, in particular to a tooth model fast cutting method based on a three-dimensional oral cavity model.
Background
With the rapid development of geometric deep learning, more and more deep learning techniques are used for orthodontics, such as: the automatic partitioning (segment) techniques mentioned in g.zanjanet al, "Deep left approach to segmented segmentation 3D point within-oral scales of teth," inproc.2nd int.conf.med.im.deep left et al (PMLR),2019, pp.557-571 the automatic partitioning (segment) has been successful over 95%, but some problems still affect the effect of segmentation, such as wisdom teeth, various teeth growth, and easy occurrence of problems at junctions between teeth. Therefore, a cutting mode which can be conveniently adjusted for the divided oral cavity model is still needed.
The existing methods have certain defects, before the automatic tooth segmentation is used, the cutting line is drawn on the surface of the oral cavity model by industrial software in a segmentation mode, then the teeth are cut, the operation time of each tooth is more than 30s, the adjustment is difficult to carry out after the cutting line is drawn, and the time for cutting one pair of teeth is more than 20 minutes. Therefore, a method for rapidly cutting teeth is urgently needed to improve the cutting and forming time of the tooth model of the oral cavity model.
Disclosure of Invention
In order to solve the technical problem, the invention provides a tooth model rapid cutting method based on a three-dimensional oral cavity model, which comprises the following steps:
acquiring a three-dimensional oral cavity model based on a segment automatic division technology, preprocessing the tooth edge of the three-dimensional oral cavity model, and acquiring an edge cutting curve of the tooth model;
simplifying the edge cutting curve into a skeleton containing a plurality of control points, establishing a cubic Bezier curve by taking the skeleton as a control polygon, and obtaining a cutting curve for cutting the tooth model by adjusting the control points to control the curve shape of the cubic Bezier curve;
the cutting curve is converted into a tubular model, and the tubular model is segmented into tooth models through a pool operation.
Preferably, the tooth margin is preprocessed by performing an opening operation and a closing operation on the tooth margin in the process of preprocessing the tooth margin of the three-dimensional oral cavity model, the preprocessing is used for solving the regional edge irregularity of the tooth margin, wherein the opening operation is used for removing the tiny protruding parts of the regional boundary of the tooth margin, and the closing operation is used for filling the tiny gaps of the regional boundary of the tooth margin by filling the tiny holes in the region of the tooth margin.
Preferably, the opening operation comprises the steps of:
acquiring a first region including a tooth model and a second region not including the tooth model based on the tooth edge, wherein a first boundary line is arranged between the first region and the second region;
acquiring a first optimum boundary line of the first region and a third region between the first optimum boundary line and the first boundary line based on the first region, wherein the third region includes the minute protruded portion of the first region;
based on the first feature of the second region, the first feature is endowed to the fine protruding part of the third region through k times of region reduction operation, and a first target region is obtained;
and based on the second characteristic of the first region, combining the second characteristic with the first region into a first edge region of the tooth edge after the second characteristic is endowed to the first target region through k times of region expansion operation, and acquiring an edge cutting curve according to the first edge region.
Preferably, the closing operation comprises the steps of:
acquiring a second optimal boundary line of the first region based on the vertex of the fine protrusion portion;
acquiring the region length of the fine protruding part based on the second optimal boundary line, and selecting a fourth region in the second region according to the region length, wherein the region length is used for indicating the vertical distance from the bottom to the top of the region where the fine protruding part is located;
and after the second characteristic is endowed to the first area and the fourth area, removing the fourth area, acquiring a second marginal area of the tooth margin, and acquiring a marginal cutting curve according to the second marginal area.
Preferably, in the process of acquiring the edge-cut curve of the tooth model, the edge-cut curve is acquired based on the first edge region and the second edge region.
