CN117876554B - Convex hull-based plate minimum bounding box calculation method and system - Google Patents
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Abstract
The invention provides a convex hull-based plate minimum bounding box calculation method and a convex hull-based plate minimum bounding box calculation system. The method and the device calculate bounding boxes of the plates accurately, efficiently and in batches by using the coordinate points of the plates, intelligently detect all possible bounding boxes of the plates, select minimum values as output, and simultaneously give out the coordinates of each vertex of the bounding boxes in a three-dimensional space to complete visual expression. The invention automatically calculates the accurate solution of the minimum bounding box of the plate and displays the minimum bounding box in the three-dimensional model, thereby bringing new technology and method innovation to the field of building industrialization, accelerating the digitizing process of the building industry and having important theoretical and practical significance.
Description
Technical Field
The invention belongs to the technical field of building industrialization, and particularly relates to a convex hull-based plate minimum bounding box calculation method and system.
Background
The building industrialization comprises design industrialization, cost analysis industrialization and digital construction industrialization, and the design mode based on the traditional 2D engineering drawing is required to be upgraded to a digital mode based on a three-dimensional digital model and integrating design, simulation and processing, so that the direct butt joint processing of the three-dimensional model is realized, and the digitization of the processing process is completed.
In the three-dimensional design of a building, the problem of determining the minimum size of a material required for processing a plate is often involved, and the application of the minimum size to plate cutting, discharging and nesting algorithm and engineering cost calculation are important processes for realizing processing digitization. The dimension is the smallest cuboid surrounding the plate, the cuboid direction is related to the plate direction, but the length, width and height of the cuboid are independent of the direction, and the length, width and height data are key parameters for processing. The cuboid is the smallest directional bounding box (Oriented Bounding Box). Therefore, the length, width and height data of the minimum bounding box need to be calculated quickly and accurately.
In the prior art, a common minimum bounding box algorithm, such as an OBB algorithm, is adopted, the input condition of the algorithm is point cloud, the direction of the bounding box is determined by solving a covariance matrix of three-dimensional coordinates of the point cloud, then the minimum size of the bounding box in each direction is obtained in three directions, and the minimum bounding box under the point cloud is obtained comprehensively. However, when solving the problem of irregular plate, the point cloud obtained by dispersing the plate is in a sheet shape, and the result obtained by the common OBB algorithm on part of the plate is a second or third small bounding box, so that the accurate optimal solution cannot be obtained, and the problems of larger blanking size of part of the plate, reduced plate utilization rate and the like are caused, thereby increasing the engineering cost.
Disclosure of Invention
The invention aims to solve the technical problems that: the method and the system are used for quickly solving the minimum bounding boxes of the plates with any shapes in the three-dimensional building model in batches.
The technical scheme adopted by the invention for solving the technical problems is as follows: a convex hull-based plate minimum bounding box calculation method comprises the following steps:
S1: acquiring a point set, and inputting three-dimensional coordinates of key points of a plate of a minimum bounding box to be calculated;
S2: based on the three-dimensional coordinates of the key points, traversing the combination of all three points in the point set to find out at least one point set division, so that the key points of the plate are distributed in two parallel planes;
s3: constructing a standard orthogonal projection matrix by using a normal vector of a parallel plane as a projection direction, and projecting all points in a point-concentrated original coordinate system to obtain a minimum bounding box height, and completing dimension reduction of a third dimension after the projection of a house jettison to obtain a two-dimensional point set;
S4: calculating a convex hull of the two-dimensional point set according to coordinates of the two-dimensional point set, calculating the length and the width of a minimum circumscribed rectangle of the two-dimensional point set according to the convex hull, and obtaining the length, the width and the height of a minimum bounding box of the round of iteration by combining the absolute value of a third dimension coordinate difference; traversing the combination of all three points in the step S2, and calculating the length, the width and the height of the minimum bounding box of the plate under each combination;
s5: selecting a global minimum bounding box according to the minimum target;
S6: and restoring the two-dimensional coordinates of the four vertexes of the current minimum circumscribed rectangle into eight vertex coordinates of the minimum bounding box under the original coordinate system through a third dimension, and completing the visualization operation.
According to the above scheme, in the step S1, the specific steps are as follows:
Let the minimum bounding box of the plate be the minimum cuboid of the bounding plate in three-dimensional space So that all key points of the plate are/>Are all in cuboid/>And cuboid/>Is the smallest volume or surface area; set cuboid/>Is/>、/>And/>The minimum bounding box problem of solving the plate is expressed as a constrained optimization problem, which comprises solving the bounding box with minimum volume
，
Or bounding box with minimal surface area
；
The minimum volume bounding box and the minimum surface area bounding box are both the smallest product of the height-determined length and width.
