CN106548484A - Product model dispersion point cloud Boundary characteristic extraction method based on two-dimentional convex closure - Google Patents

Abstract

The present invention provides a kind of product model dispersion point cloud Boundary characteristic extraction method based on two-dimentional convex closure, point cloud density is calculated by sampling analyses, traversal point cloud obtains the k neighbours of impact point, the fit Plane of impact point and its k neighbours is solved using least square method, impact point and its k neighbours are projected to into fit Plane, data for projection convex closure is obtained using value adding method, and product model scattered point cloud data Boundary characteristic extraction is realized based on convex closure.The method is applied to arbitrarily complicated product point cloud model, Boundary characteristic extraction processing efficient, stable, practical.

Description

Boundary Feature Extraction Method of Scattered Point Cloud of Product Model Based on 2D Convex Hull

technical field

The invention relates to the technical field of product reverse engineering, in particular to a method for extracting boundary features of scattered point clouds of products based on a two-dimensional convex hull.

Background technique

Reverse engineering technology mainly includes: model digitization, digital surface preprocessing and surface reconstruction and other processes. Among them, the digitization of the model is to study the measurement of the physical model. In the manufacturing industry, a common method is to use 3D scanning equipment to obtain product surface feature information. Digital surface preprocessing refers to the processing technology of measurement data. Surface reconstruction is to convert the measured data into a CAD model for actual processing and production. When using point cloud data for reconstruction, the processing of the overall data is complex and even difficult to achieve. It is necessary to first identify the boundary feature points or lines of the model, divide the data, and then process it in blocks, and finally realize the CAD modeling of the product . In addition, the point cloud boundary recognition technology has important applications in point cloud hole filling, cultural relic restoration and restoration.

Searching the prior art literature found that in the academic paper "Boundary Extraction Method of Spatial Triangular Mesh Surface" published in the academic journal "Journal of Image and Graphics of China" 2003, 8 (10), P1223-1226, by establishing the product The STL grid model of the model point cloud extracts point cloud boundary features. This method is accurate in boundary feature extraction. However, the triangulation algorithm suitable for any data point cloud has not been completely and effectively solved, and the triangulation method itself has high time complexity. It consumes a lot of system resources and runs slowly. Sun Dianzhu obtained the point cloud local surface reference point set and the fitting points Set the reference plane and project the reference point set to the plane, and extract the boundary features of the point cloud by comparing the angles of the projection data. The boundary feature point set extracted by this algorithm contains some internal points, and the extraction accuracy is low.

To sum up, the defects of the existing technology are: low precision of boundary feature extraction, small scope of application, unable to meet the needs of CAD modeling and rapid prototyping design in reverse engineering.

Contents of the invention

The invention provides a method for extracting boundary features of scattered point clouds of products based on a two-dimensional convex hull. The method is suitable for any complex product point cloud models, and the boundary feature extraction process is efficient, stable and practical.

The technical scheme of the present invention is: a kind of product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull, comprises the following steps:

Step 1, read the scattered point cloud data of the product model into the storage device, and calculate the point cloud density ρ;

Step 2, for any target point v, traverse the point cloud data, and search for the nearest k data points as the k-nearest neighbor points of the target point v;

Step 3, using the least squares method to solve the fitting plane P of the target point v and its k-nearest neighbor points;

Step 4, project the target point v and its k-nearest neighbor points to the fitting plane P, and solve the two-dimensional convex hull Q of the projected points;

Step 5, based on the convex hull Q, the boundary feature extraction of the scattered point cloud of the product model is realized.

Further, the calculation method for calculating the point cloud density ρ in step 1 is: randomly extract n points in the point cloud data, and for any point po _i extracted, traverse the point cloud data, and search for the m points closest to it, And calculate the distance d _{i, j} between each point in the nearest m points and po _i , then the point cloud density where i=0, 1, . . . n, j=0, 1, . . . m.

