CN106780746B - Blue noise sampling method based on simple mutual exclusion operation - Google Patents
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Abstract
The invention relates to a blue noise sampling method based on simple mutual exclusion operation, which is applied to a blue noise sampling area and comprises the following steps: step A, carrying out random sampling in the sampling area to obtain a sampling point set; b, selecting any sampling point in the sampling point set; c, optimizing the sampling point set according to a preset space constraint parameter; step D, if the sampling point set after optimization processing is completely converged, obtaining a sampling point set based on the convergence of the sampling points; otherwise, turning to the step C, and performing iterative optimization processing on the sampling point set subjected to the optimization processing; and E, repeating the steps B to D until the sampling point set is completely converged after optimization processing based on each sampling point, and obtaining a final blue noise sampling point set. According to the invention, the generation of high-quality blue noise sampling is realized, the space constraint is directly implemented, and the quality of re-gridding is improved.
Description
Technical Field
The invention belongs to the technical field of computer graphics processing, particularly relates to a sampling method in computer graphics processing, and particularly relates to a blue noise sampling method based on simple mutual exclusion operation.
Background
In computer graphics, vertex sets are ubiquitous. In different applications, the features that a set of points is required to have are also different. Among many point sets, an isotropic point set having a blue noise characteristic has an important application, and is widely applied to the fields of dither anti-aliasing, image point drawing, object distribution, gridding, re-gridding and the like.
Blue noise can be described by a fourier spectrum with low energy at low frequencies, a sharp peak (average distance between adjacent points) at increasing frequency, and a flat spectrum at high frequencies. From a geometric point of view, the distribution of the corresponding point sets is uniform and irregular. By uniform is meant a uniform density of point sets, with no apparent clusters or holes, as with low frequency energy. Irregularities mean that the points are not harmonious with one another and are therefore quite flat in the high frequency band, with harmonics falling off rapidly after the appearance of a peak. For clusters, the minimum neighboring distance in the point set can be used for detection, and holes can be represented by the maximum distance of neighboring points, and the two representation methods are usually used for measuring the quality of a triangular mesh with equal density. Finally, for an irregular set of points, it is also possible to represent its globally uniform nature with equal Voronoi cell volumes.
Blue Noise Sampling (Blue Noise Sampling) is typically initialized to a random set of sample points (with a flat spectrum) and then its low frequency energy is narrowed using some local constraint. The classical method of generating a poisson disk sampling point set is the tossing method, which was first proposed by Cook and was later greatly improved. However, this method is very noisy, often with large holes and too small, resulting in narrow low energy bands, and is therefore not an ideal isotropic sampling method. Then, to increase the radius of the poisson disc sample, McCool and Fiume propose to use the Lloyd's algorithm to relax the set of points to form a Voronoi (Voronoi) map of the center of gravity. However, the problem with Voronoi diagrams is that it is too regular, resulting in energy concentration at some harmonic frequencies, leading to aliasing effects. In the last years, many Optimization algorithms have been proposed to replace the Lloyd method, resulting in better Blue Noise properties, such as CCVT (Capacity Constrained Voronoi temporal characteristics), BNOT (Blue Noise through optimal transport algorithm), FPO (best effort Optimization), CCDT (Capacity Constrained Delaunay Triangulation, Constrained Delaunay triangular volume) method, etc. Furthermore, in addition to using explicit spatial constraints, there are methods that use an analog simulation approach to resemble the constraints. For example, a point set is represented by a kernel, and interaction between kernels is simulated by a statistical mechanical method, or a smooth particle fluid dynamics simulation method is used. These methods produce similar, but not identical, sets of points, resulting in different blue noise characteristics
Although there are many existing blue noise sampling methods based on simple mutual exclusion, each method has disadvantages in one or more of the following aspects: speed, memory consumption, programming complexity, sample point control, etc. To the best of our knowledge, there is no single algorithm that can ideally solve all of the above problems, and therefore a trade-off is required. For example, the FPO method achieves a maximum Poisson disc radius (no clusters), but creates holes, CCDT eliminates holes but creates clusters, and CCVT and BNOT, while being more average, do not achieve a maximum Poisson disc radius.
