CN106204742A - The radiuses such as the fixing two dimension counted maximize the Poisson disk method of sampling and system - Google Patents
The radiuses such as the fixing two dimension counted maximize the Poisson disk method of sampling and system Download PDFInfo
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Abstract
The invention discloses the radiuses such as a kind of fixing two dimension counted and maximize the Poisson disk method of sampling and sampling system.Wherein, the method includes sampled point number and the sample area specified according to user, generates the first sampling point set；Described first sampling point set is carried out Delaunay trigonometric ratio, and extracts the minor face length in Delaunay trigonometric ratio result as the first sample radius；Determine whether described first sampling point set reaches the sampling of described maximization Poisson disk；In the case of described first sampling point set reaches the sampling of described maximization Poisson disk, record described first sampling point set and described first sample radius.The technical problem that the maximization Poisson disk how realizing counting fixing is sampled is solved by the embodiment of the present invention, sampling point set can be made to have good blue noise character, have simple, be easily achieved, stable performance and the advantage that can restrain, can be applicable in the application such as image rendering and textures synthesis.
Description
Technical field
The present embodiments relate to technical field, be specifically related to the radiuses such as a kind of fixing two dimension counted and maximize Poisson circle
The radiuses such as the dish method of sampling and the fixing two dimension counted maximize Poisson disk sampling system, but are not limited to this.
Background technology
In field of Computer Graphics, the sampling of Poisson disk is basic studying a question, and the point set that sampling obtains divides
Cloth not only meets randomness but also meet uniformity, and has the frequency spectrum of blue noise characteristic.It is played the part of emphatically in a lot of actual application
The role wanted, such as image rendering [1], digital halftone [2,3], object distribution [4,5] and textures synthesis [6] etc..
One preferable Poisson disk sampling point set needs to meet three conditions: 1. zero deflection sampling property (each sampling
The point that region is not covered with has identical probability to accept a new sampled point)；2. minimum range character (adopt by any two
Distance between sampling point is more than given sample radius)；3. (sample area is covered completely by all of sampling disk to maximize character
Lid).The method of sampling meeting these three condition is referred to as maximizing Poisson disk sampling (Maximal Poisson-disk
Sampling--MPS)。
The classical way producing the sampling of Poisson disk is called throwing boomerang method (Dart Throwing--DT) [7].The base of the method
This thought is to set sample radius, randomly generates a sampled point the most every time, if new sampled point and existing sampled point
Do not conflict, then accept this sampled point, otherwise, refuse this sampled point.Boomerang method is thrown in terms of efficiency and quality not for traditional
Foot, follow-up study person proposes many effective data structures and is accelerated and improves throwing boomerang method, such as sector [8], Voronoi diagram
[9], dynamic quadtree [10,11,12], recessive quaternary tree [13], Power figure [14] etc..Although throwing boomerang method and mutation being permissible
Generate high-quality sampling point set.But, this kind of method has a common shortcoming, i.e. cannot accurately control the number of sampled point
Mesh.In consideration of it,Solstics sampling optimization (Farthest Point Optimization--is proposed Deng [15]
FPO), its main thought is the overall beeline maximizing sampling point set.But, FPO is a deterministic method, and it is every
Secondary new sampled point is inserted into " solstics " (center of circle of largest empty circle of the Delaunay trigonometric ratio that residue point set is constituted).Borrow
The thought of mirror FPO, Yan etc. [16] proposes minor face and removes algorithm (Shortest Edge Removal--SER).The method
Each selection one minor face also removes one of them end points randomly, then inserts it into " solstics ".But, SER side
Method is it cannot be guaranteed that reach to maximize sampling attribute.
In view of this, the special proposition present invention.
Relevant document sees as follows:
[1]Mitchell D P.Generating antialiased images at low sampling
densities.In Proc.the 14th ACM SIGGRAPH,1987,65-72；
[2]Yellot J.I.Spectral analysis of spatial sampling by
photoreceptors:Topological disorder prevents aliasing.Vision Research,1982,
22:1205-1210；
[3]Yellot J.I.Spectral consequences of photoreceptor sampling in the
rhesus retina.Science 221,1983,382-385；
[4]Deussen O.,Hanrahan P.,Lintermann B.,Mech R.,Pharr M.,
Prusinkiewicz P.Realistic modeling and rendering of plant
ecosystems.Proceedings of ACM SIGGRAPH 1998,1998,275-286；
[5]Cohen M.F.,Shade J.,Hiller S.,Deusseno.Wang tiles for image and
texture generation.ACM Transactions on Graphics,2003,287-294；
[6]Wu F,Dong W,Kong Y,Mei X,Yan D.M et.al.Feature-aware natural
texture synthesis.The Visual Computer,2014:1-13；
[7]Cook R.L.,Stochastic sampling in computer graphics,ACM Trans.on
Graphics,1986,5(1):69-78；
[8]Dunbar D.,Humphreys G..A spatial data structure for fast Poisson-
disk sample generation.ACM Trans.on Graphics(Proc.SIGGRAPH),2006,25(3):503-
508；
[9]Jones T.R..Efficient generation of Poisson-disk sampling
patterns.Journal of Graphics Tools,2006,11(2):27-36；
[10]White K.B.,Cline D.,Egbert P.K..Poisson disk point sets by
hierarchical dart throwing.in:Proceedings of the IEEE Symposium on
Interactive Ray Tracing,2007,129–132；
[11]GamitoM.N.,MaddockS.C.,Accurate Multidimensional Poisson-Disk
Sampling.ACM Trans.on Graphics,2009,29(1):8:1-8:19；
[12]EbeidaM.S.,PatneyA.,Mitchell S.A.,P.M.K.Andrew Davidson,Owens
J.D.,Efficient maximal Poisson-disk sampling,ACM Trans.on Graphics
(Proc.SIGGRAPH),2011,30(4):49:1–49:12；
[13]EbeidaM.S.,Mitchell S.A.,PatneyA.,Davidson A.A.,Owens J.D.,A
simple algorithm for maximal Poisson-disk sampling in high dimensions,
Computer Graphics Forum(Proc.EUROGRAPHICS),2012,31(2):785–794；
[14]Yan D.-M.,Wonka P.,Gap Processing for Adaptive Maximal Poisson-
Disk Sampling,ACM Trans.on Graphics,2013,32(5):148:1-148:15；
[15]T.,Heck D.,Deussen O.,Farthest-Point Optimized Point
Sets with Maximized Minimum Distance,in:High Performance Graphics
Proceedings,2011,35-142；
[16]Yan D.-M.,Guo J.,Jia X.,Zhang X.,Wonka P.,Blue-Noise Remeshing
with Farthest Point Optimization,Computer Graphics Forum(Proc.SGP),2014,33
(5):167-176；
[17]T.,DeussenO.,Accurate Spectral Analysis of Two-
Dimensional PointSets,Journal of Graphics,GPU,and Game Tools,2011,15(3):152-
160；
[17]A.C.,Gross M.,Analysis and synthesis of point
distributions based on pair correlation,ACM Trans.on Graphics(Proc.SIGGRAPH
Asia),2012,31(6):170。
Summary of the invention
The main purpose of the embodiment of the present invention is to provide the radiuses such as a kind of fixing two dimension counted to maximize Poisson disk
How the method for sampling, realize the technical problem of the maximization Poisson disk sampling counting fixing with solution.Additionally, the present invention implements
Example also proposes the radiuses such as a kind of fixing two dimension counted and maximizes Poisson disk sampling system.
