CN109063332A - The regularity method for improving of center of gravity Voronoi diagram - Google Patents
The regularity method for improving of center of gravity Voronoi diagram Download PDFInfo
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Abstract
The invention belongs to computer graphics disposal technology fields, and in particular to a kind of regularity method for improving of center of gravity Voronoi diagram, it is intended to solve the problems, such as how to reduce the quantity of singular point in center of gravity Voronoi diagram to promote center of gravity Voronoi diagram regularity.The method comprise the steps that constructing the center of gravity Voronoi diagram of objective body according to the triangle gridding of preset objective body and being smoothed to center of gravity Voronoi diagram；It obtains in current center of gravity Voronoi diagram according to the arrangement singular point combination of preset singular point arrangement mode；Specific singular point in singular point combination is merged or splitting operation, the singular point after being optimized combine；Center of gravity Voronoi diagram is updated according to the singular point combination after optimization and updated center of gravity Voronoi diagram is smoothed；Above-mentioned optimization process is repeated until meeting preset stop condition.The quantity of singular point can be effectively reduced in the present invention, to promote the regularity of center of gravity Voronoi diagram.
Description
Technical field
The invention belongs to computer graphics disposal technology fields, and in particular to a kind of regularity of center of gravity Voronoi diagram mentions
Lifting method.
Background technique
In field of Computer Graphics, triangle gridding is widest form in geometry discrete representation.Most of objects
It will be finally converted into triangle gridding, thus allow for efficiently rendering the numerical solution with partial differential equation.Surface mesh
(surface mesh) is calculated in modeling, animation, numerical value and other multiple fields play an important role, specifically with biological computation field
For, surface mesh just plays very important role, such as the folding of protein, the prediction of biological structure, non-precision
Solvents model etc..But many low-quality ingredients are contained in these grids, therefore the quality of these grids is in phase
To poor level.
Duality relation, the quality for promoting Voronoi diagram also just improve triangle gridding each other for Voronoi diagram and triangle gridding
Quality, i.e., the Voronoi diagram of one high quality can correspond to the triangle gridding of a high quality.The height of Voronoi diagram quality
It is low to go to evaluate there are many index, such as the size at the angle of the triangle gridding of its antithesis, the regularity of Voronoi diagram.In order to make
Voronoi diagram reaches preferable regularity, and researchers propose many methods to promote the accounting of non-singular point, for example,
The stratification that Wang Li is proposed guarantees the regularity of newly-generated point by dividing original non-singular point；What Lin Lu was proposed
Based on the optimization method of Monte Carlo random algorithm, global minima is approached by finding new Local Minimum every time.Although
Both methods contributes the regularity of model, but two methods all have its limitation.Stratification is for 3D table
CVT on surface grids is simultaneously unfriendly, and Monte Carlo minimum value method needs more the number of iterations, while the setting of parameter is very multiple
It is miscellaneous.
Correspondingly, this field needs a kind of regularity method for improving of new center of gravity Voronoi diagram to solve the above problems.
Summary of the invention
In order to solve the above problem in the prior art, in order to solve how to reduce singular point in center of gravity Voronoi diagram
Quantity to promote center of gravity Voronoi diagram regularity the problem of, the present invention provides a kind of regularities of center of gravity Voronoi diagram
Method for improving, comprising:
Step S1: the center of gravity Voronoi diagram of the objective body and right is constructed according to the triangle gridding of preset objective body
The center of gravity Voronoi diagram is smoothed；
Step S2: obtain in current center of gravity Voronoi diagram according to preset singular point arrangement mode arrangement singular point simultaneously
And the corresponding singular point of the singular point arrangement mode is obtained according to the singular point and is combined；
Step S3: merging the specific singular point in singular point combination or splitting operation, after being optimized
Singular point combination；
Step S4: the center of gravity Voronoi diagram is updated and to updated according to the singular point combination after the optimization
Center of gravity Voronoi diagram is smoothed；
Step S5: repeating step S2- step S4, until meeting preset stop condition.