Further, in the step S2, the specific steps are as follows:
S21: set at a given point set In (1)/>, dotIs/>，/>=1，2，…，; Three points/>, are selected using an iterative approachDetermination of plane/>Traversing all existing three-point combinations; is provided withRepresenting the outer product of vectors, solving for plane/>Unit normal vector/>：
；
S22: set of pairs of pointsMiddle NOT/>All points/>Calculate the dot/>To plane/>Distance/>：
；
S23: if it isOr a minimum number, then consider the point/>In plane/>Applying; if/>If the above condition is not satisfied, then pointNot in plane/>Applying;
S24: is not arranged on the plane The points on the plane/>Obtaining a point set division;
S25: judging plane And plane/>Whether parallel, if so, executing the next step; if not, step S21 is performed.
Further, in the step S2, a plane is determinedAnd plane/>The specific steps of whether the parallel is as follows: calculation plane/>All points to plane/>If plane/>All points and points/>Component vector and vector/>The inner products of (a) are the same in number and size, the plane/>And plane/>Is two parallel planes.
Further, in the step S3, the specific steps are as follows:
S31: in plane Unit normal vector/>Constructing a three-dimensional orthogonal matrix/>, as a projection direction；
For a pair ofStructure/>Make/>，/>The method meets the following conditions:
，
Or:
，
Or:
，
Will be Conversion to unit vector/>The method comprises the following steps:
；
Structure of the device ；/>Are unit vectors and are perpendicular to each other, matrix/>A transformation matrix formed for a set of orthonormal basis;
S32: set of pairs of points Linear transformation is performed on all points in the plane/>, so that the plane/>And plane/>Are all identical to plane/>Parallel;
According to Pair point set/>All points in the model are subjected to linear transformation to obtain a new point set/>：
；
Plane/>Mapping the points in (a) to a plane/>Plane/>Mapping the points in (a) to a plane/>Obtain the selection/>Height of minimum bounding box as initial point/>；
S33: discardingAxis coordinates, merging the same points to a plane/>Obtain two-dimensional point set/>。
Further, in the step S4, the specific steps are as follows:
S41: set two-dimensional point set There is/>The points are denoted as/>; Selecting the point with the smallest abscissa/>Joining two-dimensional Point set/>Convex hull/>Point/>As an iteration start point, calculate the dot/>And two-dimensional point set/>Other points/>Vector/>；
S42: will be planar/>Axial direction/>As a reference vector, a vector/>, is calculatedVector/>The cosine value of (2) is the point of least cosine value/>Adding convex hull/>And will be dot/>Set as the iteration start point of the next round, willAs a reference vector, a vector/>, is calculatedVector/>Cosine values of (2);
S43: selected such that cosine values Minimum dot/>Join/>Point/>Set as the new iteration start, vector/>Setting the new reference vector, and continuing iteration until the point/>Become the iteration starting point again to obtain a two-dimensional point set/>Convex hull of/>；
S44: two-dimensional point setOne side of the minimum circumscribed rectangle of (1) is coincident with the convex hull, and the minimum circumscribed rectangle of (2) is coincident with the convex hullIs arranged on each side of (a)Respectively carrying out iterative calculation on the length and the width to obtain a plurality of external rectangles;
s45: selecting the circumscribed rectangle with the smallest area from the plurality of circumscribed rectangles to obtain the current initial point as Time minimum bounding box length/>Width/>And high/>；
S46: and (3) judging whether the combination of all the two parallel planes obtained in the step (S2) is traversed, if so, executing the step (S5), and if not, executing the step (S2).
Further, in the step S42, the vector isVector/>Cosine value/>The method comprises the following steps:
。
further, in the step S44, edges are used Is the minimum circumscribed rectangle length/>, when the edge is coincident with the convex hullSum width/>The method comprises the following steps of:
，
；
The length of the smallest circumscribed rectangle is Broad is/>。
Further, in the step S6, the specific steps are as follows:
s61: finding the coincident edge of the minimum circumscribed rectangle and the convex hull ; The four vertex coordinates of the minimum bounding rectangle are:
，
，
，
；
s62: respectively adding third dimension coordinates of two rows of planes to the two-dimensional coordinates of the four vertexes of the current minimum circumscribed rectangle, and restoring the third dimension to be projected An axis coordinate;
s62: standard orthogonal projection matrix for left multiplication Inverse matrix/>And obtaining eight vertex coordinates of the minimum bounding box under the original coordinate system.