To achieve these goals, according to an aspect of the invention, it is provided techniques below scheme:
The radiuses such as a kind of fixing two dimension counted maximize the Poisson disk method of sampling.Described method may include that
Step 1: the sampled point number specified according to user and sample area, generates the first sampling point set；
Step 2: described first sampling point set is carried out Delaunay trigonometric ratio, and extracts in Delaunay trigonometric ratio result
Minor face length as the first sample radius；
Step 3: determine whether described first sampling point set reaches the sampling of described maximization Poisson disk；
Step 4: in the case of described first sampling point set reaches the sampling of described maximization Poisson disk, record described the
One sampling point set and described first sample radius.
Further, described method can also include:
Step 5: in the case of described first sampling point set not up to maximizes the sampling of Poisson disk, adopt from described first
Sampling point is concentrated and is removed the sampled point that in overall situation minor face, the neighborhood averaging length of side is big, obtains the second sampling point set and adopts described second
Sampling point collection carries out Delaunay trigonometric ratio, calculates space with a length of second sample radius of minor face in above-mentioned trigonometric ratio result
Region, and use throwing boomerang method by a stochastical sampling point radom insertion to the void area of described second sampling point set, obtain the 3rd
Sampling point set；
Step 6: described 3rd sampling point set carries out Delaunay trigonometric ratio, extracts in Delaunay trigonometric ratio result
Minor face is as the 3rd sample radius, to update described first sample radius and to perform described step 3.
Further, described step 2 is extracted the minor face length in Delaunay trigonometric ratio result as the first sampling half
Footpath specifically may include that
The all triangle edges length obtained after carrying out Delaunay trigonometric ratio are ranked up, by minor face length as described
First sample radius.
Further, described step 3 specifically may include that according to whether there is space triangle in described sample area,
Determine whether described first sampling point set reaches the sampling of described maximization Poisson disk.
Further, described step 5 specifically may include that
The neighborhood averaging length of side of two sampled points on described overall situation minor face is determined according to below equation:
Wherein, described N (v) represents the number on sampling neighborhood of a point limit；Described liRepresent the length on neighborhood limit；Described Eavg
Represent the neighborhood averaging length of side；Described i takes positive integer；
From described first sampling point set, remove the sampled point that in described overall situation minor face, the neighborhood averaging length of side is big, obtain institute
State the second sampling point set；
Described second sampling point set is carried out Delaunay trigonometric ratio；
Void area is calculated as the second sample radius using the minor face length in above-mentioned trigonometric ratio result；
Use described throwing boomerang method by the void area of a described stochastical sampling point radom insertion to described second sampling point set,
Obtain described 3rd sampling point set.
Further, described described second sampling point set is carried out Delaunay trigonometric ratio can also include:
Adjust adjacent the owning of sampled point place delta-shaped region that in the overall situation minor face removed, the neighborhood averaging length of side is big
The regional area that triangle is constituted.
Further, described step 6 carries out Delaunay trigonometric ratio to described 3rd sampling point set can also include:
The office that the adjacent all trianglees of described stochastical sampling point place delta-shaped region that set-up procedure 5 is inserted are constituted
Region, portion.
To achieve these goals, according to another aspect of the present invention, a kind of fixing two dimension etc. counted is additionally provided
Radius maximizes Poisson disk sampling system.This system may include that
Generation module, for the sampled point number specified according to user and sample area, generates the first sampling point set；
First extraction module, carries out Delaunay triangle for described first sampling point set generating described generation module
Change, and extract the minor face length in Delaunay trigonometric ratio result as the first sample radius；
Determine module, for determining whether described first sampling point set that described generation module generates reaches described maximization
Poisson disk is sampled；
Described, logging modle, for determining that module determines that described first sampling point set reaches described maximization Poisson disk
In the case of sampling, record described first sampling point set and the institute of described first extraction module extraction that described generation module generates
State the first sample radius.
