CN106204742B - The radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling and system - Google Patents
The radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling and system Download PDFInfo
- Publication number
- CN106204742B CN106204742B CN201610563518.5A CN201610563518A CN106204742B CN 106204742 B CN106204742 B CN 106204742B CN 201610563518 A CN201610563518 A CN 201610563518A CN 106204742 B CN106204742 B CN 106204742B
- Authority
- CN
- China
- Prior art keywords
- sampling
- sampling point
- point set
- trigonometric ratio
- short side
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000005070 sampling Methods 0.000 title claims abstract description 243
- 238000000034 method Methods 0.000 title claims abstract description 96
- 239000011800 void material Substances 0.000 claims description 23
- 238000012935 Averaging Methods 0.000 claims description 22
- 238000000605 extraction Methods 0.000 claims description 13
- 238000003780 insertion Methods 0.000 claims description 11
- 230000037431 insertion Effects 0.000 claims description 11
- 239000000284 extract Substances 0.000 claims description 10
- 238000012545 processing Methods 0.000 claims description 9
- 230000015572 biosynthetic process Effects 0.000 abstract description 4
- 238000003786 synthesis reaction Methods 0.000 abstract description 4
- 238000009877 rendering Methods 0.000 abstract description 3
- 238000010586 diagram Methods 0.000 description 19
- 238000004458 analytical method Methods 0.000 description 11
- 230000008569 process Effects 0.000 description 11
- 238000004422 calculation algorithm Methods 0.000 description 8
- 230000008859 change Effects 0.000 description 6
- 238000004590 computer program Methods 0.000 description 5
- 239000012141 concentrate Substances 0.000 description 4
- 238000009826 distribution Methods 0.000 description 4
- 230000000694 effects Effects 0.000 description 3
- 230000006870 function Effects 0.000 description 3
- 238000005457 optimization Methods 0.000 description 3
- 238000001514 detection method Methods 0.000 description 2
- 210000002837 heart atrium Anatomy 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 238000005314 correlation function Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000004744 fabric Substances 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 230000000670 limiting effect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000035772 mutation Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 238000003672 processing method Methods 0.000 description 1
- 230000002829 reductive effect Effects 0.000 description 1
- 230000000452 restraining effect Effects 0.000 description 1
- 230000002441 reversible effect Effects 0.000 description 1
- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
- 230000001755 vocal effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/30—Polynomial surface description
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Physics (AREA)
- Mathematical Analysis (AREA)
- Algebra (AREA)
- Computer Graphics (AREA)
- Geometry (AREA)
- Software Systems (AREA)
- Theoretical Computer Science (AREA)
- Information Retrieval, Db Structures And Fs Structures Therefor (AREA)
Abstract
The invention discloses a kind of radiuses such as the two dimension of fixed points to maximize the Poisson disk method of sampling and sampling system.Wherein, this method includes the sampled point number and sampling area specified according to user, generates the first sampling point set；Delaunay trigonometric ratio is carried out to first sampling point set, and it is long as the first sample radius to extract the most short side in Delaunay trigonometric ratio result；Determine whether first sampling point set reaches the maximization Poisson disk sampling；In the case where first sampling point set reaches maximization Poisson disk sampling, first sampling point set and first sample radius are recorded.It solves through the embodiment of the present invention and how to realize the technical issues of fixed maximization Poisson disk of points samples, it may make sampling point set that there is good blue noise property, have the advantages that it is simple, be easily achieved, performance is stable and can restrain, can be applied in the application such as image rendering and textures synthesis.
Description
Technical field
The present embodiments relate to technical fields, and in particular to a kind of radiuses such as two dimension of fixed points maximize Poisson circle
The radiuses such as the two dimension of the disk method of sampling and fixed points maximize Poisson disk sampling system, but are not limited to this.
Background technique
In field of Computer Graphics, the sampling of Poisson disk be one it is basic study a question, the point set sampled point
Cloth had not only met randomness but also had met uniformity, and the frequency spectrum with blue noise characteristic.It plays the part of emphatically in many practical applications
The role wanted, such as image rendering [1], digital halftone [2,3], object is distributed [4,5] and textures synthesis [6] etc..
One ideal Poisson disk sampling point set needs to meet three conditions: 1. zero deflection sampling property (each samplings
The point that region is not covered with has identical probability to receive a new sampled point)；2. minimum range property (adopt by any two
The distance between sampling point is greater than given sample radius)；3. maximizing property, (sampling area is covered completely by all sampling disks
Lid).The method of sampling for meeting these three conditions is known as maximizing Poisson disk sampling (Maximal Poisson-disk
Sampling--MPS)。
The classical way for generating the sampling of Poisson disk, which is called, throws boomerang method (Dart Throwing--DT) [7].The base of this method
This thought is setting sample radius, and a sampled point is then randomly generated every time, if new sampled point and existing sampled point
Do not conflict, then receive the sampled point, otherwise, refuses the sampled point.For traditional throwing boomerang method in terms of efficiency and quality not
Foot, follow-up study person proposes that many effective data structures are accelerated and improved to throwing boomerang method, such as sector [8], Voronoi diagram
[9], dynamic quadtree [10,11,12], recessive quaternary tree [13], Power figure [14] etc..It can be with although throwing boomerang method and its mutation
Generate the sampling point set of high quality.But such methods have the shortcomings that one it is common, i.e., can not accurately control the number of sampled point
Mesh.In consideration of it,Farthest point sampling optimization (Farthest Point Optimization-- is proposed Deng [15]
FPO), main thought is the global shortest distance for maximizing sampling point set.But FPO is a deterministic method, it is every
It is secondary that new sampled point is inserted into " farthest point " (center of circle of the largest empty circle for the Delaunay trigonometric ratio that remaining point set is constituted).It borrows
The thought of mirror FPO, Yan etc. [16] propose most short side and remove algorithm (Shortest Edge Removal--SER).This method
A most short side is selected every time and randomly removes one of endpoint, then inserts it into " farthest point ".But the side SER
Method cannot be guaranteed to reach maximization sampling attribute.
