A quasi-minimum volume bounding box optimization method for three-dimensional point sets of inclined molds

Abstract

The present invention discloses a quasi-minimum volume bounding box optimization method for a three-dimensional point set of an inclined mold, comprising the following steps: S1, based on the principle that a convex multi-deformation in two-dimensional space and a minimum enclosing rectangle must be collinear, the concept of a minimum volume constant coefficient is introduced, and a rotation axis calculation model for a quasi-minimum bounding box of a three-dimensional model is established using a linear space principle; S2, based on vertex area weighting and model detail feature evaluation, a two-dimensional projection vertex weight mathematical model is established; S3, the bounding box accuracy λ is set, a preliminary projection plane YOZ is determined based on the synchronization of the X axis based on the rotation axis calculation model, a covariance matrix model is constructed based on the two-dimensional projection vertex weight mathematical model and the projection vertex set, and then the vertex projection basis is solved, the Y and Z axes are synchronized, and the AABB algorithm is called to calculate the volume of the bounding box; S4, the Y and Z axes are used as the rotation axes to calculate the model synchronization object and S3 is iteratively repeated, thereby obtaining a quasi-minimum volume bounding box; the present invention achieves a reduction in bounding box solution time and an improvement in fitting rate.

Description

Technical Field

[0001] The present invention relates to the technical field of bounding boxes, and in particular to a method for optimizing a quasi-minimum volume bounding box of a three-dimensional point set of an inclined mold. Background Art

[0002] Since mold companies often outsource non-parametric part models to downstream manufacturers, manufacturers often estimate part blanks based on experience. This is especially true for rough machining, where the estimated impact on work time varies significantly. Currently, most 3D software uses a built-in axis alignment (AABB) algorithm to construct rough machining blanks for 3D point set part models. The axis alignment algorithm essentially traverses the model's point set, calculating in an absolute coordinate system and constructing a rectangular entity parallel to the coordinate axis. For models orthogonal to the absolute coordinate system, the estimated bounding box fit is acceptable. However, for models not orthogonal to the coordinate system, especially when the visual axis is tilted, the generated bounding box has large gaps in the corners.

[0003] The directed bounding box (OBB) algorithm has no requirements for the position of the part's main axis. The core of the algorithm is mainly to traverse the three-dimensional model face set, assign weights to each vertex based on the proportion of the area of ​​each plane, construct a covariance matrix based on the vertex set of each plane, calculate three orthogonal basis vectors, project the vertices onto the basis after normalization, calculate the xmax(min), ymax(min), and zmax(min) of each projection point under the basis, and generate a cuboid in the form parallel to the basis. The cuboid generated based on the three-dimensional model of uniform vertex set has a good fit, but the model needs to be discretized in advance and for nonlinear models with large differences in vertex distribution, accurate results cannot be obtained in one calculation, and the weight model needs to be adjusted for iterative calculation. The time complexity is (n).

[0004] Recent research on quasi-minimum bounding boxes has revealed that the minimum bounding rectangle of any closed polygon in two dimensions must be collinear with one of the polygon's edges. In three dimensions, there are two main approaches. One is to iteratively rotate the model or absolute coordinate system based on the principle of the OBB algorithm to solve the principal axis, and then use the AABB algorithm to solve the cuboid after each iterative rotation, outputting a quasi-minimum bounding box. The time complexity is generally (n3). The other is to process a 3D point set and use the processed point set as the object of the OBB algorithm. If the weight model in the algorithm has a large proportion of random factors, the weight parameter algorithm is used to iteratively output the quasi-minimum bounding box. The time complexity is generally greater than (n).

[0005] Therefore, the existing bounding box optimization method for molds has the problems of long solution time and low bounding box fitting efficiency. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a quasi-minimum volume bounding box optimization method for a three-dimensional point set of an inclined mold, which greatly reduces the solution time of the bounding box and greatly improves the fitting rate of the bounding box.