A convex hull based panel minimum bounding box computing system comprising a processor and a memory having stored therein computer instructions for executing the computer instructions stored in the memory, the system implementing the steps of a convex hull based panel minimum bounding box computing method when the computer instructions are executed by the processor.
The beneficial effects of the invention are as follows:
1. According to the convex hull-based plate minimum bounding box calculation method and system, the principle of convex hull calculation of minimum bounding rectangle is adopted, three-dimensional point cloud is projected to a two-dimensional plane to obtain the height of the bounding box by detecting a parallel plane and projecting, and then the minimum bounding rectangle is calculated to solve the minimum bounding box of the point cloud, so that the function of rapidly solving the minimum bounding box of any plate in a three-dimensional building model in batches is realized.
2. According to the invention, through vectorization of each point coordinate in a three-dimensional coordinate system, all possible parallel planes of an input point are automatically identified, the dimension-reduction projection direction is detected, dimension-reduction projection is carried out, and a three-dimensional plate with any shape is converted into a plane point set in a two-dimensional space; then calculating the minimum circumscribed rectangle according to the convex hull of the two-dimensional point set, calculating the bounding box of the plate according to the minimum target by combining the projection direction, further obtaining the coordinates of each vertex of the bounding box, and simultaneously solving the problems of minimum volume and minimum surface area; and calculating all possible projection directions, and obtaining the required minimum bounding box after comparison.
3. According to the invention, the vertex position of the minimum bounding box under the original coordinate system is obtained through matrix inverse transformation, so that the accurate calculation of the minimum bounding box size of the plate with any shape is realized, the position and the size of the minimum bounding box are marked in the original model, and the visualization is realized in the original space.
4. Aiming at the problem of losing the solving precision of the traditional method for determining the minimum bounding box by using the covariance matrix, the calculation process of the invention is matrix operation, has higher accuracy, can quickly and accurately obtain the operation result in the application of large-scale batch calculation plates, provides a feasible solution for the calculation of the minimum bounding box of the large-scale plates, has great potential in application, and accelerates the industrialization and digitization processes of the building industry.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a schematic view of the initial plate shape according to an embodiment of the present invention.
FIG. 3 is a process and minimum bounding box visualization implementation diagram of an embodiment of the present invention.
Detailed Description
The invention will be described in further detail with reference to the drawings and the detailed description.
Example 1
Referring to fig. 1, an embodiment of the present invention includes the steps of:
S1: acquiring a set of points Inputting three-dimensional coordinates of key points of the plate;
the key points of the plate include vertexes, edge points, partial surface points and the like, which are required to represent the shape characteristics of the plate and are not excessive, and the points together form a point set . The coordinates of the key points should not contain the internal points and the side points of the model, otherwise the calculation amount of the algorithm is increased, and even the algorithm is disabled.
S2: point collectionThree points/>As an initial point for determining the plane, the normal vector/>, of the plane P1 determined when the three points are selected, is calculated；
Traversing a set of pointsAll possible three-point combinations in order to determine all initial planes/>; Plane normal vector/>The calculation method of (2) is as follows:
。
S3: computing a set of points Middle NOT/>Point to plane/>To determine whether all points can be divided into parallel planes/>And plane/>If not, returning to the step S2, and reselecting three points; if so, proceed to step S4, and plane/>And plane/>The distance of (2) is the minimum bounding box height;
Determining a set of points Whether or not to divide into parallel planes/>And plane/>The detailed process of (2) is as follows:
S31: computing a set of points Middle NOT/>Point to plane/>Distance/>：
；
S32: if it isOr a minimum number, then consider/>In plane/>Applying; otherwise not in plane/>Applying; thus will/>Divided into at/>The point on and not on/>Points on;
S33: will not be at The points above are all noted as being at/>In the above, if/>All points and/>Vectors of composition and/>The inner products of (a) are the same in number and size, and are considered/>And/>Is two parallel planes;
S34: if it is And/>Is two parallel planes, then bounding box height/>For/>And/>A distance therebetween; if/>And/>Not two parallel planes, return to step S2.
In the above steps, due to calculationThey are already unitized, so/>And/>The absolute value of the inner product of (a) is/>To plane/>Is a distance of (3). Obviously, when/>All points to/>Is all the same and at/>On the same side of (1) >, indicateAndParallel, and/>And/>The distance between them is the height of the bounding box.