In view of this, the present invention is specifically proposed.
Related document is referring to 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 that providing a kind of radiuses such as the two dimension of fixed points maximizes Poisson disk
The method of sampling, to solve how to realize the technical issues of fixed maximization Poisson disk of points samples.In addition, the present invention is implemented
Example also proposes that a kind of radiuses such as the two dimension of fixed points maximize Poisson disk sampling system.
To achieve the goals above, according to an aspect of the invention, there is provided following technical scheme:
A kind of radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling.The method may include:
Step 1: the sampled point number and sampling area specified according to user generate the first sampling point set；
Step 2: Delaunay trigonometric ratio being carried out to first sampling point set, and is extracted in Delaunay trigonometric ratio result
Most short side long be used as the first sample radius；
Step 3: determining whether first sampling point set reaches the maximization Poisson disk sampling；
Step 4: in the case where first sampling point set reaches maximization Poisson disk sampling, recording described the
One sampling point set and first sample radius.
Further, the method can also include:
Step 5: in the case where first sampling point set not up to maximizes the sampling of Poisson disk, being adopted from described first
Sampling point concentrates the sampled point for removing that neighborhood averaging side length is big in global most short side, obtains the second sampling point set and adopts to described second
Sampling point collection carries out Delaunay trigonometric ratio, calculates gap with a length of second sample radius of most short side in above-mentioned trigonometric ratio result
Region, and using boomerang method is thrown by a stochastical sampling point radom insertion to the void area of second sampling point set, obtain third
Sampling point set；
Step 6: Delaunay trigonometric ratio being carried out to the third sampling point set, is extracted in Delaunay trigonometric ratio result
Most short side is as third sample radius, to update first sample radius and execute the step 3.
Further, the most short side extracted in the step 2 in Delaunay trigonometric ratio result is long as the first sampling half
Diameter can specifically include:
It will carry out all triangle edges obtained after Delaunay trigonometric ratio length to be ranked up, most short side be grown described in being used as
First sample radius.
Further, the step 3 can specifically include: according in the sampling area whether there is gap triangle,
To determine whether first sampling point set reaches the maximization Poisson disk sampling.
Further, the step 5 can specifically include:
The neighborhood averaging side length of two sampled points on the global most short side is determined according to the following formula:
Wherein, the N (v) indicates the number on sampling neighborhood of a point side；The liIndicate the length on neighborhood side；The Eavg
Indicate neighborhood averaging side length；The i takes positive integer；
From the sampled point that neighborhood averaging side length is big in the global most short side is removed in first sampling point set, institute is obtained
State the second sampling point set；
Delaunay trigonometric ratio is carried out to second sampling point set；
Void area is calculated as the second sample radius using the most short side length in above-mentioned trigonometric ratio result；
Using the throwing boomerang method by the void area of the stochastical sampling point radom insertion to second sampling point set,
Obtain the third sampling point set.
Further, described to include: to second sampling point set progress Delaunay trigonometric ratio
Delta-shaped region is adjacent where the big sampled point of neighborhood averaging side length in the global most short side that adjustment removes owns
The regional area that triangle is constituted.
Further, carrying out Delaunay trigonometric ratio to the third sampling point set in the step 6 can also include:
The office that the adjacent all triangles of delta-shaped region where the stochastical sampling point that set-up procedure 5 is inserted into are constituted
Portion region.
To achieve the goals above, according to another aspect of the present invention, a kind of two dimension etc. of fixed points is additionally provided
Radius maximizes Poisson disk sampling system.The system may include:
Generation module, sampled point number and sampling area for being specified according to user generate the first sampling point set；
First extraction module, first sampling point set for generating to the generation module carry out Delaunay triangle
Change, and it is long as the first sample radius to extract the most short side in Delaunay trigonometric ratio result；
Whether determining module, first sampling point set for determining that the generation module generates reach the maximization
The sampling of Poisson disk；
Logging modle, for determining that first sampling point set reaches the maximization Poisson disk in the determining module
In the case where sampling, first sampling point set that the generation module generates and the institute that first extraction module extracts are recorded
State the first sample radius.
Further, the system can also include:
Processing module, for determining that first sampling point set not up to maximizes Poisson disk and adopts in the determining module
In the case where sample, from the sampled point that neighborhood averaging side length is big in global most short side is removed in first sampling point set, the is obtained
Two sampling point sets and to second sampling point set carry out Delaunay trigonometric ratio, it is long with the most short side in above-mentioned trigonometric ratio result
Void area is calculated as sample radius, and uses and throws boomerang method for a stochastical sampling point radom insertion to second sampling point set
Void area, obtain third sampling point set；
Second extraction module, the third sampling point set for obtaining to the processing module carry out Delaunay triangle
Change, extracts the most short side in Delaunay trigonometric ratio result as third sample radius, to update first sample radius simultaneously
Trigger the determining module.
Further, the determining module can specifically include:
Determination unit is used for according to whether there is gap triangle in the sampling area, to determine the generation module
Whether first sampling point set generated reaches the maximization Poisson disk sampling.