Further, a kind of optimal technical scheme provided by the invention are as follows:
" obtain in current center of gravity Voronoi diagram according to preset singular point arrangement mode arrangement singular point and according to
The singular point obtains the combination of the singular point arrangement mode corresponding singular point " the step of include:
The singular point A for being 7 for each degree1, traverse the singular point A1Adjacent mesh；
If the singular point A1Adjacent mesh in there are degree be 5 singular point B1, then by the singular point A1It is adjacent
Grid set and the singular point B1Adjacent mesh set seek common ground；
Judge to whether there is in the intersection degree for 5 singular point C1, the singular point C if it exists1, then continue to judge
The singular point B1With singular point C1Adjacent mesh in the presence or absence of another degree be 7 singular point D1, the surprise if it exists
Dissimilarity D1, then by the singular point A1, singular point B1, singular point C1And singular point D1Group becomes singular point and combines.
Further, a kind of optimal technical scheme provided by the invention are as follows:
" obtain in current center of gravity Voronoi diagram according to preset singular point arrangement mode arrangement singular point and according to
The singular point obtains the combination of the singular point arrangement mode corresponding singular point " the step of include:
The singular point A for being 7 for each degree2, traverse the singular point A2Adjacent mesh；
If the singular point A2Adjacent mesh in there are degree be 5 singular point B2, then by the singular point A2It is adjacent
Grid set and the singular point B2Adjacent mesh set seek common ground；
Judge to whether there is in the intersection degree for 6 singular point C2, the singular point C if it exists2, then continue to judge
The singular point B2With singular point C2Adjacent mesh in the presence or absence of another degree be 7 singular point D2, the surprise if it exists
Dissimilarity D2, then by the singular point A2, singular point B2And singular point D2Group becomes singular point and combines.
Further, a kind of optimal technical scheme provided by the invention are as follows:
" obtain in current center of gravity Voronoi diagram according to preset singular point arrangement mode arrangement singular point and according to
The singular point obtains the combination of the singular point arrangement mode corresponding singular point " the step of include:
The singular point A for being 7 for each degree3, traverse the singular point A3Adjacent mesh；
If the singular point A3Adjacent mesh in there are degree be 5 singular point B3, then it is based on Depth Priority Searching
And according to single direction to the singular point A3Adjacent mesh traversed, if the surprise that traversal search is 5 to degree
Dissimilarity C3, then by the singular point A3, singular point B3And singular point C3Group becomes singular point and combines.
Further, a kind of optimal technical scheme provided by the invention are as follows:
" the specific singular point in singular point combination is merged or splitting operation, the singular point after being optimized
Combination " the step of include:
By singular point B in singular point combination1With singular point C1Merge into the non-singular point E that a degree is 61, described
Non-singular point E1Position and the singular point B1With singular point C1Line midpoint position it is identical.
Further, a kind of optimal technical scheme provided by the invention are as follows:
" the specific singular point in singular point combination is merged or splitting operation, the singular point after being optimized
Combination " the step of include:
By singular point B in singular point combination2With singular point C2Merge into the singular point E that a degree is 72, the surprise
Dissimilarity E2Position and the singular point B2With singular point C2Line midpoint position it is identical.
Further, a kind of optimal technical scheme provided by the invention are as follows:
" the specific singular point in singular point combination is merged or splitting operation, the singular point after being optimized
Combination " the step of include:
By the singular point A3It is split into the singular point E that a degree is 53The singular point E for being 6 with a degree4, described
Singular point E3With singular point E4About the singular point B3With singular point C3Line is symmetrical.
Further, a kind of optimal technical scheme provided by the invention are as follows:
The stop condition includes that the number of repetition step S2- step S4 reaches preset the number of iterations and/or the surprise
The quantity of dissimilarity combination is 0 and/or the regularity of the center of gravity Voronoi diagram reaches preset range；Wherein,
The regularity of the center of gravity Voronoi diagram is shown below::
Wherein, the N (v) indicates the regularity of center of gravity Voronoi diagram, the viIt indicates in the center of gravity Voronoi diagram
The degree of i-th of grid, the n are the sum of grid in the center of gravity Voronoi diagram.
Further, a kind of optimal technical scheme provided by the invention are as follows:
The method also includes:
The energy value of the center of gravity Voronoi diagram is reduced using preset iterative algorithm come to the center of gravity Voronoi diagram
It is smoothed；
Wherein, the energy value of the center of gravity Voronoi diagram is shown below:
Wherein, the ECVTIndicate the energy value of the center of gravity Voronoi diagram, the ViIndicate the center of gravity Voronoi diagram
In i-th of grid, the x indicates the ViInterior point, the ρ (x) indicate the preset ViCorresponding density function, it is described
ziIndicate the ViCenter of gravity, the n indicates the sum of grid in the center of gravity Voronoi diagram.