On the other hand, the optimization goal of the existing methods is too single, such as considering only volume constraints, or maximizing minimum distance, etc. The spatial constraints are not exhausted, so the search for blue noise sampling methods is always active to produce efficient or better blue noise characteristics.
Finally, the sampling-based re-meshing method is a most relevant application of blue noise sampling, and since the blue noise characteristic has a good distribution characteristic, a high-quality mesh (with an angle constraint and a side length constraint) can be formed through sampling. However, most of the existing methods cannot produce a grid without obtuse angles, and as far as we know, Li and Zhang first propose an algorithm which can produce a grid without obtuse angles, but the method cannot eliminate small angles in the grid at the same time. Recent work produced obtuse-angle-free re-meshing results using CVT (Central Voronoi Tesselltion, center-of-gravity Voronoi diagram) and MPS (MaximalPoisson-disk Sampling method), respectively.
Disclosure of Invention
In order to solve the above-mentioned problems in the prior art, that is, to solve the problem of how to generate high-quality blue noise samples and directly implement space constraint, the present invention provides a blue noise sampling method based on simple mutual exclusion operation, which is applied to a sampling region of blue noise, and the method includes the following steps:
step A, carrying out random sampling in the sampling area to obtain a sampling point set;
b, selecting any sampling point in the sampling point set;
c, optimizing the sampling points according to preset space constraint parameters;
step D, if the sampling points after the optimization processing are completely converged, obtaining a sampling point set based on the convergence of the sampling points; otherwise, turning to the step C, and performing iterative optimization processing on the sampling points after the optimization processing;
and E, repeating the steps B to D until the sampling point set is completely converged after optimization processing based on each sampling point, and obtaining a final blue noise sampling point set.
Preferably, the optimization process is: respectively calculating three space constraint parameters of a conflict radius, a coverage radius and a Voronoi diagram cell volume based on sampling points; and comparing the three space constraint parameters with the preset optimized space constraint parameters respectively corresponding to the three space constraint parameters, screening out unqualified sampling points in the sampling point set according to a comparison result, and adjusting the unqualified sampling points.
Preferably, in the optimization, when the three spatial constraint parameters are compared with the preset spatial constraint parameters respectively corresponding to the three spatial constraint parameters, the comparison of the three spatial constraint parameters does not have a precedence relationship.
Preferably, the set of sampling points is
The sampling region is D, and the collision radius of the sampling points is sampling point x in the optimization processingiAnd sample point xjThe distance between them;
wherein x isiFor the currently selected sample point, xjIs xiThe neighbor sampling point of (1);
the acquisition mode based on the coverage radius of the sampling points is as follows:
obtaining the currently selected sampling point xiAdjacent triangular patch tj∈DT(X)；
At tjIn the case of a triangle not having an obtuse angle, t is obtainedjThe radius r of the circumscribed circle of (a) is taken as a coverage radius based on the sampling point;
voronoi diagram cell volume of sample point is currently selected sample point xiAnd all of its neighboring sample points.
Preferably, when the three spatial constraint parameters are compared with the preset spatial constraint parameters respectively corresponding to the three spatial constraint parameters, the specific comparison method is as follows:
comparing the size relation between the conflict radius based on the sampling point and the preset conflict radius, and if the conflict radius based on the sampling point is smaller than the preset conflict radius, determining the sampling point xjUnqualified sampling points are obtained; otherwise determine the sampling point xjThe sampling points are qualified;
comparing the relation between the coverage radius based on the sampling point and the preset coverage radius, and if the coverage radius based on the sampling point is larger than the preset coverage radius, acquiring tjThe remaining two endpoints xkDetermining the endpoint xkUnqualified sampling points are obtained;
calculating the difference value between the cell volume and the average volume of the Voronoi diagram based on the sampling points, comparing the difference value with the maximum deviation of the target, and if the difference value is lower than the maximum deviation of the target, determining the currently selected sampling point xiAll the neighbor sampling points are qualified sampling points, otherwise, the currently selected sampling point x is determinediAll neighbor sample points of (1) are unqualified sample points.
Preferably, in the optimization process,
and after the unqualified sampling points in the sampling point set are screened out according to the preset space constraint parameters, moving the unqualified sampling points until the unqualified sampling points become qualified sampling points.
Preferably, step B further comprises, before:
and F, establishing Delaunay triangularization of the sampling point set.