Further, the method of solving the fitting plane P in step 3 is: set the plane equation as c ₁ x+c ₂ y+C ₃ z+c ₄ =0, and its matrix equation is HC=0, where:

Then the equation of fitting plane P is

Using the eigenvector estimation method to solve the equation of the fitting plane P, the singular value decomposition of the matrix H ^T H is obtained

Among them, U and V are orthogonal matrices, w ₁ , w ₂ , w ₃ , and w ₄ are the eigenvalues of ^HTH , and the eigenvector corresponding to the smallest eigenvalue is the least squares solution of the equation for fitting the plane P, So as to obtain the fitting plane P.

Further, in step 4, assuming that the projection set of the target point v and its k-nearest neighbor points on the fitting plane P is V _P , then the steps to solve the two-dimensional convex hull Q of the projected points are:

Step 4.1, randomly select three points that are not collinear to form an initial convex hull, and add the three sides of the initial convex hull to the convex hull set Q _E ;

Step 4.2, delete the internal points of the convex hull and the vertices of the convex hull from V _P ;

Step 4.3, if V _P is empty, the program ends, and the convex hull set Q _E is the two-dimensional convex hull Q of the projected points to be solved; otherwise, perform step 4.4;

In step _4.4 , choose a point r _t (a _t , b _t , d _t ) in VP, update the convex hull data by value-added method and return to step 4.2.

Further, in step 4.2, the method of judging whether the data point in V _P is an internal point of the convex hull is: using the formula

Calculate the center of gravity O(a _o , b _o , d _o ) of the vertex set of the convex hull set _{Q E} , where (a _l , b _l , d _l ) is the coordinate of the data point in VP, s is the coordinate of the data point in _VP number; for any data point r _t (a _t , b _t , d _t ) in V _P , all convex hull edges E in the traversal convex hull set Q _E satisfy (F ₁ a _o +F ₂ b _o +F ₃ d _o +F ₄ )(F ₁ a _t +F ₂ b _t +F ₃ d _t +F ₄ )≥0, then r _t (a _t , b _t , d _t ) is the interior point of the convex hull, otherwise r _t (a _t , b _t , d _t ) are points outside the convex hull; F ₁ a+F ₂ b+F ₃ d+F ₄ =0 means a plane passing through the convex hull edge E and perpendicular to the fitting plane P.

Further, in step 4.4, the specific steps for updating the convex hull data are:

Step 4.4.1, query the visible edge set of point r _t (a _t , b _t , d _t );

Step 4.4.2, delete each edge in the visible edge set from the convex hull set Q _E ;

Step 4.4.3, connect the point r _t (a _t , b _t , d _t ) with the two endpoints of the convex hull remaining edge set to form a new boundary, and add it to the convex hull set Q _E.

Further, in step 4.4.1, for any convex hull E, set the plane equation passing through the convex hull E and perpendicular to the fitting plane P as F ₁ a+F ₂ b+F ₃ d+F ₄ =0, Then the method of judging whether the convex hull edge E _is the visible edge of the point r _t (at , b _t , d _t ) is: calculate the center of gravity O(a _o , b _o , d _o ) of the vertex set of the convex hull set Q _E , If (F ₁ a _o +F ₂ b _o +F ₃ d _o +F ₄ )(F ₁ a _t +F ₂ b _t +F ₃ d _t +F ₄ )<0, then the convex hull E is a visible edge , otherwise, the convex hull E is invisible.

Further, in step 5, the specific method of boundary feature extraction is: if the projection of the target point v on the fitting plane P belongs to the vertex of the two-dimensional convex hull Q, then the target point v is the boundary point of the product model, and its boundary probability anglePr(v)=1.0, otherwise, let v' be the projection of the target point v on the fitting plane P, v' _g v' _g+1 be the edge on the two-dimensional convex hull Q, v' _g , v' _{g +1} is the two endpoints of the side, wherein, g=0, 1, ..., GN; when g=GN, GN+1=0, GN is the number of vertices of the convex hull; traverse each side of the two-dimensional convex hull Q , to obtain the maximum angle β _g formed by the point v′ and the line connecting the two ends of the side v′ _g v′ _g+1 , the maximum angle β _g is the maximum value of ∠v′ _g v′v′ _g+1 , then the target The boundary probability of point v is:

Compare anglePr(v) with the preset threshold σ, if anglePr(v)≥σ, then the target point v is a boundary point, otherwise the target point v is an internal point.