Further, a kind of optimal technical scheme provided by the invention are as follows:
The iterative algorithm includes Newton iterative and/or Lloyd iterative algorithm.
Compared with the immediate prior art, above-mentioned technical proposal is at least had the following beneficial effects:
The regularity method for improving of center of gravity Voronoi diagram in the present invention mainly includes the following steps: to obtain objective body
Center of gravity Voronoi diagram and the center of gravity Voronoi diagram is smoothed；Obtain meet in current center of gravity Voronoi diagram it is pre-
If singular point arrangement mode singular point combination；Specific singular point in singular point combination is merged or splitting operation,
Singular point combination after being optimized；Center of gravity Voronoi diagram is updated and to updated according to the singular point combination after optimization
Center of gravity Voronoi diagram is smoothed；Above-mentioned Optimization Steps are repeated until meeting preset stop condition.Based on above-mentioned side
Method can effectively reduce the quantity of singular point in center of gravity Voronoi diagram, promote the regularity of center of gravity Voronoi diagram.
Detailed description of the invention
Fig. 1 is a kind of key step schematic diagram of the regularity method for improving of center of gravity Voronoi diagram in the embodiment of the present invention；
Fig. 2 is to combine the key step schematic diagram optimized for 5-5-7-7 singular point in the embodiment of the present invention；
Fig. 3 is to combine the key step schematic diagram optimized for 7-5-7 singular point in the embodiment of the present invention；
Fig. 4 is to combine the key step schematic diagram optimized for 5-7-5 singular point in the embodiment of the present invention；
Fig. 5 is the experiment effect contrast schematic diagram in the embodiment of the present invention based on moai model；
Fig. 6 is the experiment effect contrast schematic diagram in the embodiment of the present invention based on kitten model；
Fig. 7 is the statistical result comparison diagram after each method optimizes on kitten model in the embodiment of the present invention.
Specific embodiment
The preferred embodiment of the present invention described with reference to the accompanying drawings.It will be apparent to a skilled person that this
A little embodiments are used only for explaining technical principle of the invention, it is not intended that limit the scope of the invention.
For each of center of gravity Voronoi diagram Voronoi unit, degree is defined as adjacent around the grid
Number of grid, degree be 6 grid in point be known as non-singular point, it is referred to as unusual for the point in the grid of other degrees
Point.The height of center of gravity Voronoi diagram regularity depends on the quantity of non-singular point in the figure, if the accounting of non-singular point is got in figure
Height, then its regularity is higher.For center of gravity Voronoi diagram, if not having singular point in figure, the regularity of the figure is most
Ideal state.
In order to reach preferable regularity, researchers propose many methods to promote the accounting of non-singular point.Specifically
For, Wang Li proposes stratification (bibliography: Wang, L, H é troy-Wheeler, F, Boyer, E.A
Hierarchical Approach for Regular Centroidal Voronoi Tessellations.Computer
Graphics Forum, 2016,35 (1): 152-165.), guarantee the rule of newly-generated point by dividing original non-singular point
Whole property.Lin Lu propose based on Monte Carlo random algorithm optimization method (bibliography: Lu L, Sun F, Pan H,
Wang W.Global Optimization of Centroidal Voronoi Tessellation with Monte
Carlo Approach.IEEE Transactions on Visualization&Computer Graphics,2012,18
(11): 1880-90.), global minima is approached by finding new Local Minimum every time.Although both methods is for model
Regularity contributed, but two methods all have its limitation.Stratification is not friendly for the CVT on 3D surface mesh
Good, Monte Carlo minimum value method needs more the number of iterations, while the setting of parameter is extremely complex.
A kind of regularity method for improving of center of gravity Voronoi diagram is disclosed in the present embodiment, this method is unusual by reducing
The quantity of point, to improve the regularity of center of gravity Voronoi diagram.In the present embodiment, firstly, defining three kinds in center of gravity
The singular point combining form often occurred in Voronoi diagram, each combining form are defined by specific arrangement mode.Then,
Taking merging for each specific combination, perhaps splitting operation carries out local disturb by way of adding some points or deleting a little
It is dynamic.Finally, updating center of gravity Voronoi diagram, smooth optimization then is carried out to it.It can produce high quality by above-mentioned process
Grid.