Compared with prior art, above-mentioned technical proposal at least has the advantages that
The embodiment of the present invention proposes a kind of radiuses such as the two dimension of fixed points and maximizes the Poisson disk method of sampling and adopt
Sample system.Wherein, the sampled point number and sampling area specified according to user, one sampling point set of random initializtion, adopt this
Sampling point collection carries out Delaunay trigonometric ratio, and it is long as sample radius to extract the most short side in Delaunay trigonometric ratio result；Really
Determine whether sampling point set reaches maximization Poisson disk sampling；Reach the feelings of the maximization Poisson disk sampling in sampling point set
Under condition, sampling point set and sample radius are recorded.The embodiment of the present invention constantly adjusts the position of sampled point by gap processing method
It sets, so that the global shortest distance is continuously increased, then void area is constantly reduced, be finally reached maximization attribute, have
Simply, it is easily achieved, performance is stable and the advantages of capable of restraining.The embodiment of the present invention solves existing maximization Poisson disk
Sampling algorithm cannot accurately control the problem of sampling number, so that sampling point set has good blue noise property, can apply
In the application such as image rendering and textures synthesis.
Detailed description of the invention
Attached drawing is as a part of the invention, and for providing further understanding of the invention, of the invention is schematic
Examples and descriptions thereof are used to explain the present invention, but does not constitute an undue limitation on the present invention.Obviously, the accompanying drawings in the following description
Only some embodiments to those skilled in the art without creative efforts, can be with
Other accompanying drawings can also be obtained according to these attached drawings.In the accompanying drawings:
Fig. 1 is to maximize Poisson disk sampling side according to the radiuses such as the two dimension counted of fixing shown in an exemplary embodiment
The flow diagram of method；
Fig. 2 is to maximize the sampling of Poisson disk according to the radiuses such as the two dimension counted of fixing shown in another exemplary embodiment
The flow diagram of method；
Fig. 3 is the schematic diagram according to the gap triangle shown in an exemplary embodiment；
Fig. 4 is the schematic diagram according to the gap primitive shown in an exemplary embodiment；
Fig. 5 a is the schematic diagram according to the big endpoint of neighborhood averaging side length in the most short side shown in an exemplary embodiment；
Fig. 5 b is according to the new sampled point sampled behind the update gap shown in an exemplary embodiment in gap
Schematic diagram；
Fig. 5 c is according to the schematic diagram being inserted into sampled point in sampling point set 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
Obtained sampling point set quality comparison schematic diagram；
Fig. 7 is the sampling according to the method for the proposition of the embodiment of the present invention shown in an exemplary embodiment on aperiodic boundary
Result schematic diagram；
Fig. 8 is the relative radius according to the method for FPO and proposition of the embodiment of the present invention shown in an exemplary embodiment
Distribution schematic diagram；
Fig. 9 is to carry out PCF to the point set that sampling number is 0.5K, 1K, 2K, 20K according to shown in an exemplary embodiment
The result schematic diagram of analysis；
Figure 10 is to maximize the sampling of Poisson disk according to the radiuses such as the two dimension counted of fixing shown in an exemplary embodiment
The structural schematic diagram of system；
Figure 11 is to be adopted according to the radiuses such as the two dimension the counted maximization Poisson disk of fixing shown in another exemplary embodiment
The structural schematic diagram of sample system.
These attached drawings and verbal description are not intended to the protection scope limiting the invention in any way, but by reference to
Specific embodiment is that those skilled in the art illustrate idea of the invention.
Specific embodiment
The technical issues of with reference to the accompanying drawing and specific embodiment is solved to the embodiment of the present invention, used technical side
Case and the technical effect of realization carry out clear, complete description.Obviously, described embodiment is only one of the application
Divide embodiment, is not whole embodiments.Based on the embodiment in the application, those of ordinary skill in the art are not paying creation
Property labour under the premise of, all other equivalent or obvious variant the embodiment obtained is fallen within the scope of protection of the present invention.
The embodiment of the present invention can be embodied according to the multitude of different ways being defined and covered by claim.
It should be noted that in the following description, understanding for convenience, giving many details.But it is very bright
Aobvious, realization of the invention can be without these details.
It should also be noted that, in the absence of clear limitations or conflicts, each embodiment in the present invention and
Technical characteristic therein can be combined with each other and form technical solution.
In practical applications, existing maximization Poisson disk sampling algorithm cannot accurately control sampling number.For this purpose,
The embodiment of the present invention proposes that a kind of radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling.As illustrated in fig. 1 and 2,
This method can be realized by step S100 to step S150.Wherein:
S100: the sampled point number and sampling area specified according to user generate the first sampling point set.
In this step, sampling area can disposably be specified in the form of random number according to the shape of sampling area
The coordinate (such as: x, y-coordinate) of an interior point, to obtain a random point.N times are executed repeatedly, can be obtained N number of random
Point.
As an example it is supposed that the sampling number specified of user is N, sampling area Ω, sampling point set (namely random point
Integrate) as X；Then, the N number of point of stochastical sampling in sampling area Ω, obtains sampling point set
S110: Delaunay trigonometric ratio is carried out to the first sampling point set, and is extracted in Delaunay trigonometric ratio result most
Short side is long to be used as the first sample radius.
Wherein, Delaunay trigonometric ratio (DT) be in sampling area Ω finite point set P carry out triangulation so that
Point in sampling area Ω is strictly in the outside of any one triangle circumscribed circle in DT (P).Delaunay trigonometric ratio is maximum
The minimum angle for having changed this triangulation intermediate cam shape, avoids the occurrence of the triangle of " extremely thin " as far as possible.Its name derives from
BorisDelaunay is algorithm as known in the art in honour of him from the work in this field in 1934, no longer superfluous herein
It states.
In this step, extracting that most short side in Delaunay trigonometric ratio result is long specifically can be with as the first sample radius
Include: that will carry out all triangle edges obtained after Delaunay trigonometric ratio length to be ranked up, most short side length is adopted as first
Sample radius.