Compared with the prior art, the present invention has the following advantages:

1) The least square method is used to obtain the fitting plane, and the scattered point cloud boundary feature extraction of the product model is obtained through the convex hull of the plane projection data, which has the advantages of simple geometric structure and convenient processing;

2) By constructing the center of gravity of the convex hull, the visible surface recognition is realized, and then the convex hull construction of the projection data is realized, which avoids the time consumption caused by vector calculation to find the visible edge in the traditional convex hull construction process, and has the characteristics of high operating efficiency and reliable accuracy ;

3) Calculate the density of scattered point clouds by sampling data, and traverse the point cloud model to obtain the target data k-nearest neighbors, which can be applied to point cloud models of various complex surfaces, and the data adaptability is strong.

Description of drawings

Fig. 1 is a flowchart of a specific embodiment of the present invention.

Fig. 2 is a schematic diagram of a product point cloud model according to a specific embodiment of the present invention.

Fig. 3 is a schematic diagram of the boundary feature extraction results of the product point cloud model according to a specific embodiment of the present invention.

detailed description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.

As shown in Figure 1, the process of the method for extracting the boundary features of the scattered point cloud of the product model based on the two-dimensional convex hull provided by the present invention is: the data reading program reads the point cloud data output by the product digitization device into the storage device, and forms A linear linked list that can be used for data access; perform data sampling on point cloud data and calculate point cloud density. For any target point v, use the k-nearest neighbor query program to obtain its k-nearest neighbor data points, and use the least squares method to fit The least squares fitting plane P of the target point v and its k-nearest neighbors, project the target point v and its k-nearest neighbors to the fitting plane P; use the value-added method to solve the two-dimensional convex hull Q of the projected data, based on the two-dimensional convex Package Q realizes the feature extraction of the scattered point cloud boundary of the product model.

The specific steps are:

Step 1, read the scattered point cloud data of the product model into the storage device, and calculate the point cloud density ρ.

The calculation method of the point cloud density ρ in this step is: randomly extract n points in the scattered point cloud of the product model, for any point po _i extracted, traverse the scattered point cloud data of the product model, and search for the m points closest to it , and calculate the distance d _{i, j} between each point in the nearest m points and po _i , then the point cloud dense expansion where i=0, 1, . . . n, j=0, 1, . . . m. The values of m and n are adjusted according to the point cloud distribution. Generally, n takes 1/1000 of the total number of point clouds, and m takes 8-20 to meet the requirements.

Step 2, for any target point v, traverse the scattered point cloud data of the product model, and search for the k nearest data points as the k-nearest neighbor points of the target point v.

Step 3, using the least squares method to solve the fitting plane P of the target point v and its k-nearest neighbor points.

The solution method of fitting plane P is: set the plane equation as c ₁ x+c ₂ y+c ₃ z+c ₄ =0, and its matrix equation is HC=0, where:

Then the equation of fitting plane P is

Using the eigenvector estimation method to solve the equation of the fitting plane P, the singular value decomposition of the matrix H ^T H is obtained

Among them, U and V are orthogonal matrices, w ₁ , w ₂ , w ₃ , and w ₄ are the eigenvalues of ^HTH , and the eigenvector corresponding to the smallest eigenvalue is the least squares solution of the equation for fitting the plane P, So as to obtain the fitting plane P.

Step 4. Project the target point v and its k-nearest neighbor points to the fitting plane P, and solve the two-dimensional convex hull Q of the projected points.

In this step, set the projection set of the target point v and its k-nearest neighbor points on the fitting plane P as V _P , then the solution steps of the two-dimensional convex hull Q of the projected points are:

Step 4.1, randomly select three points that are not collinear to form an initial convex hull, and add the three sides of the initial convex hull to the convex hull set Q _E .