[0007] To achieve the above object, the present invention adopts a technical solution: a method for optimizing a quasi-minimum volume bounding box of a three-dimensional point set of an inclined mold, comprising the following steps:

[0008] S1. Based on the principle that convex polygon deformation in two-dimensional space and the minimum bounding rectangle must be collinear, the concept of minimum volume constant coefficient is introduced, and the linear space principle is used to establish a quasi-minimum bounding box rotation axis calculation model for three-dimensional models;

[0009] S2. Establish a two-dimensional projection vertex weight mathematical model based on vertex area weighting and model detail feature evaluation;

[0010] S3. Set the bounding box precision λ, synchronize the X axis based on the rotation axis calculation model to determine the preliminary projection plane YOZ, build a covariance matrix model based on the two-dimensional projection vertex weight mathematical model and the projection vertex set, then solve the vertex projection basis, synchronize the Y and Z axes, and call the AABB algorithm to calculate the volume of the bounding box;

[0011] S4. Calculate the model synchronization object using the Y axis and the Z axis as the rotation axis and iteratively repeat S3 to obtain a bounding box with a quasi-minimum volume.

[0012] Preferably, the specific steps of step S1 are as follows:

[0013] S101. Let S be the three-dimensional point set of the part, let B be the minimum bounding box of S, let L be the distance between the two farthest points in the point set S, let l be the longest common edge between B and S, whose endpoints are s and t, then |st| ≤ L ≤ √3|st|;

[0014] S102. Let G be the gridding of B, with a grid side length of £ / (2√d), where d is the dimension. Let x, y be any two points in B, and xG, yG be the two points in G closest to x, y, then |xy|-l≤|xGyG|≤|xy|+l;

[0015] S103. Since L(G)≥L(S)-l, l≤(£ / 2)L(S), replace xy with s and t, then

[0016] |st|≥|sGtG|-l= L(G)-l≥L(S)-2l≥(1-£)L(S), that is, |st|≥(1-£)L(S), then L(G) is the (1-£) approximation of L(S);

[0017] S104. Let plane H be perpendicular to st, let Q be the projection of S on H, from which we can get the convex polygon formed on plane H and the projected quadrilateral of B has the following characteristics: √2|s't'|≥L(Q); let vector u be the normal vector of plane H, let The projected quadrilateral of B has an area of ​​R, then the quasi-minimum bounding box B*=6√6B(S,{st,u}); when one of the vertices of B is translated in a direction parallel to the edge, the volume does not change, then

[0018] ;

[0019] but ;

[0020] S105. Since S is contained in G and contained in B*, then V(G)≤V(B)≤V(B*)≤ V(G);

[0021] S106, V(G)≤V(B)≤V(B*)≤ V(G) extends to the d-1 dimension and outputs the Cartesian product of the d-1 dimension and the projection direction vector. Since in two-dimensional space, the minimum bounding rectangle of the plane and the convex polygon have at least one collinear edge, that is, the Cartesian product is 0, then in d-dimensional space, the Cartesian product of the quasi-minimum bounding box axis and the d-dimensional point set normal is 0, that is, the quasi-minimum bounding box of the three-dimensional model has at least one pair of edges and the model convex plane normal vector or cylinder axis quantity whose Cartesian product is 0;

[0022] S107. Traverse all faces of the model and calculate the areas of all faces to obtain a set S{s1, s2…si…sn};

[0023] S108. Calculate the normal direction of the flat surface and the axial direction of the cylindrical or conical surface to obtain a vector set F{f1, f2…fi…fn}. The vector set F corresponds to the elements of the set S one by one, that is, si is the weight of fi;

[0024] S109, merging vectors in the same direction to obtain a new set F'{f 'i}, and summing the corresponding weights in the same direction to obtain a new set S'{S 'i};

[0025] S110, find the maximum value of S'{S'i}, output the corresponding f'i according to the mapping relationship between S' and F', and the vector is the rotation axis direction vector. Normalize f'i to obtain the rotation axis calculation model i.

[0026] Preferably, step S2 includes the following process:

[0027] S201. Construct a vertex region. The vertex region s to which the vertex P belongs is s = s1 + s2 + s3 + s4. Any region si is a polygon formed by the perpendicular bisectors of the adjacent sides of the supporting vertex and its adjacent sides. Taking region s1 as an example, its area calculation formula is:

[0028] ; Therefore, for vertex P, the area s=Σsi, which is the sum of all sub-areas;

[0029] S202, based on The area of ​​any vertex Pi on the three-dimensional model can be expressed as Si= ;

[0030] S203. Based on the Voronoi polygon, the vertex area weight Qi = si / s can be obtained;

[0031] S204, the model detail features introduce the evaluation coefficient ei;

[0032] S205. Based on the evaluation coefficient and the vertex area weighting, a vertex weight mathematical model wi=Qi*ei can be obtained.