S120: determine whether having reached the maximum Poisson disk samples the first sampling point set.If so, thening follow the steps
S130；Otherwise, step S140 is executed.
Wherein, reach to maximize Poisson disk and sample and refer to that there is no gap triangles in Delaunay trigonometric ratio result.
As soon as if the center Voronoi of triangle is not covered by the sampling disk of Atria vertex correspondence, then the triangle
It is gap triangle.The corresponding sampling disk of point refers to centered on point, using present sample radius as the circle of radius.Fig. 3 shows
Show gap triangle to example property.Wherein, Pi、Pj、PkIndicate three vertex of triangle t, CtIndicate the one of Voronoi diagram
A vertex.
Specifically, this step can be according to whether there is gap triangle, to determine whether to have reached in sampling area
Maximize the sampling of Poisson disk.
S130: the first sampling point set of record and the first sample radius.
S140: from the sampled point that neighborhood averaging side length is big in global most short side is removed in the first sampling point set, second is obtained
Sampling point set and Delaunay trigonometric ratio is carried out to the second sampling point set, with a length of second sampling half of the most short side of above-mentioned trigonometric ratio
Diameter calculates void area, and using throwing boomerang method for the void area of a stochastical sampling point radom insertion to the second sampling point set,
Obtain third sampling point set.
Specifically, this step may include:
S141: the neighborhood averaging side length of two sampled points on global most short side is determined according to the following formula:
Wherein, N (v) indicates the number on sampling neighborhood of a point side；liIndicate the length on neighborhood side；EavgIndicate neighborhood averaging
Side length；I takes positive integer.
In this step, the neighborhood averaging side length of two endpoints of global most short side, above-mentioned public affairs are determined according to above-mentioned formula
N (v) in formula namely indicates the neighborhood of endpoint v while (endpoint when setting is the number of v).
S142: from the sampled point that neighborhood averaging side length is big in global most short side is removed in the first sampling point set, second is obtained
Sampling point set.
Illustratively, find shortest side in Delaunay trigonometric ratio (DT) result, the shortest side there are two endpoint,
Each endpoint has respective neighborhood respectively, compares the neighborhood averaging side length of the two endpoints, and big neighborhood averaging side length institute is right
The endpoint answered removes, i.e., this endpoint is deleted from sampling point set X.
S143: Delaunay trigonometric ratio is carried out to the second sampling point set.
In the specific implementation process, this step re-starts Delaunay trigonometric ratio to the sampling point set for removing endpoint,
And execute gap detection operation.When re-starting Delaunay trigonometric ratio, need to readjust in the global most short side of removal
The regional area that the adjacent all triangles of delta-shaped region where the big sampled point of neighborhood averaging side length are constituted.
It should be noted that the change of Delaunay trigonometric ratio (DT) as caused by delete operation is dynamic and local
, the time complexity of update is (1) O.
S144: void area is calculated with a length of second sample radius of most short side in above-mentioned trigonometric ratio result.
This step in the specific implementation process, by execute gap primitive (as shown in Figure 4) extraction operation, come extract not by
Sample the void area of disk covering；It is long as the most short side of trigonometric ratio result obtained in step S143 to set sample radius.
Gap processing is described in detail with reference to the accompanying drawing.
Theory based on Voronoi diagram, Yan etc. [14] give necessary and sufficient condition existing for gap.If a triangle t
Meet Π (t) > 0, then t is a gap triangle, can calculate void area by handling gap triangle.
Wherein, Π (t) is defined as:
- r > 0 (1) Π (t)=dis (p, ct)
Wherein, t indicates triangle；A vertex of p expression triangle t；R indicates sample radius；ctIndicate Voronoi diagram
A vertex, the also referred to as center Voronoi of triangle t；dis(p,ct) indicate p to ctEuclidean distance.
Wherein, void area refers to: the part area of the sampling disk covering on vertex is not sampled in sampling area Ω
Domain.The sampling disk on sampling vertex refers to that centered on sampled point, the sample radius of current record is the circle of radius.
Above-mentioned formula (1) can be described as: if the center Voronoi of a triangle is not by Atria vertex pair
The sampling disk covering answered, then the triangle is exactly gap triangle.
Gap processing is respectively that gap detection and gap primitive extract mainly comprising two operations.
Gap is detected and is operated, mainly analysis current sampling point, which is concentrated, whether there is gap and their specific position
It sets.If there is no gap, then having reached the maximum of sampling point set can be confirmed.Because in the Voronoi of gap triangle
The heart can be in the outside (as shown in the small figure in middle position in Fig. 3) of gap triangle, so a gap triangle may not anticipate
Taste this triangle itself include uncovered region.Meanwhile a void area may include several triangles
The center Voronoi, correspondingly, this gap just has several gap triangles to be corresponding to it.
Therefore, in actual operation, all Delaunay triangles are traversed, the corresponding center Voronoi and Π are calculated
(t).If Π (t) meets (1) formula, it is marked as gap triangle, to obtain a series of gap triangle.
For gap primitive extraction operation, all gaps are divided into several simple and nonoverlapping convex polygons
(it is at most six sides), and assign them to each gap triangle.Fig. 4, which is schematically illustrated, to be surrounded from dark line segment
Triangle, quadrangle, pentagon to the different types of gap primitive of hexagon.For a gap triangle, extract with
The time complexity of corresponding gap primitive be constant (each gap primitive at most has six sides), so entire gap base
The time complexity that member is extracted is O (n), wherein the number of n expression gap triangle.
S145: using boomerang method is thrown by the void area of a stochastical sampling point radom insertion to the second sampling point set, the is obtained
Three sampling point sets.