The regularity method for improving of center of gravity Voronoi diagram provided by the invention is illustrated with reference to the accompanying drawing.
Refering to attached drawing 1, Fig. 1 illustrates a kind of regularity method for improving of center of gravity Voronoi diagram in the present embodiment
Key step, as shown in Figure 1, under the regularity method for improving of one of the present embodiment center of gravity Voronoi diagram may include
State step:
Step S101: the center of gravity Voronoi diagram and counterweight of objective body are constructed according to the triangle gridding of preset objective body
Heart Voronoi diagram is smoothed.
Specifically, the three-dimensional triangulation shape surface mesh for giving an objective body, random sampled point, root are taken in surface mesh
Center of gravity Voronoi diagram is constructed according to sampled point, and the center of gravity Voronoi diagram is smoothed.The purpose of smoothing processing is drop
The energy of centre of gravity Voronoi diagram makes grid keep the property of center of gravity Voronoi diagram, more specifically, to center of gravity Voronoi
The step of figure is smoothed include:
Step Sa1: the energy value of center of gravity Voronoi diagram is calculated；
Step Sa2: point in center of gravity Voronoi diagram in grid and the center of gravity of corresponding grid are made based on preset iterative algorithm
Position is overlapped；
Wherein, shown in the energy value of center of gravity Voronoi diagram such as formula (1):
Wherein, ECVTIndicate the energy value of center of gravity Voronoi diagram, ViIndicate i-th of grid in center of gravity Voronoi diagram, x table
Show the ViInterior point, ρ (x) indicate ViCorresponding density function, ziIndicate ViCenter of gravity, n indicate center of gravity Voronoi diagram in net
The sum of lattice.
The parameter in Newton iterative method algorithm and/or Lloyd iterative algorithm optimization formula (1) can be passed through in the present embodiment
X, the process of iteration can all make parameter x close to the center of gravity z of corresponding grid each timei, as the center of gravity z of parameter x and corresponding gridiPosition
Iterative process terminates when setting coincidence.
Step S102: the singular point arranged in current center of gravity Voronoi diagram according to preset singular point arrangement mode is obtained
And it obtains the corresponding singular point of the singular point arrangement mode according to singular point to combine.
Specifically, it according to preset one or more singular point integrated modes, finds in current center of gravity Voronoi diagram to excellent
The singular point of change combines.It is preset in the present embodiment according to the degree of grid each in center of gravity Voronoi diagram and critical relation
Three kinds of singular points combinations, including the combination of 5-5-7-7 singular point, the combination of 7-5-7 singular point, the combination of 5-7-5 singular point.
Obtaining the step of 5-5-7-7 singular point combines includes:
The singular point A for being 7 for each degree1, traverse singular point A1Adjacent mesh；
If singular point A1Adjacent mesh in there are degree be 5 singular point B1, then by singular point A1Adjacent mesh set
With singular point B1Adjacent mesh set seek common ground；Further, the process of intersection is taken are as follows: with A1Adjacent grid set is
ΩA, with B1Adjacent grid set is ΩB, for ΩAIn each grid PiIf PiAlso in ΩBIn, then by PiIt is added to set
ΩA∩BIn, ΩA∩BThat is required intersection；
Judge to whether there is in the intersection degree for 5 singular point C1, singular point C if it exists1, then continue to judge singular point
B1With singular point C1Adjacent mesh in the presence or absence of another degree be 7 singular point D1, singular point D if it exists1, then will be odd
Dissimilarity A1, singular point B1, singular point C1And singular point D1Group becomes 5-5-7-7 singular point and combines.
Obtaining the step of 7-5-7 singular point combines includes:
The singular point A for being 7 for each degree2, traverse singular point A2Adjacent mesh；
If singular point A2Adjacent mesh in there are degree be 5 singular point B2, then by singular point A2Adjacent mesh set
With singular point B2Adjacent mesh set seek common ground；
Judge to whether there is in the intersection degree for 6 singular point C2, singular point C if it exists2, then continue to judge singular point
B2With singular point C2Adjacent mesh in the presence or absence of another degree be 7 singular point D2, singular point D if it exists2, then will be odd
Dissimilarity A2, singular point B2And singular point D2Group becomes 7-5-7 singular point and combines.