S4: constructing standard orthogonal projection matrixPoint set/>All the points are projected, the third dimension is abandoned, all the points are converted into two-dimensional points, and a two-dimensional point set/>, is obtained; Will/>The same points in (a) are combined to obtain a point set/>；
In the step S4, a standard orthogonal projection matrix is constructedThe detailed process of projection dimension reduction and merging the same points is as follows:
S41: assume that Then/>At least one of which is other than 0. An AND/>, can then be constructed according to the following procedurePerpendicular Unit vector/>：
；
Or:
；
Or:
；
S42: will be Converted into unit vector and then recorded as/>Let/>Matrix/>A transformation matrix formed by a group of standard orthogonal bases, namely the required standard orthogonal projection matrix/>。
S43: according toPair point set/>All points in the model are subjected to linear transformation to obtain a new point set/>。
；
S44: discardingMidpoint/>The direction coordinates transform all points into points in a two-dimensional plane. Calculating the distance between each point, removing the repeated points (the distance is 0), and obtaining a two-dimensional point set/>。
Wherein,Will/>, in the original coordinate SystemPlanar transformation into/>Plane,/>Planar transformation into and/>Planes parallel to the plane; abandoning/>Directional coordinates, then Point set/>All points in the two-dimensional plane are projected as points on the two-dimensional plane, and the dimension reduction processing is completed.
S5: computing a set of pointsConvex hull/>；
In the step S5, in order to obtain the minimum bounding rectangle of the two-dimensional point set, it is necessary to calculateConvex hull of (a). The detailed calculation process is as follows:
s51: selecting The point with the smallest middle abscissa is used as the iteration starting point/>Will/>Join/>。
S52: will beAxial direction/>As an initial reference vector,/>For points other than any px' in P ", calculate/>And/>Cosine values of (a) are provided.
S53: will minimize the cosine valueJoin/>And will/>Set as the iteration start point of the next round, willAs the next round of reference vectors, step S52 is repeated until/>Retum/>。
S54: obtained byNamely, point set/>Is a convex hull of (a).
S6: according to convex hullsCalculating the minimum circumscribed rectangle, wherein the length and width of the minimum circumscribed rectangle are the length/>, of the minimum bounding boxSum width/>；
In the step S6, since one side of the minimum bounding rectangle is overlapped with the side of the convex hull, the minimum bounding rectangle can be calculated according to the convex hull, and the detailed calculation process is as follows:
S61: sequentially selecting each edge in the convex hull
S62: with edgesThe calculation process of the minimum bounding rectangle when the bounding rectangle is overlapped with the edges is as follows, all the edges are traversed according to the process, and the minimum bounding rectangle length and width combination with the same number of the edges is obtained:
S63: the length of the minimum circumscribed rectangle is Broad is/>。
This results in all possible combinations of length and width of the smallest bounding rectangle. Selected such thatMinimum/>And/>Namely the length and width of the smallest external rectangle.
S7：、/>And/>I.e. select/>The length, width and height of the minimum bounding box serving as the initial point are returned to the step S2 to calculate the minimum bounding box when other initial points are combined, and the step S8 is carried out after all possible combinations are calculated;
in the step S7, the step S6 is performed 、/>Obtained in step S3/>I.e. the initial point is/>And (3) obtaining all possible situations of the minimum bounding box by traversing possible combinations.
S8: and (3) comparing the minimum bounding boxes obtained in the step (S7), and selecting a minimum value according to the target of the minimum volume or the minimum surface area. Visualization is based on the minimum circumscribed rectangleAnd (5) calculating.
In the step S8, the existence of the minimum bounding box may be obtained according to the target selection step S7. If the visualization is required to be completed in the original coordinate system, the method comprises the following steps:
S81: finding the coincident edge of the minimum circumscribed rectangle and the convex hull according to the selected minimum bounding box 。
S82: the vertex coordinates of the minimum bounding rectangle are:
the four points are the vertices of the minimum bounding rectangle.
S83: the four-point third dimension is added with two projected images respectivelyThe axis height, the obtained is the eight vertex coordinates of the projected minimum bounding box, and then the projection matrix/>Inverse matrix/>And obtaining eight vertex coordinates of the minimum bounding box under the original coordinate system, and connecting the eight points to complete the visualization.
Example 2
The flow chart of the method is shown in fig. 1, and the schematic diagram of the plate shape is shown in fig. 2. Table 1 is the coordinate data of the initial plate, and the algorithm of the present invention is used to calculate the volume minimum bounding box according to the data shown in table 1, and the specific implementation process is as follows:
TABLE 1 initial coordinate data
S1: importing coordinate data as shown in table 1;
S2: taking three initial points, such as (-458.362, -200.0, -160.345), (298.0, -200.0, 560.0), (-207.845, -200.0, -474.138), where the normal vector is (0, 1, 0);
S3: determining the distance from other points to the three points according to the normal vector, and when the three points are taken as the judgment result, dividing all the points into two parallel planes, and continuing to carry out the step S4;
S4: the obtained orthogonal projection matrix is as follows:
Discarding the third dimension after projection and merging the same points;
s5: the convex hulls obtained according to the above method are shown in table 2;
table 2 two-dimensional coordinates of points found in convex hull
S6: the length and width of the minimum external rectangle obtained by calculation are 1079.5 and 400.0 respectively;
s7: when the initial three points are combined, the length and width heights of the minimum bounding box are 1079.5, 400.0 and 35.0;
S8: after comparing all the possible cases, the length, width and height of the minimum volume bounding box can be 1079.5, 400.0 and 35.0 respectively, and the visualization condition is shown in fig. 3, and the vertex table 3 of the minimum bounding box is shown.
TABLE 3 three-dimensional coordinates of vertices of minimum volume bounding boxes
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic, and should not limit the implementation process of the embodiment of the present application.
The above embodiments are merely for illustrating the design concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, the scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications according to the principles and design ideas of the present invention are within the scope of the present invention.
Claims (9)
1. A convex hull-based plate minimum bounding box calculation method is characterized by comprising the following steps of: the method comprises the following steps:
S1: acquiring a point set, and inputting three-dimensional coordinates of key points of a plate of a minimum bounding box to be calculated;
S2: based on the three-dimensional coordinates of the key points, traversing the combination of all three points in the point set to find out at least one point set division, so that the key points of the plate are distributed in two parallel planes;
s3: constructing a standard orthogonal projection matrix by using a normal vector of a parallel plane as a projection direction, and projecting all points in a point-concentrated original coordinate system to obtain a minimum bounding box height, and completing dimension reduction of a third dimension after the projection of a house jettison to obtain a two-dimensional point set; the method comprises the following specific steps:
S31: in plane Unit normal vector/>Constructing a three-dimensional orthogonal matrix/>, as a projection direction；
For a pair ofStructure/>Make/>，/>The method meets the following conditions:
，
Or:
，
Or:
，
Will be Conversion to unit vector/>The method comprises the following steps:
；
further structure ；/>Are unit vectors and are perpendicular to each other, matrix/>A transformation matrix formed for a set of orthonormal basis;
S32: set of pairs of points Linear transformation is performed on all points in the plane/>, so that the plane/>And plane/>Are all identical to plane/>Parallel;
According to Pair point set/>All points in the model are subjected to linear transformation to obtain a new point set/>：
；
Plane/>Mapping the points in (a) to a plane/>Plane/>Mapping the points in (a) to a plane/>Obtaining and selectingHeight of minimum bounding box as initial point/>；
S33: discardingAxis coordinates, merging the same points to a plane/>Obtain two-dimensional point set/>；
S4: calculating a convex hull of the two-dimensional point set according to coordinates of the two-dimensional point set, calculating the length and the width of a minimum circumscribed rectangle of the two-dimensional point set according to the convex hull, and obtaining the length, the width and the height of a minimum bounding box of the round of iteration by combining the absolute value of a third dimension coordinate difference; traversing the combination of all three points in the step S2, and calculating the length, the width and the height of the minimum bounding box of the plate under each combination;
s5: selecting a global minimum bounding box according to the minimum target;
S6: and restoring the two-dimensional coordinates of the four vertexes of the current minimum circumscribed rectangle into eight vertex coordinates of the minimum bounding box under the original coordinate system through a third dimension, and completing the visualization operation.
2. The convex hull-based panel minimum bounding box calculation method as claimed in claim 1, wherein: in the step S1, the specific steps are as follows:
Let the minimum bounding box of the plate be the minimum cuboid of the bounding plate in three-dimensional space So that all key points of the plate are/>Are all in cuboid/>And cuboid/>Is the smallest volume or surface area; set cuboid/>Is/>、/>And/>The minimum bounding box problem of solving the plate is expressed as a constrained optimization problem, which comprises solving the bounding box with minimum volume
，
Or bounding box with minimal surface area
；
The minimum volume bounding box and the minimum surface area bounding box are both the smallest product of the height-determined length and width.