Preferably, in the process of simplifying the edge cutting curve into a skeleton containing a plurality of control points, the edge cutting curve is simplified according to a DP algorithm, wherein the DP algorithm comprises the following steps:
s101, setting a thinning threshold value, and dividing an edge cutting curve into a plurality of curves to be processed;
s102, connecting the first point and the last point of the curve to be processed into a straight line in a virtual mode, solving the distance between the middle point between the first point and the last point and the straight line, and finding out the maximum distance value dmax;
s103, if dmax is less than threshold, the intermediate point is discarded; if dmax is larger than or equal to threshold, dividing the curve into two parts by taking the middle point corresponding to dmax as a boundary point, and repeating the steps S102-S103 on the two parts of the curve until all the middle points are processed, and taking the boundary point as a control point to construct the framework.
Preferably, in the process of establishing the cubic Bezier curve, the control points are connected in sequence, and the coordinates of the control points are obtained;
acquiring a first vertex coordinate of a first vertex and a second vertex coordinate of a second vertex for generating a cubic Bezier curve according to the control point coordinates;
constructing a cubic Bezier curve according to the first vertex coordinate, the control point coordinate and the second vertex coordinate;
and moving the first vertex and the second vertex to the surface of the tooth model by adjusting the control points to obtain a cutting curve.
Preferably, the expression of the first vertex coordinates is:
Figure BDA0003368094420000041
the expression for the second vertex coordinates is:
Figure BDA0003368094420000042
wherein, PiIs the ith control point coordinate, QiAs first vertex coordinates, Qi+1Is the second vertex coordinate.
Preferably, the expression of the cubic bezier curve is:
B(t)＝Pi*(1-t)3+3*Qi*t*(1-t)2+3*Qi+1*t2*(1-t)+Pi+1*t3 t∈[0，1]。
preferably, in the process of obtaining the cutting curve, the positions of the cutting curve, which are not tightly fitted with the tooth model, are collected, the positions are subjected to edge subdivision, and the cutting curve is obtained after points of the edges are wrapped on the surface of the tooth model, wherein the process of adjusting the positions which are not tightly fitted comprises the following steps:
s201, moving the vertex of the edge to the surface of the tooth model;
s202, collecting the distance between the center of the edge and the tooth model, obtaining a first edge with the distance larger than the pipe radius of the tubular model, and subdividing the first edge into two parts based on the center;
s203, the steps S201-S202 are repeated until the cutting curve is attached to the surface of the tooth model.
The invention discloses the following technical effects:
compared with the prior art, the method for rapidly and manually adjusting and cutting the three-dimensional oral cavity model which is automatically divided (segment) is provided by the invention. And extracting a smooth boundary curve by using the marked region, extracting a plurality of control points from the curve, and adjusting the position of the control point to adjust the curve shape so as to adjust the range of the selected region. The problems of errors in automatic identification, multiple manual adjustment steps and low speed are solved, and the tooth cutting speed is greatly increased when the dental orthodontic software is used for processing the oral scanning model.
The invention greatly improves the speed of segmentation, including the time spent by automatic division of the deep network model, and in addition, the technology can cut a pair of teeth in 4 minutes. And drawing a tooth dividing line under the condition of no automatic division, and only selecting 10-20 control points, wherein the average time is only 9 s. In the case of the existing division, the cutting line is automatically generated, and the average time for manually adjusting one tooth is only 3S.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 illustrates a problem with the prior art in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of a cutting line and a control point according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of the open operation of an embodiment of the present invention;
FIG. 4 is a schematic diagram of a closing operation according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating a step of extracting a cutting curve according to an embodiment of the present invention;
FIG. 6 is a depiction of the Douglas algorithm in accordance with an embodiment of the present invention;
FIG. 7 is a graph illustrating curve changes for adjusting control points according to an embodiment of the present invention;
FIG. 8 is a diagram illustrating the effect of steps according to an embodiment of the present invention;
fig. 9 is a diagram of method steps according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
As shown in FIGS. 1-9, the present invention is directed to a method for rapid manual adjustment and cutting of automatically partitioned (segment) three-dimensional models. And extracting a smooth boundary curve by using the marked region, extracting a plurality of control points from the curve, and adjusting the positions of the control points to adjust the curve shape, thereby adjusting the range of the selected region and quickly cutting out the tooth.