Obtaining the step of 5-7-5 singular point combines includes:
The singular point A for being 7 for each degree3, traverse singular point A3Adjacent mesh；
If singular point A3Adjacent mesh in there are degree be 5 singular point B3, then based on Depth Priority Searching and
According to single direction to singular point A3Adjacent mesh traversed, if the singular point C that traversal search is 5 to degree3, then
By singular point A3, singular point B3And singular point C3Group becomes 5-7-5 singular point and combines.
Step S103: merging the specific singular point in singular point combination or splitting operation, the surprise after being optimized
Dissimilarity combination.
Specifically, 5-5-7-7 singular point is combined, the edge of the combination shares 18 sides, this quantity with three simultaneously
The nonsingular grid number of edges of row is consistent, it is possible to make one by merging the singular point that two intermediate degrees are 5
The singular point that degree is 6 combines to optimize 5-5-7-7 singular point.It is influenced relatively for other grids of surrounding in this way
It is small, the regularity of surrounding grid will not be influenced.
Refering to attached drawing 2, Fig. 2, which is illustrated, combines the key step optimized for 5-5-7-7 singular point, such as schemes
Shown in 2, for above-mentioned 5-5-7-7 singular point combination optimization the step of include:
By singular point combine in singular point B1With singular point C1Merge into the non-singular point E that a degree is 61, non-singular point
E1Position and singular point B1With singular point C1Line midpoint position it is identical.
Specifically, 7-5-7 singular point is combined, the edge of the combination shares 19 sides, this quantity and a 6-7-6
Nonsingular grid number of edges it is consistent, it is possible to by merging the singular point that intermediate degree is 5 and the non-singular point that degree is 6
To optimize the combination of 7-5-7 singular point.It is influenced for other grids of surrounding so relatively small, surrounding net will not be influenced
The regularity of lattice.
Refering to attached drawing 3, Fig. 3, which is illustrated, combines the key step optimized, such as Fig. 3 for 7-5-7 singular point
It is shown, for above-mentioned 7-5-7 singular point combination optimization the step of include:
By singular point combine in singular point B2With singular point C2Merge into the singular point E that a degree is 72, singular point E2's
Position and singular point B2With singular point C2Line midpoint position it is identical.
Specifically, 5-7-5 singular point is combined, the singular point that two degrees are 5 in the combination is located at the surprise that degree is 7
The opposite side of dissimilarity, it is possible to which converting an isolated degree for the combination of these three singular points by way of adding some points is 5
Singular point.It is influenced for other grids of surrounding so relatively small, the regularity of surrounding grid will not be influenced.
Attached drawing 4 is participated in, Fig. 4 example, which is shown, combines the key step optimized for 5-7-5 singular point, such as Fig. 4 institute
Show, for above-mentioned 5-7-5 singular point combination optimization the step of include:
By singular point A3It is split into the singular point E that a degree is 53The singular point E for being 6 with a degree4, singular point E3
With singular point E4About the singular point B3With singular point C3Line is symmetrical.
Step S104: center of gravity Voronoi diagram is updated and to updated center of gravity according to the singular point combination after optimization
Voronoi diagram is smoothed.
Specifically, after the disturbance optimization of above-mentioned Three models, center of gravity is updated according to the singular point combination after optimization
Voronoi diagram.Because updated center of gravity Voronoi diagram inevitably causes energy lift, can for the energy of promotion
By by Newton method and/or Lloyd algorithm by iteration in a manner of optimize.CVT model can kept good in this way
The regularity of lift scheme under network.
Specifically, the step of being smoothed to updated center of gravity Voronoi diagram include:
The energy value of center of gravity Voronoi diagram is calculated using formula (1)；
The point in the center of gravity Voronoi diagram in grid is overlapped with the center of gravity of the grid based on preset iterative algorithm.More
It is possible to further pass through the parameter x in Newton iterative method algorithm and/or Lloyd iterative algorithm iteration optimization formula (1),
The process of iteration can all make parameter x close to the center of gravity z of corresponding grid each timei, as the center of gravity z of parameter x and corresponding gridiPosition
Iterative process terminates when coincidence.
It should be noted that above-mentioned iterative algorithm can be single use Newton iterative；It is also possible to individually make
With Lloyd iterative algorithm；Also the combination of Newton iterative and Lloyd iterative algorithm can be used, such as first carry out about 10 times
Lloyd iterative operation reuses about 30 Newton methods and optimizes to Voronoi diagram.
Step S105: repeating step S102- step S104, until meeting preset stop condition.
Specifically, stop condition include repeat step S102- step S104 number reach preset the number of iterations and/or
The quantity of above-mentioned singular point combination is 0 and/or the regularity of center of gravity Voronoi diagram reaches preset range.It should be noted that setting
It when stop condition, can adjust accordingly according to actual needs, such as stop condition only needs to meet and repeats step S102- step
The number of S104 reaches 2 times or stop condition only need the regularity for meeting center of gravity Voronoi diagram reach a preset range or
The quantity of above-mentioned singular point combination is 0 etc..
As described above, the most ideal situation is that the point in center of gravity Voronoi diagram in grid is non-singular point.And for surprise
For dissimilarity, then its degree is better closer to 6, for example than 4 degree points of 5 degree of points are more preferable, and than 8 degree points of 7 degree of points are more preferable, so these values
The cumulative Appreciation gist that can be used as measuring current center of gravity Voronoi diagram regularity.
The regularity of center of gravity Voronoi diagram can be calculated by method shown in formula (2):
Wherein, N (v) indicates the regularity of center of gravity Voronoi diagram, viIndicate the degree of i-th of grid in center of gravity Voronoi diagram
Number, n indicate the sum of grid in center of gravity Voronoi diagram.
Based on the regularity method for improving of above-mentioned center of gravity Voronoi diagram, can eliminate well common some unusual
Point combination, and compared with existing method, it can produce better mesh shape.In order to preferably show invention effect, it incite somebody to action this
The method of invention is compared with existing advanced method (such as stratification, Monte Carlo random algorithm).From qualitative and fixed
Two aspects are measured to be shown.
Refering to attached drawing 5, Fig. 5 illustrates the experiment effect comparison diagram based on moai model, as shown in figure 5, by from
From left to right, sequence from top to bottom successively indicates traditional CVT method, stratification, Monte Carlo method, 1 iteration knot of the invention
The effect displaying of fruit, 32 iteration results of the invention, present invention iteration results.Wherein, white grid representation non-singular point, ash
Color grid representation singular point.
With continued reference to attached drawing 6, Fig. 6 illustrates the experiment effect comparison diagram based on kitten model, such as Fig. 6 institute
Show, by from left to right, sequence from top to bottom successively indicates traditional CVT method, stratification, Monte Carlo method, the present invention 1
The effect displaying of secondary iteration result, 32 iteration results of the invention, present invention iteration results.Wherein, white grid representation is non-
Singular point, grey grid representation singular point.
With continued reference to attached drawing 7, Fig. 7 illustrates the statistical result after various methods optimize on kitten model,
As shown in fig. 7, traditional CVT method, stratification, Monte Carlo method, the present invention 1 time are successively indicated in abscissa from left to right repeatedly
For result, 2 iteration results of the invention, 3 iteration results of the invention；Ordinate indicates 5 degree of singular points, 6 degree of singular points and 7
Spend singular point ratio shared in kitten model respectively.
In conjunction with attached drawing 5, attached drawing 6 and attached drawing 7 it can be seen that method and traditional CVT method, stratification, illiteracy of the invention
Special calot's method is compared, and method of the invention can further promote the regularity of grid on an existing basis, to realize more preferable
Effect.
It should be noted that the hardware of the regularity method for improving carrying out practically of center of gravity Voronoi diagram of the invention and
Programming language is unrestricted, and the regularity promotion side that any programming language realizes center of gravity Voronoi diagram of the invention can be used
Method.Experiment porch in the present embodiment is the central processing unit with Intel i73.60GHz, 16GB RAM and 64
The computer of 10 operating system of windows.Two-dimentional triangle gridding is devised using CGAL computational geometry algorithms library on the platform
Generation system.
Those skilled in the art should be able to recognize that, side described in conjunction with the examples disclosed in the embodiments of the present disclosure
Method step, can be realized with electronic hardware, computer software, or a combination of the two, in order to clearly demonstrate electronic hardware and
The interchangeability of software generally describes each exemplary composition and step according to function in the above description.These
Function is executed actually with electronic hardware or software mode, specific application and design constraint depending on technical solution.
Those skilled in the art can use different methods to achieve the described function each specific application, but this reality
Now it should not be considered as beyond the scope of the present invention.
Term " includes " or any other like term are intended to cover non-exclusive inclusion, so that including a system
The process, method of column element not only includes those elements, but also other elements including being not explicitly listed, or further includes
The intrinsic element of these process, methods.
So far, it has been combined preferred embodiment shown in the drawings and describes technical solution of the present invention, still, this field
Technical staff is it is easily understood that protection scope of the present invention is expressly not limited to these specific embodiments.Without departing from this
Under the premise of the principle of invention, those skilled in the art can make equivalent change or replacement to the relevant technologies feature, these
Technical solution after change or replacement will fall within the scope of protection of the present invention.
Claims (10)
1. a kind of regularity method for improving of center of gravity Voronoi diagram, characterized by comprising:
Step S1: the center of gravity Voronoi diagram of the objective body is constructed according to the triangle gridding of preset objective body and to described
Center of gravity Voronoi diagram is smoothed；
Step S2: it obtains in current center of gravity Voronoi diagram according to the singular point and root of the arrangement of preset singular point arrangement mode
The corresponding singular point combination of the singular point arrangement mode is obtained according to the singular point；
Step S3: merging the specific singular point in singular point combination or splitting operation, unusual after being optimized
Point combination；
Step S4: the center of gravity Voronoi diagram is updated and to updated center of gravity according to the singular point combination after the optimization
Voronoi diagram is smoothed；
Step S5: repeating step S2- step S4, until meeting preset stop condition.
2. the regularity method for improving of center of gravity Voronoi diagram according to claim 1, which is characterized in that " obtain current weight
It is unusual that this is obtained according to the singular point of preset singular point arrangement mode arrangement in heart Voronoi diagram and according to the singular point
The step of point arrangement mode corresponding singular point combination " includes:
The singular point A for being 7 for each degree1, traverse the singular point A1Adjacent mesh；
If the singular point A1Adjacent mesh in there are degree be 5 singular point B1, then by the singular point A1Adjacent mesh
Set and the singular point B1Adjacent mesh set seek common ground；
Judge to whether there is in the intersection degree for 5 singular point C1, the singular point C if it exists1, then continue described in judgement
Singular point B1With singular point C1Adjacent mesh in the presence or absence of another degree be 7 singular point D1, the singular point if it exists
D1, then by the singular point A1, singular point B1, singular point C1And singular point D1Group becomes singular point and combines.
3. the regularity method for improving of center of gravity Voronoi diagram according to claim 1, which is characterized in that " obtain current weight
It is unusual that this is obtained according to the singular point of preset singular point arrangement mode arrangement in heart Voronoi diagram and according to the singular point
The step of point arrangement mode corresponding singular point combination " includes:
The singular point A for being 7 for each degree2, traverse the singular point A2Adjacent mesh；
If the singular point A2Adjacent mesh in there are degree be 5 singular point B2, then by the singular point A2Adjacent mesh
Set and the singular point B2Adjacent mesh set seek common ground；
Judge to whether there is in the intersection degree for 6 singular point C2, the singular point C if it exists2, then continue described in judgement
Singular point B2With singular point C2Adjacent mesh in the presence or absence of another degree be 7 singular point D2, the singular point if it exists
D2, then by the singular point A2, singular point B2And singular point D2Group becomes singular point and combines.
4. the regularity method for improving of center of gravity Voronoi diagram according to claim 1, which is characterized in that " obtain current weight
It is unusual that this is obtained according to the singular point of preset singular point arrangement mode arrangement in heart Voronoi diagram and according to the singular point
The step of point arrangement mode corresponding singular point combination " includes:
The singular point A for being 7 for each degree3, traverse the singular point A3Adjacent mesh；
If the singular point A3Adjacent mesh in there are degree be 5 singular point B3, then based on Depth Priority Searching and
According to single direction to the singular point A3Adjacent mesh traversed, if the singular point that traversal search is 5 to degree
C3, then by the singular point A3, singular point B3And singular point C3Group becomes singular point and combines.