Further, described system can also include:
Described, processing module, for determining that module determines that described first sampling point set not up to maximizes Poisson disk and adopts
In the case of sample, from described first sampling point set, remove the overall situation sampled point that the neighborhood averaging length of side is big in minor face, obtain the
Two sampling point set and described second sampling point set is carried out Delaunay trigonometric ratio are long with the minor face in above-mentioned trigonometric ratio result
Calculate void area as sample radius, and use throwing boomerang method by a stochastical sampling point radom insertion to described second sampling point set
Void area, obtain the 3rd sampling point set；
Second extraction module, carries out Delaunay triangle for described 3rd sampling point set obtaining described processing module
Changing, the minor face in extraction Delaunay trigonometric ratio result is as the 3rd sample radius, to update described first sample radius also
Trigger and described determine module.
Further, described determine that module specifically may include that
Determine unit, for according to whether described sample area exists space triangle, determine described generation module
Whether described first sampling point set generated reaches the sampling of described maximization Poisson disk.
Compared with prior art, technique scheme at least has the advantages that
The embodiment of the present invention proposes the radiuses such as a kind of fixing two dimension counted and maximizes the Poisson disk method of sampling and adopt
Sample system.Wherein, the sampled point number specified according to user and sample area, one sampling point set of random initializtion, this is adopted
Sampling point collection carries out Delaunay trigonometric ratio, and extracts the minor face length in Delaunay trigonometric ratio result as sample radius；Really
Determine whether sampling point set reaches to maximize the sampling of Poisson disk；The feelings of described maximization Poisson disk sampling are reached in sampling point set
Under condition, record sampling point set and sample radius.The embodiment of the present invention, by space processing method, constantly adjusts the position of sampled point
Put so that overall situation beeline is continuously increased, and then makes void area constantly reduce, is finally reached maximization attribute, has
Simply, be easily achieved, stable performance and the advantage that can restrain.The embodiment of the present invention solves existing maximization Poisson disk
The problem that sampling algorithm can not accurately control sampling number so that sampling point set has good blue noise character, can apply
In image rendering and textures synthesis etc. are applied.
Accompanying drawing explanation
Accompanying drawing, as the part of the present invention, is used for providing further understanding of the invention, and the present invention's is schematic
Embodiment and explanation thereof are used for explaining the present invention, but do not constitute inappropriate limitation of the present invention.Obviously, the accompanying drawing in describing below
It is only some embodiments, to those skilled in the art, on the premise of not paying creative work, it is also possible to
Other accompanying drawings are obtained according to these accompanying drawings.In the accompanying drawings:
Fig. 1 is to maximize Poisson disk sampling side according to radiuses such as the fixing two dimensions counted shown in an exemplary embodiment
The schematic flow sheet of method；
Fig. 2 is to maximize the sampling of Poisson disk according to radiuses such as the fixing two dimensions counted shown in another exemplary embodiment
The schematic flow sheet of method；
Fig. 3 is the schematic diagram according to the space triangle shown in an exemplary embodiment；
Fig. 4 is the schematic diagram according to the space primitive shown in an exemplary embodiment；
Fig. 5 a is the schematic diagram of the end points big according to the neighborhood averaging length of side in the minor face shown in an exemplary embodiment；
Fig. 5 b is according to the new sampled point obtained of sampling in space behind the renewal space shown in an exemplary embodiment
Schematic diagram；
Fig. 5 c is according to the schematic diagram being inserted in sampling point set by sampled point shown in an exemplary embodiment；
Fig. 6 is according to the method proposed according to SER, FPO, MPS and the embodiment of the present invention shown in an exemplary embodiment
The sampling point set mass ratio relatively schematic diagram obtained；
Fig. 7 is the sampling on border aperiodic of the method according to the embodiment of the present invention proposition shown in an exemplary embodiment
Result schematic diagram；
Fig. 8 is the relative radius of the method proposed according to the FPO shown in an exemplary embodiment and the embodiment of the present invention
Distribution situation schematic diagram；
Fig. 9 is according to shown in an exemplary embodiment, the point set that sampling number is 0.5K, 1K, 2K, 20K being carried out PCF
The result schematic diagram analyzed；
Figure 10 is to maximize the sampling of Poisson disk according to radiuses such as the fixing two dimensions counted shown in an exemplary embodiment
The structural representation of system；
Figure 11 is to maximize Poisson disk according to radiuses such as the fixing two dimensions counted shown in another exemplary embodiment to adopt
The structural representation of sample system.
These accompanying drawings and word describe and are not intended as limiting the scope of the invention by any way, but pass through reference
Specific embodiment is that those skilled in the art illustrate idea of the invention.
Detailed description of the invention
Below in conjunction with the accompanying drawings and the specific embodiment technical side that the embodiment of the present invention solved the technical problem that, is used
The technique effect of case and realization carries out clear, complete description.Obviously, described embodiment is only of the application
Divide embodiment, be not whole embodiments.Based on the embodiment in the application, those of ordinary skill in the art are not paying creation
Property work on the premise of, the embodiment of other equivalents all of being obtained or substantially modification all falls within protection scope of the present invention.
The embodiment of the present invention can embody according to the multitude of different ways being defined and covered by claim.
It should be noted that in the following description, understand for convenience, give many details.But it is the brightest
Aobvious, the realization of the present invention can not have these details.
Also, it should be noted the most clearly limiting or in the case of not conflicting, each embodiment in the present invention and
Technical characteristic therein can be mutually combined and form technical scheme.
In actual applications, existing maximization Poisson disk sampling algorithm can not accurately control sampling number.To this end,
The embodiment of the present invention proposes the radiuses such as a kind of fixing two dimension counted and maximizes the Poisson disk method of sampling.As illustrated in fig. 1 and 2,
The method can be realized to step S150 by step S100.Wherein:
S100: the sampled point number specified according to user and sample area, generate the first sampling point set.
In this step, disposably sample area can be specified with the form of random number according to the shape of sample area
The coordinate (such as: x, y-coordinate) of an interior point, thus obtain a random point.Repeatedly perform n times, i.e. can get N number of at random
Point.