3. The convex hull-based panel minimum bounding box calculation method as claimed in claim 2, wherein: in the step S2, the specific steps are as follows:
S21: set at a given point set In (1)/>, dotIs/>，/>=1，2，…，/>; Three points/>, are selected using an iterative approachDetermination of plane/>Traversing all existing three-point combinations; let/>Representing the outer product of vectors, solving for plane/>Unit normal vector/>：
；
S22: set of pairs of pointsMiddle NOT/>All points/>Calculate the dot/>To plane/>Distance/>：
；
S23: if it isOr a minimum number, then consider the point/>In plane/>Applying; if/>If the above condition is not satisfied, then point/>Not in plane/>Applying;
S24: is not arranged on the plane The points on the plane/>Obtaining a point set division;
S25: judging plane And plane/>Whether parallel, if so, executing the next step; if not, step S21 is performed.
4. A convex hull based panel minimum bounding box calculation method according to claim 3, wherein: in the step S2, a plane is determinedAnd plane/>The specific steps of whether the parallel is as follows: calculation plane/>All points to planeIf plane/>All points and points/>Component vector and vector/>The inner products of (a) are the same in number and size, the plane/>And plane/>Is two parallel planes.
5. The convex hull-based panel minimum bounding box calculation method as claimed in claim 1, wherein: in the step S4, the specific steps are as follows:
S41: set two-dimensional point set There is/>The points are denoted as/>; Selecting the point with the smallest abscissaJoining two-dimensional Point set/>Convex hull/>Point/>As an iteration start point, calculate the dot/>And two-dimensional point set/>Other points/>Vector/>；
S42: will be planar/>Axial direction/>As a reference vector, a vector/>, is calculatedVector/>The cosine value of (2) is the point of least cosine value/>Adding convex hull/>And will be dot/>Put as the start of the next iteration, will/>As a reference vector, a vector/>, is calculatedVector/>Cosine values of (2);
S43: selected such that cosine values Minimum dot/>Join/>Point/>Set as the new iteration start point, vectorSetting the new reference vector, and continuing iteration until the point/>Become the iteration starting point again to obtain a two-dimensional point set/>Convex hull of (1) is；
S44: two-dimensional point setOne side of the minimum circumscribed rectangle of (1) is coincident with the convex hull, and the minimum circumscribed rectangle of (2) is coincident with the convex hullIs arranged on each side of (a)Respectively carrying out iterative calculation on the length and the width to obtain a plurality of external rectangles;
s45: selecting the circumscribed rectangle with the smallest area from the plurality of circumscribed rectangles to obtain the current initial point as Time minimum bounding box length/>Width/>And high/>；
S46: and (3) judging whether the combination of all the two parallel planes obtained in the step (S2) is traversed, if so, executing the step (S5), and if not, executing the step (S2).
6. The convex hull-based panel minimum bounding box calculation method of claim 5, wherein: in the step S42, vectorsVector/>Cosine value/>The method comprises the following steps:
。
7. the convex hull-based panel minimum bounding box calculation method of claim 5, wherein: in the step S44, edges are used Is the minimum circumscribed rectangle length/>, when the edge is coincident with the convex hullSum width/>The method comprises the following steps of:
，
；
The length of the smallest circumscribed rectangle is Broad is/>。
8. The convex hull-based panel minimum bounding box calculation method of claim 7, wherein: in the step S6, the specific steps are as follows:
s61: finding the coincident edge of the minimum circumscribed rectangle and the convex hull ; The four vertex coordinates of the minimum bounding rectangle are:
，
，
，
；
s62: respectively adding third dimension coordinates of two rows of planes to the two-dimensional coordinates of the four vertexes of the current minimum circumscribed rectangle, and restoring the third dimension to be projected An axis coordinate;
s62: standard orthogonal projection matrix for left multiplication Inverse matrix/>And obtaining eight vertex coordinates of the minimum bounding box under the original coordinate system.
9. A convex hull based panel minimum bounding box computing system comprising a processor and a memory, characterized in that: the memory has stored therein computer instructions, the processor being configured to execute the computer instructions stored in the memory, the system implementing the steps of a convex hull based panel minimum bounding box calculation method as claimed in any of claims 1 to 8 when the computer instructions are executed by the processor.
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| CN202410275872.2A CN117876554B (en) | 2024-03-12 | 2024-03-12 | Convex hull-based plate minimum bounding box calculation method and system |
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