[0033] Preferably, the specific steps of step S3 are as follows:

[0034] S301, setting the bounding box output accuracy to λ;

[0035] S302, select the X axis and synchronize it with the rotation axis calculation model i;

[0036] S303, projecting the vertices of the three-dimensional model onto the YOZ plane to obtain a two-dimensional vertex set Q{qxi};

[0037] S304, perform mean processing on the Y and Z coordinates of the two-dimensional vertex set, and declination on the vertex set to obtain a new set Q'{q'i}, and construct a covariance mathematical model based on the weight model: R=1 / nΣi=1wi2qxzi.qxyi; then construct a covariance matrix A[cov(y,z)]= based on the covariance mathematical model. ;

[0038] S305. Since the covariance matrix A is a symmetric matrix, there exists a pair of orthogonal eigenvectors. Solve the eigenvalues ​​of the matrix A to obtain a pair of orthogonal vectors j and z. Normalize j and z.

[0039] S306. Synchronize the Y and Z axes with the two orthogonal bases j and z, call the AABB function, and solve the bounding box Bx of the model in the new coordinate system. The volume accuracy λx = Vobject / VB. Compare λx with λ. If λx ≥ λ, output Bx.

[0040] Preferably, the specific steps of step S4 are as follows:

[0041] S401, if λx<λ, select the Y axis and synchronize it with the rotation axis calculation model i;

[0042] S402, project the vertices of the three-dimensional model onto the XOZ plane to obtain a two-dimensional vertex set Q{qyi}. Subsequent processing steps are the same as S304-S306. Finally, the volume accuracy λy=Vobject / VB. Compare λy with λ. If λy≥λ, output By.

[0043] S403, if λy<λ, then select the Z axis and synchronize it with the rotation axis calculation model i;

[0044] S404. Project the 3D model vertices onto the XOY plane to obtain a 2D vertex set Q{qzi}. Subsequent processing steps are the same as S304-S306. The volumetric accuracy λz = Vobject / VB. Compare λz with λ. If λz ≥ λ, output Bz.

[0045] S405. If λx, λy, and λz are all less than λ, then MAX{λx, λy, λz} and output the corresponding Bi (where i is x, y, and z).

[0046] Due to the application of the above technical solution, the present invention has the following advantages compared with the prior art:

[0047] The quasi-minimum volume bounding box optimization method for the three-dimensional point set of an inclined mold of the present invention uses the linear space principle to establish a quasi-minimum volume bounding box rotation axis calculation model of the three-dimensional model, and then selects the part rotation axis based on the rotation axis calculation model, and uses this to determine the projection surface, thereby converting the three-dimensional vertex set into a two-dimensional vertex set.

[0048] The PCA algorithm is used for all points in the two-dimensional vertex set, that is, a covariance matrix is ​​constructed. The geometric information of the points that may be lost in the projection is weighted in the form of Voronoi polygons and feature information assignments to solve two orthogonal vectors. Finally, the original standard coordinates are synchronized with the inertial axis, and the AABB algorithm is called to output directly. The entire calculation time from the rotation axis plus the projection is at most 3n, which ultimately greatly reduces the bounding box solution time and greatly improves the bounding box fitting rate, thereby achieving optimization of the minimum volume bounding box. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The technical solution of the present invention will be further described below with reference to the accompanying drawings:

[0050] Figure 1 A schematic diagram of a flow chart of an embodiment of the present invention;

[0051] Figure 2 is a top view of the polyhedron in S2 in one embodiment of the present invention;

[0052] Figure 3 Schematic diagram of the process of S3 and S4 in one embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0054] The present invention provides a method for optimizing a quasi-minimum volume bounding box of a three-dimensional point set of an inclined mold, so as to solve the problem in the prior art that the time complexity of the quasi-minimum bounding box outputted by the inclined mold is generally high.

[0055] For ease of understanding, the specific process in the embodiment of this application is described below. Figure 1 , a quasi-minimum volume bounding box optimization method for a three-dimensional point set of an inclined mold in an embodiment of the present application includes the following steps: S1, based on the principle that convex polygon deformation and the minimum enclosing rectangle in two-dimensional space must be collinear, the concept of minimum volume constant coefficient is introduced, and the linear space principle is used to establish a quasi-minimum bounding box rotation axis calculation model for the three-dimensional model; S2, based on vertex area weighting and model detail feature evaluation, a two-dimensional projection vertex weight mathematical model is established; S3, the bounding box accuracy λ is set, and the preliminary projection plane YOZ is determined based on the X-axis synchronization of the rotation axis calculation model, and a covariance matrix model is constructed based on the two-dimensional projection vertex weight mathematical model and the projection vertex set, and then the vertex projection basis is solved, the Y and Z axes are synchronized, and the AABB algorithm is called to calculate the volume of the bounding box; S4, the Y and Z axes are used as the rotation axis calculation model, and S3 is iteratively repeated for the model synchronization object, so as to obtain a quasi-minimum volume bounding box.