As an example it is supposed that the sampling number that user specifies is N, sample area is Ω, sampling point set (namely random point
Integrate) as X；Then, in sample area Ω, the N number of point of stochastical sampling, obtains sampling point set
S110: the first sampling point set is carried out Delaunay trigonometric ratio, and extract in Delaunay trigonometric ratio result
Minor face length is as the first sample radius.
Wherein, Delaunay trigonometric ratio (DT) is that the finite point set P in sample area Ω is carried out triangulation so that
Point in sample area Ω is strictly in the outside of any one triangle circumscribed circle in DT (P).Delaunay trigonometric ratio is maximum
Change the minimum angle of this triangulation intermediate cam shape, avoid the occurrence of the triangle of " the thinnest " as far as possible.Its name derives from
BorisDelaunay, in honour of him from the work in this field in 1934, is algorithm as known in the art, the most superfluous at this
State.
In this step, the minor face length in Delaunay trigonometric ratio result is extracted the most permissible as the first sample radius
Including: all triangle edges length obtained after carrying out Delaunay trigonometric ratio are ranked up, and minor face length are adopted as first
Sample radius.
S120: whether having been maxed out Poisson disk is sampled to determine the first sampling point set.The most then perform step
S130；Otherwise, step S140 is performed.
Wherein, reach to maximize the sampling of Poisson disk to refer to Delaunay trigonometric ratio result does not exist space triangle.
If the Voronoi center of a triangle is not covered by the sampling disk of Atria vertex correspondence, then this triangle is just
It it is space triangle.Sampling disk corresponding to Dian refers to the circle centered by point, with present sample radius as radius.Fig. 3 shows
Show to example space triangle.Wherein, Pi、Pj、PkRepresent three summits of triangle t, CtRepresent the one of Voronoi diagram
Individual summit.
Specifically, this step can determine whether to have reached according to whether there is space triangle in sample area
Maximize the sampling of Poisson disk.
S130: record the first sampling point set and the first sample radius.
S140: remove the sampled point that in overall situation minor face, the neighborhood averaging length of side is big from the first sampling point set, obtain second
Sampling point set and the second sampling point set is carried out Delaunay trigonometric ratio, with a length of second sampling half of the minor face of above-mentioned trigonometric ratio
Footpath calculates void area, and use throwing boomerang method by the void area of a stochastical sampling point radom insertion to the second sampling point set,
Obtain the 3rd sampling point set.
Specifically, this step may include that
S141: determine the neighborhood averaging length of side of the overall situation two sampled points on minor face according to below equation:
Wherein, N (v) represents the number on sampling neighborhood of a point limit；liRepresent the length on neighborhood limit；EavgRepresent neighborhood averaging
The length of side；I takes positive integer.
In this step, the neighborhood averaging length of side of the overall situation two end points of minor face, above-mentioned public affairs are determined according to above-mentioned formula
N (v) in formula namely represents the number on the neighborhood limit (setting the end points on limit as v) of end points v.
S142: remove the sampled point that in overall situation minor face, the neighborhood averaging length of side is big from the first sampling point set, obtain second
Sampling point set.
Exemplarily, finding the shortest limit in Delaunay trigonometric ratio (DT) result, there are two end points on this shortest limit,
Each end points has respective neighborhood respectively, compares the neighborhood averaging length of side of the two end points, by right for big neighborhood averaging length of side institute
The end points answered removes, and i.e. deletes this end points from sampling point set X.
S143: the second sampling point set is carried out Delaunay trigonometric ratio.
In specific implementation process, this step re-starts Delaunay trigonometric ratio to the sampling point set removing end points,
And perform space detection operation.When re-starting Delaunay trigonometric ratio, need to readjust in the overall situation removed minor face
The regional area that all trianglees that sampled point place delta-shaped region that the neighborhood averaging length of side is big is adjacent are constituted.
It should be noted that the change of the Delaunay trigonometric ratio (DT) caused by deletion action is dynamic and local
, the time complexity of renewal is O (1).
S144: calculate void area with a length of second sample radius of minor face in above-mentioned trigonometric ratio result.
This step in specific implementation process, by perform space primitive (as shown in Figure 4) extract operation, extract not by
The void area that sampling disk covers；The minor face setting the sample radius trigonometric ratio result as obtaining in step S143 is long.
Below in conjunction with the accompanying drawings space is processed and be described in detail.
Theory based on Voronoi diagram, Yan etc. [14] gives the necessary and sufficient condition that space exists.If a triangle t
Meet Π (t) > 0, then t is a space triangle, can calculate void area by processing space triangle.
Wherein, the definition of Π (t) is:
Π (t)=dis (p, ct)-r > 0 (1)
Wherein, t represents triangle；P represents a summit of triangle t；R represents sample radius；ctRepresent Voronoi diagram
A summit, the Voronoi center of also referred to as triangle t；dis(p,ct) represent p to ctEuclidean distance.
Wherein, void area refers to: be not sampled the part district that the sampling disk on summit covers in sample area Ω
Territory.The sampling disk on sampling summit refers to centered by sampled point, and the sample radius of current record is the circle of radius.
Above-mentioned formula (1) can be described as: if the Voronoi center of a triangle is not by Atria summit pair
The sampling disk answered covers, then this triangle is exactly space triangle.
Space processes and mainly comprises two operations, and it is respectively space detection and space primitive extracts.
For space detection operation, mainly analyze current sampling point concentrates whether there is space and their concrete position
Put.If there is no space, then can confirm that having been maxed out of sampling point set.Because in the Voronoi of space triangle
The heart can be in the outside (as shown in the little figure in centre position in Fig. 3) of space triangle, so a space triangle may not be anticipated
Taste this triangle and self is included uncovered region.Meanwhile, a void area may comprise several trianglees
Voronoi center, correspondingly, this space just has several space trianglees the most corresponding.