Step 4.2, delete the internal points and vertices of the convex hull from V _P . The method of judging the internal points of the convex hull is: using the formula

Calculate the center of gravity O(a _o , b _o , d _o ) of the vertex set of the convex hull set _{Q E} , where (a _l , b _l , d _l ) is the coordinate of the data point in VP, s is the coordinate of the data point in _VP number; for any data point r _t (a _t , b _t , d _t ) in V _P , all convex hull edges E in the traversal convex hull set Q _E satisfy (F ₁ a _o +F ₂ b _o +F ₃ d _o +F ₄ )(F ₁ a _t +F ₂ b _t +F ₃ d _t +F ₄ )≥0, then r _t (a _t , b _t , d _t ) is an internal point, otherwise r _t (a _t , b _t , d _t ) are external points; where F ₁ a+F ₂ b+F ₃ d+F ₄ =0 is a plane passing through the convex hull E and perpendicular to the fitting plane P.

Step 4.3, if V _P is empty, the program ends, otherwise, go to step 4.4.

In step _4.4 , choose a point r _t (a _t , b _t , d _t ) in VP, update the convex hull data by value-added method and return to step 4.2. The specific steps of convex hull data update are:

Step 4.4.1, query the visible edge set of point r _t (a _t , b _t , d _t ). For any convex hull E, the plane equation passing through the convex hull E and perpendicular to the fitting plane P is F ₁ a+F ₂ b+F ₃ d+F ₄ =0, then whether the convex hull E is a point r _t The judgment method of the visible edge of (a _t , b _t , d _t ) is: calculate the center of gravity O(a _o , b _o , d _o ) of the vertex set of the convex hull set Q _E , if (F ₁ a _o +F ₂ b _o +F ₃ d _o +F ₄ )(F ₁ a _t +F ₂ b _t +F ₃ d _t +F ₄ )<0, then the convex hull E is visible, otherwise, the convex hull E is invisible side.

Step 4.4.2, delete each edge in the visible edge set from Q _E.

Step 4.4.3, connect the point r _t (a _t , b _t , d _t ) with the two endpoints of the remaining edge set of the convex hull to form a new boundary and add it to Q _E.

Step 5, based on the convex hull Q, the boundary feature extraction of the scattered point cloud of the product model is realized.

The specific method of boundary feature extraction in this step is: if the projection point of the target point v belongs to the vertex of the two-dimensional convex hull Q, then the target point v is the boundary point of the product model, and its boundary probability anglePr(v)=1.0, otherwise, set v ' is the projection of the target point v on the fitting plane P, v' _g v' _g+1 is the edge on the convex hull, v' _g and v' _g+1 are the two endpoints of the edge, where g=0 , 1,..., GN; where GN is the number of convex hull vertices. When g=GN, GN+1=0, that is, the last point in the set of ordered points constituting the two-dimensional convex hull Q forms an edge with the 0th point to perform the following angle calculation and comparison; traverse the two-dimensional convex hull Q , get the maximum angle β _g formed by the point v′ and the line connecting the two ends of the convex hull v′ _g v′ _g+1 , and the maximum angle β _g is ∠v′ _g v′v′ _g+1 The maximum value, then the boundary probability of the target point v is:

Compare anglePr(v) with the preset threshold σ, if anglePr(v)≥σ, then the target point v is a boundary point, otherwise the target point v is an internal point. The value of σ can be adjusted according to the point cloud density. When the density is high, the value should be appropriately larger, generally 0.8 to 1.0.

The following takes the product point cloud model shown in Figure 2 as an example to extract the boundary features of the product point cloud model.