[0056] In step S1, the specific operation process is as follows:

[0057] S101. Let S be the three-dimensional point set of the part, let B be the minimum bounding box of S, let L be the distance between the two farthest points in the point set S, let l be the longest common edge of B and S, and let its endpoints be s and t, then |st|≤L≤√3|st|(1-1).

[0058] S102. Let G be the gridding of B, with the grid side length being £ / (2√d), d being the dimension, let x, y be any two points in B, and xG, yG be the two points in G closest to x, y, then |xy|-l≤|xGyG|≤|xy|+l.

[0059] S103, L(G) ≥ L(S)-l, l ≤ (£ / 2)L(S), replace s and t with xy, then |st| ≥ |sGtG|-l = L(G)-l ≥ L(S)-2l ≥ (1-£)L(S), that is, |st| ≥ (1-£)L(S) (1-2);

[0060] Thus, from formulas (1-1) and (1-2), we can obtain that L(G) is an approximate value of (1-£) of L(S).

[0061] S104. Let plane H be perpendicular to st, and let Q be the projection of S on H. From this, we can obtain that the convex polygon formed on plane H and the projected quadrilateral of B have the following characteristics: √2|s't'|≥L(Q).

[0062] Let vector u be the normal vector of plane H, let The projected quadrilateral of B has an area of ​​R, then the quasi-minimum bounding box B*=6√6B(S,{st,u}); Obviously, when one of the vertices of B is translated in a direction parallel to the edge, the volume will not change, then

[0063] ;but

[0064] ;

[0065] S105. Since S is contained in G and contained in B*, then V(G)≤V(B)≤V(B*)≤ V(G)(1-3);

[0066] S106. Extend formula (1-3) to the d-1 dimension, and output the Cartesian product of the d-1 dimension and the projection direction vector. Since in two-dimensional space, the minimum enclosing rectangle of the plane and the convex polygon have at least one collinear side, that is, the Cartesian product is 0, then in d-dimensional space, the Cartesian product of the quasi-minimum bounding box axis and the d-dimensional point set normal is 0, that is, the quasi-minimum bounding box of the three-dimensional model has at least one pair of sides whose Cartesian product with the model convex plane normal vector or cylinder axis is 0.

[0067] 1S07. Traverse all faces of the model and calculate the areas of all faces to obtain the set S{s1, s2…si…sn}.

[0068] S108. Calculate the normal direction of the flat surface and the axial direction of the cylindrical or conical surface to obtain the vector set F{f1, f2…fi…fn}. The vector set F corresponds to the elements of the set S one by one, that is, si is the weight of fi.

[0069] S109. Merge the vectors in the same direction to obtain a new set F'{f 'i}, and sum the corresponding weights in the same direction to obtain a new set S'{S 'i}.

[0070] S110, find the maximum value of S'{S'i}, output the corresponding f'i according to the mapping relationship between S' and F', and the vector is the rotation axis direction vector. Normalize f'i to obtain the rotation axis calculation model i.

[0071] based on Figure 2 In step S2, since the traditional area weighted method repeatedly calculates the weighted area of ​​coplanar vertices, the distance between any point in the polygon area of ​​the Voronoi polygon and the polygon site is closer than the distance to the adjacent polygon site. If the vertex is set as the polygon site, then any vertex has a strongly associated area to which it belongs. The model plane is reconstructed based on the Voronoi polygon, and the area contained in any vertex is independent.

[0072] Therefore, a two-dimensional projection vertex weight mathematical model is established, which specifically includes the following steps:

[0073] S201, construct the vertex area based on Figure 2 , which is a top view of a polyhedron. The vertex area s to which the vertex P belongs is s=s1+s2+s3+s4, where any si area is a polygon consisting of the perpendicular bisectors of the adjacent sides of the supporting vertex and its adjacent sides. Taking the s1 area as an example, its area calculation formula is: (2-1); Therefore, for vertex P, the area of ​​the region s=Σsi, which is the sum of all sub-regions.