Therefore, in practical operation, travel through all of Delaunay triangle, calculate corresponding Voronoi center and Π
(t).If Π (t) meets (1) formula, then it is marked as space triangle, thus obtains a series of space triangle.
Operation is extracted for space primitive, all of space is divided into several simple and nonoverlapping convex polygons
(it is at most six limits), and assign them to each space triangle.Fig. 4 schematically illustrates and surrounds from dark line segment
Triangle, tetragon, pentagon are to hexagon different types of space primitive.For a space triangle, extract with
The time complexity of gap primitive of correspondence be constant (each space primitive at most has six limits), so whole space base
The time complexity that unit extracts is O (n), and wherein, n represents the number of space triangle.
S145: use and throw boomerang method by the void area of a stochastical sampling point radom insertion to the second sampling point set, obtain the
Three sampling point set.
In the void area that step S144 is extracted, randomly generate a sampled point, and this sampled point is inserted into sampled point
In collection X, namely use and throw boomerang method by this sampled point radom insertion to the void area obtained with present sample radius calculation,
Thus obtain the 3rd sampling point set.
S150: the 3rd sampling point set carries out Delaunay trigonometric ratio, that extracts in Delaunay trigonometric ratio result is the shortest
While as the 3rd sample radius, to update the first sample radius and to perform step S120.
In this step, when returning execution step S120, using the 3rd sampling point set as the first sampling point set, by the 3rd
Sample radius, as the first sample radius, continues to determine whether that having been maxed out Poisson disk is sampled, until it reaches terminate
Condition.
The change of the Delaunay trigonometric ratio caused by update is also dynamic and locally, its local updating time
Between complexity be O (1).
Specifically, this step is when carrying out Delaunay trigonometric ratio to the 3rd sampling point set, it is also possible to including: needs are again
The regional area that all trianglees that the newly inserted stochastical sampling point place delta-shaped region of set-up procedure S140 is adjacent are constituted.
Fig. 5 a-5c schematically illustrates the most complete iterative process.Wherein, the Polygons Representation of Dark grey approximates
Void area, grayish circle represents sampling disk.Neighborhood averaging limit during the some P in dotted line frame is the minor face chosen in Fig. 5 a
The end points grown up.First remove a P, and local updating DT, draw disk with the current a length of sample radius of minor face.Then,
Update space, and sampling obtains new some Q, as shown in the dotted line frame in Fig. 5 b in space.Finally, Q point is inserted into sampled point
Concentrate, as shown in Figure 5 c.This completes an iteration process.
For the border of region Ω aperiodic in the case of, at sharp-pointed corner point (such as: four angle points of tetragon)
Sampling, and be fixed, these points are not involved in follow-up optimization process.Secondly, execution iterative optimization method, then, will
The sampled point that Voronoi unit intersects with border projects on border, re-executes the method that the embodiment of the present invention proposes.Repeat
Carrying out above procedure, until relative radius does not has significant change, this process typically has only to repeat 5 in actual applications
～can restrain for 10 times.After projection process, relative radius can be increased further.
Fig. 6 schematically illustrates the method proposed according to SER [16], FPO [15], MPS [14] and the embodiment of the present invention
The sampling point set mass ratio relatively schematic diagram that (i.e. OURS) obtains.Wherein, sample area is the square area of cycle boundary, sampling
Counting is 1024, owing to MPS method can not accurately control sampling number, so it is counted is approximately 1024.Fig. 6 divides from top to bottom
It is not: sampling point set, PSA analysis result [17], PCF analysis result [18].Wherein, PSA analyzes and includes: power spectrum (the of Fig. 6
Two row), radius average (the third line of Fig. 6) and anisotropy (fourth line of Fig. 6)；PCF analyzes and includes: become pair correlation function
(fifth line of Fig. 6) and scrambling (the 6th row of Fig. 6).From the secondary series of Fig. 6 it can be seen that compared to additive method, FPO
The point set that method obtains is more regular.It addition, from the analysis result of sampling point set result and PCF it can be seen that SER and MPS not
Systematicness (randomness) is the strongest, and their PCF quickly tends to smooth and scrambling is slightly larger；The embodiment of the present invention proposes
The scrambling of method (i.e. OURS) take second place, FPO is last, the method that main cause is MPS and the embodiment of the present invention proposes
New sampled point randomly generates, and comparing FPO has more randomness.Although it should be noted that SER and MPS method
Sampling policy is entirely different, but they have closely similar point set quality.It addition, from the analysis result of PSA it can be seen that
Sampling point set produced by the method that the embodiment of the present invention proposes has good blue noise quality.
In the way of preferred embodiment, mesh quality it is analyzed below and compares.
The sampled point of method (i.e. OURS) four kinds of methods of SER, FPO, MPS and embodiment of the present invention proposition added up by table 1
Collection and the quality of triangle meshes.Sampling number is 4096, takes the meansigma methods of 100 operation results.Wherein, δX=dmin/dmax
Represent relative radius, dminRepresent any point of point set X between overall beeline,Represent any point
Theoretical maximum minimum range between to.For weighing the quality of a triangle, atRepresent triangle t's
Area, ptRepresent the semi-perimeter of t, ltRepresent that the longest edge of t is long；QminAnd QavgRepresent minimum and average triangle shape quality respectively.
θminAnd θmaxRepresent minimum and maximum angle respectively,Represent minimum angles average of all trianglees.θ<30 ° and θ>
90 ° represent θ respectivelyminLess than 30 ° with θmaxTriangle ratio more than 90 °.V567% represents the summit percentage that the number of degrees are 5,6,7
Ratio.Wherein, for δX, the quality of FPO be the highest, the embodiment of the present invention propose method (i.e. OURS) take second place, MPS and SER
Essentially identical.FPO adjusts point set by maximizing beeline, and therefore the relative radius of the method can reach very
Greatly, and the embodiment of the present invention propose method between FPO and MPS.From table 1 it follows that the result of SER and MPS is very
Close, and SER is slightly better than MPS, as shown in Figure 6.It addition, except θmin, the method that the embodiment of the present invention proposes is (i.e.