Preferably, step E is followed by:
and G, updating the Delaunay triangularization of the blue noise sampling point set.
Compared with the prior art, the invention has at least the following advantages:
through the design of the invention, the generation of high-quality blue noise sampling is realized, the space constraint is directly implemented, and the quality of re-gridding is improved.
Drawings
FIG. 1 is a schematic flow chart of a blue noise sampling method based on simple mutual exclusion operation according to the present invention;
FIG. 2 is a schematic diagram of the present invention of blue noise sampling method based on simple mutual exclusion operation to optimize collision, coverage and volume by repositioning neighbor points;
FIG. 3 is a comparison of statistical results of different blue noise sampling methods based on simple mutual exclusion;
FIG. 4 is a graph of the results of spectral analysis and anti-aliasing analysis under different parameters;
FIG. 5 is a comparison of the dot plots of the present method with other methods;
FIG. 6 is a comparison of statistical parameters for different re-gridding methods;
FIG. 7 is a graph of the results of different re-gridding methods.
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.
The invention provides a blue noise sampling method based on simple mutual exclusion operation, which is applied to a blue noise sampling region, and the following describes a specific implementation mode of the invention in detail by combining with the attached drawings.
As shown in fig. 1, the method specifically includes the following steps:
and A, carrying out random sampling in the sampling area to obtain a sampling point set.
And F, establishing Delaunay triangularization of the sampling point set.
And B, selecting any sampling point in the sampling point set.
And C, optimizing the sampling points according to preset space constraint parameters.
Wherein the optimization process is as follows: respectively calculating three space constraint parameters of a conflict radius, a coverage radius and a Voronoi diagram cell volume based on sampling points; comparing the three space constraint parameters with the preset space constraint parameters respectively corresponding to the three space constraint parameters, screening out unqualified sampling points in the sampling point set according to the comparison result, and adjusting the unqualified sampling points; further, in the optimization processing, when the three spatial constraint parameters are compared with the preset spatial constraint parameters respectively corresponding to the three spatial constraint parameters, the comparison processing of the three spatial constraint parameters does not have a precedence relationship.
Set of sampling points as
The sampling region is D, and in the optimization process, the conflict radius of the sampling point is XiAnd sample point xjThe distance between them;
wherein x isiFor the currently selected sample point, xjIs xiThe neighbor sampling point of (1);
the acquisition mode based on the coverage radius of the sampling points is as follows:
obtaining the currently selected sampling point xiAdjacent triangular patch tj∈DT(X)；
At tjIn the case of a triangle not having an obtuse angle, t is obtainedjThe radius r of the circumscribed circle of (a) is taken as a coverage radius based on the sampling point;
voronoi diagram cell volume of sample point is currently selected sample point xiAnd the volume between all its neighboring sample points.
Further, when the three spatial constraint parameters are compared with the preset spatial constraint parameters respectively corresponding to the three spatial constraint parameters, the specific comparison method is as follows:
comparing the size relation between the conflict radius based on the sampling point and the preset conflict radius, and if the conflict radius based on the sampling point is smaller than the preset conflict radius, determining the sampling point xjUnqualified sampling points are obtained; otherwise determine the sampling point xjThe sampling points are qualified;
comparing the relation between the coverage radius based on the sampling point and the preset coverage radius, and if the coverage radius based on the sampling point is larger than the preset coverage radius, acquiring tjThe remaining two endpoints xkDetermining the endpoint xkUnqualified sampling points are obtained;
calculating the difference value between the cell volume and the average volume of the Voronoi diagram based on the sampling points, comparing the difference value with the maximum deviation of the target, and if the difference value is lower than the maximum deviation of the target, determining the currently selected sampling point xiAll the neighbor sampling points are qualified sampling points, otherwise, the currently selected sampling point x is considerediAll neighbor sample points of (1) are unqualified sample points.
Further, in the optimization process,
and after the unqualified sampling points in the sampling point set are screened out according to the preset space constraint parameters, moving the unqualified sampling points until the unqualified sampling points become qualified sampling points.
And D, if the sampling points after the optimization processing are completely converged, obtaining a sampling point set based on the convergence of the sampling points.
And C, if the sampling points after the optimization processing are not completely converged, turning to the step C, and performing iterative optimization processing on the sampling points after the optimization processing.