A sampled point is randomly generated in the void area that step S144 is extracted, and this sampled point is inserted into sampled point
Collect in X, that is, use throwing boomerang method by the sampled point radom insertion to the void area being calculated with present sample radius,
To obtain third sampling point set.
S150: carrying out Delaunay trigonometric ratio to third sampling point set, extracts most short in Delaunay trigonometric ratio result
Side is as third sample radius, to update the first sample radius and execute step S120.
In this step, when returning to step S120, using third sampling point set as the first sampling point set, by third
Sample radius continues to determine whether that having reached the maximum Poisson disk samples, until reaching termination as the first sample radius
Condition.
The change of the Delaunay trigonometric ratio as caused by insertion operation is also dynamic and part, local updating when
Between complexity be (1) O.
Specifically, this step can also include: to need again when carrying out Delaunay trigonometric ratio to third sampling point set
The regional area that the adjacent all triangles of delta-shaped region where the stochastical sampling point that set-up procedure S140 is newly inserted into are constituted.
Fig. 5 a-5c schematically illustrates primary complete iterative process.Wherein, the Polygons Representation of Dark grey is approximate
Void area, grayish circle indicate sampling disk.Point P in Fig. 5 a in dotted line frame is neighborhood averaging side in the most short side chosen
The endpoint grown up.Point P, and local updating DT are removed first, and disk is drawn with the current a length of sample radius of most short side.Then,
Gap is updated, and samples to obtain new point Q in gap, as shown in the dotted line frame in Fig. 5 b.Finally, Q point is inserted into sampled point
It concentrates, as shown in Figure 5 c.This completes an iteration processes.
In situation aperiodic for the boundary of region Ω, sharp corner point (such as: four angle points of quadrangle)
It is sampled, and is fixed, these points are not involved in subsequent optimization process.Secondly, iterative optimization method is executed, it then, will
The sampled point that Voronoi unit intersects with boundary projects on boundary, the method for re-executing proposition of the embodiment of the present invention.It repeats
Above procedure is carried out, until relative radius does not have significant change, this process generally only needs to repeat 5 in practical applications
It can restrain for~10 times.After projection process, it can further increase relative radius.
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 quality comparison schematic diagram that (i.e. OURS) is obtained.Wherein, sampling area is the square area of cycle boundary, sampling
Points are 1024, since MPS method cannot accurately control sampling number, so its points is approximately 1024.Fig. 6 divides from top to bottom
Not are as follows: sampling point set, PSA analysis result [17], PCF analysis result [18].Wherein, PSA analysis includes: power spectrum (the of Fig. 6
Two rows), radius average (the third line of Fig. 6) and anisotropy (fourth line of Fig. 6)；PCF analysis includes: into pair correlation function
(fifth line of Fig. 6) and scrambling (the 6th row of Fig. 6).It can be seen that from the secondary series of Fig. 6 compared to other methods, FPO
The point set that method obtains is more regular.In addition, can be seen that SER and MPS not from the analysis result of sampling point set result and PCF
Systematicness (randomness) is most strong, their PCF tends to be flat quickly and scrambling is slightly larger；The embodiment of the present invention proposes
The scrambling of method (i.e. OURS) take second place, FPO is finally, main cause is MPS and the method that the embodiment of the present invention proposes
New sampled point is randomly generated, and has more randomnesss compared to FPO.Although it is worth noting that, SER and MPS method
Sampling policy is entirely different, but they have closely similar point set quality.In addition, can be seen that from the analysis result of PSA
Sampling point set caused by the method that the embodiment of the present invention proposes has good blue noise quality.
Mesh quality is analyzed compared in a manner of preferred embodiment below.
Table 1 has counted the sampled point of method (i.e. OURS) four kinds of methods of SER, FPO, MPS and proposition of the embodiment of the present invention
The quality of collection and triangle meshes.Sampling number is 4096, takes the average value of 100 operation results.Wherein, δX=dmin/dmax
Indicate relative radius, dminIndicate the global shortest distance between point set X any point pair,Indicate any point
Theoretical maximum minimum range between.For measuring the quality of a triangle, atIndicate triangle t's
Area, ptIndicate the semi-perimeter of t, ltIndicate the longest side length of t；QminAnd QavgRespectively indicate minimum and average triangle shape quality.
θminAnd θmaxMinimum and maximum angle is respectively indicated,Indicate being averaged for the minimum angles of all triangles.θ<30 ° and θ>
90 ° respectively indicate θminLess than 30 ° and θmaxTriangle ratio greater than 90 °.V567% indicates that degree is 5,6,7 vertex percentage
Than.Wherein, for δX, FPO quality be it is highest, the embodiment of the present invention propose method (i.e. OURS) take second place, MPS and SER
It is essentially identical.FPO is to adjust point set by maximizing the shortest distance, therefore the relative radius of this method can achieve 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
It is close, and SER is slightly better than MPS, as shown in Figure 6.In addition, in addition to θmin, the method that the embodiment of the present invention proposes is (i.e.
OURS most performance indicators) are superior to SER and MPS.As Fig. 7 schematically illustrates the side of proposition of the embodiment of the present invention
Method aperiodic boundary sampled result, wherein being from left to right respectively as follows: Wavy, Face, Dolphin, S.Meanwhile it counting and having adopted
The quality of sampling point collection and triangle meshes, as shown in table 2.Table 2 illustrates the method for proposition of the embodiment of the present invention for aperiodic
The validity of edge sampling.