[0074] S202, based on (2-1), the area of ​​any vertex Pi on the three-dimensional model can be expressed as Si= .

[0075] S203. Based on the Voronoi polygon, the vertex area weight Qi=Si / S can be obtained.

[0076] S204: For model details with complex features, an evaluation coefficient ei is introduced. In this embodiment, the relevant details include holes and slots, which are defined using the face-edge rule as shown in the following table:

[0077] Feature Rule Evaluation Table

[0078]

[0079] 206. Based on the evaluation coefficient and vertex area weighting, the vertex weight mathematical model wi=Qi*ei can be obtained.

[0080] based on Figure 3 In this embodiment, the specific steps in step S3 are as follows:

[0081] S301. Set the bounding box output accuracy to λ.

[0082] S302 , selecting the X axis and synchronizing it with the rotation axis calculation model i.

[0083] S303 , projecting the vertices of the three-dimensional model onto the YOZ plane to obtain a two-dimensional vertex set Q{qxi}.

[0084] S304. Perform mean processing on the Y and Z coordinates of the two-dimensional vertex set, and declination on the vertex set to obtain a new set Q'{q'i}. Construct a covariance mathematical model based on the weight model: R=1 / nΣi=1wi2qxzi.qxyi. Construct a covariance matrix A[cov(y,z)]= based on the covariance mathematical model. .

[0085] 305. Since the covariance matrix A is a symmetric matrix, there must be a pair of orthogonal eigenvectors. Solve the eigenvalues ​​of the matrix A to obtain a pair of orthogonal vectors j and z, and normalize j and z.

[0086] 306. Synchronize the Y and Z axes with the two orthogonal bases j and z, call the AABB function, and solve the bounding box Bx of the model in the new coordinate system. The volume accuracy λx = Vobject / VB. Compare λx with λ. If λx ≥ λ, output Bx.

[0087] In step S4, the Y axis and the Z axis are used as the rotation axis respectively to calculate the model synchronization i object and iteratively repeat step S3. The specific process is as follows:

[0088] S401, if λx<λ, select the Y axis and synchronize it with the rotation axis calculation model i;

[0089] S402 : Project the 3D model vertices onto the XOZ plane to obtain a 2D vertex set Q{qyi}. Subsequent processing steps are the same as S304 - S306 . Volume accuracy λy = Vobject / VB . Compare λy with λ. If λy ≥ λ, output By.

[0090] S403, if λy<λ, then select the Z axis and synchronize it with the rotation axis calculation model i;

[0091] S404. Project the 3D model vertices onto the XOY plane to obtain a 2D vertex set Q{qzi}. Subsequent processing steps are the same as S304-S306. The volumetric accuracy λz = Vobject / VB. Compare λz with λ. If λz ≥ λ, output Bz.

[0092] S405. If λx, λy, and λz are all less than λ, then MAX{λx, λy, λz} and output the corresponding Bi (i is x, y, z).

[0093] To sum up, the quasi-minimum volume bounding box optimization method of the inclined mold three-dimensional point set of the present invention uses the linear space principle to establish a quasi-minimum bounding box rotation axis calculation model of the three-dimensional model, and then selects the part rotation axis based on the rotation axis calculation model, and uses this to determine the projection surface, and converts the three-dimensional vertex set into a two-dimensional vertex set.

[0094] The PCA algorithm is used for all points in the two-dimensional vertex set, that is, a covariance matrix is ​​constructed. The geometric information of the points that may be lost in the projection is weighted in the form of Voronoi polygons and feature information assignments to solve two orthogonal vectors. Finally, the original standard coordinates are synchronized with the inertial axis, and the AABB algorithm is called to output directly. The entire calculation time from the rotation axis plus the projection is at most 3n, which ultimately greatly reduces the bounding box solution time and greatly improves the bounding box fitting rate, thereby achieving optimization of the minimum volume bounding box.

[0095] In addition, for parts that are not orthogonal to the absolute coordinate system, the generated bounding box has a high degree of fit, and the parts at the edge corners fit the bounding box. For parts with a large number of vertices, although a covariance matrix is ​​constructed, the vertices are pre-processed for dimensionality reduction. The dimensionality reduction process here is to use the linear space principle in S1 to establish a quasi-minimum bounding box rotation axis calculation model for the three-dimensional model, and then select the part rotation axis based on the rotation axis calculation model, and use this to determine the projection surface, converting the three-dimensional vertex set into a two-dimensional vertex set. Based on this, the algorithm calculation time is greatly reduced and the efficiency of the bounding box solution is improved.