OURS) most performance indications are superior to SER and MPS.As Fig. 7 schematically illustrates the side that the embodiment of the present invention proposes
Method, in the sampled result on border aperiodic, is the most from left to right respectively as follows: Wavy, Face, Dolphin, S.Meanwhile, added up and adopted
Sampling point collection and the quality of triangle meshes, as shown in table 2.Table 2 illustrates that method that the embodiment of the present invention proposes is for aperiodic
The effectiveness of edge sampling.
Table 1:
Table 2:
The embodiment of the present invention has also added up the distribution situation of the relative radius of the method for FPO and embodiment of the present invention proposition,
As shown in Figure 8.Wherein, the result of the first row correspondence FPO；The result of the method that the second row correspondence embodiment of the present invention proposes.Directly
The abscissa of side's figure is relative radius, and vertical coordinate is the experiment number in the range of specific phase pair radius.From left to right, sampled point
Number is respectively N=0.5k, 2k, 10k.Each situation performs 1000 times.As can be seen from Figure 8 the relative radius of FPO compares
Concentrate, and the relative radius of the method that the embodiment of the present invention proposes has a relatively large constant interval, main cause to be these
New sampled point is inserted randomly into void area rather than fixing position (sampled point by the method that inventive embodiments proposes
The center of circle of collection largest empty circle).To a certain extent, also illustrate that the method that the embodiment of the present invention proposes has higher randomness.
In the way of preferred embodiment, stability is analyzed below.The embodiment of the present invention has added up hundreds of points to number
Coefficient of variation CV (Coefficient of Variation) of each performance indications of the point set of 100000 points, last such as table 1
Shown in a line.Its computational methods are, the meansigma methods of performance indications is divided by corresponding standard deviation.The coefficient of variation weighs different point set
The degree of variation of performance indications, the coefficient of variation is the least, and variation (deviation) degree is the least, and it to a certain extent can be with parser
Stability because for a kind of sampling algorithm, the different number of sampling point set obtained should have basically identical matter
Amount.As it can be seen from table 1 for each index, the method corresponding CV value that the embodiment of the present invention proposes be the lowest (<
3.5%) method that, this explanation embodiment of the present invention proposes is the most stable.Meanwhile, stablizing for further verification algorithm
Property, the point set of sampling number N=0.5K, 1K, 2K, 20K can be carried out PCF analysis, its result is as shown in Figure 9.The first row pair
Answer PCF, the second row correspondence Irregularity.It can be seen in figure 9 that the PCF analysis result that difference is counted is basically identical.
Although in above-described embodiment, each step is described according to the mode of above-mentioned precedence, but this area
Those of skill will appreciate that, in order to realize the effect of the present embodiment, perform not necessarily in such order between different steps,
It can simultaneously (parallel) perform or perform with reverse order, these simply change all protection scope of the present invention it
In.
Based on the technology design identical with embodiment of the method, the embodiment of the present invention also provides for a kind of fixing two dimension etc. counted
Radius maximizes Poisson disk sampling system.This system can perform said method embodiment.As shown in Figure 10, this system is permissible
Including generation module the 11, first extraction module 12, determine module 13 and logging modle 14.Wherein, generation module 11 is for basis
Sampled point number that user specifies and sample area, generate the first sampling point set.First extraction module 12 is for generation module
11 the first sampling point set generated carry out Delaunay trigonometric ratio, and extract the work of minor face length in Delaunay trigonometric ratio result
It it is the first sample radius.Determine whether the first sampling point set that module 13 generates for determining generation module 11 reaches to maximize pool
Pine disk sampling.Logging modle 14 is for determining that module 13 determines that the first sampling point set reaches to maximize the sampling of Poisson disk
In the case of, record the first sampling point set and the first sampling half of the first extraction module 12 extraction that described generation module 11 generates
Footpath.
In an optional embodiment, it is also possible to processing module 15 and is set on the basis of said system embodiment
Two extraction modules 16.Wherein, processing module 15 is for determining that module 13 determines that the first sampling point set not up to maximizes Poisson
In the case of disk sampling, from the first sampling point set, remove the sampled point that in overall situation minor face, the neighborhood averaging length of side is big, obtain
Second sampling point set and the second sampling point set is carried out Delaunay trigonometric ratio, with the minor face of above-mentioned trigonometric ratio result a length of
Two sample radius calculate void area, and use throwing boomerang method by the sky of a stochastical sampling point radom insertion to the second sampling point set
Gap region, obtains the 3rd sampling point set.Second extraction module 16 is carried out for the 3rd sampling point set obtaining processing module 15
Delaunay trigonometric ratio, extracts minor face in Delaunay trigonometric ratio result as the 3rd sample radius, to update described the
One sample radius triggering determine module 13.
In an optional embodiment, in said system embodiment, cover half block can also include determining unit really.Should
Determine that unit, for whether there is space according in sample area, determines whether the first sampling point set that generation module generates reaches
To maximizing the sampling of Poisson disk.
It should be noted that the radiuses such as the fixing two dimension counted of above-described embodiment offer maximize the sampling of Poisson disk it is
System, when sampling, is only illustrated with the division of above-mentioned each functional module, in actual applications, and can be as required
And above-mentioned functions distribution is completed by different functional modules, the internal structure of system will be divided into different function moulds
Block, to complete all or part of function described above.
It will be understood by those skilled in the art that the radiuses such as the above-mentioned fixing two dimension counted maximize Poisson disk sampling system
Also include some other known features, such as processor, controller, memorizer etc., in order to unnecessarily obscure the reality of the disclosure
Executing example, known to these, structure is not shown in Figure 10-11.