Table 1:
Table 2:
The embodiment of the present invention has also counted the distribution situation of the relative radius of the method for FPO and proposition of the embodiment of the present invention,
As shown in Figure 8.Wherein, the first row corresponds to the result of FPO；Second row corresponds to the result of the method for proposition of the embodiment of the present invention.Directly
The abscissa of square figure is relative radius, and ordinate is the experiment number within the scope of specific relative radius.From left to right, sampled point
Number is respectively N=0.5k, 2k, 10k.Every case executes 1000 times.As can be seen from Figure 8 the relative radius of FPO compares
It concentrates, and the relative radius for the method that the embodiment of the present invention proposes has a relatively large constant interval, main cause is this
New sampled point is inserted randomly into void area by the method that inventive embodiments propose, rather than fixed position (sampled point
Collect the center of circle of largest empty circle).To a certain extent, also illustrate that the method that the embodiment of the present invention proposes has stronger randomness.
Stability is analyzed in a manner of preferred embodiment below.The embodiment of the present invention has counted hundreds of points to number
The coefficient of variation CV (Coefficient of Variation) of each performance indicator of the point set of 100000 points, it is last such as table 1
Shown in a line.Its calculation method is that the average value of performance indicator is divided by corresponding standard deviation.The coefficient of variation measures different point sets
The degree of variation of performance indicator, the coefficient of variation is smaller, and variation (deviation) degree is smaller, it can analyze algorithm to a certain extent
Stability because for a kind of sampling algorithm, obtained different number of sampling point set should have almost the same matter
Amount.As it can be seen from table 1 for each index, the corresponding CV value of method that the embodiment of the present invention proposes be very it is low (<
3.5%), this illustrates that the method that the embodiment of the present invention proposes is very stable.Meanwhile for the stabilization of further verification algorithm
Property, PCF analysis can be carried out to the point set of sampling number N=0.5K, 1K, 2K, 20K, result is as shown in Figure 9.The first row pair
PCF is answered, the second row corresponds to Irregularity.It can be seen in figure 9 that the PCF analysis result of different points is almost the same.
Although each step is described in the way of above-mentioned precedence in above-described embodiment, this field
Technical staff is appreciated that the effect in order to realize the present embodiment, executes between different steps not necessarily in such order,
It (parallel) execution simultaneously or can be executed with reverse order, these simple variations all protection scope of the present invention it
It is interior.
Based on technical concept identical with embodiment of the method, the embodiment of the present invention also provides a kind of two dimension etc. of fixed points
Radius maximizes Poisson disk sampling system.The system can execute above method embodiment.As shown in Figure 10, which can be with
Including generation module 11, the first extraction module 12, determining module 13 and logging modle 14.Wherein, generation module 11 is used for basis
The sampled point number and sampling area that user specifies generate the first sampling point set.First extraction module 12 is used for generation module
11 the first sampling point sets generated carry out Delaunay trigonometric ratio, and extract the long work of the most short side in Delaunay trigonometric ratio result
For the first sample radius.Determining module 13 is used to determine whether the first sampling point set that generation module 11 generates to reach maximization pool
Loose disk sampling.Logging modle 14, which is used to determine that the first sampling point set reaches in determining module 13, maximizes the sampling of Poisson disk
In the case of, record the first sampling point set that the generation module 11 generates and the first sampling half that the first extraction module 12 extracts
Diameter.
In an alternative embodiment, processing module 15 and can also be set on the basis of the above system embodiment
Two extraction modules 16.Wherein, processing module 15 is used to determine that the first sampling point set not up to maximizes Poisson in determining module 13
In the case that disk samples, from the sampled point that neighborhood averaging side length is big in global most short side is removed in the first sampling point set, obtain
Second sampling point set and Delaunay trigonometric ratio is carried out to the second sampling point set, with the most short side of above-mentioned trigonometric ratio result a length of the
Two sample radius calculate void area, and using throwing boomerang method for the sky of a stochastical sampling point radom insertion to the second sampling point set
Gap region obtains third sampling point set.The third sampling point set that second extraction module 16 is used to obtain processing module 15 carries out
Delaunay trigonometric ratio, extracts the most short side in Delaunay trigonometric ratio result as third sample radius, to update described the
One sample radius simultaneously triggers determining module 13.
In an alternative embodiment, the determining module in the above system embodiment can also include determination unit.It should
Determination unit is used for according to whether there is gap in sampling area, and whether the first sampling point set to determine that generation module generates reaches
It is sampled to Poisson disk is maximized.
It should be noted that the radiuses such as two dimension of fixed points provided by the above embodiment maximize Poisson disk sampling system
System only the example of the division of the above functional modules, in practical applications, can according to need when being sampled
And complete above-mentioned function distribution by different functional modules, i.e., the internal structure of system is divided into different function moulds
Block, to complete all or part of the functions described above.
It will be understood by those skilled in the art that the radiuses such as two dimension of above-mentioned fixed points maximize Poisson disk sampling system
It further include some other known features, such as processor, controller, memory etc., in order to unnecessarily obscure the reality of the disclosure
Example is applied, these well known structures are not shown in Figure 10-11.
It should be understood that the quantity of the modules in Figure 10-11 is only schematical.According to actual needs, can have
There is any number of each module.
The above system embodiment can be used for executing above method embodiment, technical principle, it is solved the technical issues of
And the technical effect generated is similar, person of ordinary skill in the field can be understood that, for the convenience and letter of description
Clean, the specific work process of the system of foregoing description and related explanation can refer to corresponding processes in the foregoing method embodiment,
Details are not described herein.
It should be pointed out that system embodiment and embodiment of the method for the invention are described respectively above, but it is right
The details of one embodiment description can also be applied to another embodiment.For module involved 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
It is appreciated that the module or step in the embodiment of the present invention can also be decomposed or be combined again.Such as the mould of above-described embodiment
Block can be merged into a module, can also be further split into multiple submodule.