And E, repeating the steps B to D until the sampling point set is completely converged after optimization processing based on each sampling point, and obtaining a final blue noise sampling point set.
Wherein, said step E further comprises the following steps:
and G, updating the Delaunay triangularization of the blue noise sampling point set.
In the invention, the position of the mobile neighbor sampling point is used for replacing the mobile selected sampling point, and the method for moving the neighbor sampling point is greatly different from the original method: after one iteration, each sampling point can optimize local neighbor sampling points, and then the global optimization of the sampling points in the sampling point set is quickly achieved through subsequent iterations. Therefore, after each sample point is visited, a portion of the sample points over the sampling region are always optimized, which results in faster convergence than merely moving the selected sample point itself.
The basic model of the invention is serial, in each iteration step, for a sampling point, the neighboring sampling point is continuously optimized, as shown in fig. 2, three kinds of space constraints are realized by the following three optimization steps.
The radius conflict optimization moves the radius conflicting sampling points out of the preset conflicting radius, and the steps are as follows if the 'push' operation is general:
1. initializing a sampling point set X of n points;
2. establishing Delaunay triangularization DT (X);
3. traverse each point xi∈X；
4. Traverse xiEach neighbor sample point xj；
5. Setting offset
6. Computing an inter-point vector
7. If mould
Then
xj＝xj+shift；
8. If xiNeighbor x ofjJumping to the step 4 if the traversal is not finished;
9. updating Delaunay triangularization DT (X);
10. if xiJumping to the step 3 if the traversal is not finished;
11. if xiIf the traversal is finished but some points do not meet the requirements and the movement needs to be continued, jumping to the step 3, and traversing all the sampling points x againi；
The coverage radius optimization moves the sampling point into the preset coverage radius, and the steps are as follows if the operation is pulled:
1. initializing a sampling point set X of n points;
2. establishing Delaunay triangularization DT (X);
3. traverse each point xi∈X；
4. Traverse xiEach of the adjoining triangular patches t ofj∈DT(X)；
5. If t isjIs obtuse triangle, skip the current tjGo to step 4;
6. otherwise, if tjRadius r of the circumscribed circle of (1) is larger than rcIf yes, executing step 7, otherwise, jumping to step 16;
7. setting c as tjThe center of the circumscribed circle of (1);
8.r＝|c-xi|；
9. set scale rc/r；
10. Traverse tjThe remaining two endpoints xk；
11.
12.
13.xk＝xk+shift；
14. If xkJumping to the step 10 if the traversal is not finished;
15. if t isjJumping to the step 4 if the traversal is not finished;
16. updating Delaunay triangularization DT (X);
17. if xiJumping to the step 3 if the traversal is not finished;
18. if xiAfter the traversal is finished, but the point still does not meet the requirement, and the movement needs to be continued, the step 3 is skipped, and all the sampling points x are traversed againi；
Volume optimization visually uses the Voronoi internal ratio as a container for holding water, so that the force applied to each boundary is the same, and the cell volume of the Voronoi diagram can be increased or decreased by pushing or pulling the neighbor sampling points, and the steps are as follows:
1. initializing a sampling point set X of n points;
2. establishing Delaunay triangularization DT (X);
3. traverse each point xi∈X；
4. Setting A to be the volume of the current Voronoi cell;
5. the difference between the current volume and the average volume is calculated,
6. if d isABelow the target maximum deviation, skip the current xiGo to step 3;
7. otherwise, the cell perimeter L ═ Σ L is calculatedi；
8. Calculating the pressure P ═ d of unit side lengthA/L；
9. Traverse xiEach neighbor sample point xj；
10. Computing an inter-point vector
11. Let ljIs xjThe corresponding Voronoi cell side length;
12. calculating xjUpper force F ═ P × lj；
13. Is provided with
14.xj＝xj+shift；
15. If xiNeighbor x ofjJumping to step 9 if the traversal is not finished;
16. updating Delaunay triangularization DT (X);
17. if xiJumping to the step 3 if the traversal is not finished;
18. if xiAfter the traversal is finished, but the point still does not meet the requirement, and the movement needs to be continued, the step 3 is skipped, and all the sampling points x are traversed againi。
Because the three optimization steps can be implemented by using the same data structureNow, the above three steps can be easily combined at will, and the three targets of each sampling point are optimized in turn, so that the conflict radius r can be maximizedfMinimizing the radius of coverage rcAnd makes the density of the sampling points uniform.
The invention provides a specific embodiment, and particularly provides the effectiveness of the algorithm through a series of experimental verification, wherein an experimental platform is a computer with an Intel i7-37703.40GHz central processing unit, a 16GB RAM and a 64-bit windows 7 operating system. A C + + validation program was designed on this platform using a CGAL computational geometry algorithm library.
Firstly, the invention is compared with other blue noise methods in main characteristics, each performance parameter of blue noise sampling is summarized in figure 3, Push-pull- {1,2,3} is an example of the invention under different parameters, d of the first two columnsminAnd davgRespectively, the minimum and average nearest neighbor distances. Large dminValue indicates no cluster in the point set, large davgThe points of illustration are uniform in space. r iscThe radius of coverage is as small as possible. Heck et al propose two blue noise optimization objectives: effective nyquist frequency veffAnd oscillation omega at high frequency, high effective Nyquist frequency ve ffRepresenting a wide low band, while a smaller oscillation omega for high frequencies represents less aliasing β ═ rc/rfThe present invention can reach 0.67 without losing the blue noise characteristic, which is better when the ratio of the coverage radius and the collision radius is smaller. To measure irregularities, the present invention introduces BOO in the last column, which reflects how similar to an ideal hexagonal grid arrangement, and whose value is 0,1]Meanwhile, if BOO is less than 0.6, the point set is indicated to have irregularity, and as can be seen from the figure, other sampling methods except the CVT method all meet the requirement of irregularity. Compared with other methods, the parameter indexes in the frequency domain and the spatial domain of the invention have better performance.
Secondly, the spectrum analysis and the anti-aliasing experiment prove that the proposed method can eliminate the aliasing effect, and FIG. 4 shows the power spectrum and the anti-aliasing effect of the point set under different parametersAnd (6) testing. Wherein the antialiasing experiment uses a one-time sampling per pixel and a Mitchell filter reconstruction function (x, y) → sin (x)2+y2). Because it can represent a correspondingly wide frequency, the antialiased reconstructed image can be well evaluated for the degree of aliasing. It can be seen that the present invention can achieve high quality frequency domain characteristics, very close to the current advanced methods such as BNOT and FPH, illustrating the ability of the present method to produce controllable blue noise characteristics. It has also been found that increasing the collision radius is effective in reducing low frequency noise, but at the cost of introducing aliasing. Fortunately, the method can be implemented by reducing rcTo eliminate noise does not introduce excessive aliasing. The method can better trade off between noise and aliasing by adjusting the parameters. Furthermore, the method can be applied to image point mapping, as shown in fig. 5, and compared with the existing method, the method can map high-quality point mapping with blue noise distribution.
Finally, the present invention compared to existing regridding techniques, studies the performance of different surface regridding methods in generating mesh quality, including maximum poisson disk sampling (MPS), Farthest Point Optimization (FPO), volume-limited CVT (capcvt), diskturning for disk density adjustment, and CVT (CVT) that penalizes Voronoi short edgesnob). FIG. 6 shows statistics of the quality of the re-gridding, QminAnd QavgThe minimum and average triangle masses, θ, are shownminAnd thetamaxIs the angle of the minimum and maximum,
represents the average of the minimum angles, θ, of all triangles＜30°% is the percentage of angles smaller than 30 degrees, θ>90°% is the percentage of obtuse angle, V567% is the percentage of degrees at 5, 6, 7 vertices, dRMSIs the root mean square distance, dHIs the Hausdorff distance of the input surface and the re-gridding result. FIG. 6 shows some examples of the re-gridding results, and it can be seen from the comparison of statistical parameters that the present invention can effectively eliminate obtuse triangles, and compared with other re-gridding methods with blue noise characteristicsBetter triangle and angle quality is achieved. And CVTnobIn contrast, the present invention has similar qualities, and not only does it show that fig. 7 shows the present invention ratio CVTnobThe method has larger irregularity, and the characteristic can be better applied to simulation, such as fracture simulation and fluid simulation.
In conclusion, the results of the embodiment of the invention have important application values in the fields of animation, physical simulation, medical and biological data analysis, scientific simulation and the like.
Those of skill in the art will appreciate that the various illustrative modules, and method steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps 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 (5)
1. A blue noise sampling method based on simple mutual exclusion operation in graphic processing is characterized in that the method is applied to a sampling area of blue noise and comprises the following steps:
step A, carrying out random sampling in the sampling area to obtain a sampling point set;
b, selecting any sampling point in the sampling point set;
c, optimizing the sampling points according to preset space constraint parameters;
step D, if the sampling points after the optimization processing are completely converged, obtaining a sampling point set based on the convergence of the sampling points; otherwise, turning to the step C, and performing iterative optimization processing on the sampling points after the optimization processing;
e, repeating the steps B-D until the sampling point set is completely converged after optimization processing based on each sampling point to obtain a final blue noise sampling point set;
wherein the optimization process is as follows: respectively calculating three space constraint parameters of a conflict radius, a coverage radius and a Voronoi diagram cell volume based on sampling points; comparing the three space constraint parameters with the preset space constraint parameters respectively corresponding to the three space constraint parameters, screening out unqualified sampling points in the sampling point set according to the comparison result, and adjusting the unqualified sampling points;
the set of sampling points is
The sampling region is D, and the collision radius of the sampling points is sampling point x in the optimization processingiAnd sample point xjThe distance between them;
wherein x isiFor the currently selected sample point, xjIs xiThe neighbor sampling point of (1);
the acquisition mode based on the coverage radius of the sampling points is as follows:
obtaining the currently selected sampling point xiAdjacent triangular patch tj∈DT(X)；
At tjIn the case of a triangle not having an obtuse angle, t is obtainedjThe radius r of the circumscribed circle of (a) is taken as a coverage radius based on the sampling point;
voronoi diagram cell volume of sample point is currently selected sample point xiThe volume between the sampling point and all the neighboring sampling points;
when the three spatial constraint parameters are compared with the preset spatial constraint parameters respectively corresponding to the three spatial constraint parameters, the specific comparison mode is as follows:
comparing the size relation between the conflict radius based on the sampling point and the preset conflict radius, and if the conflict radius based on the sampling point is smaller than the preset conflict radius, determining the sampling point xjUnqualified sampling points are obtained; otherwise determine the sampling point xjThe sampling points are qualified;
comparing the relation between the coverage radius based on the sampling point and the preset coverage radius, and if the coverage radius based on the sampling point is larger than the preset coverage radius, acquiring tjThe remaining two endpoints xkDetermining the endpoint xkUnqualified sampling points are obtained;
calculating the difference value between the cell volume and the average volume of the Voronoi diagram based on the sampling points, comparing the difference value with the maximum deviation of the target, and if the difference value is lower than the maximum deviation of the target, determining the currently selected sampling point xiAll the neighbor sampling points are qualified sampling points, otherwise, the currently selected sampling point x is considerediAll neighbor sample points of (1) are unqualified sample points.
2. The method according to claim 1, wherein in the optimization process, when the three spatial constraint parameters are compared with preset spatial constraint parameters respectively corresponding to the three spatial constraint parameters, there is no precedence relationship in the comparison process of the three spatial constraint parameters.
3. The method of claim 1, wherein in the optimization process,
and after the unqualified sampling points in the sampling point set are screened out according to the preset space constraint parameters, moving the unqualified sampling points until the unqualified sampling points become qualified sampling points.
4. The method for blue noise sampling based on simple mutual exclusion operation according to claim 1, wherein said step B is preceded by the steps of:
and F, establishing Delaunay triangularization of the sampling point set.
5. The method for blue noise sampling based on simple mutual exclusion operation according to claim 4, wherein said step E is followed by further comprising:
and G, updating the Delaunay triangularization of the blue noise sampling point set.
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| CN103839292A (en) * | 2014-03-06 | 2014-06-04 | 中国科学院自动化研究所 | Method for sampling contour surface and generating high-quality triangular mesh |
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| CN104240299A (en) * | 2014-08-29 | 2014-12-24 | 中国科学院自动化研究所 | Remeshing method based on maximal Poisson-disk sampling |
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| CN103839292A (en) * | 2014-03-06 | 2014-06-04 | 中国科学院自动化研究所 | Method for sampling contour surface and generating high-quality triangular mesh |
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