Read the product point cloud data into the storage structure, the point cloud data is 58720, randomly extract 60 points from it, and traverse the point cloud data for any point po _i (i=0, 1, ..., 60) extracted, and search 8 points closest to it, and calculate the distance d _{i, j} (j=0, 1, ..., 8) between each point and po _i , then the point cloud is densely expanded The obtained point cloud density is 0.036mm. For any target point v, traverse the point cloud data, and obtain k data points closest to the target point v as k-nearest neighbors of v, where k is 12. The target point v and its k-nearest neighbors are regarded as a set V _P , and the fitting plane P of the set is solved by the least square method, and the target point v and its k-nearest neighbors are projected to the fitting plane P. The value-added method is used to solve the convex hull of the projected data. The specific method is: ① randomly select 3 points that are not collinear to form the initial convex hull, and add the three sides of the initial convex hull to the convex hull set Q _E ; ② add the internal points of the convex hull and the convex hull vertices are deleted from V _P ; ③ If V _P is empty, the program ends, otherwise step ④ is executed; ④ Choose a point r _t (a _t , b _t , d _t ) in V _P and use the value-added method to perform The convex hull data is updated and returns to step ②. After obtaining the projection data convex hull, judge the relationship between the target point v, the projection point and the convex hull v′ and the convex hull, if it belongs to the convex hull vertex, then the boundary probability of the point is 1.0, and the boundary extraction ends; otherwise, set v′ to be The projection of the target point v on the fitting plane P, v′ _g v′ _g+1 is the edge on the convex hull, v′ _g and v′ _g+1 are the two endpoints of the edge, where g=0,1 , ..., GN; when g=GN, GN+1=0, GN is the number of vertices of the convex hull; traverse each edge of the two-dimensional convex hull Q, and obtain the point v' and the convex hull edge v' _g v' _{g+ 1} The maximum angle β _g formed by the line connecting the two ends, the maximum angle β _g is the maximum value of ∠v′ _g v′v′ _g+1 , then the boundary probability of the target point v is:

Compare anglePr(v) with the preset threshold σ, if anglePr(v)≥σ, then the target point v is a boundary point, otherwise the target point v is an internal point. It can be seen from the point cloud density that the point cloud distribution is relatively dense, so the value of σ increases correspondingly, taking 0.95.

The above disclosure is only a preferred embodiment of the present invention, but the present invention is not limited thereto, any non-creative changes that those skilled in the art can think of, and some improvements and modifications made without departing from the principle of the present invention , should fall within the protection scope of the present invention.

Claims (8)