The invention provides a tooth model rapid cutting method based on a three-dimensional oral cavity model, which comprises the following steps:
acquiring a three-dimensional oral cavity model based on a segment automatic division technology, preprocessing the tooth edge of the three-dimensional oral cavity model, and acquiring an edge cutting curve of the tooth model;
simplifying the edge cutting curve into a skeleton containing a plurality of control points, establishing a cubic Bezier curve by taking the skeleton as a control polygon, and obtaining a cutting curve for cutting the tooth model by adjusting the control points to control the curve shape of the cubic Bezier curve;
the cutting curve is converted into a tubular model, and the tubular model is segmented into tooth models through a pool operation.
Further preferably, in the process of preprocessing the tooth margin of the three-dimensional oral cavity model, the tooth margin is preprocessed by performing an opening operation and a closing operation on the tooth margin, the preprocessing is used for solving the regional edge irregularity of the tooth margin, wherein the opening operation is used for removing the tiny protruding parts of the regional boundary of the tooth margin, and the closing operation is used for filling the tiny gaps of the regional boundary of the tooth margin by filling the tiny leaks in the region of the tooth margin.
Further preferably, the opening operation comprises the steps of:
acquiring a first region including a tooth model and a second region not including the tooth model based on the tooth edge, wherein a first boundary line is arranged between the first region and the second region;
acquiring a first optimum boundary line of the first region and a third region between the first optimum boundary line and the first boundary line based on the first region, wherein the third region includes the minute protruded portion of the first region;
based on the first feature of the second region, the first feature is endowed to the fine protruding part of the third region through k times of region reduction operation, and a first target region is obtained;
and based on the second characteristic of the first region, combining the second characteristic with the first region into a first edge region of the tooth edge after the second characteristic is endowed to the first target region through k times of region expansion operation, and acquiring an edge cutting curve according to the first edge region.
Further preferably, the closing operation comprises the steps of:
acquiring a second optimal boundary line of the first region based on the vertex of the fine protrusion portion;
acquiring the region length of the fine protruding part based on the second optimal boundary line, and selecting a fourth region in the second region according to the region length, wherein the region length is used for indicating the vertical distance from the bottom to the top of the region where the fine protruding part is located;
and after the second characteristic is endowed to the first area and the fourth area, removing the fourth area, acquiring a second marginal area of the tooth margin, and acquiring a marginal cutting curve according to the second marginal area.
Further preferably, in the process of acquiring the edge-cut curve of the tooth model, the edge-cut curve is acquired based on the first edge region and the second edge region.
Further preferably, in the process of simplifying the edge cutting curve into a skeleton containing a plurality of control points, the edge cutting curve is simplified according to a DP algorithm, wherein the DP algorithm comprises the following steps:
s101, setting a thinning threshold value, and dividing an edge cutting curve into a plurality of curves to be processed;
s102, connecting the first point and the last point of the curve to be processed into a straight line in a virtual mode, solving the distance between the middle point between the first point and the last point and the straight line, and finding out the maximum distance value dmax;
s103, if dmax is less than threshold, the intermediate point is discarded; if dmax is larger than or equal to threshold, dividing the curve into two parts by taking the middle point corresponding to dmax as a boundary point, and repeating the steps S102-S103 on the two parts of the curve until all the middle points are processed, and taking the boundary point as a control point to construct the framework.
Further preferably, in the process of establishing the cubic Bezier curve, the control points are connected in sequence, and the coordinates of the control points are obtained;
acquiring a first vertex coordinate of a first vertex and a second vertex coordinate of a second vertex for generating a cubic Bezier curve according to the control point coordinates;
constructing a cubic Bezier curve according to the first vertex coordinate, the control point coordinate and the second vertex coordinate;
and moving the first vertex and the second vertex to the surface of the tooth model by adjusting the control points to obtain a cutting curve.