[0096] As described above, the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for optimizing the quasi-minimum volume bounding box of a three-dimensional point set of an inclined mold, characterized by: The steps include: S1. Based on the principle that convex polygons and minimum bounding rectangles in two-dimensional space must be collinear, the concept of minimum volume constant coefficient is introduced, and a quasi-minimum bounding box rotation axis calculation model for a three-dimensional model is established using the principle of linear space. The specific steps include the following: S101. Traverse all faces of the model and calculate the areas of all faces to obtain the set S{s1, s2…si…sn}; S102. Calculate the normal direction of the flat surface and the axial direction of the cylindrical or conical surface to obtain a vector set F{f1, f2…fi…fn}. The vector set F corresponds to the elements of the set S one by one, that is, si is the weight of fi; S103, merging vectors in the same direction to obtain a new set F'{f 'i}, and summing the corresponding weights in the same direction to obtain a new set S'{S 'i}; S104, find the maximum value of S'{S'i}, output the corresponding f'i according to the mapping relationship between S' and F', this vector is the rotation axis direction vector, and normalize f'i to obtain the rotation axis calculation model i; S2. Establish a two-dimensional projection vertex weight mathematical model based on vertex area weighting and model detail feature evaluation; the specific steps are as follows: S201, constructing a vertex area; S202, the area of ​​any vertex Pi on the three-dimensional model is expressed as Si; S203. Based on the Voronoi polygon, the vertex area weight Qi = Si / s can be obtained; S204, introducing an evaluation coefficient ei based on the detailed features of the model; S205, based on the evaluation coefficient and the vertex area weighting, a vertex weight mathematical model wi=Qi*ei can be obtained; S3. Set the bounding box precision λ, synchronize the X axis based on the rotation axis calculation model to determine the preliminary projection plane YOZ, build a covariance matrix model based on the two-dimensional projection vertex weight mathematical model and the projection vertex set, then solve the vertex projection basis, synchronize the Y and Z axes, and call the AABB algorithm to calculate the volume of the bounding box. The specific steps are as follows: S301, setting the bounding box output accuracy to λ; S302, select the X axis and synchronize it with the rotation axis calculation model i; S303, projecting the vertices of the three-dimensional model onto the YOZ plane to obtain a two-dimensional vertex set Q{qxi}; S304, perform mean processing on the Y and Z coordinates of the two-dimensional vertex set, and perform declination on the vertex set to obtain a new set Q'{q'i}, and construct a covariance mathematical model based on the weight model: ; i = 1, 2, ...; then construct the covariance matrix A[cov(y,z)]= based on the covariance mathematical model ; S305. Since the covariance matrix A is a symmetric matrix, there exists a pair of orthogonal eigenvectors. Solve the eigenvalues ​​of the matrix A to obtain a pair of orthogonal vectors j and z. Normalize j and z. S306. Synchronize the Y and Z axes with the two orthogonal bases j and z, call the AABB function, and solve the bounding box Bx of the model in the new coordinate system. The volume accuracy λx = Vobject / VB. Compare λx with λ. If λx ≥ λ, output Bx. S4. Calculate the model synchronization object using the Y axis and the Z axis as the rotation axis and iteratively repeat S3 to obtain a bounding box with a quasi-minimum volume.

2. The method for optimizing the quasi-minimum volume bounding box of a three-dimensional point set of an inclined mold according to claim 1, wherein: The specific steps of step S4 are as follows: S401, if λx<λ, select the Y axis and synchronize it with the rotation axis calculation model i; S402, project the vertices of the three-dimensional model onto the XOZ plane to obtain a two-dimensional vertex set Q{qyi}. Subsequent processing steps are the same as S304-S306. Finally, the volume accuracy λy=Vobject / VB. Compare λy with λ. If λy≥λ, output By. S403, if λy<λ, then select the Z axis and synchronize it with the rotation axis calculation model i; S404, project the vertices of the three-dimensional model onto the XOY plane to obtain a two-dimensional vertex set Q{qzi}. Subsequent processing steps are the same as S304-S306. Volume accuracy λz = Vobject / VB. Compare λz with λ. If λz ≥ λ, output Bz. S405. If λx, λy, and λz are all less than λ, then MAX{λx, λy, λz} and output the corresponding Bi, where i is x, y, and z.

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