1. A product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull, is characterized in that, comprises the following steps: Step 1, read the scattered point cloud data of the product model into the storage device, and calculate the point cloud density ρ; Step 2, for any target point v, traverse the point cloud data, and search for the nearest k data points as the k-nearest neighbor points of the target point v; Step 3, using the least squares method to solve the fitting plane P of the target point v and its k-nearest neighbor points; Step 4, project the target point v and its k-nearest neighbor points to the fitting plane P, and solve the two-dimensional convex hull Q of the projected points; Step 5, based on the convex hull Q, the boundary feature extraction of the scattered point cloud of the product model is realized. 2. the product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull according to claim 1, is characterized in that, the calculation method of calculating point cloud density ρ in step 1 is: randomly extract n in point cloud data Points, for any point po _i extracted, traverse the point cloud data, search for the nearest m points, and calculate the distance d _i,j between each point of the nearest m points and po _i , then the point cloud density where i=0, 1, . . . n, j=0, 1, . . . m. 3. the product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull according to claim 1, is characterized in that, the solution method of fitting plane P in step 3 is: set plane equation as c _x +c ₂ y+c ₃ z+c ₄ =0, its matrix equation is HC=0, where: $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& \mathrm{<span\; class="notranslate">\; 1</span>}\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}& {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}& \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ Then the equation of fitting plane P is $\mathrm{<span\; class="notranslate">\; h</span>}\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right]$ Using the eigenvector estimation method to solve the equation of the fitting plane P, the singular value decomposition of the matrix H ^T H is obtained ${\mathrm{<span\; class="notranslate">\; h</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; u</span>}\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\end{array}\right]{\mathrm{<span\; class="notranslate">\; V</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$ Among them, U and V are orthogonal matrices, w ₁ , w ₂ , w ₃ , and w ₄ are the eigenvalues of ^HTH , and the eigenvector corresponding to the smallest eigenvalue is the least squares solution of the equation for fitting the plane P, So as to obtain the fitting plane P. 4. the product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull according to claim 1, is characterized in that, in step 4, set target point v and k-nearest neighbor point thereof on fitting plane P The projection set is V _P , then the steps to solve the two-dimensional convex hull Q of the projected points are: Step 4.1, randomly select three points that are not collinear to form an initial convex hull, and add the three sides of the initial convex hull to the convex hull set Q _E ; Step 4.2, delete the internal points of the convex hull and the vertices of the convex hull from V _P ; Step 4.3, if V _P is empty, the program ends, and the convex hull set Q _E is the two-dimensional convex hull Q of the projected points to be solved; otherwise, perform step 4.4; In step 4.4, choose a point r _t (a _t ,b _t ,d _t ) from V _P , use the value-added method to update the convex hull data and return to step 4.2. 5. the product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull according to claim 4, it is characterized in that, in step 4.2, the _judging method whether data point is convex hull internal point among the VP is: adopt formula ${\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}$ Calculate the center of gravity O(a _o ,b _o ,d _o ) of the vertex set of the convex hull set _{Q E} , where (a _l , b _l , d _l ) are the coordinates of the data points in VP, and s is the coordinates of the data points in _VP number; for any data point r _t (a _t ,b _t ,d _t ) in V _P , all convex hull edges E in the traversal convex hull set Q _E satisfy (F ₁ a _o +F ₂ b _o +F ₃ d _o +F ₄ )(F ₁ a _t +F ₂ b _t +F ₃ d _t +F ₄ )≥0, then r _t (a _t ,b _t ,d _t ) is the interior point of the convex hull, otherwise r _t (a _t , b _t , d _t ) are points outside the convex hull; F ₁ a+F ₂ b+F ₃ d+F ₄ =0 means a plane passing through the convex hull edge E and perpendicular to the fitting plane P. 6. the product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull according to claim 4, is characterized in that, in step 4.4, the specific steps of convex hull data update are: Step 4.4.1, query the visible edge set of point r _t (a _t ,b _t ,d _t ); Step 4.4.2, delete each edge in the visible edge set from the convex hull set Q _E ; Step 4.4.3, connect the point r _t (a _t ,b _t ,d _t ) with the two endpoints of the convex hull remaining edge set to form a new boundary, and add it to the convex hull set Q _E. 7. The product model scattered point cloud boundary feature extraction method based on two-dimensional convex hull according to claim 6, characterized in that, in step 4.4.1, for any convex hull edge E, set the convex hull edge E and vertical Since the plane equation of the fitting plane P is F ₁ a+F ₂ b+F ₃ d+F ₄ ＝0, whether the convex hull E is the visible side of the point r _t (a _t ,b _t ,d _t ) The judgment method is: calculate the center of gravity O(a _o ,b _o ,d _o ) of the vertex set of the convex hull set Q _E , if (F ₁ a _o +F ₂ b _o +F ₃ d _o +F ₄ )(F ₁ a _t +F ₂ b _t +F ₃ d _t +F ₄ )<0, then the convex hull E is a visible edge, otherwise, the convex hull E is an invisible edge. 8. The method for extracting boundary features of scattered point clouds of product models based on two-dimensional convex hulls according to claim 1, characterized in that, in step 5, the specific method of boundary feature extraction is: if the target point v is on the fitting plane P The projection on belongs to the vertex of the two-dimensional convex hull Q, then the target point v is the boundary point of the product model, and its boundary probability anglePr(v)=1.0, otherwise, let v' be the projection of the target point v on the fitting plane P , v′ _g v′ _g+1 is the edge on the two-dimensional convex hull Q, v′ _g and v′ _g+1 are the two endpoints of the edge, where g=0,1,…,GN; when g= When GN, GN+1=0, GN is the number of vertices of the convex hull; traverse each edge of the two-dimensional convex hull Q, and obtain the maximum angle between the point v' and the line connecting the two ends of the edge v' _g v' _g+1 β _g , the maximum included angle β _g is the maximum value of ∠v _g ′v′v′ _g+1 , then the boundary probability of the target point v is: $\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; l</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; v</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 1.0</span>}<span\; class="notranslate">\; )</span>$ Compare anglePr(v) with the preset threshold σ, if anglePr(v)≥σ, then the target point v is a boundary point, otherwise the target point v is an internal point.