Technical solution is provided for the embodiments of the invention above to be described in detail.Although applying herein specific
A example the principle of the present invention and embodiment are expounded, still, the explanation of above-described embodiment be only applicable to help manage
Solve the principle of the embodiment of the present invention；Meanwhile to those skilled in the art, according to an embodiment of the present invention, it is being embodied
It can be made a change within mode and application range.
It should be noted that the flowchart or block diagram being referred to herein is not limited solely to form shown in this article,
Other can also be carried out to divide and/or combine.
It should be noted that: label and text in attached drawing are intended merely to be illustrated more clearly that the present invention, are not intended as pair
The improper restriction of the scope of the present invention.
Again it should be noted that description and claims of this specification and term " first " in above-mentioned attached drawing, "
Two " etc. be to be used to distinguish similar objects, rather than be used to describe or indicate specific sequence or precedence.It should be understood that this
The data that sample uses can be interchanged in appropriate circumstances, so that the embodiment of the present invention described herein can be in addition at this
In illustrate or description those of other than sequence implement.
The terms "include", "comprise" or any other like term are intended to cover non-exclusive inclusion, so that
Process, method, article or equipment/device including a series of elements not only includes those elements, but also including not bright
The other elements really listed, or further include the intrinsic element of these process, method, article or equipment/devices.
As used herein, term " module " may refer to the software object executed on a computing system or routine.
Disparate modules described herein can be embodied as to the object executed on a computing system or process (for example, as independence
Thread).While it is preferred that realize system and method described herein with software, but with hardware or software and hard
The realization of the combination of part is also possible and can be conceived to.
Each step of the invention can be realized with general computing device, for example, they can concentrate on it is single
On computing device, such as: personal computer, server computer, handheld device or portable device, laptop device or more
Processor device can also be distributed over a network of multiple computing devices, they can be to be different from sequence herein
Shown or described step is executed, perhaps they are fabricated to each integrated circuit modules or will be more in them
A module or step are fabricated to single integrated circuit module to realize.Therefore, the present invention is not limited to any specific hardware and soft
Part or its combination.
Programmable logic device can be used to realize in method provided by the invention, and it is soft also to may be embodied as computer program
Part or program module (it include routines performing specific tasks or implementing specific abstract data types, programs, objects, component or
Data structure etc.), such as embodiment according to the present invention can be a kind of computer program product, run the computer program
Product executes computer for demonstrated method.The computer program product includes computer readable storage medium, should
It include computer program logic or code section on medium, for realizing the method.The computer readable storage medium can
To be the built-in medium being mounted in a computer or the removable medium (example that can be disassembled from basic computer
Such as: using the storage equipment of hot plug technology).The built-in medium includes but is not limited to rewritable nonvolatile memory,
Such as: RAM, ROM, flash memory and hard disk.The removable medium includes but is not limited to: and optical storage media (such as: CD-
ROM and DVD), magnetic-optical storage medium (such as: MO), magnetic storage medium (such as: tape or mobile hard disk), can with built-in
Rewrite the media (such as: storage card) of nonvolatile memory and the media (such as: ROM box) with built-in ROM.
Particular embodiments described above has carried out further in detail the purpose of the present invention, technical scheme and beneficial effects
It describes in detail bright, it should be understood that the above is only a specific embodiment of the present invention, is not intended to restrict the invention, it is all
Within the spirit and principles in the present invention, any modification, equivalent substitution, improvement and etc. done should be included in guarantor of the invention
Within the scope of shield.
Claims (8)
1. a kind of radiuses such as two dimension of fixed points maximize the Poisson disk method of sampling, which is characterized in that the method is at least
Include:
Step 1: the sampled point number and sampling area specified according to user generate the first sampling point set；
Step 2: Delaunay trigonometric ratio being carried out to first sampling point set, and is extracted in Delaunay trigonometric ratio result most
Short side is long to be used as the first sample radius；
Step 3: determining whether first sampling point set reaches the maximization Poisson disk sampling；
Step 4: in the case where first sampling point set reaches maximization Poisson disk sampling, recording described first and adopt
Sampling point collection and first sample radius；
Step 5: in the case where first sampling point set not up to maximizes the sampling of Poisson disk, from first sampled point
The sampled point for removing that neighborhood averaging side length is big in global most short side is concentrated, obtains the second sampling point set and to second sampled point
Collection carries out Delaunay trigonometric ratio, calculates gap with a length of second sample radius of most short side in Delaunay trigonometric ratio result
Region, and using boomerang method is thrown by a stochastical sampling point radom insertion to the void area of second sampling point set, obtain third
Sampling point set；
Step 6: Delaunay trigonometric ratio being carried out to the third sampling point set, is extracted most short in Delaunay trigonometric ratio result
Side is as third sample radius, to update first sample radius and execute the step 3.
2. the method according to claim 1, wherein being extracted in Delaunay trigonometric ratio result in the step 2
Most short side it is long be used as the first sample radius, specifically include: all triangle edges obtained after Delaunay trigonometric ratio will be carried out
Length is ranked up, and regard most short side length as first sample radius.
3. the method according to claim 1, wherein the step 3 specifically includes: according in the sampling area
With the presence or absence of gap triangle, to determine whether first sampling point set reaches the maximization Poisson disk sampling.
4. the method according to claim 1, wherein the step 5 specifically includes:
The neighborhood averaging side length of two sampled points on the global most short side is determined according to the following formula:
Wherein, the N (v) indicates the number on sampling neighborhood of a point side；The liIndicate the length on neighborhood side；The EavgIndicate adjacent
Domain average side length；The i takes positive integer；
From the sampled point that neighborhood averaging side length is big in the global most short side is removed in first sampling point set, described the is obtained
Two sampling point sets；
Delaunay trigonometric ratio is carried out to second sampling point set；
Void area is calculated as the second sample radius using the most short side length in above-mentioned trigonometric ratio result；
The one stochastical sampling point radom insertion is obtained to the void area of second sampling point set using the throwing boomerang method
The third sampling point set.