5. the regularity method for improving of center of gravity Voronoi diagram according to claim 2, which is characterized in that " to described unusual
Specific singular point in point combination merges or splitting operation, and the singular point after optimize combines " the step of include:
By singular point B in singular point combination1With singular point C1Merge into the non-singular point E that a degree is 61, the non-surprise
Dissimilarity E1Position and the singular point B1With singular point C1Line midpoint position it is identical.
6. the regularity method for improving of center of gravity Voronoi diagram according to claim 3, which is characterized in that " to described unusual
Specific singular point in point combination merges or splitting operation, and the singular point after optimize combines " the step of include:
By singular point B in singular point combination2With singular point C2Merge into the singular point E that a degree is 72, the singular point
E2Position and the singular point B2With singular point C2Line midpoint position it is identical.
7. the regularity method for improving of center of gravity Voronoi diagram according to claim 4, which is characterized in that " to described unusual
Specific singular point in point combination merges or splitting operation, and the singular point after optimize combines " the step of include:
By the singular point A3It is split into the singular point E that a degree is 53The singular point E for being 6 with a degree4, described unusual
Point E3With singular point E4About the singular point B3With singular point C3Line is symmetrical.
8. the regularity method for improving of center of gravity Voronoi diagram described in any one of -7 according to claim 1, which is characterized in that
The stop condition includes that the number of repetition step S2- step S4 reaches preset the number of iterations and/or singular point combination
Quantity be that 0 and/or the regularity of the center of gravity Voronoi diagram reach preset range；Wherein,
The regularity of the center of gravity Voronoi diagram is shown below::
Wherein, the N (v) indicates the regularity of center of gravity Voronoi diagram, the viIt indicates in the center of gravity Voronoi diagram i-th
The degree of grid, the n are the sum of grid in the center of gravity Voronoi diagram.
9. the regularity method for improving of center of gravity Voronoi diagram described in any one of -7 according to claim 1, which is characterized in that
The method also includes:
The energy value of the center of gravity Voronoi diagram is reduced using preset iterative algorithm to carry out to the center of gravity Voronoi diagram
Smoothing processing；
Wherein, the energy value of the center of gravity Voronoi diagram is shown below:
Wherein, the ECVTIndicate the energy value of the center of gravity Voronoi diagram, the ViIt indicates i-th in the center of gravity Voronoi diagram
A grid, the x indicate the ViInterior point, the ρ (x) indicate the preset ViCorresponding density function, the ziIt indicates
The ViCenter of gravity, the n indicates the sum of grid in the center of gravity Voronoi diagram.
10. the regularity method for improving of center of gravity Voronoi diagram according to claim 9, which is characterized in that the iteration is calculated
Method includes Newton iterative and/or Lloyd iterative algorithm.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111080509A (en) * | 2019-12-10 | 2020-04-28 | 中国科学院自动化研究所 | Multithreading parallel computing method and system for three-dimensional cutting Voronoi diagram |
| CN111967148A (en) * | 2020-07-31 | 2020-11-20 | 电子科技大学 | Voronoi graph particle merging algorithm for particle simulation |
| CN115293985A (en) * | 2022-08-11 | 2022-11-04 | 北京拙河科技有限公司 | Super-resolution noise reduction method and device for image optimization |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111080509A (en) * | 2019-12-10 | 2020-04-28 | 中国科学院自动化研究所 | Multithreading parallel computing method and system for three-dimensional cutting Voronoi diagram |
| CN111080509B (en) * | 2019-12-10 | 2022-03-08 | 中国科学院自动化研究所 | Multithreading parallel computing method and system for three-dimensional cutting Voronoi diagram |
| CN111967148A (en) * | 2020-07-31 | 2020-11-20 | 电子科技大学 | Voronoi graph particle merging algorithm for particle simulation |
| CN111967148B (en) * | 2020-07-31 | 2023-07-07 | 电子科技大学 | Particle simulation Voronoi diagram particle merging algorithm |
| CN115293985A (en) * | 2022-08-11 | 2022-11-04 | 北京拙河科技有限公司 | Super-resolution noise reduction method and device for image optimization |
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