It should be understood that the quantity of the modules in Figure 10-11 is only schematically.According to actual needs, can have
There is any number of each module.
Said system embodiment may be used for performing said method embodiment, its know-why, is solved the technical problem that
And the technique effect of generation is similar, person of ordinary skill in the field is it can be understood that arrive, for the convenience described and letter
Clean, the specific works process of the system of foregoing description and relevant explanation, it is referred to the corresponding process in preceding method embodiment,
Do not repeat them here.
It is to be noted that above system embodiment and embodiment of the method to the present invention is described the most respectively, but right
The details of one embodiment description also apply be applicable to another embodiment.For the module related in the embodiment of the present invention, step
Title, it is only for distinguish modules or step, be not intended as inappropriate limitation of the present invention.Those skilled in the art
The module being appreciated that in the embodiment of the present invention or step can also be decomposed or combine.The mould of such as above-described embodiment
Block can merge into a module, it is also possible to is further split into multiple submodule.
The technical scheme provided the embodiment of the present invention above is described in detail.Although applying concrete herein
Individual example principle and the embodiment of the present invention are set forth, but, the explanation of above-described embodiment be only applicable to help reason
Solve the principle of the embodiment of the present invention；For those skilled in the art, according to the embodiment of the present invention, it is being embodied as
All can make a change within mode and range of application.
It should be noted that referred to herein to flow chart or block diagram be not limited solely to form shown in this article, its
Can also be carried out other divide and/or combination.
It can further be stated that: labelling and word in accompanying drawing are intended merely to be illustrated more clearly that the present invention, and it is right to be not intended as
The improper restriction of scope.
Again it should be noted that term " first " in description and claims of this specification and above-mentioned accompanying drawing, "
Two " it is etc. for distinguishing similar object rather than for describing or representing specific order or precedence.Should be appreciated that this
The data that sample uses can be exchanged in appropriate circumstances, in order to embodiments of the invention described herein can be with except at this
In illustrate or describe those beyond order implement.
Term " includes ", " comprising " or any other like term are intended to comprising of nonexcludability, so that
Process, method, article or equipment/device including a series of key elements not only include those key elements, but also include the brightest
Other key element really listed, or also include the key element that these processes, method, article or equipment/device are intrinsic.
As used herein, term " module " may refer to software object or the routine performed on a computing system.
Disparate modules described herein can be embodied as the object that performs on a computing system or process (such as, as independence
Thread).While it is preferred that realize system and method described herein with software, but with hardware or software and hard
The realizing also possible and can be conceived to of the combination of part.
Each step of the present invention can realize with general calculating device, and such as, they can concentrate on single
Calculate on device, such as: personal computer, server computer, handheld device or portable set, laptop device or many
Processor device, it is also possible to be distributed on the network that multiple calculating device is formed, they can be to be different from order herein
Step shown or described by execution, or they are fabricated to respectively each integrated circuit modules, or by many in them
Individual module or step are fabricated to single integrated circuit module and realize.Therefore, the invention is not restricted to any specific hardware and soft
Part or its combination.
The method that the present invention provides can use PLD to realize, it is also possible to is embodied as computer program soft
Part or program module (it include performing particular task or realize the routine of particular abstract data type, program, object, assembly or
Data structure etc.), can be such as a kind of computer program according to embodiments of the invention, run this computer program
Product makes computer perform for the method demonstrated.Described computer program includes computer-readable recording medium, should
Comprise computer program logic or code section on medium, be used for realizing described method.Described computer-readable recording medium can
To be the built-in medium being mounted in a computer or the removable medium (example that can disassemble from basic computer
As: use the storage device of hot plug technology).Described built-in medium includes but not limited to rewritable nonvolatile memory,
Such as: RAM, ROM, flash memory and hard disk.Described removable medium includes but not limited to: optical storage media is (such as: CD-
ROM and DVD), magnetic-optical storage medium (such as: MO), magnetic storage medium (such as: tape or portable hard drive), have built-in can
Rewrite the media (such as: storage card) of nonvolatile memory and there are the media (such as: ROM box) of built-in ROM.
Particular embodiments described above, has been carried out the purpose of the present invention, technical scheme and beneficial effect the most in detail
Describe in detail bright, be it should be understood that the specific embodiment that the foregoing is only the present invention, be not limited to the present invention, all
Within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. done, should be included in the guarantor of the present invention
Within the scope of protecting.
Claims (10)
1. the radius such as the fixing two dimension counted maximizes the Poisson disk method of sampling, it is characterised in that described method is at least
Including:
Step 1: the sampled point number specified according to user and sample area, generates the first sampling point set；
Step 2: described first sampling point set is carried out Delaunay trigonometric ratio, and extract in Delaunay trigonometric ratio result
Minor face length is as the first sample radius；
Step 3: determine whether described first sampling point set reaches the sampling of described maximization Poisson disk；
Step 4: in the case of described first sampling point set reaches the sampling of described maximization Poisson disk, record described first and adopt
Sampling point collection and described first sample radius.
Method the most according to claim 1, it is characterised in that described method also includes:
Step 5: in the case of described first sampling point set not up to maximizes the sampling of Poisson disk, from described first sampled point
Concentrate and remove the sampled point that in overall situation minor face, the neighborhood averaging length of side is big, obtain the second sampling point set and to described second sampled point
Collection carries out Delaunay trigonometric ratio, calculates space with a length of second sample radius of minor face in Delaunay trigonometric ratio result
Region, and use throwing boomerang method by a stochastical sampling point radom insertion to the void area of described second sampling point set, obtain the 3rd
Sampling point set；
Step 6: described 3rd sampling point set carries out Delaunay trigonometric ratio, that extracts in Delaunay trigonometric ratio result is the shortest
While as the 3rd sample radius, to update described first sample radius and to perform described step 3.