5. according to the method described in claim 4, it is characterized in that, described carry out Delaunay tri- to second sampling point set
Angling, further includes:
The adjacent all triangles of delta-shaped region where the big sampled point of neighborhood averaging side length in the global most short side that adjustment removes
The regional area that shape is constituted.
6. the method according to claim 1, wherein being carried out in the step 6 to the third sampling point set
Delaunay trigonometric ratio, further includes:
The partial zones that the adjacent all triangles of delta-shaped region where the stochastical sampling point that set-up procedure 5 is inserted into are constituted
Domain.
7. a kind of radiuses such as two dimension of fixed points maximize Poisson disk sampling system, which is characterized in that the system is at least
Include:
Generation module, sampled point number and sampling area for being specified according to user generate the first sampling point set；
First extraction module, first sampling point set for generating to the generation module carry out Delaunay trigonometric ratio,
And it is long as the first sample radius to extract the most short side in Delaunay trigonometric ratio result；
Whether determining module, first sampling point set for determining that the generation module generates reach the maximization Poisson
Disk sampling；
Logging modle, for determining that first sampling point set reaches the maximization Poisson disk sampling in the determining module
In the case where, it records first sampling point set that the generation module generates and first extraction module extracts described the
One sample radius；
Processing module maximizes the sampling of Poisson disk for determining that first sampling point set is not up in the determining module
In the case of, from the sampled point that neighborhood averaging side length is big in global most short side is removed in first sampling point set, obtains second and adopt
Sampling point collection and Delaunay trigonometric ratio is carried out to second sampling point set, adopted so that the most short side of above-mentioned trigonometric ratio is long as second
Sample radius calculates void area, and using throwing boomerang method for the sky of a stochastical sampling point radom insertion to second sampling point set
Gap region obtains third sampling point set；
Second extraction module, the third sampling point set for obtaining to the processing module carry out Delaunay trigonometric ratio,
The most short side in Delaunay trigonometric ratio result is extracted as third sample radius, to update first sample radius and trigger
The determining module.
8. system according to claim 7, which is characterized in that the determining module specifically includes:
Determination unit is used for according to whether there is gap triangle in the sampling area, to determine that the generation module generates
First sampling point set whether reach maximization Poisson disk sampling.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610563518.5A CN106204742B (en) | 2016-07-18 | 2016-07-18 | The radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling and system |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610563518.5A CN106204742B (en) | 2016-07-18 | 2016-07-18 | The radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling and system |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106204742A CN106204742A (en) | 2016-12-07 |
| CN106204742B true CN106204742B (en) | 2019-03-08 |
Family
ID=57474710
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610563518.5A Active CN106204742B (en) | 2016-07-18 | 2016-07-18 | The radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling and system |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106204742B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108288287B (en) * | 2018-01-16 | 2021-08-06 | 合肥工业大学 | Power graph-based tile texture generation 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 |
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 |
|---|
| Farthest-Point Optimized Point Sets with Maximized Minimum Distance;Thomas SchlOmer et al;《Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics》;20111231;第135-142页 * |
| Gap Processing for Adaptive Maximal Poisson-Disk Sampling;DONG-MING YAN et al;《ACM Transactions on Graphics》;20130930;第32卷(第5期);正文第1-14页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106204742A (en) | 2016-12-07 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Corsini et al. | Efficient and flexible sampling with blue noise properties of triangular meshes | |
| KR102238693B1 (en) | Method and apparatus for extracting feature regions in point cloud | |
| Li et al. | SURE-based optimization for adaptive sampling and reconstruction | |
| Zhang et al. | Multi-normal estimation via pair consistency voting | |
| CN110147721A (en) | A kind of three-dimensional face identification method, model training method and device | |
| US8970593B2 (en) | Visualization and representation of data clusters and relations | |
| Salman et al. | Feature preserving mesh generation from 3D point clouds | |
| Wang et al. | Shape detection from raw lidar data with subspace modeling | |
| CN105096268A (en) | Denoising smoothing method of point cloud | |
| WO2010094713A1 (en) | Rendering caustics in computer graphics with photon mapping by relaxation | |
| Pound et al. | A patch-based approach to 3D plant shoot phenotyping | |
| CN106204742B (en) | The radiuses such as the two dimension of fixed points maximize the Poisson disk method of sampling and system | |
| Zhao et al. | A saliency detection based method for 3d surface simplification | |
| CN116188716B (en) | Method and device for reconstructing three-dimensional model of irregular complex building | |
| Pusch et al. | Improving the sketch-based interface: Forming curves from many small strokes | |
| Liu et al. | An edge-sensitive simplification method for scanned point clouds | |
| CN106415606B (en) | A kind of identification based on edge, system and method | |
| CN115861571A (en) | Semantic-aware triangulation network model building entity reconstruction method | |
| CN105719349B (en) | Based on the tetrahedral grid method and system for maximizing the sampling of Poisson disk | |
| Xu et al. | Towards globally optimal normal orientations for thin surfaces | |
| Geng et al. | Approximate poisson disk sampling on mesh | |
| Liao et al. | Fast hierarchical animated object decomposition using approximately invariant signature | |
| CN104036552B (en) | Method for generating blue noise meshes on basis of farthest point optimization | |
| Skrodzki | Neighborhood data structures, manifold properties, and processing of point set surfaces | |
| US8730235B2 (en) | Method for determining point connectivity on a two manifold in 3D space |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |