CN107688693B - Automatic folding method of three-dimensional model - Google Patents
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Abstract
The invention relates to the field of computer graphics, and particularly provides an automatic folding method of a three-dimensional model. Aims to solve the problem that the occupied space of objects is large. The method comprises the steps of establishing a three-dimensional model of an object, extracting the symmetrical relation and the connection relation of components in the three-dimensional model, establishing hinge points among connecting components, generating a relation graph and a rotating shaft of the components according to the hinge points, solving the folding sequence, the folding shaft and the folding angle of each component, and finally realizing the automatic folding of the three-dimensional model. According to the invention, by the automatic folding method of the three-dimensional model, the folding sequence, the folding axis and the folding angle of the object can be comprehensively optimized, meanwhile, the non-collision folding path of the part is generated in advance in the folding optimization process by analyzing the compressibility and the convex hull property of the part of the object, so that the object can be further divided, and the space occupied by the object is further reduced.
Description
Technical Field
The invention relates to the field of computer graphics, and particularly provides an automatic folding method of a three-dimensional model.
Background
In recent years, small-area house types are more popular with the rising of house prices, under the environment, how to better utilize the limited space is very important, and the folding of the object can help us to better utilize the limited space. For example, the desk and chair which are not commonly used in the living room usually occupy a large space, and if the desk and chair are folded for storage when not needed and unfolded for placement when needed, a large amount of space can be saved. Meanwhile, in the transportation process of the objects, if some equipment with large occupied space is disassembled for transportation, a large amount of space can be saved, and the difficulty in the transportation process of the objects can be reduced.
Therefore, how to provide a solution to the above problems is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In order to solve the above problems in the prior art, that is, to solve the problem that an object occupies a large space, the invention provides an automatic folding method of a three-dimensional model, which comprises the following steps:
establishing a three-dimensional model of an object, detecting the symmetrical relation and the connection relation of each part in the three-dimensional model, and establishing hinge points among the connection parts;
generating a relation graph and a rotating shaft of the parts according to the hinge points, and solving the folding sequence, the folding shaft and the folding angle of each part according to the relation graph and the rotating shaft;
folding the three-dimensional model according to the folding order, the folding axis and the folding angle.
In a preferred embodiment of the above method, after the "building a three-dimensional model of an object" and before the "detecting a symmetry relationship and a connection relationship of each component in the three-dimensional model", the method further includes:
and carrying out convex hull decomposition on the part by using an HACD (Hadoop distributed compact disc) level approximate convex decomposition algorithm.
In a preferred embodiment of the above method, after the "solving a folding order, a folding axis, and a folding angle of each of the components", and before the "folding the three-dimensional model according to the folding order, the folding axis, and the folding angle", the method further includes:
and analyzing compressibility and convex hull of the part, and if the compressibility and the convex hull of the part meet the folding requirement, further dividing the part.
In a preferred embodiment of the above method, the further dividing method comprises:
and selecting an intersection point close to the center of the part from the intersection points of the convex hulls of the part, and dividing the part along the direction with the largest change of the part.
In a preferred embodiment of the above method, the "detecting a symmetric relationship between components in the three-dimensional model" includes:
and judging whether a potential symmetry plane exists between the components, if so, continuously judging whether the components meet a symmetry constraint relation, and if so, determining that the components have a symmetry relation.
In a preferred embodiment of the above method, the "establishing a hinge point between the connecting parts" includes:
combining polygons with the same normal vector in the part into a first combined polygon, combining polygons with a normal vector opposite to the part in the part connected with the part into a second combined polygon, representing the first combined polygon and the second combined polygon by using a bounding box with a direction, and determining the hinge point according to the intersection area of the first combined polygon and the second combined polygon.
In a preferred embodiment of the above method, the "generating a relationship diagram of the components from the hinge points" includes:
and generating a relation graph of the parts by a breadth first algorithm according to the hinge points.
In a preferred embodiment of the above method, after the "generating the relationship diagram of the components according to the hinge points" and before the "solving the folding order, the folding axis, and the folding angle of each of the components", the method further includes:
and calculating the maximum external force which can be borne by the three-dimensional model through a bullet collision detection algorithm.
In a preferred embodiment of the above method, the "solving the folding order of each of the components" includes:
calculating the folding order of each of the parts by a genetic algorithm.
In a preferred embodiment of the above method, the method of finding the folding axis and the folding angle of each of the members includes:
traversing a rotation axis and a rotation angle of a cyclic structure not included in the three-dimensional model;
solving a folding energy function and a functional feasibility function of the three-dimensional model according to the rotating shaft and the rotating angle;
and if the combined energy of the folding energy function and the functional feasibility function is obtained through solving, selecting a rotating shaft and a rotating angle corresponding to the maximum combined energy as the folding shaft and the folding angle of the three-dimensional model.
According to the invention, by the automatic folding method of the three-dimensional model, the folding sequence, the folding axis and the folding angle of the object can be comprehensively optimized, meanwhile, the non-collision folding path of the part is generated in advance in the folding optimization process by analyzing the compressibility and the convex hull property of the part of the object, so that the object can be further divided, and the space occupied by the object is further reduced.
Drawings
FIG. 1 is a schematic flow chart of a method for automatically folding a three-dimensional model according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of information extraction of a method for automatically folding a three-dimensional model according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram illustrating a method for automatically folding a three-dimensional model according to an embodiment of the present invention;
FIG. 4 is a schematic structural diagram of a rotating shaft of the method for automatically folding a three-dimensional model according to an embodiment of the present invention;
FIG. 5 is a schematic structural diagram illustrating a folding sequence of a method for automatically folding a three-dimensional model according to an embodiment of the present invention;
FIG. 6 is a flowchart illustrating the folding steps of the method for automatically folding a three-dimensional model according to an embodiment of the present invention.
Detailed Description
Preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the present invention, and are not intended to limit the scope of the present invention.
As shown in fig. 1, a schematic flow chart of a method for automatically folding a three-dimensional model according to an embodiment of the present invention includes:
step S1: establishing a three-dimensional model of an object, detecting the symmetrical relation and the connection relation of each part in the three-dimensional model, and establishing hinge points among the connection parts;
fig. 2 is a schematic flow chart illustrating the information extraction process of the method for automatically folding a three-dimensional model according to an embodiment of the present invention, wherein step S21 represents the input three-dimensional model, step S22 represents the determination of hinge points, step S23 represents the extraction of relationship diagram, and step S24 represents the extraction of symmetric relationship. By establishing the three-dimensional model of the object and carrying out one-to-one correspondence on the segmentation areas of the three-dimensional model and the parts of the object, the object can be divided into a plurality of parts for analysis, so that the relation among the parts can be found, and the object can be folded and analyzed more favorably. By analyzing and extracting the symmetry relationship and the connection relationship of each part in the model and establishing hinge points between the connection parts, a relationship diagram between each part can be generated, and a rotation axis of the foldable part is determined, wherein the rotation axis is selected as a folding axis when the three-dimensional model is folded.
Step S2: generating a relation graph and a rotating shaft of the components according to the hinge points, and solving the folding sequence, the folding shaft and the folding angle of each component according to the relation graph and the rotating shaft;
fig. 3 is a schematic structural diagram of the method for automatically folding a three-dimensional model according to an embodiment of the present invention, in which 31 denotes two selected components, 32 denotes a first combined polygon, and 33 denotes a second combined polygon. In practical application, in order to facilitate subsequent analysis and calculation, the parts connected with the components are abstracted into hinge points, and then a relationship diagram of the components and a corresponding rotating shaft are generated according to the hinge points, so that a complex object in reality can be converted into a model easy to analyze and calculate, wherein the relationship diagram can visually express the connection relationship between the components of the object, the rotating shaft can analyze the mode in which the model can rotate and fold, and after the relationship diagram and the rotating shaft of the object components are obtained, the folding sequence, the folding shaft and the folding angle of each component can be further solved by combining a corresponding algorithm.
Step S3: and realizing automatic folding of the three-dimensional model according to the folding sequence, the folding shaft and the folding angle.
After the folding sequence, the folding axis and the folding angle of each part are obtained, the optimal method for folding each part of the object can be obtained, the effect that the occupied space is the minimum after the object is folded is achieved, meanwhile, the method can complete automatic folding of the original three-dimensional model after the folding sequence, the folding axis and the folding angle are obtained, and the three-dimensional model with the smaller occupied space after folding is obtained.
As a preferred embodiment, after "building a three-dimensional model of an object" and before "detecting the symmetry relationship and connection relationship of each component in the three-dimensional model", the method further includes:
and (3) performing convex hull decomposition on the part by using an HACD (Hierarchical approximate convex decomposition) algorithm to avoid collision in the part folding process.
In the process of folding the object, it is necessary to ensure that the parts do not collide during the process of folding. The HACD algorithm can perform convex hull decomposition to decompose a component into a group of convex hulls, wherein the convex hulls are any two points on the boundary or inside any polygon, and all points on a line segment connecting the two points are contained in the boundary or inside the polygon. After the convex hull of the part is decomposed, whether the folded part collides or not can be more visually known, and then the space occupied by the collided part can be reduced.
As a preferred embodiment, after "solving the folding order, the folding axis and the folding angle of each component", before "implementing the automatic folding of the three-dimensional model", the method further comprises:
and performing compressibility and convex hull analysis on the part, and if the compressibility and convex hull of the part meet the folding requirements, further dividing the part.
In practical application, some models which cannot be effectively folded exist, the compressibility and the convex hull of the part can be analyzed, if the compressibility and the convex hull of the part meet requirements, the part is further segmented, the model is folded, and therefore the space occupied by the model is reduced.
Specifically, compressibility is determined by the folding angle of each component, generally, a perpendicular relationship exists between most components, so that the ideal folding angle is 90 degrees, and folding the components at an angle of 90 degrees can maximally achieve spatial compression, but in practical application, the folded components should not have intersecting parts and cannot achieve a folding angle of 90 degrees, so that the component with the smallest folding angle is selected for further segmentation.
Specifically, convex hull analysis is to emit rays from the component, select the sum of the lengths of the rays intersecting the convex hull in the component as the measure of the convex hull performance of the component, and select the component with the smallest sum of the lengths of the rays to further segment the component in order to ensure that the convex hull formed by the component is as close as possible to the component after folding.
As a preferred embodiment, the method of further dividing is:
the direction in which the feature changes most is selected, and the segmentation is performed from the intersection of the convex hulls of the features and near the center of the features.
During specific segmentation, only one Component is selected to divide the Component into two parts at each time, and the segmentation direction is the direction in which the Component changes most, wherein the specific segmentation direction can be solved through a Principal Component Analysis (PCA) algorithm, and the PCA algorithm transforms original data into a group of linearly independent representations of various dimensions through linear transformation, can be used for extracting main characteristic components of the data and is commonly used for dimension reduction of high-dimensional data. The division positions are the intersection points of different convex hulls in the component and are as close as possible to the center of the component, and in order to ensure that the symmetrical groups in the original component have the same operation, the symmetrical components can be divided by using a similar division method.
As a preferred embodiment, "detecting the symmetry relationship of each part in the three-dimensional model" includes:
and judging whether a potential symmetry plane exists between the components, if so, judging whether the components meet the symmetry constraint relation, and if so, judging that the components have the symmetry relation.
During the process of decomposing the relationship diagram of the components, folding and dividing the components, the detection of each component in the three-dimensional model is neededThe invention obtains corresponding symmetry groups by analyzing the mirror symmetry between different components, wherein, whether a potential symmetry plane exists between the components needs to be judged first, and the judgment method of the potential symmetry plane is as follows: selecting the center points of the two parts, which are respectively denoted as ciAnd cjIf a plane is a unit vector corresponding to the connection line of the midpoint points of two members
And passes through the coordinate point ci+0.5·(cj-ci) If so, it can be determined that a potential symmetry plane exists, and on the premise that the potential symmetry plane exists, it is determined whether points on corresponding components satisfy a constraint relationship, and then it is determined whether the components satisfy a symmetry relationship, where the specific determination method is: if at point p on any partiCan find corresponding points p on other componentsjMake it satisfy the constraint relation pj＝pi+||pj-piAnd if | is n, the corresponding parts can be considered to satisfy the symmetry relation.
As a preferred embodiment, "a hinge point is established between the connection parts" by:
the method comprises the steps of combining polygons with the same normal vector in a part into a first combined polygon, combining polygons with the normal vector opposite to the part in the part connected with the part into a second combined polygon, representing the first combined polygon and the second combined polygon by using a bounding box with a direction, and determining a hinge point according to the intersection area of the first combined polygon and the second combined polygon.
Fig. 4 is a schematic structural diagram of a rotating shaft of the method for automatically folding a three-dimensional model according to an embodiment of the present invention. The hinge points connecting different parts can be obtained by analyzing the intersection areas of the meshes of the adjacent parts, in order to facilitate the calculation of the intersection areas, the algorithm combines the polygonal areas with the same normal direction into a first combined polygon and uses the bounding box with the direction to represent the first combined polygon, then analyzes the polygons with opposite normal vectors in the parts connected with the parts and combines the polygons into a second polygon, the bounding box with the direction also represents the second combined polygon, and the hinge points are determined by the intersection areas of the first combined polygon and the second combined polygon. The bounding box is an algorithm for solving an optimal bounding space of the discrete point set, and can approximately replace a complex geometric object by a geometric body with a slightly larger volume and simple characteristics, and the geometric body with the slightly larger volume and simple characteristics is called the bounding box. Since each hinge point is generated by intersection of polygons, the intersected quadrilateral region can be represented as four nodes, and in contrast, the rotation axis corresponding to the hinge point can be determined by four nodes of the quadrilateral, and each hinge point can generate a rotation axis rotating in 9 directions.
As a preferred embodiment, "generating a relationship diagram of components according to hinge points" includes:
and generating a relation graph of the components according to the hinge points through a breadth first algorithm.
The breadth-first algorithm is a graph search algorithm that may begin at the root node, traverse the nodes of the tree along the width of the tree, and terminate if a target is found. The relationship graph between the components can be generated by a breadth first algorithm, and in the present invention, the root node is the component which is not included in the symmetric group and has the largest bounding box.
As a preferred embodiment, after "generating a relationship diagram of components according to hinge points", before "solving the folding order, folding axis and folding angle of each component", the method further comprises:
and calculating the maximum external force which can be borne by the three-dimensional model through a bullet collision detection algorithm.
During the folding process of the object, the load bearing analysis needs to be performed on the folded part of the object, namely the maximum external force which can be borne by the whole model. Through a bullet collision detection algorithm, the magnitude of the external force can be continuously increased on the model until the model collapses, and the maximum external force which can be borne by the model is tested.
As a preferred embodiment, the folding order of each component is solved by:
the folding order of the individual components is calculated by a genetic algorithm.