Further preferably, the expression of the first vertex coordinates is:
Figure BDA0003368094420000091
the expression for the second vertex coordinates is:
Figure BDA0003368094420000092
wherein, PiIs the ith control point coordinate, QiAs first vertex coordinates, Qi+1Is the second vertex coordinate.
Further preferably, the expression of the cubic bezier curve is:
B(t)＝Pi*(1-t)3+3*Qi*t*(1-t)2+3*Qi+1*t2*(1-t)+Pi+1*t3 t∈[0，1]。
further preferably, in the process of obtaining the cutting curve, the positions of the cutting curve and the tooth model which are not tightly fitted are collected, the positions are subjected to edge subdivision, points of the edges are wrapped on the surface of the tooth model, and then the cutting curve is obtained, wherein the process of adjusting the positions which are not tightly fitted comprises the following steps:
s201, moving the vertex of the edge to the surface of the tooth model;
s202, collecting the distance between the center of the edge and the tooth model, obtaining a first edge with the distance larger than the pipe radius of the tubular model, and subdividing the first edge into two parts based on the center;
s203, the steps S201-S202 are repeated until the cutting curve is attached to the surface of the tooth model.
The invention also includes a rapid cutting system for a tooth model based on a three-dimensional oral cavity model, comprising:
the modeling module is used for collecting a three-dimensional oral cavity model based on segment automatic division technology;
the pretreatment module is used for pretreating the tooth edge of the three-dimensional oral cavity model to obtain an edge cutting curve of the tooth model;
the data processing module is used for simplifying the edge cutting curve into a skeleton containing a plurality of control points, establishing a cubic Bezier curve by taking the skeleton as a control polygon, and acquiring a cutting curve for cutting the tooth model by adjusting the control points to control the curve shape of the cubic Bezier curve;
and the model cutting module is used for converting the cutting curve into a tubular model and segmenting the tubular model into the tooth model through the pool operation.
Example 1: the invention provides a method, which comprises the following steps:
1.1, generating a smooth cutting curve according to the result of automatic division (segment)
The automatic division (segment) result of the oral cavity model is obtained, but the automatically divided edges are different in topology, so that a method for solving the regional edge difference by adopting open operation and close operation is adopted. Performing an opening operation, namely performing k times of region reduction operation, and then performing k times of region expansion operation; the meaning of the on operation is that a thin protruding part of the region boundary can be removed. The closing operation is to perform k times of region expanding operation and then k times of region reducing operation. The meaning of the close operation is to fill a fine hole in the region and fill a fine gap on the boundary.
And performing opening operation and closing operation on the selected area on the mesh. The problem of raggedness in edge topology is solved.
The edge topology is flat, but from the edge point coordinate perspective, the edge is still not flat. The edge of the edge is extracted to generate a curve, and the curve is smoothened.
1.2, simplifying the cutting curve into a skeleton containing a few control points, establishing a cubic Bessel curve by taking the skeleton as a control polygon, and controlling the curve shape by adjusting the control points.
The simplified curve: Douglas-Peuker (DP algorithm), is the classic algorithm for thinning linear elements. The method is used for processing a large number of redundant geometric data points, so that the aim of reducing the data volume can be fulfilled, and a skeleton capable of retaining geometric shapes to a great extent is provided.
Douglas procedure:
step one, setting a thinning threshold value
Step two, connecting the first point and the last point of the curve to be processed into a straight line in a virtual mode, solving the distance between all the middle points and the straight line, and finding out the maximum distance value dmax
If dmax is less than threshold, the middle points on the curve are all rounded off; if dmax is larger than or equal to threshold, dividing the curve into two parts by taking the point as a boundary, and repeating the steps two and three on the two parts of the curve until all the points are processed
Reduction curve: the control points of the cubic Bezier curve are sequentially connected in sequence, and the coordinates of the control points are respectively (P)1,P2,P3…Pn),PiWhere i is the control point number, and there are n control points.
Want to calculate PiTo Pi+1The curve of (2) requires the generation of two additional vertices Qi，Qi+1。
Figure BDA0003368094420000121
Figure BDA0003368094420000122
(Pi，Qi，Qi+1，Pi+1) A cubic bezier curve is established for the vertices:
B(t)＝Pi*(1-t)3+3*Qi*t*(1-t)2+3*Qi+1*t2*(1-t)+Pi+1*t3 t∈[0，1]。
such a curve must pass through Pi，Pi+1Two control points. The shape of the curve can be conveniently adjusted by adjusting the control points. Finally, the curve (multi-segment broken line) is made to fit the oral cavity model surface, i.e. the vertex on the line moves to the nearest oral cavity model surface (also called shrink wrapping operation), and the curve follows the surface of the oral cavity modelThe control point is changed by the movement of the control point, so that the cutting curve can be adjusted quickly.
1.3 successful cutting of teeth with the cutting Curve
The cutting curve is transformed into a tubular model with a certain diameter, and the model is divided into tooth parts by using a bone operation. The cutting curve should conform to the model surface as much as possible, and the point on the curve that is furthest from the oral cavity model should be less than the radius of the tubular model so that the teeth are completely separated from the oral cavity into two parts. Therefore, the edges need to be subdivided in places where the edges are not tightly attached, and points on the edges need to be shrunk to the surface of the model.
And (3) curve fitting:
1) move the vertex on the line to the nearest oral model surface (also known as a shrink wrap operation)
2) Subdividing the edge whose distance from the edge center to the model exceeds a set pipe radius r into two parts
3) And circulating the steps 1) and 2) until the curve (the multi-segment broken line) is fit with the surface of the oral cavity model.
The existing method is complex in operation, long in operation time and slow in operation speed in a cutting line drawing mode. Each tooth requires more than 30 seconds of operation time, and after the dividing line is drawn, the adjustment is difficult to perform, and the cutting of one pair of teeth requires more than 20 minutes. The technology greatly improves the segmentation speed, only 10-20 control points are needed to be selected under the condition of no automatic calibration, and the operation only needs 9s on average. Under the condition of automatic calibration, a cutting line is automatically generated, and the average time of manually adjusting one tooth is only 3S.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus once an item is defined in one figure, it need not be further defined and explained in subsequent figures, and moreover, the terms "first", "second", "third", etc. are used merely to distinguish one description from another and are not to be construed as indicating or implying relative importance.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the present invention in its spirit and scope. Are intended to be covered by the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A tooth model fast cutting method based on a three-dimensional oral cavity model is characterized by comprising the following steps:
acquiring a three-dimensional oral cavity model based on a segment automatic division technology, preprocessing the tooth edge of the three-dimensional oral cavity model, and acquiring an edge cutting curve of the tooth model;
simplifying the edge cutting curve into a skeleton containing a plurality of control points, establishing a cubic Bezier curve by taking the skeleton as a control polygon, and controlling the curve shape of the cubic Bezier curve by adjusting the control points to obtain a cutting curve for cutting the tooth model;
converting the cutting curve into a tubular model, and segmenting the tubular model into the tooth model through a pool operation;
preprocessing the tooth margin by performing opening and closing operations on the tooth margin in the process of preprocessing the tooth margin of the three-dimensional oral cavity model, wherein the preprocessing is used for solving regional margin irregularity of the tooth margin, the opening operation is used for removing a fine protruding part of the regional boundary of the tooth margin, and the closing operation is used for filling a fine gap of the regional boundary of the tooth margin by filling a fine leak in the regional boundary of the tooth margin;
the opening operation comprises the following steps:
acquiring a first region including the tooth model and a second region not including the tooth model based on the tooth edge, wherein a first boundary line is arranged between the first region and the second region;
acquiring a first optimum boundary line of the first region and a third region between the first optimum boundary line and the first boundary line based on the first region, wherein the third region includes the fine protruding part of the first region;
based on the first feature of the second region, the first feature is endowed to the fine protruding part of the third region through k times of region reduction operation, and a first target region is obtained;
and based on the second feature of the first region, combining the second feature with the first region to form a first edge region of the tooth edge after the second feature is endowed to the first target region through k times of region expansion operation, and acquiring the edge cutting curve according to the first edge region.
2. The method for rapidly cutting the tooth model based on the three-dimensional oral cavity model according to claim 1, characterized in that:
the closing operation includes the steps of:
acquiring a second optimal boundary line of the first region based on a vertex of the fine protrusion part;
acquiring the region length of the fine protruding part based on the second optimal boundary line, and selecting a fourth region in the second region according to the region length, wherein the region length is used for indicating the vertical distance from the bottom of the region where the fine protruding part is located to the vertex;
and after the second characteristic is endowed to the first area and the fourth area, removing the fourth area, acquiring a second marginal area of the tooth margin, and acquiring the marginal cutting curve according to the second marginal area.
3. The method for rapidly cutting the tooth model based on the three-dimensional oral cavity model according to claim 2, characterized in that:
in the process of obtaining the edge-cut curve of the tooth model, the edge-cut curve is obtained according to the first edge region and the second edge region.
4. The method for rapidly cutting the tooth model based on the three-dimensional oral cavity model according to claim 3, characterized in that:
in the process of simplifying the edge cutting curve into a skeleton containing a plurality of control points, the edge cutting curve is simplified according to a DP algorithm, wherein the DP algorithm comprises the following steps:
s101, setting a thinning threshold value, and dividing the edge cutting curve into a plurality of curves to be processed;
s102, connecting the first point and the last point of the curve to be processed into a straight line in a virtual mode, solving the distance between the middle point between the first point and the last point and the straight line, and finding out a maximum distance value dmax;
s103, if dmax is less than threshold, the intermediate point is discarded; if dmax is larger than or equal to threshold, dividing the curve into two parts by taking the intermediate point corresponding to dmax as a boundary point, and repeating the steps S102-S103 on the two parts of the curve until all the intermediate points are processed, and taking the boundary point as the control point to construct the framework.
5. The method for rapidly cutting the tooth model based on the three-dimensional oral cavity model according to claim 4, characterized in that:
in the process of establishing the cubic Bezier curve, the control points are connected in sequence, and the coordinates of the control points are obtained;
acquiring a first vertex coordinate of a first vertex and a second vertex coordinate of a second vertex for generating the cubic Bezier curve according to the control point coordinate;
constructing the cubic Bezier curve according to the first vertex coordinate, the control point coordinate and the second vertex coordinate;
and moving the first vertex and the second vertex to the surface of the tooth model by adjusting the control point to obtain the cutting curve.
6. The method for rapidly cutting the tooth model based on the three-dimensional oral cavity model according to claim 5, characterized in that:
the expression of the first vertex coordinates is:
Figure FDA0003571258610000041
the expression of the second vertex coordinates is:
Figure FDA0003571258610000042
wherein, PiIs the ith control point coordinate, QiIs the first vertex coordinate, Qi+1Is the second vertex coordinate.
7. The method for rapidly cutting the tooth model based on the three-dimensional oral cavity model according to claim 6, characterized in that:
the expression of the cubic Bezier curve is as follows:
B(t)＝Pi*(1-t)3+3*Qi*t*(1-t)2+3*Qi+1*t2*(1-t)+Pi+1*t3 t∈[0，1]。
8. the method for rapidly cutting the tooth model based on the three-dimensional oral cavity model according to claim 7, characterized in that:
in the process of obtaining the cutting curve, collecting the positions of the cutting curve which are not tightly fitted with the tooth model, carrying out edge subdivision on the positions, wrapping points of the edges on the surface of the tooth model, and obtaining the cutting curve, wherein the process of adjusting the positions which are not tightly fitted comprises the following steps:
s201, moving the vertex of the edge to the surface of the tooth model;
s202, collecting the distance between the center of the edge and the tooth model, obtaining a first edge of which the distance is larger than the pipe radius of the tubular model, and subdividing the first edge into two parts based on the center;
s203, the steps S201-S202 are repeated until the cutting curve is attached to the surface of the tooth model.
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