Method the most according to claim 1, it is characterised in that extract in Delaunay trigonometric ratio result in described step 2
Minor face length as the first sample radius, specifically include: all triangle edges obtained after Delaunay trigonometric ratio being carried out
Length is ranked up, by minor face length as described first sample radius.
Method the most according to claim 1, it is characterised in that described step 3 specifically includes: according in described sample area
Whether there is space triangle, determine whether described first sampling point set reaches the sampling of described maximization Poisson disk.
Method the most according to claim 2, it is characterised in that described step 5 specifically includes:
The neighborhood averaging length of side of two sampled points on described overall situation minor face is determined according to below equation:
Wherein, described N (v) represents the number on sampling neighborhood of a point limit；Described liRepresent the length on neighborhood limit；Described EavgRepresent neighbour
Territory average side length；Described i takes positive integer；
From described first sampling point set, remove the sampled point that in described overall situation minor face, the neighborhood averaging length of side is big, obtain described
Two sampling point set；
Described second sampling point set is carried out Delaunay trigonometric ratio；
Void area is calculated as the second sample radius using the minor face length in above-mentioned trigonometric ratio result；
Use described throwing boomerang method by a described stochastical sampling point radom insertion to the void area of described second sampling point set, obtain
Described 3rd sampling point set.
Method the most according to claim 5, it is characterised in that described described second sampling point set is carried out Delaunay tri-
Keratinization, also includes:
Adjust all triangles that sampled point place delta-shaped region that in the overall situation minor face that removes, the neighborhood averaging length of side is big is adjacent
The regional area that shape is constituted.
Method the most according to claim 2, it is characterised in that in described step 6, described 3rd sampling point set is carried out
Delaunay trigonometric ratio, also includes:
The partial zones that the adjacent all trianglees of described stochastical sampling point place delta-shaped region that set-up procedure 5 is inserted are constituted
Territory.
8. the radius such as the fixing two dimension counted maximizes Poisson disk sampling system, it is characterised in that described system is at least
Including:
Generation module, for the sampled point number specified according to user and sample area, generates the first sampling point set；
First extraction module, carries out Delaunay trigonometric ratio for described first sampling point set generating described generation module,
And extract the minor face length in Delaunay trigonometric ratio result as the first sample radius；
Determine module, for determining whether described first sampling point set that described generation module generates reaches described maximization Poisson
Disk is sampled；
Described, logging modle, for determining that module determines that described first sampling point set reaches the sampling of described maximization Poisson disk
In the case of, record described first sampling point set that described generation module generates and described first extraction module extracts described the
One sample radius.
System the most according to claim 8, it is characterised in that described system also includes:
Described, processing module, for determining that module determines that described first sampling point set not up to maximizes the sampling of Poisson disk
In the case of, from described first sampling point set, remove the sampled point that in overall situation minor face, the neighborhood averaging length of side is big, obtain second and adopt
Sampling point collection and described second sampling point set is carried out Delaunay trigonometric ratio, adopts using the minor face length of above-mentioned trigonometric ratio as second
Sample radius calculates void area, and uses throwing boomerang method by the sky of a stochastical sampling point radom insertion to described second sampling point set
Gap region, obtains the 3rd sampling point set；
Second extraction module, carries out Delaunay trigonometric ratio for described 3rd sampling point set obtaining described processing module,
Minor face in extraction Delaunay trigonometric ratio result is as the 3rd sample radius, to update described first sample radius and to trigger
Described determine module.
System the most according to claim 8, it is characterised in that described determine that module specifically includes:
Determine unit, for according to whether described sample area exists space triangle, determine that described generation module generates
Described first sampling point set whether reach described maximization Poisson disk sampling.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108288287A (en) * | 2018-01-16 | 2018-07-17 | 合肥工业大学 | A kind of ceramic tile Texture Generating Approach based on Power figures |
| CN109740427A (en) * | 2018-11-26 | 2019-05-10 | 浙江财经大学 | Standard well screen based on blue noise sampling selects visual analysis method |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN104036552A (en) * | 2014-06-23 | 2014-09-10 | 中国科学院自动化研究所 | Method for generating blue noise meshes on basis of farthest point optimization |
| 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 |
| CN105719349A (en) * | 2016-01-19 | 2016-06-29 | 中国科学院自动化研究所 | Tetrahedral meshing method and system based on maximum Poisson disc sampling |
-
2016
- 2016-07-18 CN CN201610563518.5A patent/CN106204742B/en active Active
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN104036552A (en) * | 2014-06-23 | 2014-09-10 | 中国科学院自动化研究所 | Method for generating blue noise meshes on basis of farthest point optimization |
| 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 |
| CN105719349A (en) * | 2016-01-19 | 2016-06-29 | 中国科学院自动化研究所 | Tetrahedral meshing method and system based on maximum Poisson disc sampling |
Non-Patent Citations (2)
| Title |
|---|
| DONG-MING YAN ET AL: "Gap Processing for Adaptive Maximal Poisson-Disk Sampling", 《ACM TRANSACTIONS ON GRAPHICS》 * |
| THOMAS SCHLOMER ET AL: "Farthest-Point Optimized Point Sets with Maximized Minimum Distance", 《PROCEEDINGS OF THE ACM SIGGRAPH SYMPOSIUM ON HIGH PERFORMANCE GRAPHICS》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108288287A (en) * | 2018-01-16 | 2018-07-17 | 合肥工业大学 | A kind of ceramic tile Texture Generating Approach based on Power figures |
| CN109740427A (en) * | 2018-11-26 | 2019-05-10 | 浙江财经大学 | Standard well screen based on blue noise sampling selects visual analysis method |
| CN109740427B (en) * | 2018-11-26 | 2020-10-23 | 浙江财经大学 | Standard well screening visual analysis method based on blue noise sampling |
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