Fig. 5 is a schematic structural diagram illustrating a folding sequence of the method for automatically folding a three-dimensional model according to an embodiment of the present invention. For folding of the object, different folding sequences may result in different folding effects, thereby affecting the compressibility of the object after final folding. The invention can optimize the space of the folded object and the bearing capacity change of the folded object through a genetic algorithm, namely the difference between the space of the folded object and the convex hull contained in the space of the folded object is as small as possible. The genetic algorithm takes a randomly generated folding sequence as an initialized population, takes a subset of the components with the component subset base number of 1 or 2 as a candidate of the folding sequence, selects a group of sequences for hybridization by roulette, realizes variation by exchanging the positions of the sequence subsets, and stops when the similarity of the new and old populations is more than a certain proportion three times in succession, wherein the similarity is the ratio of the same sample number to the total sample number in the two populations, the specific proportion is set by a user, and the general proportion is more than 90%.
As a preferred embodiment, the solution method of the folding axis and the folding angle is:
traversing a rotating shaft and a rotating angle of a circulating structure which is not contained in the three-dimensional model;
solving a folding energy function and a functional feasibility function of the three-dimensional model according to the rotating shaft and the rotating angle;
and if the maximum energy of the folding energy function and the functional feasibility function is obtained through solving, selecting a rotating shaft and a rotating angle when the combined energy is maximum as the folding shaft and the folding angle of the three-dimensional model.
Specifically, the folding energy function is a weighted sum of the volume of the convex hull of the folded object, the volume of the convex hull formed by the current folding part and other parts, and the larger the volume of the convex hull is, the higher the folding energy is. The functional feasibility energy function requires that the bearing capacity of the folded object is kept as constant as possible, and the function of the bearing capacity of the model at the position i can be obtained by testing the bearing capacity at different positions of the modelLine performance metric function E2iAs shown in equation (1):
wherein, | | fo，i||2Is the amplitude of the bearing capacity of the original model, | | fc，i||2Is the amplitude of the bearing force of the folded model, is epsilonfRatio of variation allowed for bearing force, fo，iIs the bearing force vector of the original model, fc，iIs the bearing force vector of the folded model, when the bearing force of the original model after folding is still kept in a certain range, E2，iIs 0, otherwise the corresponding result is considered unreasonable, i.e. infinite.
Specifically, as shown in fig. 6, a schematic flow chart of the folding step of the method for automatically folding a three-dimensional model according to an embodiment of the present invention is shown. In step S61, the original three-dimensional model is built, and steps S62 to S65 are performed in order. During the folding process, the operation is only allowed to be carried out according to the rotation of the hinge point, and for the realization of the rotation operation, the component transformation operation needs to be realized by using a layering method or a complex motion constraint solver determined according to the position of the component in the relation graph. The position of a component in the relationship graph is determined by whether it is in a cyclic structure. If there are any two elements A, B in the graph, element A, B is in a loop structure, traversing the graph from a to B or B to a. The hierarchical transformation method applies similar constraints to the components and the sub-nodes thereof which are not in the cyclic structure, and the complex motion constraint solver can effectively process the transformation of the components contained in the cyclic structure. In the invention, a rotation axis and a rotation angle of a circulating structure which is not contained in the three-dimensional model are traversed by using a hierarchical transformation method, wherein the rotation angle is searched at an interval of 5 degrees, and when the calculated folding energy function and the calculated functional feasibility function have the maximum energy, the rotation axis and the rotation angle with the maximum combined energy are selected as the folding axis and the folding angle of the three-dimensional model.
According to the invention, by the automatic folding method of the three-dimensional model, the folding sequence, the folding axis and the folding angle of the object can be comprehensively optimized, meanwhile, the non-collision folding path of the part is generated in advance in the folding optimization process by analyzing the compressibility and the convex hull property of the part of the object, so that the object can be further divided, and the space occupied by the object is further reduced.
Those of skill in the art will appreciate that the method steps of the examples described in connection with the embodiments disclosed herein may be embodied in electronic hardware, computer software, or combinations of both, and that the components and steps of the examples have been described above generally in terms of their functionality in order to clearly illustrate the interchangeability of electronic hardware and software. Whether such functionality is implemented as electronic hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
So far, the technical solutions of the present invention have been described in connection with the preferred embodiments shown in the drawings, but it is easily understood by those skilled in the art that the scope of the present invention is obviously not limited to these specific embodiments. Equivalent changes or substitutions of related technical features can be made by those skilled in the art without departing from the principle of the invention, and the technical scheme after the changes or substitutions can fall into the protection scope of the invention.
Claims (9)
1. A method for automatically folding a three-dimensional model is characterized by comprising the following steps:
establishing a three-dimensional model of an object, detecting the symmetrical relation and the connection relation of each part in the three-dimensional model, and establishing hinge points among the connection parts;
generating a relation graph and a rotating shaft of the parts according to the hinge points, and solving the folding sequence, the folding shaft and the folding angle of each part according to the relation graph and the rotating shaft;
folding the three-dimensional model according to the folding order, the folding axis and the folding angle;
wherein, the method for establishing the hinge point between the connecting parts comprises the following steps:
combining polygons with the same normal vector in the part into a first combined polygon, combining polygons with a normal vector opposite to the part in the part connected with the part into a second combined polygon, representing the first combined polygon and the second combined polygon by using a bounding box with a direction, and determining the hinge point according to the intersection area of the first combined polygon and the second combined polygon.
2. The method for automatically folding the three-dimensional model according to claim 1, wherein after the step of building the three-dimensional model of the object and before the step of detecting the symmetry relationship and the connection relationship of each component in the three-dimensional model, the method further comprises the steps of:
and carrying out convex hull decomposition on the part by using an HACD (Hadoop distributed compact disc) level approximate convex decomposition algorithm.
3. The method for automatically folding a three-dimensional model according to claim 1, wherein after solving a folding order, a folding axis and a folding angle of each of the components and before folding the three-dimensional model according to the folding order, the folding axis and the folding angle, the method further comprises:
and analyzing compressibility and convex hull of the part, and if the compressibility and the convex hull of the part meet the folding requirement, further dividing the part.
4. The method for automatically folding the three-dimensional model according to claim 3, wherein the step of "further dividing the part" comprises:
and selecting an intersection point close to the center of the part from the intersection points of the convex hulls of the part, and dividing the part along the direction with the largest change of the part.
5. The method for automatically folding the three-dimensional model according to claim 4, wherein the step of detecting the symmetry relationship of each part in the three-dimensional model comprises the following steps:
and judging whether a potential symmetry plane exists between the components, if so, continuously judging whether the components meet a symmetry constraint relation, and if so, determining that the components have a symmetry relation.
6. The method for automatically folding the three-dimensional model according to claim 1, wherein the step of generating the relationship diagram of the part according to the hinge point comprises the following steps:
and generating a relation graph of the parts by a breadth first algorithm according to the hinge points.
7. The method for automatically folding a three-dimensional model according to claim 6, wherein after the step of generating the relationship diagram of the components according to the hinge points and before the step of solving the folding sequence, the folding axis and the folding angle of each of the components, the method further comprises:
and calculating the maximum external force which can be borne by the three-dimensional model through a bullet collision detection algorithm.
8. The method for automatically folding a three-dimensional model according to any one of claims 1 to 7, wherein said "solving the folding order of each of said parts" is carried out by:
calculating the folding order of each of the parts by a genetic algorithm.
9. The method for automatically folding a three-dimensional model according to any one of claims 1 to 7, wherein the folding axis and the folding angle of each part are solved by:
traversing a rotation axis and a rotation angle of a cyclic structure not included in the three-dimensional model;
solving a folding energy function and a functional feasibility function of the three-dimensional model according to the rotating shaft and the rotating angle;
and if the combined energy of the folding energy function and the functional feasibility function is obtained through solving, selecting a rotating shaft and a rotating angle corresponding to the maximum combined energy as the folding shaft and the folding angle of the three-dimensional model.
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